Stress corrosion cracking

Stress corrosion cracking

A close-up of the surface of a steel pipeline showing indications of stress corrosion cracking (two clusters of small black lines) revealed by magnetic particle inspection. Cracks which would normally have been invisible are detectable due to the magnetic particles clustering at the crack openings. The scale at the bottom is in millimetres.

Stress corrosion cracking (SCC) is the growth of crack formation in a corrosive environment. It can lead to unexpected sudden failure of normally ductile metals subjected to a tensile stress, especially at elevated temperature. SCC is highly chemically specific in that certain alloys are likely to undergo SCC only when exposed to a small number of chemical environments. The chemical environment that causes SCC for a given alloy is often one which is only mildly corrosive to the metal otherwise. Hence, metal parts with severe SCC can appear bright and shiny, while being filled with microscopic cracks. This factor makes it common for SCC to go undetected prior to failure. SCC often progresses rapidly, and is more common among alloys than pure metals. The specific environment is of crucial importance, and only very small concentrations of certain highly active chemicals are needed to produce catastrophic cracking, often leading to devastating and unexpected failure.[1]

The stresses can be the result of the crevice loads due to stress concentration, or can be caused by the type of assembly or residual stresses from fabrication (e.g. cold working); the residual stresses can be relieved by annealing or other surface treatments.

Metals attacked

Certain austenitic stainless steels and aluminium alloys crack in the presence of chlorides, mild steel cracks in the presence of alkali (boiler cracking) and nitrates, copper alloys crack in ammoniacal solutions (season cracking). This limits the usefulness of austenitic stainless steel for containing water with higher than few ppm content of chlorides at temperatures above 50 °C. Worse still, high-tensile structural steels crack in an unexpectedly brittle manner in a whole variety of aqueous environments, especially containing chlorides. With the possible exception of the latter, which is a special example of hydrogen cracking, all the others display the phenomenon of subcritical crack growth, i.e. small surface flaws propagate (usually smoothly) under conditions where fracture mechanics predicts that failure should not occur. That is, in the presence of a corrodent, cracks develop and propagate well below KIc. In fact, the subcritical value of the stress intensity, designated as KIscc, may be less than 1% of KIc, as the following table shows:

Alloy KIc


SCC environment KIscc


13Cr steel 60 3% NaCl 12
18Cr-8Ni 200 42% MgCl2 10
Cu-30Zn 200 NH4OH, pH7 1
Al-3Mg-7Zn 25 Aqueous halides 5
Ti-6Al-1V 60 0.6M KCl 20

Polymers attacked

A similar process (environmental stress cracking) occurs in polymers, when products are exposed to specific solvents or aggressive chemicals such as acids and alkalis. As with metals, attack is confined to specific polymers and particular chemicals. Thus polycarbonate is sensitive to attack by alkalis, but not by acids. On the other hand, polyesters are readily degraded by acids, and SCC is a likely failure mechanism. Polymers are susceptible to environmental stress cracking where attacking agents do not necessarily degrade the materials chemically. Nylon is sensitive to degradation by acids, a process known as hydrolysis, and nylon mouldings will crack when attacked by strong acids.

Close-up of broken nylon fuel pipe connector caused by SCC

For example, the fracture surface of a fuel connector showed the progressive growth of the crack from acid attack (Ch) to the final cusp (C) of polymer. In this case the failure was caused by hydrolysis of the polymer by contact with sulfuric acid leaking from a car battery. The degradation reaction is the reverse of the synthesis reaction of the polymer:

Condensation polymerization diacid diamine.svg
Amide hydrolysis.svg

Cracks can be formed in many different elastomers by ozone attack, another form of SCC in polymers. Tiny traces of the gas in the air will attack double bonds in rubber chains, with natural rubber, styrene-butadiene rubber, and nitrile butadiene rubber being most sensitive to degradation. Ozone cracks form in products under tension, but the critical strain is very small. The cracks are always oriented at right angles to the strain axis, so will form around the circumference in a rubber tube bent over. Such cracks are very dangerous when they occur in fuel pipes because the cracks will grow from the outside exposed surfaces into the bore of the pipe, so fuel leakage and fire may follow. The problem of ozone cracking can be prevented by adding anti-ozonants to the rubber before vulcanization. Ozone cracks were commonly seen in automobile tire sidewalls, but are now seen rarely thanks to the use of these additives. On the other hand, the problem does recur in unprotected products such as rubber tubing and seals.

Ceramics attacked

This effect is significantly less common in ceramics which are typically more resilient to chemical attack. Although phase changes are common in ceramics under stress these usually result in toughening rather than failure (see Zirconium dioxide). Recently studies have shown that the same driving force for this toughening mechanism can also enhance oxidation of reduced cerium oxide resulting in slow crack growth and spontaneous failure of dense ceramic bodies.[2]

Crack growth

The subcritical nature of propagation may be attributed to the chemical energy released as the crack propagates. That is,

elastic energy released + chemical energy = surface energy + deformation energy

The crack initiates at KIscc and thereafter propagates at a rate governed by the slowest process, which most of the time is the rate at which corrosive ions can diffuse to the crack tip. As the crack advances so K rises (because crack length appears in the calculation of stress intensity). Finally it reaches KIc, whereupon fast fracture ensues and the component fails. One of the practical difficulties with SCC is its unexpected nature. Stainless steels, for example, are employed because under most conditions they are "passive", i.e. effectively inert. Very often one finds a single crack has propagated while the rest of the metal surface stays apparently unaffected. The crack propagates perpendicular to the applied stress.


SCC is the result of a combination of three factors – a susceptible material, exposure to a corrosive environment, and tensile stresses above a threshold. If any one of these factors are eliminated, SCC initiation becomes impossible. There are, consequently, a number of approaches that can be used to prevent or at least delay the onset of SCC. In an ideal world a stress corrosion cracking control strategy will start operating at the design stage, and will focus on the selection of material, the limitation of stress and the control of the environment. The skill of the engineer then lies in selecting the strategy that delivers the required performance at minimum cost. In this context it should be noted that part of the performance requirements relate to the acceptability of failure. The primary containment pressure vessel in a nuclear reactor obviously requires a very low risk of failure. For the pressed brass decorative trim on a light switch, the occasional stress corrosion crack is not going to be a serious problem, although frequent failures would have an undesirable impact on product returns and the manufacturer's image. The conventional approach to controlling the problem has been to develop new alloys that are more resistant to SCC. This is a costly proposition and can require a massive time investment to achieve only marginal success.

Selection and control of material

The first line of defence in controlling stress corrosion cracking is to be aware of the possibility at the design and construction stages. By choosing a material that is not susceptible to SCC in the service environment, and by processing and fabricating it correctly, subsequent SCC problems can be avoided. Unfortunately, it is not always quite that simple. Some environments, such as high temperature water, are very aggressive, and will cause SCC of most materials. Mechanical requirements, such as a high yield strength, can be very difficult to reconcile with SCC resistance (especially where hydrogen embrittlement is involved).

Control of stress

As one of the requirements for stress corrosion cracking is the presence of stress in the components, one method of control is to eliminate that stress, or at least reduce it below the threshold stress for SCC. This is not usually feasible for working stresses (the stress that the component is intended to support), but it may be possible where the stress causing cracking is a residual stress introduced during welding or forming. Residual stresses can be relieved by stress-relief annealing, and this is widely used for carbon steels. These have the advantage of a relatively high threshold stress for most environments, consequently it is relatively easy to reduce the residual stresses to a low enough level. In contrast austenitic stainless steels have a very low threshold stress for chloride SCC. This, combined with the high annealing temperatures that are necessary to avoid other problems, such as sensitization and sigma phase embrittlement, means that stress relief is rarely successful as a method of controlling SCC for this system. For large structures, for which full stress-relief annealing is difficult or impossible, partial stress relief around welds and other critical areas may be of value. However, this must be done in a controlled way to avoid creating new regions of high residual stress, and expert advice is advisable if this approach is adopted. Stresses can also be relieved mechanically. For example, hydrostatic testing beyond yield will tend to ‘even-out’ the stresses and thereby reduce the peak residual stress. Similarly laser peening, shot-peening, or grit-blasting tend to introduce a surface compressive stress, and are beneficial for the control of SCC. The uniformity with which these processes are applied is important. If, for example, only the weld region is shot-peened, damaging tensile stresses may be created at the border of the peened area. The compressive residual stresses imparted by laser peening are precisely controlled both in location and intensity, and can be applied to mitigate sharp transitions into tensile regions. Laser peening imparts deep compressive residual stresses on the order of 10 to 20 times deeper than conventional shot peening making it significantly more beneficial at preventing SCC.[3] Laser peening is widely used in the aerospace and power generation industries in gas fired turbine engines.[4]

Control of environment

The most direct way of controlling SCC through control of the environment is to remove or replace the component of the environment that is responsible for the problem, though this is not usually feasible. Where the species responsible for cracking are required components of the environment, environmental control options consist of adding inhibitors, modifying the electrode potential of the metal, or isolating the metal from the environment with coatings.

For example, chloride stress corrosion cracking of austenitic stainless steel has been experienced in hot-water jacketed pipes carrying molten chocolate in the food industry. It is difficult to control the temperature, while changing pipe material or eliminating residual stresses associated with welding and forming the pipework is costly and incurs plant downtime. However, this is a rare case where environment may be modified: an ion exchange process may be used to remove chlorides from the heating water.

Testing of susceptible materials

One of the primary methods used to detect and remove materials that are susceptible to SCC is corrosion testing. A variety of SCC corrosion tests exist for different metal alloy.


The collapsed Silver Bridge, as seen from the Ohio side

A classic example of SCC is season cracking of brass cartridge cases, a problem experienced by the British army in India in the early 19th century. It was initiated by ammonia from dung and horse manure decomposing at the higher temperatures of the spring and summer. There was substantial residual stress in the cartridge shells as a result of cold forming. The problem was solved by annealing the shells to ameliorate the stress.

A 32-inch diameter gas transmission pipeline, north of Natchitoches, Louisiana, belonging to the Tennessee Gas Pipeline exploded and burned from SCC on March 4, 1965, killing 17 people. At least 9 others were injured, and 7 homes 450 feet from the rupture were destroyed.[5][6]

SCC caused the catastrophic collapse of the Silver Bridge in December 1967, when an eyebar suspension bridge across the Ohio river at Point Pleasant, West Virginia, suddenly failed. The main chain joint failed and the whole structure fell into the river, killing 46 people in vehicles on the bridge at the time. Rust in the eyebar joint had caused a stress corrosion crack, which went critical as a result of high bridge loading and low temperature. The failure was exacerbated by a high level of residual stress in the eyebar. The disaster led to a nationwide reappraisal of bridges.[7]

Suspended ceilings in indoor swimming pools are safety-relevant components. As was demonstrated by the collapses of the ceiling of the Uster (Switzerland) indoor swimming pool (1985) and again at Steenwijk (Netherlands, 2001), attention must be paid to selecting suitable materials and inspecting the state of such components. The reason for the failures was stress corrosion cracking of metal fastening components made of stainless steel.[8] The active chemical was chlorine added to the water as a disinfectant.

See also


  1. ^ ASM International, Metals Handbook (Desk Edition) Chapter 32 (Failure Analysis), American Society for Metals
  2. ^ Munnings, C.; Badwal, S. P. S.; Fini, D. (20 February 2014). "Spontaneous stress-induced oxidation of Ce ions in Gd-doped ceria at room temperature". Ionics. 20 (8): 1117–1126. doi:10.1007/s11581-014-1079-2. 
  3. ^ EPRI | Search Results: Compressor Dependability: Laser Shock Peening Surface Treatment
  4. ^
  5. ^
  6. ^ The Washington Observer - Google News Archive Search
  7. ^ Lewis, Peter Rhys, Reynolds, K, and Gagg, C, Forensic Materials Engineering: Case studies, CRC Press (2004).
  8. ^ M. Faller and P. Richner: Material selection of safety-relevant components in indoor swimming pools, Materials and Corrosion 54 (2003) S. 331 - 338.(only online in German (3.6 MB)) (ask for a copy of the English version)
  • ASM International, Metals Handbook (Desk Edition) Chapter 32 (Failure Analysis), American Society for Metals, (1997) pp 32–24 to 32-26
  • ASM Handbook Volume 11 "Failure Analysis and Prevention" (2002) "Stress-Corrosion Cracking" Revised by W.R. Warke, American Society of Metals. Pages 1738-1820

External links

Stress–strain analysis

Stress–strain analysis

Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.

Stress analysis is a primary task for civil, mechanical and aerospace engineers involved in the design of structures of all sizes, such as tunnels, bridges and dams, aircraft and rocket bodies, mechanical parts, and even plastic cutlery and staples. Stress analysis is also used in the maintenance of such structures, and to investigate the causes of structural failures.

Typically, the starting point for stress analysis are a geometrical description of the structure, the properties of the materials used for its parts, how the parts are joined, and the maximum or typical forces that are expected to be applied to the structure. The output data is typically a quantitative description of how the applied forces spread throughout the structure, resulting in stresses, strains and the deflections of the entire structure and each component of that structure. The analysis may consider forces that vary with time, such as engine vibrations or the load of moving vehicles. In that case, the stresses and deformations will also be functions of time and space.

In engineering, stress analysis is often a tool rather than a goal in itself; the ultimate goal being the design of structures and artifacts that can withstand a specified load, using the minimum amount of material or that satisfies some other optimality criterion.

Stress analysis may be performed through classical mathematical techniques, analytic mathematical modelling or computational simulation, experimental testing, or a combination of methods.

The term stress analysis is used throughout this article for the sake of brevity, but it should be understood that the strains, and deflections of structures are of equal importance and in fact, an analysis of a structure may begin with the calculation of deflections or strains and end with calculation of the stresses.


General principles

Stress analysis is specifically concerned with solid objects. The study of stresses in liquids and gases is the subject of fluid mechanics.

Stress analysis adopts the macroscopic view of materials characteristic of continuum mechanics, namely that all properties of materials are homogeneous at small enough scales. Thus, even the smallest particle considered in stress analysis still contains an enormous number of atoms, and its properties are averages of the properties of those atoms.

In stress analysis one normally disregards the physical causes of forces or the precise nature of the materials. Instead, one assumes that the stresses are related to strain of the material by known constitutive equations.

By Newton's laws of motion, any external forces that act on a system must be balanced by internal reaction forces,[1] or cause the particles in the affected part to accelerate. In a solid object, all particles must move substantially in concert in order to maintain the object's overall shape. It follows that any force applied to one part of a solid object must give rise to internal reaction forces that propagate from particle to particle throughout an extended part of the system. With very rare exceptions (such as ferromagnetic materials or planet-scale bodies), internal forces are due to very short range intermolecular interactions, and are therefore manifested as surface contact forces between adjacent particles — that is, as stress.[2]

Fundamental problem

The fundamental problem in stress analysis is to determine the distribution of internal stresses throughout the system, given the external forces that are acting on it. In principle, that means determining, implicitly or explicitly, the Cauchy stress tensor at every point.

The external forces may be body forces (such as gravity or magnetic attraction), that act throughout the volume of a material;[3] or concentrated loads (such as friction between an axle and a bearing, or the weight of a train wheel on a rail), that are imagined to act over a two-dimensional area, or along a line, or at single point. The same net external force will have a different effect on the local stress depending on whether it is concentrated or spread out.

Types of structures

In civil engineering applications, one typically considers structures to be in static equilibrium: that is, are either unchanging with time, or are changing slowly enough for viscous stresses to be unimportant (quasi-static). In mechanical and aerospace engineering, however, stress analysis must often be performed on parts that are far from equilibrium, such as vibrating plates or rapidly spinning wheels and axles. In those cases, the equations of motion must include terms that account for the acceleration of the particles. In structural design applications, one usually tries to ensure the stresses are everywhere well below the yield strength of the material. In the case of dynamic loads, the material fatigue must also be taken into account. However, these concerns lie outside the scope of stress analysis proper, being covered in materials science under the names strength of materials, fatigue analysis, stress corrosion, creep modeling, and other.

Experimental methods

Stress analysis can be performed experimentally by applying forces to a test element or structure and then determining the resulting stress using sensors. In this case the process would more properly be known as testing (destructive or non-destructive). Experimental methods may be used in cases where mathematical approaches are cumbersome or inaccurate. Special equipment appropriate to the experimental method is used to apply the static or dynamic loading.

There are a number of experimental methods which may be used:

  • Tensile testing is a fundamental materials science test in which a sample is subjected to uniaxial tension until failure. The results from the test are commonly used to select a material for an application, for quality control, or to predict how a material will react under other types of forces. Properties that are directly measured via a tensile test are the ultimate tensile strength, maximum elongation and reduction in cross-section area. From these measurements, properties such as Young's modulus, Poisson's ratio, yield strength, and the strain-hardening characteristics of the sample can be determined.
  • Strain gauges can be used to experimentally determine the deformation of a physical part. A commonly used type of strain gauge is a thin flat resistor that is affixed to the surface of a part, and which measures the strain in a given direction. From the measurement of strain on a surface in three directions the stress state that developed in the part can be calculated.
  • Neutron diffraction is a technique that can be used to determine the subsurface strain in a part.
Stress in plastic protractor causes birefringence.
  • The photoelastic method relies on the fact that some materials exhibit birefringence on the application of stress, and the magnitude of the refractive indices at each point in the material is directly related to the state of stress at that point. The stresses in a structure can be determined by making a model of the structure from such a photoelastic material.
  • Dynamic mechanical analysis (DMA) is a technique used to study and characterize viscoelastic materials, particularly polymers. The viscoelastic property of a polymer is studied by dynamic mechanical analysis where a sinusoidal force (stress) is applied to a material and the resulting displacement (strain) is measured. For a perfectly elastic solid, the resulting strains and the stresses will be perfectly in phase. For a purely viscous fluid, there will be a 90 degree phase lag of strain with respect to stress. Viscoelastic polymers have the characteristics in between where some phase lag will occur during DMA tests.

Mathematical methods

While experimental techniques are widely used, most stress analysis is done by mathematical methods, especially during design.

Differential formulation

The basic stress analysis problem can be formulated by Euler's equations of motion for continuous bodies (which are consequences of Newton's laws for conservation of linear momentum and angular momentum) and the Euler-Cauchy stress principle, together with the appropriate constitutive equations.

These laws yield a system of partial differential equations that relate the stress tensor field to the strain tensor field as unknown functions to be determined. Solving for either then allows one to solve for the other through another set of equations called constitutive equations. Both the stress and strain tensor fields will normally be continuous within each part of the system and that part can be regarded as a continuous medium with smoothly varying constitutive equations.

The external body forces will appear as the independent ("right-hand side") term in the differential equations, while the concentrated forces appear as boundary conditions. An external (applied) surface force, such as ambient pressure or friction, can be incorporated as an imposed value of the stress tensor across that surface. External forces that are specified as line loads (such as traction) or point loads (such as the weight of a person standing on a roof) introduce singularities in the stress field, and may be introduced by assuming that they are spread over small volume or surface area. The basic stress analysis problem is therefore a boundary-value problem.

Elastic and linear cases

A system is said to be elastic if any deformations caused by applied forces will spontaneously and completely disappear once the applied forces are removed. The calculation of the stresses (stress analysis) that develop within such systems is based on the theory of elasticity and infinitesimal strain theory. When the applied loads cause permanent deformation, one must use more complicated constitutive equations, that can account for the physical processes involved (plastic flow, fracture, phase change, etc.)

Engineered structures are usually designed so that the maximum expected stresses are well within the realm of linear elastic (the generalization of Hooke’s law for continuous media) behavior for the material from which the structure will be built. That is, the deformations caused by internal stresses are linearly related to the applied loads. In this case the differential equations that define the stress tensor are also linear. Linear equations are much better understood than non-linear ones; for one thing, their solution (the calculation of stress at any desired point within the structure) will also be a linear function of the applied forces. For small enough applied loads, even non-linear systems can usually be assumed to be linear.

Built-in stress (preloaded)

Example of a Hyperstatic Stress Field.

A preloaded structure is one that has, internal forces, stresses and strains imposed within it by various means prior to application of externally applied forces. For example, a structure may have cables that are tightened, causing forces to develop in the structure, before any other loads are applied. Tempered glass is a commonly found example of a preloaded structure that has tensile forces and stresses that act on the plane of the glass and in the central plane of glass that causes compression forces to act on the external surfaces of that glass.

The mathematical problem represented is typically ill-posed because it has an infinitude of solutions. In fact, in any three-dimensional solid body one may have infinitely many (and infinitely complicated) non-zero stress tensor fields that are in stable equilibrium even in the absence of external forces. These stress fields are often termed hyperstatic stress fields[4] and they co-exist with the stress fields that balance the external forces. In linear elasticity, their presence is required to satisfy the strain/displacement compatibility requirements and in limit analysis their presence is required to maximise the load carrying capacity of the structure or component.

Example of a Hyperstatic Moment Field.

Such built-in stress may occur due to many physical causes, either during manufacture (in processes like extrusion, casting or cold working), or after the fact (for example because of uneven heating, or changes in moisture content or chemical composition). However, if the system can be assumed to behave in a linear fashion with respect to the loading and response of the system, then effect of preload can be accounted for by adding the results of a preloaded structure and the same non-preloaded structure.

If linearity cannot be assumed, however, any built-in stress may affect the distribution of internal forces induced by applied loads (for example, by changing the effective stiffness of the material) or even cause an unexpected material failure. For these reasons, a number of techniques have been developed to avoid or reduce built-in stress, such as annealing of cold-worked glass and metal parts, expansion joints in buildings, and for bridges.


Simplified modeling of a truss by unidimensional elements under uniaxial uniform stress.

Stress analysis is simplified when the physical dimensions and the distribution of loads allow the structure to be treated as one- or two-dimensional. In the analysis of a bridge, its three dimensional structure may be idealized as a single planar structure, if all forces are acting in the plane of the trusses of the bridge. Further, each member of the truss structure might then be treated a uni-dimensional members with the forces acting along the axis of each member. In which case, the differential equations reduce to a finite set of equations with finitely many unknowns.

If the stress distribution can be assumed to be uniform (or predictable, or unimportant) in one direction, then one may use the assumption of plane stress and plane strain behavior and the equations that describe the stress field are then a function of two coordinates only, instead of three.

Even under the assumption of linear elastic behavior of the material, the relation between the stress and strain tensors is generally expressed by a fourth-order stiffness tensor with 21 independent coefficients (a symmetric 6 × 6 stiffness matrix). This complexity may be required for general anisotropic materials, but for many common materials it can be simplified. For orthotropic materials such as wood, whose stiffness is symmetric with respect to each of three orthogonal planes, nine coefficients suffice to express the stress–strain relationship. For isotropic materials, these coefficients reduce to only two.

One may be able to determine a priori that, in some parts of the system, the stress will be of a certain type, such as uniaxial tension or compression, simple shear, isotropic compression or tension, torsion, bending, etc. In those parts, the stress field may then be represented by fewer than six numbers, and possibly just one.

Solving the equations

In any case, for two- or three-dimensional domains one must solve a system of partial differential equations with specified boundary conditions. Analytical (closed-form) solutions to the differential equations can be obtained when the geometry, constitutive relations, and boundary conditions are simple enough. For more complicated problems one must generally resort to numerical approximations such as the finite element method, the finite difference method, and the boundary element method.

Factor of safety

The ultimate purpose of any analysis is to allow the comparison of the developed stresses, strains, and deflections with those that are allowed by the design criteria. All structures, and components thereof, must obviously be designed to have a capacity greater than what is expected to develop during the structure's use to obviate failure. The stress that is calculated to develop in a member is compared to the strength of the material from which the member is made by calculating the ratio of the strength of the material to the calculated stress. The ratio must obviously be greater than 1.0 if the member is to not fail. However, the ratio of the allowable stress to the developed stress must be greater than 1.0 as a factor of safety (design factor) will be specified in the design requirement for the structure. All structures are designed to exceed the load those structures are expected to experience during their use. The design factor (a number greater than 1.0) represents the degree of uncertainty in the value of the loads, material strength, and consequences of failure. The stress (or load, or deflection) the structure is expected to experience are known as the working, the design or limit stress. The limit stress, for example, is chosen to be some fraction of the yield strength of the material from which the structure is made. The ratio of the ultimate strength of the material to the allowable stress is defined as the factor of safety against ultimate failure.

Laboratory tests are usually performed on material samples in order to determine the yield and ultimate strengths of those materials. A statistical analysis of the strength of many samples of a material is performed to calculate the particular material strength of that material. The analysis allows for a rational method of defining the material strength and results in a value less than, for example, 99.99% of the values from samples tested. By that method, in a sense, a separate factor of safety has been applied over and above the design factor of safety applied to a particular design that uses said material.

The purpose of maintaining a factor of safety on yield strength is to prevent detrimental deformations that would impair the use of the structure. An aircraft with a permanently bent wing might not be able to move its control surfaces, and hence, is inoperable. While yielding of material of structure could render the structure unusable it would not necessarily lead to the collapse of the structure. The factor of safety on ultimate tensile strength is to prevent sudden fracture and collapse, which would result in greater economic loss and possible loss of life.

An aircraft wing might be designed with a factor of safety of 1.25 on the yield strength of the wing and a factor of safety of 1.5 on its ultimate strength. The test fixtures that apply those loads to the wing during the test might be designed with a factor of safety of 3.0 on ultimate strength, while the structure that shelters the test fixture might have an ultimate factor of safety of ten. These values reflect the degree of confidence the responsible authorities have in their understanding of the load environment, their certainty of the material strengths, the accuracy of the analytical techniques used in the analysis, the value of the structures, the value of the lives of those flying, those near the test fixtures, and those within the building.

The factor of safety is used to calculate a maximum allowable stress:

Load transfer

The evaluation of loads and stresses within structures is directed to finding the load transfer path. Loads will be transferred by physical contact between the various component parts and within structures. The load transfer may be identified visually or by simple logic for simple structures. For more complex structures more complex methods, such as theoretical solid mechanics or numerical methods may be required. Numerical methods include direct stiffness method which is also referred to as the finite element method.

The object is to determine the critical stresses in each part, and compare them to the strength of the material (see strength of materials).

For parts that have broken in service, a forensic engineering or failure analysis is performed to identify weakness, where broken parts are analysed for the cause or causes of failure. The method seeks to identify the weakest component in the load path. If this is the part which actually failed, then it may corroborate independent evidence of the failure. If not, then another explanation has to be sought, such as a defective part with a lower tensile strength than it should for example.

Uniaxial stress

A linear element of a structure is one that is essentially one dimensional and is often subject to axial loading only. When a structural element is subjected to tension or compression its length will tend to elongate or shorten, and its cross-sectional area changes by an amount that depends on the Poisson's ratio of the material. In engineering applications, structural members experience small deformations and the reduction in cross-sectional area is very small and can be neglected, i.e., the cross-sectional area is assumed constant during deformation. For this case, the stress is called engineering stress or nominal stress and is calculated using the original cross section.

where P is the applied load, and Ao is the original cross-sectional area.

In some other cases, e.g., elastomers and plastic materials, the change in cross-sectional area is significant. If the true stress is desired, it must be calculated using the true cross-sectional area instead of the initial cross-sectional area, as:



is the nominal (engineering) strain, and
is nominal (engineering) stress.

The relationship between true strain and engineering strain is given by


In uniaxial tension, true stress is then greater than nominal stress. The converse holds in compression.

Graphical representation of stress at a point

Mohr's circle, Lame's stress ellipsoid (together with the stress director surface), and Cauchy's stress quadric are two-dimensional graphical representations of the state of stress at a point. They allow for the graphical determination of the magnitude of the stress tensor at a given point for all planes passing through that point. Mohr's circle is the most common graphical method.

Mohr's circle, named after Christian Otto Mohr, is the locus of points that represent the state of stress on individual planes at all their orientations. The abscissa, , and ordinate, , of each point on the circle are the normal stress and shear stress components, respectively, acting on a particular cut plane with a unit vector with components .

Lame's stress ellipsoid

The surface of the ellipsoid represents the locus of the endpoints of all stress vectors acting on all planes passing through a given point in the continuum body. In other words, the endpoints of all stress vectors at a given point in the continuum body lie on the stress ellipsoid surface, i.e., the radius-vector from the center of the ellipsoid, located at the material point in consideration, to a point on the surface of the ellipsoid is equal to the stress vector on some plane passing through the point. In two dimensions, the surface is represented by an ellipse (Figure coming).

Cauchy's stress quadric

Stress Trajectories in a Plate Membrane

The Cauchy's stress quadric, also called the stress surface, is a surface of the second order that traces the variation of the normal stress vector as the orientation of the planes passing through a given point is changed.

The complete state of stress in a body at a particular deformed configuration, i.e., at a particular time during the motion of the body, implies knowing the six independent components of the stress tensor , or the three principal stresses , at each material point in the body at that time. However, numerical analysis and analytical methods allow only for the calculation of the stress tensor at a certain number of discrete material points. To graphically represent in two dimensions this partial picture of the stress field different sets of contour lines can be used:[5]

  • Isobars are curves along which the principal stress, e.g., is constant.
  • Isochromatics are curves along which the maximum shear stress is constant. This curves are directly determined using photoelasticity methods.
  • Isopachs are curves along which the mean normal stress is constant
  • Isostatics or stress trajectories[6] are a system of curves which are at each material point tangent to the principal axes of stress - see figure [7]
  • Isoclinics are curves on which the principal axes make a constant angle with a given fixed reference direction. These curves can also be obtained directly by photoelasticity methods.
  • Slip lines are curves on which the shear stress is a maximum.

See also


  1. ^ Donald Ray Smith and Clifford Truesdell (1993) "An Introduction to Continuum Mechanics after Truesdell and Noll". Springer. ISBN 0-7923-2454-4
  2. ^ I-Shih Liu (2002), "Continuum Mechanics". Springer ISBN 3-540-43019-9
  3. ^ Fridtjov Irgens (2008), "Continuum Mechanics". Springer. ISBN 3-540-74297-2
  4. ^ Ramsay, Angus. "Hyperstatic Stress Fields". Retrieved 6 May 2017. 
  5. ^ John Conrad Jaeger, N. G. W. Cook, and R. W. Zimmerman (2007), "Fundamentals of Rock Mechanics" (4th edition) Wiley-Blackwell. ISBN 0-632-05759-9
  6. ^ Maunder, Edward. "Visualisation of stress fields - from stress trajectories to strut and tie models.". Retrieved 15 April 2017. 
  7. ^ Ramsay, Angus. "Stress Trajectories". Ramsay Maunder Associates. Retrieved 15 April 2017. 

Impact (mechanics)

Impact (mechanics)

Head impact can cause concussion. Sports helmets help protect against brain injury.[1]

In mechanics, an impact is a high force or shock applied over a short time period when two or more bodies collide. Such a force or acceleration usually has a greater effect than a lower force applied over a proportionally longer period. The effect depends critically on the relative velocity of the bodies to one another.

At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, and this deformation will absorb most or all of the force of the collision. Viewed from a conservation of energy perspective, the kinetic energy of the projectile is changed into heat and sound energy, as a result of the deformations and vibrations induced in the struck object. However, these deformations and vibrations cannot occur instantaneously. A high-velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it would otherwise be, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that materials actually are more brittle on short time scales than on long time scales: this is related to time-temperature superposition. Impact resistance decreases with an increase in the modulus of elasticity, which means that stiffer materials will have less impact resistance. Resilient materials will have better impact resistance.

Different materials can behave in quite different ways in impact when compared with static loading conditions. Ductile materials like steel tend to become more brittle at high loading rates, and spalling may occur on the reverse side to the impact if penetration doesn't occur. The way in which the kinetic energy is distributed through the section is also important in determining its response. Projectiles apply a Hertzian contact stress at the point of impact to a solid body, with compression stresses under the point, but with bending loads a short distance away. Since most materials are weaker in tension than compression, this is the zone where cracks tend to form and grow.


Crane with a pile driver
1/2" drive pistol-grip air impact wrench

A nail is pounded with a series of impacts, each by a single hammer blow. These high velocity impacts overcome the static friction between the nail and the substrate. A pile driver achieves the same end, although on a much larger scale, the method being commonly used during civil construction projects to make building and bridge foundations. An impact wrench is a device designed to impart torque impacts to bolts to tighten or loosen them. At normal speeds, the forces applied to the bolt would be dispersed, via friction, to the mating threads. However, at impact speeds, the forces act on the bolt to move it before they can be dispersed. In ballistics, bullets utilize impact forces to puncture surfaces that could otherwise resist substantial forces. A rubber sheet, for example, behaves more like glass at typical bullet speeds. That is, it fractures, and does not stretch or vibrate.

Impacts causing damage

Chevrolet Malibu involved in a rollover crash

Road traffic accidents usually involve impact loading, such as when a car hits a traffic bollard, water hydrant or tree, the damage being localized to the impact zone. When vehicles collide, the damage is proportionate to the relative velocity of the vehicles, the damage increasing as the square of the velocity since it is the impact kinetic energy (1/2 mv2) which is the variable of importance. Much design effort is made to improve the impact resistance of cars so as to minimize user injury. It can be achieved in several ways: by enclosing the driver and passengers in a safety cell for example. The cell is reinforced so it will survive in high speed crashes, and so protect the users. Parts of the body shell outside the cell are designed to crumple progressively, absorbing most of the kinetic energy which must be dissipated by the impact.

Various impact test are used to assess the effects of high loading, both on products and standard slabs of material. The Charpy test and Izod test are two examples of standardized methods which are used widely for testing materials. Ball or projectile drop tests are used for assessing product impacts.

The Columbia disaster was caused by impact damage when a chunk of polyurethane foam impacted the carbon fibre composite wing of the space shuttle. Although tests had been conducted before the disaster, the test chunks were much smaller than the chunk that fell away from the booster rocket and hit the exposed wing.

Mock-up of a space shuttle leading edge made with an RCC-panel taken from Discovery showing impact damage during a test

When fragile items are shipped, impacts and drops can cause product damage. Protective packaging and cushioning help reduce the peak acceleration by extending the duration of the shock or impact.[2]

See also


  1. ^ Consumer Product Safety Commission. "Safety Standard for Bicycle Helmets" (PDF). Final Rule 16 CFR Part 1203. Archived from the original (PDF) on 24 September 2006. Retrieved 2006.  Check date values in: |access-date= (help)
  2. ^ "Package Cushioning Design". MIL-HDBK 304C. DoD. 1997. 
  • Goldsmith, W. (1960). Impact: The Theory and Physical Behaviour of Colliding Solids Dover Publications, ISBN 0-486-42004-3
  • Poursartip, A. (1993). Instrumented Impact Testing at High Velocities, Journal of Composites Technology and Research, 15(1).
  • Toropov, AI. (1998). Dynamic Calibration of Impact Test Instruments, Journal of Testing and Evaluation, 24(4).

Hydrogen embrittlement

Hydrogen embrittlement

Hydrogen Induced Cracks (HIC)
Steels were embrittled with hydrogen through cathodic charging. Heat treatments (baking) was used to reduce hydrogen content. Lower bake times resulted in quicker fracture times due to higher hydrogen content.[1]

Hydrogen embrittlement is the process by which metals such as steel become brittle and fracture due to the introduction and subsequent diffusion of hydrogen into the metal. This is often a result of accidental introduction of hydrogen during forming and finishing operations. This issue is caused by material properties (diffusion of hydrogen), environment, and stress. This phenomenon was first described in 1875.[2]


During hydrogen embrittlement, hydrogen is introduced to the surface of a metal and individual hydrogen atoms diffuse through the metal. Because the solubility of hydrogen increases at higher temperatures, raising the temperature can increase the diffusion of hydrogen. When assisted by a concentration gradient where there is significantly more hydrogen outside the metal than inside, hydrogen diffusion can occur even at lower temperatures. These individual hydrogen atoms within the metal gradually recombine to form hydrogen molecules, creating pressure from within the metal. This pressure can increase to levels where the metal has reduced ductility, toughness, and tensile strength, up to the point where it cracks open (hydrogen-induced cracking, or HIC).[3] Though hydrogen atoms embrittle a variety of substances, including steel,[4][5][6] aluminium (at high temperatures only[7]), and titanium,[8] hydrogen embrittlement of high-strength steel is of the most importance. Austempered iron is also susceptible, though austempered steel (and possibly other austempered metals) display increased resistance to hydrogen embrittlement.[9] Steel with an ultimate tensile strength of less than 1000 MPa (~145,000 psi) or hardness of less than 23 HRC is not generally considered susceptible to hydrogen embrittlement. In tensile tests carried out on several structural metals under high-pressure molecular hydrogen environment, it has been shown that austenitic stainless steels, aluminium (including alloys), copper (including alloys, e.g. beryllium copper) are not susceptible to hydrogen embrittlement along with a few other metals.[10][11] As an example of severe hydrogen embrittlement, the elongation at failure of 17-4PH precipitation hardened stainless steel was measured to drop from 17% to only 1.7% when smooth specimens were exposed to high-pressure hydrogen.

However, recent computational research (using Parrinello-Rahman molecular dynamics) has shown that instead of leading to a decrease in ductility, there is local enhancement of ductility in areas that are hydrogen saturated. This increase in ductility leads to areas where there is a reduction in the critical tensile stress which leads to failure to occur at lower than expected stresses.[12]

Hydrogen embrittlement can occur during various manufacturing operations or operational use - anywhere that the metal comes into contact with atomic or molecular hydrogen. Processes that can lead to this include cathodic protection, phosphating, pickling, and electroplating. A special case is arc welding, in which the hydrogen is released from moisture, such as in the coating of welding electrodes.[8][13] To minimize this, special low-hydrogen electrodes are used for welding high-strength steels. Other mechanisms of introduction of hydrogen into metal are galvanic corrosion, as well as chemical reactions with acids or other chemicals. One of these chemical reactions involves hydrogen sulfide in sulfide stress cracking (SSC), an important process for the oil and gas industries.[14]


Hydrogen embrittlement can be prevented through several methods, all of which are centered on minimizing contact between the metal and hydrogen, particularly during fabrication. Embrittling procedures such as acid pickling should be avoided, as should increased contact with elements such as sulfur and phosphate. The use of proper electroplating solution and procedures can also help to prevent hydrogen embrittlement.[15] Furthermore, metal substrates (generally ferrous sulfide or other sulfides) can be applied to metal in order to prevent hydrogen embrittlement.[16][17]

If the metal has not yet started to crack, embrittlement can be reversed by removing the hydrogen source and causing the hydrogen within the metal to diffuse out through heat treatment.[18] This de-embrittlement process, known as "baking", is used to overcome the weaknesses of methods such as electroplating which introduce hydrogen to the metal, but is not always entirely effective.[19]

In the case of welding, often pre- and post-heating the metal is applied to allow the hydrogen to diffuse out before it can cause any damage. This is specifically done with high-strength steels and low alloy steels such as the chrome/molybdenum/vanadium alloys. Due to the time needed to re-combine hydrogen atoms into the hydrogen molecules, hydrogen cracking due to welding can occur over 24 hours after the welding operation is completed.

Another way of preventing this problem is through materials selection. This will build an inherent resistance to this process and reduce the need of post processing or constant monitoring for failure. Certain metals or alloys are highly susceptible to this issue so choosing a material that is minimally affected while retaining the desired properties would also provide an optimal solution. Much research has been done to catalog the compatibility of certain metals with hydrogen.[20]


  • In 2013, six months prior to opening, the East Span of the Oakland Bay Bridge failed during testing. Catastrophic failures occurred in in the span, after only two weeks of service, with the failure attributed to embrittlement, possibly from the environment.[21]

Related phenomena

If steel is exposed to hydrogen at high temperatures, hydrogen will diffuse into the alloy and combine with carbon to form tiny pockets of methane at internal surfaces like grain boundaries and voids. This methane does not diffuse out of the metal, and collects in the voids at high pressure and initiates cracks in the steel. This selective leaching process is known as hydrogen attack, or high temperature hydrogen attack and leads to decarburization of the steel and loss of strength and ductility.

Copper alloys which contain oxygen can be embrittled if exposed to hot hydrogen. The hydrogen diffuses through the copper and reacts with inclusions of Cu2O, forming H2O (water), which then forms pressurized bubbles at the grain boundaries. This process can cause the grains to literally be forced away from each other, and is known as steam embrittlement (because steam is produced, not because exposure to steam causes the problem).

A large number of alloys of vanadium, nickel, and titanium absorb significant amounts of hydrogen. This can lead to large volume expansion and damage to the crystal structure leading to the alloys becoming very brittle. This is a particular issue when looking for non-palladium based alloys for use in hydrogen separation membranes.[22]


There are two ASTM standards for testing embrittlement due to hydrogen gas. The Standard Test Method for Determination of the Susceptibility of Metallic Materials to Hydrogen Gas Embrittlement (HGE) Test,[23] uses a diaphragm loaded with a differential pressure. The Standard Test Method for Determination of Susceptibility of Metals to Embrittlement in Hydrogen Containing Environments at High Pressure, High Temperature, or Both[24] uses a cylindrical tensile specimen tested into an enclosure pressurized with hydrogen or helium.

Another ASTM standard exists for quantitatively testing for the Hydrogen Embrittlement threshold stress for the onset of Hydrogen-Induced Cracking due to platings and coatings from Internal Hydrogen Embrittlement (IHE) and Environmental Hydrogen Embrittlement (EHE) - F1624-06 Standard Test Method for Measurement of Hydrogen Embrittlement Threshold in Steel by the Incremental Step Loading Technique.[25][26] and ASTM STP 962, "Hydrogen Embrittlement: Prevention and Control."

  • NACE TM0284-2003 (NACE International) Resistance to Hydrogen-Induced Cracking
  • ISO 11114-4:2005 (ISO)Test methods for selecting metallic materials resistant to hydrogen embrittlement.
  • Standard Test Method for Process Control Verification to Prevent Hydrogen Embrittlement in Plated or Coated Fasteners[27]
  • Standard Test Method for Mechanical Hydrogen Embrittlement Evaluation of Plating/Coating Processes and Service Environments[28]

See also


  1. ^ Morlett, J. O. (1958). "Hydrogen Embrittlement in Steels". SteeIInst. 189: 37. 
  2. ^ "Study reveals clues to cause of hydrogen embrittlement" (Press release). McGill University. November 19, 2012. Retrieved November 20, 2012. 
  3. ^ Vergani, Laura; Colombo, Chiara; et al. (2014). "Hydrogen effect on fatigue behavior of a quenched and tempered steel". Procedia Engineering. Elsevier. 74 (XVII International Colloquium on Mechanical Fatigue of Metals (ICMFM17)): 468–71. doi:10.1016/j.proeng.2014.06.299. Retrieved 9 May 2015. 
  4. ^ Djukic, M.B.; et al. (2014). "Hydrogen embrittlement of low carbon structural steel". Procedia Materials Science. Elsevier. 3 (20th European Conference on Fracture): 1167–1172. doi:10.1016/j.mspro.2014.06.190. Retrieved 9 May 2015. 
  5. ^ Djukic, M.B.; et al. (2015). "Hydrogen damage of steels: A case study and hydrogen embrittlement model". Engineering Failure Analysis. Elsevier. 58 (Recent case studies in Engineering Failure Analysis): 485–498. doi:10.1016/j.engfailanal.2015.05.017. Retrieved 9 May 2015. 
  6. ^ Djukic, Milos B.; et al. (2016). "Hydrogen Embrittlement of Industrial Components: Prediction, Prevention, and Models". Corrosion. NACE International. 72 (7; Environment Assisted Cracking): 943–961. doi:10.5006/1958. Retrieved 9 May 2015. 
  7. ^ Ambat, Rajan; Dwarakadasa (February 1996). "Effect of Hydrogen in aluminium and aluminium alloys: A review". Bulletin of Materials Science. Springer India. 19 (1): 103–114. 
  8. ^ a b Eberhart, Mark (2003). Why Things Break. New York: Harmony Books. p. 65. ISBN 1-4000-4760-9. 
  9. ^ Tartaglia, John; Lazzari, Kristen; et al. (March 2008). "A Comparison of Mechanical Properties and Hydrogen Embrittlement Resistance of Austempered vs Quenched and Tempered 4340 Steel". Metallurgical and Materials Transactions A. Springer US. 39 (3): 559–76. Bibcode:2008MMTA...39..559T. ISSN 1073-5623. doi:10.1007/s11661-007-9451-8. 
  10. ^ Jewett, R.P. (1973). Hydrogen Environment Embrittlement of Metals. NASA CR-2163. 
  11. ^ Gillette, J.L.; Kolpa, R.L. (November 2007). "Overview of interstate hydrogen pipeline systems" (PDF). Retrieved 2013-12-16. 
  12. ^ ZHONG, C.; et al. (1 April 2013). "Technical Reference for Hydrogen Compatiblity of Materials". Nature. 362: 435–437. 
  13. ^ Weman, Klas (2011). Welding Processes Handbook. Elsevier. p. 115. ISBN 978-0-85709-518-3. 
  14. ^ "Standard Test Method for Process Control Verification to Prevent Hydrogen Embrittlement in Plated or Coated Fasteners". Retrieved 24 February 2015. 
  15. ^ Main contributor: Clive D. Pearce (2006). "Hydrogen Embrittlement: An Overview from a Mechanical Fastenings Aspect" (PDF). The Fastener Engineering and Research Association. Confederation of British Metalforming. Retrieved 9 May 2015. 
  16. ^ Bhardwaj, B.P. (2014). The Complete Book on Ferroalloys. Khamla Nagar, New Delhi: Niir Project Consultancy Services. p. 12. ISBN 978-93-81039-29-8. Retrieved 10 May 2015. 
  17. ^ US Patent 4335754, Alfred C. C. Tseung; Anthony I. Onuchukwu & Ho C. Chan, "Prevention of hydrogen embrittlement of metals in corrosive environments", published 1982-06-22, issued 1983-02-02, assigned to Alfred C. C. Tseung and Anthony I. Onuchukwu 
  18. ^ Chalaftris, George (December 2003). "Abstract". Evaluation of Aluminium–Based Coatings for Cadmium Replacement (PhD thesis). Cranfield University School of Industrial and Manufacturing Science. Retrieved 9 May 2015. 
  19. ^ Federal Engineering and Design Support. "Embrittlement" (PDF). Fastenal. Fastenal Company Engineering Department. Retrieved 9 May 2015. 
  20. ^ Marchi, C. San (2012). "Technical Reference for Hydrogen Compatiblity of Materials" (PDF). 
  21. ^ Yun Chung (2 December 2014). "Validity of Caltrans' Environmental Hydrogen Embrittlement Test on Grade BD Anchor Rods in the SAS Span" (PDF). 
  22. ^ Dolan, Michael D.; Kochanek, Mark A.; Munnings, Christopher N.; McLennan, Keith G.; Viano, David M. (February 2015). "Hydride phase equilibria in V–Ti–Ni alloy membranes". Journal of Alloys and Compounds. 622: 276–281. doi:10.1016/j.jallcom.2014.10.081. 
  23. ^ "ASTM F1459 - 06(2012): Standard Test Method for Determination of the Susceptibility of Metallic Materials to Hydrogen Gas Embrittlement (HGE)". Retrieved 2015-02-24. 
  24. ^ "ASTM G142 - 98(2011) Standard Test Method for Determination of Susceptibility of Metals to Embrittlement in Hydrogen Containing Environments at High Pressure, High Temperature, or Both". Retrieved 2015-02-24. 
  25. ^ ASTM STP 543, "Hydrogen Embrittlement Testing"
  26. ^ Raymond L (1974). Hydrogen Embrittlement Testing. ASTM International. ISBN 978-0-8031-0373-3. 
  27. ^ "ASTM F1940 - 07a(2014) Standard Test Method for Process Control Verification to Prevent Hydrogen Embrittlement in Plated or Coated Fasteners". Retrieved 2015-02-24. 
  28. ^

Further reading

  • ASM international, ASM Handbook #13: Corrosion, ASM International, 1998

External links



A fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.[1] Fracture strength or breaking strength is the stress when a specimen fails or fractures.

The word fracture is often applied to bones of living creatures (i.e. a bone fracture), or to crystalline materials, such as gemstones or metal. Sometimes, individual crystals fracture without the structure actually separating into two or more pieces. Depending on the substance, a fracture reduces strength (most substances) or inhibits transmission of waves, such as light (optical crystals). A detailed understanding of how fracture occurs in materials may be assisted by the study of fracture mechanics.

Fracture strength

Stress vs. strain curve typical of aluminum
1. Ultimate tensile strength
2. Yield strength
3. Proportional limit stress
4. Fracture
5. Offset strain (typically 0.2%)

Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture.[2] This is usually determined for a given specimen by a tensile test, which charts the stress-strain curve (see image). The final recorded point is the fracture strength.

Ductile materials have a fracture strength lower than the ultimate tensile strength (UTS), whereas in brittle materials the fracture strength is equivalent to the UTS.[2] If a ductile material reaches its ultimate tensile strength in a load-controlled situation,[Note 1] it will continue to deform, with no additional load application, until it ruptures. However, if the loading is displacement-controlled,[Note 2] the deformation of the material may relieve the load, preventing rupture.


Brittle fracture

Brittle fracture in glass
Fracture of an aluminum crank arm of a bicycle, where Bright= brittle fracture, Dark= fatigue fracture.

In brittle fracture, no apparent plastic deformation takes place before fracture. In brittle crystalline materials, fracture can occur by cleavage as the result of tensile stress acting normal to crystallographic planes with low bonding (cleavage planes). In amorphous solids, by contrast, the lack of a crystalline structure results in a conchoidal fracture, with cracks proceeding normal to the applied tension. The sinking of RMS Titanic in 1912 from an iceberg collision is widely reported to have been due to brittle fracture of the hull's steel plates.[3]

The theoretical strength of a crystalline material is (roughly)

where: -

is the Young's modulus of the material,
is the surface energy, and
is the equilibrium distance between atomic centers.

On the other hand, a crack introduces a stress concentration modeled by

(For sharp cracks)

where: -

is the loading stress,
is half the length of the crack, and
is the radius of curvature at the crack tip.

Putting these two equations together, we get

Looking closely, we can see that sharp cracks (small ) and large defects (large ) both lower the fracture strength of the material.

Recently, scientists have discovered supersonic fracture, the phenomenon of crack propagation faster than the speed of sound in a material.[4] This phenomenon was recently also verified by experiment of fracture in rubber-like materials.

Brittle fracture may be avoided by limiting pressure and temperature within limits. Each system has a brittle fracture prevention limit curve defined by the weakest components at given temperatures and pressures allowing for the largest undetected preexisting flaw in each component.

Ductile fracture

Ductile failure of a specimen strained axially

In ductile fracture, extensive plastic deformation (necking) takes place before fracture. The terms rupture or ductile rupture describe the ultimate failure of ductile materials loaded in tension. Rather than cracking, the material "pulls apart," generally leaving a rough surface. In this case there is slow propagation and an absorption of a large amount energy before fracture.[citation needed] The ductility of a material is also referred to as toughness.

Schematic representation of the steps in ductile fracture (in pure tension)

Many ductile metals, especially materials with high purity, can sustain very large deformation of 50–100% or more strain before fracture under favorable loading condition and environmental condition. The strain at which the fracture happens is controlled by the purity of the materials. At room temperature, pure iron can undergo deformation up to 100% strain before breaking, while cast iron or high-carbon steels can barely sustain 3% of strain.[citation needed]

Because ductile rupture involves a high degree of plastic deformation, the fracture behavior of a propagating crack as modelled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation ahead of the crack as it propagates.

The basic steps in ductile fracture are: void formation, void coalescence (also known as crack formation), crack propagation, and failure, often resulting in a cup-and-cone shaped failure surface.

Crack separation modes

There are three ways of applying a force to enable a crack to propagate:

Fracture crack separation modes
  • Mode I crack – Opening mode (a tensile stress normal to the plane of the crack)
  • Mode II crack – Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front)
  • Mode III crack – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)

Crack initiation and propagation accompany fracture. The manner by which the crack propagates through the material gives great insight into the mode of fracture. In ductile materials (ductile fracture), the crack moves slowly and is accompanied by a large amount of plastic deformation around the crack tip. The crack will usually not extend unless an increased stress is applied. On the other hand, in dealing with brittle fracture, cracks spread very rapidly with little or no plastic deformation. The cracks that propagate in a brittle material will continue to grow and increase in magnitude once they are initiated. In a part made of a ductile material, the crack may progress to a section of the part where stresses a slighly lower and stop due to the blunting effect of plastic deformations at the crack tip. Another important mannerism of crack propagation is the way in which the advancing crack travels through the material. A crack that passes through the grains within the material is undergoing transgranular fracture. However, a crack that propagates along the grain boundaries is termed an intergranular fracture.

See also


  1. ^ A simple load-controlled tensile situation would be to support a specimen from above, and hang a weight from the bottom end. The load on the specimen is then independent of its deformation.
  2. ^ A simple displacement-controlled tensile situation would be to attach a very stiff jack to the ends of a specimen. As the jack extends, it controls the displacement of the specimen; the load on the specimen is dependent on the deformation.


  1. ^ Cherepanov, G.P., Mechanics of Brittle Fracture 
  2. ^ a b Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003), Materials and Processes in Manufacturing (9th ed.), Wiley, p. 32, ISBN 0-471-65653-4. 
  3. ^ [1]
  4. ^ C. H. Chen; H. P. Zhang; J. Niemczura; K. Ravi-Chandar; M. Marder (November 2011). "Scaling of crack propagation in rubber sheets". Europhysics Letters. 96 (3): 36009. Bibcode:2011EL.....9636009C. doi:10.1209/0295-5075/96/36009. 

Further reading

  • Dieter, G. E. (1988) Mechanical Metallurgy ISBN 0-07-100406-8
  • A. Garcimartin, A. , L. Bellon and S. Cilberto (1997) " Statistical Properties of Fracture Precursors ". Physical Review Letters, 79, 3202 (1997)
  • Callister, Jr., William D. (2002) Materials Science and Engineering: An Introduction. ISBN 0-471-13576-3
  • Peter Rhys Lewis, Colin Gagg, Ken Reynolds, CRC Press (2004), Forensic Materials Engineering: Case Studies.

External links



Heat exchanger in a steam power plant, fouled by macro fouling
Condenser tube with residues of biofouling (cut open)
Condenser tube with calcium carbonate scaling (cut open)
Brass tube with corrosion traces (cut open)
Cost relations between the individual types of fouling

Fouling is the accumulation of unwanted material on solid surfaces to the detriment of function. The fouling materials can consist of either living organisms (biofouling) or a non-living substance (inorganic or organic). Fouling is usually distinguished from other surface-growth phenomena, in that it occurs on a surface of a component, system or plant performing a defined and useful function, and that the fouling process impedes or interferes with this function.

Other terms used in the literature to describe fouling include: deposit formation, encrustation, crudding, deposition, scaling, scale formation, slagging, and sludge formation. The last six terms have a more narrow meaning than fouling within the scope of the fouling science and technology, and they also have meanings outside of this scope; therefore, they should be used with caution.

Fouling phenomena are common and diverse, ranging from fouling of ship hulls, natural surfaces in the marine environment (marine fouling), fouling of heat-transfer components through ingredients contained in the cooling water or gases, and even the development of plaque or calculus on teeth, or deposits on solar panels on Mars, among other examples.

This article is primarily devoted to the fouling of industrial heat exchangers, although the same theory is generally applicable to other varieties of fouling. In the cooling technology and other technical fields, a distinction is made between macro fouling and micro fouling. Of the two, micro fouling is the one which is usually more difficult to prevent and therefore more important.

Components subject to fouling

Following are examples of components that may be subject to fouling and the corresponding effects of fouling:

  • Heat exchanger surfaces – reduces thermal efficiency, decreases heat flux, increases temperature on the hot side, decreases temperature on the cold side, induces under-deposit corrosion, increases use of cooling water;
  • Piping, flow channels – reduces flow, increases pressure drop, increases upstream pressure, increases energy expenditure, may cause flow oscillations, slugging in two-phase flow, cavitation; may increase flow velocity elsewhere, may induce vibrations, may cause flow blockage;
  • Ship hulls – creates additional drag, increases fuel usage, reduces maximum speed;[1]
  • Turbines – reduces efficiency, increases probability of failure;
  • Solar panels – decreases the electrical power generated;
  • Reverse osmosis membranes – increases pressure drop, increases energy expenditure, reduces flux, membrane failure (in severe cases);[2]
  • Electrical heating elements – increases temperature of the element, increases corrosion, reduces lifespan;
  • Nuclear fuel in pressurized water reactors – axial offset anomaly,[3] may need to de-rate the power plant;
  • Injection/spray nozzles (e.g., a nozzle spraying a fuel into a furnace) – incorrect amount injected, malformed jet, component inefficiency, component failure;
  • Venturi tubes, orifice plates – inaccurate or incorrect measurement of flow rate;
  • Pitot tubes in airplanes – inaccurate or incorrect indication of airplane speed;
  • Spark plug electrodes in cars – engine misfiring;[4]
  • Production zone of petroleum reservoirs and oil wells – decreased petroleum production with time; plugging; in some cases complete stoppage of flow in a matter of days;[5]
  • Teeth – promotes tooth or gum disease, decreases aesthetics;
  • Living organisms – deposition of excess minerals (e.g., calcium, iron, copper) in tissues is (sometimes controversially) linked to aging/senescence.

Macro fouling

Macro fouling is caused by coarse matter of either biological or inorganic origin, for example industrially produced refuse. Such matter enters into the cooling water circuit through the cooling water pumps from sources like the open sea, rivers or lakes. In closed circuits, like cooling towers, the ingress of macro fouling into the cooling tower basin is possible through open canals or by the wind. Sometimes, parts of the cooling tower internals detach themselves and are carried into the cooling water circuit. Such substances can foul the surfaces of heat exchangers and may cause deterioration of the relevant heat transfer coefficient. They may also create flow blockages, redistribute the flow inside the components, or cause fretting damage.

  • Manmade refuse;
  • Detached internal parts of components;
  • Tools and other "foreign objects" accidentally left after maintenance;
  • Algae;
  • Mussels;
  • Leaves, parts of plants up to entire trunks.

Micro fouling

As to micro fouling, distinctions are made between:[6]

  • Scaling or precipitation fouling, as crystallization of solid salts, oxides and hydroxides from water solutions, for example, calcium carbonate or calcium sulfate;
  • Particulate fouling, i.e., accumulation of particles, typically colloidal particles, on a surface;
  • Corrosion fouling, i.e., in-situ growth of corrosion deposits, for example, magnetite on carbon steel surfaces;
  • Chemical reaction fouling, for example, decomposition or polymerization of organic matter on heating surfaces;
  • Solidification fouling - when components of the flowing fluid with a high-melting point freeze onto a subcooled surface;
  • Biofouling, like settlements of bacteria and algae;
  • Composite fouling, whereby fouling involves more than one foulant or fouling mechanism.

Precipitation fouling

Limescale buildup inside a pipe both reduces liquid flow through the pipe, as well as reduces thermal conduction from the liquid to the outer pipe shell. Both effects will reduce the pipe's overall thermal efficiency when used as a heat exchanger.
Temperature dependence of the solubility of calcium sulfate (3 phases) in pure water. The water is pressurized so that it can be maintained in the liquid state at the elevated temperatures.

Scaling or precipitation fouling involves crystallization of solid salts, oxides and hydroxides from solutions. These are most often water solutions, but non-aqueous precipitation fouling is also known. Precipitation fouling is a very common problem in boilers and heat exchangers operating with hard water and often results in limescale.

Through changes in temperature, or solvent evaporation or degasification, the concentration of salts may exceed the saturation, leading to a precipitation of solids (usually crystals).

As an example, the equilibrium between the readily soluble calcium bicarbonate - always prevailing in natural water - and the poorly soluble calcium carbonate, the following chemical equation may be written:

The calcium carbonate that forms through this reaction precipitates. Due to the temperature dependence of the reaction, and increasing volatility of CO2 with increasing temperature, the scaling is higher at the hotter outlet of the heat exchanger than at the cooler inlet.

In general, the dependence of the salt solubility on temperature or presence of evaporation will often be the driving force for precipitation fouling. The important distinction is between salts with "normal" or "retrograde" dependence of solubility on temperature. The salts with the "normal" solubility increase their solubility with increasing temperature and thus will foul the cooling surfaces. The salts with "inverse" or "retrograde" solubility will foul the heating surfaces. An example of the temperature dependence of solubility is shown in the figure. Calcium sulfate is a common precipitation foulant of heating surfaces due to its retrograde solubility.

Precipitation fouling can also occur in the absence of heating or vaporization. For example, calcium sulfate decreases it solubility with decreasing pressure. This can lead to precipitation fouling of reservoirs and wells in oil fields, decreasing their productivity with time.[7] Fouling of membranes in reverse osmosis systems can occur due to differential solubility of barium sulfate in solutions of different ionic strength.[2] Similarly, precipitation fouling can occur because of solubility changes induced by other factors, e.g., liquid flashing, liquid degassing, redox potential changes, or mixing of incompatible fluid streams.

The following lists some of the industrially common phases of precipitation fouling deposits observed in practice to form from aqueous solutions:

The deposition rate by precipitation is often described by the following equations:

Surface crystallisation:


m - mass of the material (per unit surface area), kg/m2
t - time, s
Cb - concentration of the substance in the bulk of the fluid, kg/m3
Ci - concentration of the substance at the interface, kg/m3
Ce - equilibrium concentration of the substance at the conditions of the interface, kg/m3
n1, n2 - order of reaction for the crystallisation reaction and the overall deposition process, respectively, dimensionless
kt, kr, kd - kinetic rate constants for the transport, the surface reaction, and the overall deposition reaction, respectively; with the dimension of m/s (when n1 and n2 = 1)

Particulate fouling

Fouling by particles suspended in water ("crud") or in gas progresses by a mechanism different than precipitation fouling. This process is usually most important for colloidal particles, i.e., particles smaller than about 1 μm in at least one dimension (but which are much larger than atomic dimensions). Particles are transported to the surface by a number of mechanisms and there they can attach themselves, e.g., by flocculation or coagulation. Note that the attachment of colloidal particles typically involves electrical forces and thus the particle behaviour defies the experience from the macroscopic world. The probability of attachment is sometimes referred to as "sticking probability", P:[6]

where kd and kt are the kinetic rate constants for deposition and transport, respectively. The value of P for colloidal particles is a function of both the surface chemistry, geometry, and the local thermohydraulic conditions.

An alternative to using the sticking probability is to use a kinetic attachment rate constant, assuming the first order reaction:[9][10]

and then the transport and attachment kinetic coefficients are combined as two processes occurring in series:


  • dm/dt is the rate of the deposition by particles, kg m−2 s−1,
  • ka, kt and kd are the kinetic rate constants for deposition, m/s,
  • Ci and Cb are the concentration of the particle foulant at the interface and in the bulk fluid, respectively; kg m3.

Being essentially a surface chemistry phenomenon, this fouling mechanism can be very sensitive to factors that affect colloidal stability, e.g., zeta potential. A maximum fouling rate is usually observed when the fouling particles and the substrate exhibit opposite electrical charge, or near the point of zero charge of either of them.

Particles larger than those of colloidal dimensions may also foul e.g., by sedimentation ("sedimentation fouling") or straining in small-size openings.

With time, the resulting surface deposit may harden through processes collectively known as "deposit consolidation" or, colloquially, "aging".

The common particulate fouling deposits formed from aqueous suspensions include:

Fouling by particles from gas aerosols is also of industrial significance. The particles can be either solid or liquid. The common examples can be fouling by flue gases, or fouling of air-cooled components by dust in air. The mechanisms are discussed in article on aerosol deposition.

Corrosion fouling

Corrosion deposits are created in-situ by the corrosion of the substrate. They are distinguished from fouling deposits, which form from material originating ex-situ. Corrosion deposits should not be confused with fouling deposits formed by ex-situ generated corrosion products. Corrosion deposits will normally have composition related to the composition of the substrate. Also, the geometry of the metal-oxide and oxide-fluid interfaces may allow practical distinction between the corrosion and fouling deposits. An example of corrosion fouling can be formation of an iron oxide or oxyhydroxide deposit from corrosion of the carbon steel underneath. Corrosion fouling should not be confused with fouling corrosion, i.e., any of the types of corrosion that may be induced by fouling.

Chemical reaction fouling

Chemical reactions may occur on contact of the chemical species in the process fluid with heat transfer surfaces. In such cases, the metallic surface sometimes acts as a catalyst. For example, corrosion and polymerization occurs in cooling water for the chemical industry which has a minor content of hydrocarbons. Systems in petroleum processing are prone to polymerization of olefins or deposition of heavy fractions (asphaltenes, waxes, etc.). High tube wall temperatures may lead to carbonizing of organic matter. Food industry, for example milk processing, also experiences fouling problems by chemical reactions.

Fouling through an ionic reaction with an evolution of an inorganic solid is commonly classified as precipitation fouling (not chemical reaction fouling).

Solidification fouling

Solidification fouling occurs when a component of the flowing fluid "freezes" onto a surface forming a solid fouling deposit. Examples may include solidification of wax (with a high melting point) from a hydrocarbon solution, or of molten ash (carried in a furnace exhaust gas) onto a heat exchanger surface. The surface needs to have a temperature below a certain threshold; therefore, it is said to be subcooled in respect to the solidification point of the foulant.


A fragment of a canal lock in Northern France, covered with zebra mussels

Biofouling or biological fouling is the undesirable accumulation of micro-organisms, algae and diatoms, plants, and animals on surfaces, for example ships' hulls, or piping and reservoirs with untreated water. This can be accompanied by microbiologically influenced corrosion (MIC).

Bacteria can form biofilms or slimes. Thus the organisms can aggregate on surfaces using colloidal hydrogels of water and extracellular polymeric substances (EPS) (polysaccharides, lipids, nucleic acids, etc.). The biofilm structure is usually complex.

Bacterial fouling can occur under either aerobic (with oxygen dissolved in water) or anaerobic (no oxygen) conditions. In practice, aerobic bacteria prefer open systems, when both oxygen and nutrients are constantly delivered, often in warm and sunlit environments. Anaerobic fouling more often occurs in closed systems when sufficient nutrients are present. Examples may include sulfate-reducing bacteria (or sulfur-reducing bacteria), which produce sulfide and often cause corrosion of ferrous metals (and other alloys). Sulfide-oxidizing bacteria (e.g., Acidithiobacillus), on the other hand, can produce sulfuric acid, and can be involved in corrosion of concrete.

Zebra mussels serve as an example of larger animals that have caused widespread fouling in North America.

Composite fouling

Composite fouling is common. This type of fouling involves more than one foulant or more than one fouling mechanism[11] working simultaneously. The multiple foulants or mechanisms may interact with each other resulting in a synergistic fouling which is not a simple arithmetic sum of the individual components.

Fouling on Mars

NASA Mars Exploration Rovers (Spirit and Opportunity) experienced (presumably) abiotic fouling of solar panels by dust particles from the Martian atmosphere.[12] Some of the deposits subsequently spontaneously cleaned off. This illustrates the universal nature of the fouling phenomena.

Quantification of fouling

The most straightforward way to quantify fairly uniform fouling is by stating the average deposit surface loading, i.e., kg of deposit per m² of surface area. The fouling rate will then be expressed in kg/m²s, and it is obtained by dividing the deposit surface loading by the effective operating time. The normalized fouling rate (also in kg/m²s) will additionally account for the concentration of the foulant in the process fluid (kg/kg) during preceding operations, and is useful for comparison of fouling rates between different systems. It is obtained by dividing the fouling rate by the foulant concentration. The fouling rate constant (m/s) can be obtained by dividing the normalized fouling rate by the mass density of the process fluid (kg/m³).

Deposit thickness (μm) and porosity (%) are also often used for description of fouling amount. The relative reduction of diameter of piping or increase of the surface roughness can be of particular interest when the impact of fouling on pressure drop is of interest.

In heat transfer equipment, where the primary concern is often the effect of fouling on heat transfer, fouling can be quantified by the increase of the resistance to the flow of heat (m²K/W) due to fouling (termed "fouling resistance"), or by development of heat transfer coefficient (W/m²K) with time.

If under-deposit or crevice corrosion is of primary concern, it is important to note non-uniformity of deposit thickness (e.g., deposit waviness), localized fouling, packing of confined regions with deposits, creation of occlusions, "crevices", "deposit tubercles",[13] or sludge piles. Such deposit structures can create environment for underdeposit corrosion of the substrate material, e.g., intergranular attack, pitting, stress corrosion cracking, or localized wastage. Porosity and permeability of the deposits will likely influence the probability of underdeposit corrosion. Deposit composition can also be important - even minor components of the deposits can sometimes cause severe corrosion of the underlying metal (e.g., vanadium in deposits of fired boilers causing hot corrosion).

There is no general rule on how much deposit can be tolerated, it depends on the system. In many cases, a deposit even a few micrometers thick can be troublesome. A deposit in a millimeter-range thickness will be of concern in almost any application.

Progress of fouling with time

Deposit on a surface does not always develop steadily with time. The following fouling scenarios can be distinguished, depending on the nature of the system and the local thermohydraulic conditions at the surface:

  • Induction period. Sometimes, a near-nil fouling rate is observed when the surface is new or very clean. This is often observed in biofouling and precipitation fouling. After the "induction period", the fouling rate increases.
  • "Negative" fouling. This can occur when fouling rate is quantified by monitoring heat transfer. Relatively small amounts of deposit can improve heat transfer, relative to clean surface, and give an appearance of "negative" fouling rate and negative total fouling amount. Negative fouling is often observed under nucleate-boiling heat-transfer conditions (deposit improves bubble nucleation) or forced-convection (if the deposit increases the surface roughness and the surface is no longer "hydraulically smooth"). After the initial period of "surface roughness control", the fouling rate usually becomes strongly positive.
  • Linear fouling. The fouling rate can be steady with time. This is a common case.
  • Falling fouling. Under this scenario, the fouling rate decreases with time, but never drops to zero. The deposit thickness does not achieve a constant value. The progress of fouling can be often described by two numbers: the initial fouling rate (a tangent to the fouling curve at zero deposit loading or zero time) and the fouling rate after a long period of time (an oblique asymptote to the fouling curve).
  • Asymptotic fouling. Here, the fouling rate decreases with time, until it finally reaches zero. At this point, the deposit thickness remains constant with time (a horizontal asymptote). This is often the case for relatively soft or poorly adherent deposits in areas of fast flow. The asymptote is usually interpreted as the deposit loading at which the deposition rate equals the deposit removal rate.
  • Accelerating fouling. Under this scenario, the fouling rate increases with time; the rate of deposit buildup accelerates with time (perhaps until it becomes transport limited). Mechanistically, this scenario can develop when fouling increases the surface roughness, or when the deposit surface exhibits higher chemical propensity to fouling than the pure underlying metal.
  • Seesaw fouling. Here, fouling loading generally increases with time (often assuming a generally linear or falling rate), but, when looked at in more detail, the fouling progress is periodically interrupted and takes the form of sawtooth curve. The periodic sharp variations in the apparent fouling amount often correspond to the moments of system shutdowns, startups or other transients in operation. The periodic variations are often interpreted as periodic removal of some of the deposit (perhaps deposit re-suspension due to pressure pulses, spalling due thermal stresses, or exfoliation due to redox transients). Steam blanketing has been postulated to occur between the partially spalled deposits and the heat transfer surface. However, other reasons are possible, e.g., trapping of air inside the surface deposits during shutdowns, or inaccuracy of temperature measurements during transients ("temperature streaming").[14]

Fouling modelling

Schematics of the fouling process consisting of simultaneous foulant deposition and deposit removal.

Fouling of a system can be modelled as consisting of several steps:

  • Generation or ingress of the species that causes fouling ("foulant sourcing");
  • Foulant transport with the stream of the process fluid (most often by advection);
  • Foulant transport from the bulk of the process fluid to the fouling surface. This transport is often by molecular or turbulent-eddy diffusion, but may also occur by inertial coasting/impaction, particle interception by the surface (for particles with finite sizes), electrophoresis, thermophoresis, diffusiophoresis, Stefan flow (in condensation and evaporation), sedimentation, Magnus force (acting on rotating particles), thermoelectric effect,[15][16] and other mechanisms.
  • Induction period, i.e., a near-nil fouling rate at the initial period of fouling (observed only for some fouling mechanisms);
  • Foulant crystallisation on the surface (or attachment of the colloidal particle, or chemical reaction, or bacterial growth);
  • Sometimes fouling autoretardation, i.e., reduction (or potentially enhancement) of crystallisation/attachment rate due to changes in the surface conditions caused by the fouling deposit;
  • Deposit dissolution (or re-entrainment of loosely attached particles);
  • Deposit consolidation on the surface (e.g., through Ostwald ripening or differential solubility in temperature gradient) or cementation, which account for deposit losing its porosity and becoming more tenacious with time;
  • Deposit spalling, erosion wear, or exfoiliation.

Deposition consists of transport to the surface and subsequent attachment. Deposit removal is either through deposit dissolution, particle re-entrainment, or deposit spalling, erosive wear, or exfoliation. Fouling results from foulant generation, foulant deposition, deposit removal, and deposit consolidation.

For the modern model of fouling involving deposition with simultaneous deposit re-entrainment and consolidation,[17] the fouling process can be represented by the following scheme:

      [ rate of deposit accumulation ] = [ rate of deposition ] - [ rate of re-entrainment of unconsolidated deposit ]

      [ rate of accumulation of unconsolidated deposit ] = [ rate of deposition ] - [ rate of re-entrainment of unconsolidated deposit ] - [ rate of consolidation of unconsolidated deposit ]

Following the above scheme, the basic fouling equations can be written as follows (for steady-state conditions with flow, when concentration remains constant with time):


  • m is the mass loading of the deposit (consolidated and unconsolidated) on the surface (kg/m2);
  • t is time (s);
  • kd is the deposition rate constant (m/s);
  • ρ is the fluid density (kg/m3);
  • Cm - mass fraction of foulant in the fluid (kg/kg);
  • λr is the re-entrainment rate constant (1/s);
  • mr is the mass loading of the removable (i.e., unconsolidated) fraction of the surface deposit (kg/m2); and
  • λc is the consolidation rate constant (1/s).

This system of equations can be integrated (taking that m = 0 and mr = 0 at t = 0) to the form:

where λ = λr + λc.

This model reproduces either linear, falling, or asymptotic fouling, depending on the relative values of k, λr, and λc. The underlying physical picture for this model is that of a two-layer deposit consisting of consolidated inner layer and loose unconsolidated outer layer. Such a bi-layer deposit is often observed in practice. The above model simplifies readily to the older model of simultaneous deposition and re-entrainment[18] (which neglects consolidation) when λc=0. In the absence of consolidation, the asymptotic fouling is always anticipated by this older model and the fouling progress can be described as:

where m* is the maximum (asymptotic) mass loading of the deposit on the surface (kg/m2).

Economic and environmental importance of fouling

Fouling is ubiquitous and generates tremendous operational losses, not unlike corrosion. For example, one estimate puts the losses due to fouling of heat exchangers in industrialized nations to be about 0.25% of their GDP.[19] Another analysis[20] estimated (for 2006) the economical loss due to boiler and turbine fouling in China utilities at 4.68 billion dollars, which is about 0.169% the country GDP .

The losses initially result from impaired heat transfer, corrosion damage (in particular under-deposit and crevice corrosion), increased pressure drop, flow blockages, flow redistribution inside components, flow instabilities, induced vibrations (possibly leading to other problems, e.g., fatigue[21]), fretting, premature failure of electrical heating elements, and a large number of other often unanticipated problems. In addition, the ecological costs should be (but typically are not) considered. The ecological costs arise from the use of biocides for the avoidance of biofouling, from the increased fuel input to compensate for the reduced output caused by fouling, and an increased use of cooling water in once-through cooling systems.

For example, "normal" fouling at a conventionally fired 500 MW (net electrical power) power station unit accounts for output losses of the steam turbine of 5 MW and more. In a 1,300 MW nuclear power station, typical losses could be 20 MW and up (up to 100% if the station shuts down due to fouling-induced component degradation). In seawater desalination plants, fouling may reduce the gained output ratio by two-digit percentages (the gained output ratio is an equivalent that puts the mass of generated distillate in relation to the steam used in the process). The extra electrical consumption in compressor-operated coolers is also easily in the two-digit area. In addition to the operational costs, also the capital cost increases because the heat exchangers have to be designed in larger sizes to compensate for the heat-transfer loss due to fouling. To the output losses listed above, one needs to add the cost of down-time required to inspect, clean, and repair the components (millions of dollars per day of shutdown in lost revenue in a typical power plant), and the cost of actually doing this maintenance. Finally, fouling is often a root cause of serious degradation problems that may limit the life of components or entire plants.

Fouling control

The most fundamental and usually preferred method of controlling fouling is to prevent the ingress of the fouling species into the cooling water circuit. In steam power stations and other major industrial installations of water technology, macro fouling is avoided by way of pre-filtration and cooling water debris filters. Some plants employ foreign-object exclusion program (to eliminate the possibility of salient introduction of unwanted materials, e.g., forgetting tools during maintenance). Acoustic monitoring is sometimes employed to monitor for fretting by detached parts. In the case of micro fouling, water purification is achieved with extensive methods of water treatment, microfiltration, membrane technology (reverse osmosis, electrodeionization) or ion-exchange resins. The generation of the corrosion products in the water piping systems is often minimized by controlling the pH of the process fluid (typically alkanization with ammonia, morpholine, ethanolamine or sodium phosphate), control of oxygen dissolved in water (for example, by addition of hydrazine), or addition of corrosion inhibitors.

For water systems at relatively low temperatures, the applied biocides may be classified as follows: inorganic chlorine and bromide compounds, chlorine and bromide cleavers[disambiguation needed], ozone and oxygen cleavers, unoxidizable biocides. One of the most important unoxidizable biocides is a mixture of chloromethyl-isothiazolinone and methyl-isothiazolinone. Also applied are dibrom nitrilopropionamide and quaternary ammonium compounds. For underwater ship hulls bottom paints are applied.

[22] can reduce fouling in many systems, mainly by interfering with the crystallization, attachment, or consolidation steps of the fouling process. Examples for water systems are: chelating agents (for example, EDTA), long-chain aliphatic amines or polyamines (for example, , helamin, and other "film-forming" amines), organic phosphonic acids (for example, etidronic acid), or polyelectrolytes (for example, polyacrylic acid,[23] polymethacrylic acid, usually with a molecular weight lower than 10000). For fired boilers, aluminum or magnesium additives can lower the melting point of ash and promote creation of deposits which are easier to remove. See also process chemicals.

Magnetic water treatment has been a subject of controversy as to its effectiveness for fouling control since the 1950s. The prevailing opinion is that it simply "does not work".[24] Nevertheless, some studies suggest that it may be effective under some conditions to reduce buildup of calcium carbonate deposits.[25]

On the component design level, fouling can often (but not always) be minimized by maintaining a relatively high (for example, 2 m/s) and uniform fluid velocity throughout the component. Stagnant regions need to be eliminated. Components are normally overdesigned to accommodate the fouling anticipated between cleanings. However, a significant overdesign can be a design error because it may lead to increased fouling due to reduced velocities. Periodic on-line pressure pulses or backflow can be effective if the capability is carefully incorporated at the design time. Blowdown capability is always incorporated into steam generators or evaporators to control the accumulation of non-volatile impurities that cause or aggravate fouling. Low-fouling surfaces (for example, very smooth, implanted with ions, or of low surface energy like Teflon) are an option for some applications. Modern components are typically required to be designed for ease of inspection of internals and periodic cleaning. On-line fouling monitoring systems are designed for some application so that blowing or cleaning can be applied before unpredictable shutdown is necessary or damage occurs.

Chemical or mechanical cleaning processes for the removal of deposits and scales are recommended when fouling reaches the point of impacting the system performance or an onset of significant fouling-induced degradation (e.g., by corrosion). These processes comprise pickling with acids and complexing agents, cleaning with high-velocity water jets ("water lancing"), recirculating ("blasting") with metal, sponge or other balls, or propelling offline mechanical "bullet-type" tube cleaners. Whereas chemical cleaning causes environmental problems through the handling, application, storage and disposal of chemicals, the mechanical cleaning by means of circulating cleaning balls or offline "bullet-type" cleaning can be an environmentally friendlier alternative. In some heat-transfer applications, mechanical mitigation with dynamic scraped surface heat exchangers is an option. Also ultrasonic or abrasive cleaning methods are available for many specific applications.

See also


  1. ^ "Marine fouling and its prevention"; prepared for Bureau of Ships, Navy Dept, Woods Hole Oceanographic Institution, United States, Navy Dept. Bureau of Ship, 1952. (pdf)
  2. ^ a b Siobhán Francesca E. Boerlage, "Scaling and Particulate Fouling in Membrane Filtration Systems", Taylor & Francis; 2001, ISBN 90-5809-242-9 (Google books)
  3. ^ Joshua M. Hawkes, "The Simulation and Study of Conditions Leading to Axial Offset Anomaly in Pressurized Water Reactors", Georgia Institute of Technology Master of Science Thesis, December 2004. (pdf)
  4. ^ "Spark Plug Faces", brochure "Bosch Spark Plugs 0307", Part 1 (pdf)
  5. ^ G.A. Mansoori "Physicochemical Basis of Arterial Blockage / Fouling. Prediction and Prevention." Department of Chemical Engineering, University of Illinois at Chicago, on-line publication, September 2001 (pdf)
  6. ^ a b T.R. Bott, "Fouling of Heat Exchangers (Chemical Engineering Monographs)", Elsevier Science, 1995.
  7. ^ J. Moghadasi, H. Müller-Steinhagen, M. Jamialahmadi, and A. Sharif, "Scale Deposition in Porous Media and their Removal by EDTA Injection ", ECI Engineering Conferences International Symposium Series, Heat Exchanger Fouling and Cleaning VII, July 1–6, 2007 - Tomar, Portugal. (pdf)
  8. ^ "Modeling PWR Fuel Corrosion Product Deposition and Growth Processes (5)", Technical Report 1009734, Electric Power Research Institute, Palo Alto, California, USA, 2004.
  9. ^ Eli Ruckenstein and Dennis C. Prieve, "Rate of deposition of Brownian particles under the action of London and double-layer forces", J. Chem. Soc., Faraday Trans. 2, 1973, 69, 1522-1536 (abstract).
  10. ^ Bruce D. Bowen and Norman Epstein, "Fine particle deposition in smooth parallel-plate channels", Journal of Colloid and Interface Science, Volume 72, Issue 1,15 October 1979, Pages 81-97 (abstract)
  11. ^ Hong Lu, "Composite Fouling of Heat Exchanger Surfaces", Nova Science Books, New York, 2007.
  12. ^ Mars Pathfinder - Dust Settling (MAE)
  13. ^ H. M. Herro (Nalco Chemical Company), "Deposit-Related Corrosion in Industrial Cooling Water Systems", Presented at the National Association of Corrosion Engineers Corrosion ’89 meeting, New Orleans, Louisiana, April 17–21, 1989 ((pdf).
  14. ^ "Steam Generator Thermal Performance Degradation Case Studies", Report TR-110018, Electric Power Research Institute, Palo Alto, California, USA, 1998 (abstract).
  15. ^ V.P. Brusakov, "Law for the Deposition of Materials on Heat-Transmitting Surfaces under the Action of Thermoelectric Effects", Atomnaya Energiya, Vol.30, No.1, pp.10-14, January 1971.
  16. ^ D.H. Lister, ""Corrosion products in power generating systems". In: Fouling of Heat Exchanger Equipment", E.F. Somerscales and J.G. Knudsen (eds.), Hemisphere Pub. Corp., Washington, DC, USA, 1981, pp.135-200.
  17. ^ C.W. Turner, S.J. Klimas, "Modelling the Effect of Surface Chemistry on Particle Fouling Under Flow-Boiling Conditions", Proceeding of Heat Exchanger Fouling: Fundamental Approaches and Technical Solutions, 2001, July 8–13, Davos, Switzerland, AECL Report 12171.
  18. ^ D.O.Kern and R.E. Seaton, "A theoretical analysis of thermal surface fouling", Brit. Chem. Eng., 14, 5, 258, 1959.
  19. ^ H. Mueller-Steinhagen and A.P. Watkinson, "Fouling of Heat Exchanger--New Approaches to Solve Old Problem", Heat Transfer Engineering, 26(2), 2005.
  20. ^ Xu Zhi-Ming, ZHANG Zhong-Bin, and YANG Shan-Rang, "Costs due to utility fouling in China", ECI Engineering Conferences International Symposium Series, Heat Exchanger Fouling and Cleaning VII, July 1–6, 2007 - Tomar, Portugal. (pdf)
  21. ^ Herve BODINEAU and Thierry SOLLIER, "Tube support plate clogging up of French steam generators", Eurosafe webpage
  22. ^ J.C. Cowan and D.J. Weintritt, "Water-Formed Scale Deposits. A Comprehensive Study of the Prevention, Control, Removal and Use of Mineral Scale", Gulf Publishing Company, Houston, Texas, 1976.
  23. ^ "Dispersants for Tube Fouling Control: Volume 2: Short-Term Trial at ANO-2", Report 1003144, Electric Power Research Institute, Palo Alto, California, USA, 2001 (abstract)
  24. ^ "Magnetic Water Treatment Archived 2011-12-15 at the Wayback Machine.", Public Works Technical Bulletin 420-49-34, U.S. Army Corps of Engineers, 15 June 2001.
  25. ^ A. Szkatula, M. Balanda, M. Kopec, "Magnetic treatment of industrial water. Silica activation". Eur. Phys. J.Applied Physics, 1, vol. 18, p. 41-49, 2002 (abstract)

External links

Fatigue (material)

Fatigue (material)

In materials science, fatigue is the weakening of a material caused by repeatedly applied loads. It is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The nominal maximum stress values that cause such damage may be much less than the strength of the material typically quoted as the ultimate tensile stress limit, or the yield stress limit.

Fatigue occurs when a material is subjected to repeated loading and unloading. If the loads are above a certain threshold, microscopic cracks will begin to form at the stress concentrators such as the surface, persistent slip bands (PSBs), interfaces of constituents in the case of composites, and grain interfaces in the case of metals.[1] Eventually a crack will reach a critical size, the crack will propagate suddenly, and the structure will fracture. The shape of the structure will significantly affect the fatigue life; square holes or sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Round holes and smooth transitions or fillets will therefore increase the fatigue strength of the structure.

Fatigue life

The American Society for Testing and Materials defines fatigue life, Nf, as the number of stress cycles of a specified character that a specimen sustains before failure of a specified nature occurs.[2] For some materials, notably steel and titanium, there is a theoretical value for stress amplitude below which the material will not fail for any number of cycles, called a fatigue limit, endurance limit, or fatigue strength.[3]

Engineers have used any of three methods to determine the fatigue life of a material: the stress-life method, the strain-life method, and the linear-elastic fracture mechanics method.[4] One method to predict fatigue life of materials is the Uniform Material Law (UML).[5] UML was developed for fatigue life prediction of aluminium and titanium alloys by the end of 20th century and extended to high-strength steels,[6] and cast iron.[7]

Characteristics of fatigue

Fracture of an aluminium crank arm. Dark area of striations: slow crack growth. Bright granular area: sudden fracture.
  • In metal alloys, and for the simplifying case when there are no macroscopic or microscopic discontinuities, the process starts with dislocation movements at the microscopic level, which eventually form persistent slip bands that become the nucleus of short cracks.
  • Macroscopic and microscopic discontinuities (at the crystalline grain scale) as well as component design features which cause stress concentrations (holes, keyways, sharp changes of load direction etc.) are common locations at which the fatigue process begins.
  • Fatigue is a process that has a degree of randomness (stochastic), often showing considerable scatter even in seemingly identical sample in well controlled environments.
  • Fatigue is usually associated with tensile stresses but fatigue cracks have been reported due to compressive loads.[8]
  • The greater the applied stress range, the shorter the life.
  • Fatigue life scatter tends to increase for longer fatigue lives.
  • Damage is cumulative. Materials do not recover when rested.
  • Fatigue life is influenced by a variety of factors, such as temperature, surface finish, metallurgical microstructure, presence of oxidizing or inert chemicals, residual stresses, scuffing contact (fretting), etc.
  • Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue limit below which continued loading does not lead to fatigue failure.
  • High cycle fatigue strength (about 104 to 108 cycles) can be described by stress-based parameters. A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of around 20–50 Hz. Other sorts of machines—like resonant magnetic machines—can also be used, to achieve frequencies up to 250 Hz.
  • Low cycle fatigue (loading that typically causes failure in less than 104 cycles) is associated with localized plastic behavior in metals; thus, a strain-based parameter should be used for fatigue life prediction in metals. Testing is conducted with constant strain amplitudes typically at 0.01–5 Hz.

Timeline of fatigue research history

Micrographs showing how surface fatigue cracks grow as material is further cycled. From Ewing & Humfrey, 1903
  • 1837: Wilhelm Albert publishes the first article on fatigue. He devised a test machine for conveyor chains used in the Clausthal mines.[9]
  • 1839: Jean-Victor Poncelet describes metals as being 'tired' in his lectures at the military school at Metz.
  • 1842: William John Macquorn Rankine recognises the importance of stress concentrations in his investigation of railroad axle failures. The Versailles train wreck was caused by fatigue failure of a locomotive axle.[10]
  • 1843: Joseph Glynn reports on the fatigue of an axle on a locomotive tender. He identifies the keyway as the crack origin.
  • 1848: The Railway Inspectorate reports one of the first tyre failures, probably from a rivet hole in tread of railway carriage wheel. It was likely a fatigue failure.
  • 1849: Eaton Hodgkinson is granted a "small sum of money" to report to the UK Parliament on his work in "ascertaining by direct experiment, the effects of continued changes of load upon iron structures and to what extent they could be loaded without danger to their ultimate security".
  • 1854: Braithwaite reports on common service fatigue failures and coins the term fatigue.[11]
  • 1860: Systematic fatigue testing undertaken by Sir William Fairbairn and August Wöhler.
  • 1870: Wöhler summarises his work on railroad axles. He concludes that cyclic stress range is more important than peak stress and introduces the concept of endurance limit.[9]
  • 1903: Sir James Alfred Ewing demonstrates the origin of fatigue failure in microscopic cracks.
  • 1910: proposes a log-log relationship for S-N curves, using Wöhler's test data.[12]
  • 1940: Sidney M. Cadwell publishes first rigorous study of fatigue in rubber.[13]
  • 1945: popularises Palmgren's (1924) linear damage hypothesis as a practical design tool.
  • 1952: An S-N curve model.[14]
  • 1954: The world's first commercial jetliner, the de Havilland Comet, suffers disaster as three planes break up in mid-air, causing de Havilland and all other manufacturers to redesign high altitude aircraft and in particular replace square apertures like windows with oval ones.
  • 1954: and explain fatigue crack-growth in terms of plastic strain in the tip of cracks.
  • 1961: P. C. Paris proposes methods for predicting the rate of growth of individual fatigue cracks in the face of initial scepticism and popular defence of Miner's phenomenological approach.
  • 1968: Tatsuo Endo and devise the rainflow-counting algorithm and enable the reliable application of Miner's rule to random loadings.[15]
  • 1970: elucidates the mechanisms and importance of crack closure in slowing the growth of a fatigue crack due to the wedging effect of plastic deformation left behind the tip of the crack.
  • 1973: and observe that fatigue life under multiaxial conditions is governed by the experience of the plane receiving the most damage, and that both tension and shear loads on the critical plane must be considered.[16]

High-cycle fatigue

Historically, most attention has focused on situations that require more than 104 cycles to failure where stress is low and deformation is primarily elastic.

Stress-cycle (S-N) curve

In high-cycle fatigue situations, materials performance is commonly characterized by an S-N curve, also known as a Wöhler curve . This is a graph of the magnitude of a cyclic stress (S) against the logarithmic scale of cycles to failure (N).

S-N curve for a brittle aluminium with an ultimate tensile strength of 320 MPa

S-N curves are derived from tests on samples of the material to be characterized (often called ) where a regular sinusoidal stress is applied by a testing machine which also counts the number of cycles to failure. This process is sometimes known as coupon testing. Each coupon test generates a point on the plot though in some cases there is a runout where the time to failure exceeds that available for the test (see censoring). Analysis of fatigue data requires techniques from statistics, especially survival analysis and linear regression.

The progression of the S-N curve can be influenced by many factors such as stress ratio (mean stress), loading frequency, temperature, corrosion, residual stresses, and the presence of notches. A constant fatigue life (CFL) diagram[17] is useful for the study of stress ratio effect. The Goodman-Line is a method used to estimate the influence of the mean stress on the fatigue strength.

Probabilistic nature of fatigue

As coupons sampled from a homogeneous frame will display a variation in their number of cycles to failure, the S-N curve should more properly be a Stress-Cycle-Probability (S-N-P) curve to capture the probability of failure after a given number of cycles of a certain stress. Probability distributions that are common in data analysis and in design against fatigue include the log-normal distribution, extreme value distribution, Birnbaum–Saunders distribution, and Weibull distribution.

Complex loadings

Spectrum loading

In practice, a mechanical part is exposed to a complex, often random, sequence of loads, large and small. In order to assess the safe life of such a part:

  1. Complex loading is reduced to a series of simple cyclic loadings using a technique such as rainflow analysis;
  2. A histogram of cyclic stress is created from the rainflow analysis to form a fatigue damage spectrum;
  3. For each stress level, the degree of cumulative damage is calculated from the S-N curve; and
  4. The effect of the individual contributions are combined using an algorithm such as Miner's rule.

For multiaxial loading

Since S-N curves are typically generated for uniaxial loading, some equivalence rule is needed whenever the loading is multiaxial. For simple, proportional loading histories (lateral load in a constant ratio with the axial), may be applied. For more complex situations, such as nonproportional loading, Critical plane analysis must be applied.

Miner's Rule

In 1945, popularised a rule that had first been proposed by A. Palmgren in 1924. The rule, variously called Miner's rule or the Palmgren-Miner linear damage hypothesis, states that where there are k different stress magnitudes in a spectrum, Si (1 ≤ ik), each contributing ni(Si) cycles, then if Ni(Si) is the number of cycles to failure of a constant stress reversal Si (determined by uni-axial fatigue tests), failure occurs when:

C is experimentally found to be between 0.7 and 2.2. Usually for design purposes, C is assumed to be 1. This can be thought of as assessing what proportion of life is consumed by a linear combination of stress reversals at varying magnitudes.

Although Miner's rule may be a useful approximation in many circumstances, it has several major limitations:

  1. It fails to recognise the probabilistic nature of fatigue and there is no simple way to relate life predicted by the rule with the characteristics of a probability distribution. Industry analysts often use design curves, adjusted to account for scatter, to calculate Ni(Si).
  2. The sequence in which high vs. low stress cycles are applied to a sample in fact affect the fatigue life, for which Miner's Rule does not account. In some circumstances, cycles of low stress followed by high stress cause more damage than would be predicted by the rule.[18] It does not consider the effect of an overload or high stress which may result in a compressive residual stress that may retard crack growth. High stress followed by low stress may have less damage due to the presence of compressive residual stress.

Constant Fatigue Life (CFL) diagram and Goodman relation

A CFL diagram is useful for stress ratio effect on S-N curve.[19] Also, in the presence of a steady stress superimposed on the cyclic loading, the Goodman relation can be used to estimate a failure condition. It plots stress amplitude against mean stress with the fatigue limit and the ultimate tensile strength of the material as the two extremes. Alternative failure criteria include Soderberg and Gerber.[20]

Paris' Law

Typical fatigue crack growth rate graph

In Fracture mechanics, Anderson, Gomez, and Paris derived relationships for the stage II crack growth with cycles N, in terms of the cyclical component ΔK of the Stress Intensity Factor K[21]

where a is the crack length and m is typically in the range 3 to 5 (for metals), which states that the rate of crack growth with respect to the cycles of load applied is a function of the stress intensity factor; this is named Paris' law.

This relationship was later modified by Forman in 1967[22] to make better allowance for the mean stress, by introducing a factor depending on (1 − R) where R = min stress/max stress, in the denominator.

Strain-cycle (ε-N) curve

Due to the proportionality between stress and strain, high cycle fatigue can also be expressed as strain amplitude vs. number of cycles. High cycle fatigue can be approximated by equating the total strain to just the elastic strain. Using this approximation, 12Δεelasticσf'E(2Nf)b


Δεelastic is the change in elastic strain per cycle
σf' is a parameter that scales with tensile strength obtained by fitting experimental data
E is the Young's modulus
Nf is the number of cycles to failure
b is the slope of the log-log curve again determined by fitting

The figure below shows high cycle fatigue as the right-most linear portion. Any test performed in the bottom left region (i.e. with a low enough strain amplitude and number of cycles) below the dark line has a high probability to avoid failure.

Graph showing fatigue failure as a function of strain amplitude.

As shown in the figure above (the left-most linear section) and as described in the next section, the total strain is approximated to be equal to just the plastic strain. For regions between high and low cycle fatigue, an unweighted sum of the high cycle and low cycle expressions gives a reasonable approximation with a built-in safety factor.[23]

Low-cycle fatigue

Where the stress is high enough for plastic deformation to occur, the accounting of the loading in terms of stress is less useful and the strain in the material offers a simpler and more accurate description. This type of fatigue is normally experienced by components which undergo a relatively small number of straining cycles. Low-cycle fatigue is usually characterised by the Coffin-Manson relation (published independently by in 1954[24] and in 1953):[25]


  • Δεp /2 is the plastic strain amplitude;
  • εf' is an empirical constant known as the fatigue ductility coefficient, the failure strain for a single reversal;
  • 2N is the number of reversals to failure (N cycles);
  • c is an empirical constant known as the fatigue ductility exponent, commonly ranging from −0.5 to −0.7 for metals in time independent fatigue. Slopes can be considerably steeper in the presence of creep or environmental interactions.

A similar relationship for materials such as Zirconium is used in the nuclear industry.[26]

Fatigue and fracture mechanics

The account above is purely empirical and, though it allows life prediction and design assurance, life improvement or design optimisation can be enhanced using Fracture mechanics. Fatigue of materials can be described as having four stages.

  1. Crack nucleation,
  2. Stage I crack-growth,
  3. Stage II crack-growth, and
  4. Ultimate ductile failure.

Design against fatigue

Dependable design against fatigue-failure requires thorough education and supervised experience in structural engineering, mechanical engineering, or materials science. There are four principal approaches to life assurance for mechanical parts that display increasing degrees of sophistication:[27]

  1. Design to keep stress below threshold of fatigue limit (infinite lifetime concept);
  2. Fail-safe, graceful degradation, and fault-tolerant design: Instruct the user to replace parts when they fail. Design in such a way that there is no single point of failure, and so that when any one part completely fails, it does not lead to catastrophic failure of the entire system.
  3. Safe-life design: Design (conservatively) for a fixed life after which the user is instructed to replace the part with a new one (a so-called lifed part, finite lifetime concept, or "safe-life" design practice); planned obsolescence and disposable product are variants that design for a fixed life after which the user is instructed to replace the entire device;
  4. Damage tolerant design: Instruct the user to inspect the part periodically for cracks and to replace the part once a crack exceeds a critical length. This approach usually uses the technologies of nondestructive testing and requires an accurate prediction of the rate of crack-growth between inspections. The designer sets some aircraft maintenance checks schedule frequent enough that parts are replaced while the crack is still in the "slow growth" phase. This is often referred to as damage tolerant design or "retirement-for-cause".

Stopping fatigue

Fatigue cracks that have begun to propagate can sometimes be stopped by drilling holes, called drill stops, in the path of the fatigue crack.[28] This is not recommended as a general practice because the hole represents a stress concentration factor which depends on the size of the hole and geometry, though the hole is typically less of a stress concentration than the removed tip of the crack. The possibility remains of a new crack starting in the side of the hole. It is always far better to replace the cracked part entirely.

Material change

Changes in the materials used in parts can also improve fatigue life. For example, parts can be made from better fatigue rated metals. Complete replacement and redesign of parts can also reduce if not eliminate fatigue problems. Thus helicopter rotor blades and propellers in metal are being replaced by composite equivalents. They are not only lighter, but also much more resistant to fatigue. They are more expensive, but the extra cost is amply repaid by their greater integrity, since loss of a rotor blade usually leads to total loss of the aircraft. A similar argument has been made for replacement of metal fuselages, wings and tails of aircraft.[29]

Peening treatment of welds and metal components

Example of a HFMI treated steel highway bridge to avoid fatigue along the weld transition.

Increases in fatigue life and strength are proportionally related to the depth of the compressive residual stresses imparted by surface enhancement processes such as shot peening but particularly by laser peening. Shot peening imparts compressive residual stresses approximately 0.005 inches deep, laser peening imparts compressive residual stresses from 0.040 to 0.100 inches deep, or deeper. Laser peening provide significant fatigue life extension through shock wave mechanics which plastically deform the surface of the metal component changing the material properties.[30] Laser peening can be applied to existing parts without redesign requirements or incorporated into new designs to allow for lighter materials or thinner designs to achieve comparable engineering results.

High frequency mechanical impact (HFMI) treatment of welds

The durability and life of dynamically loaded, welded steel structures are determined often by the welds, particular by the weld transitions. By selective treatment of weld transitions with the High Frequency Mechanical Impact (HFMI) treatment method,[31][32] the durability of many designs can be increased significantly. This method is universally applicable, requires only specific equipment and offers high reproducibility and a high degree of quality control.

Deep Cryogenic treatment

The use of Deep Cryogenic treatment has been shown to increase resistance to fatigue failure. Springs used in industry, auto racing and firearms have been shown to last up to six times longer when treated. Heat checking, which is a form of thermal cyclic fatigue has been greatly delayed.[33]

Notable fatigue failures

Versailles train crash

Versailles train disaster
Drawing of a fatigue failure in an axle by Joseph Glynn, 1843

Following the King's celebrations at the Palace of Versailles, a train returning to Paris crashed in May 1842 at Meudon after the leading locomotive broke an axle. The carriages behind piled into the wrecked engines and caught fire. At least 55 passengers were killed trapped in the carriages, including the explorer Jules Dumont d'Urville. This accident is known in France as the "Catastrophe ferroviaire de Meudon". The accident was witnessed by the British locomotive engineer Joseph Locke and widely reported in Britain. It was discussed extensively by engineers, who sought an explanation.

The derailment had been the result of a broken locomotive axle. Rankine's investigation of broken axles in Britain highlighted the importance of stress concentration, and the mechanism of crack growth with repeated loading. His and other papers suggesting a crack growth mechanism through repeated stressing, however, were ignored, and fatigue failures occurred at an ever-increasing rate on the expanding railway system. Other spurious theories seemed to be more acceptable, such as the idea that the metal had somehow "crystallized". The notion was based on the crystalline appearance of the fast fracture region of the crack surface, but ignored the fact that the metal was already highly crystalline.

de Havilland Comet

The recovered (shaded) parts of the wreckage of G-ALYP and the site (arrowed) of the failure

Two de Havilland Comet passenger jets broke up in mid-air and crashed within a few months of each other in 1954. As a result, systematic tests were conducted on a fuselage immersed and pressurised in a water tank. After the equivalent of 3,000 flights, investigators at the Royal Aircraft Establishment (RAE) were able to conclude that the crash had been due to failure of the pressure cabin at the forward Automatic Direction Finder window in the roof. This 'window' was in fact one of two apertures for the aerials of an electronic navigation system in which opaque fibreglass panels took the place of the window 'glass'. The failure was a result of metal fatigue caused by the repeated pressurisation and de-pressurisation of the aircraft cabin. Also, the supports around the windows were riveted, not bonded, as the original specifications for the aircraft had called for. The problem was exacerbated by the punch rivet construction technique employed. Unlike drill riveting, the imperfect nature of the hole created by punch riveting caused manufacturing defect cracks which may have caused the start of fatigue cracks around the rivet.

The fuselage roof fragment of G-ALYP on display in the Science Museum in London, showing the two ADF windows at-which the initial failure occurred.[34]

The Comet's pressure cabin had been designed to a safety factor comfortably in excess of that required by British Civil Airworthiness Requirements (2.5 times the cabin proof test pressure as opposed to the requirement of 1.33 times and an ultimate load of 2.0 times the cabin pressure) and the accident caused a revision in the estimates of the safe loading strength requirements of airliner pressure cabins.

In addition, it was discovered that the stresses around pressure cabin apertures were considerably higher than had been anticipated, especially around sharp-cornered cut-outs, such as windows. As a result, all future jet airliners would feature windows with rounded corners, greatly reducing the stress concentration. This was a noticeable distinguishing feature of all later models of the Comet. Investigators from the RAE told a public inquiry that the sharp corners near the Comets' window openings acted as initiation sites for cracks. The skin of the aircraft was also too thin, and cracks from manufacturing stresses were present at the corners.

Alexander L. Kielland oil platform capsizing

Fractures on the right side of the Alexander L. Kielland rig

The Alexander L. Kielland was a Norwegian semi-submersible drilling rig that capsized whilst working in the Ekofisk oil field in March 1980 killing 123 people. The capsizing was the worst disaster in Norwegian waters since World War II. The rig, located approximately 320 km east of Dundee, Scotland, was owned by the Stavanger Drilling Company of Norway and was on hire to the United States company Phillips Petroleum at the time of the disaster. In driving rain and mist, early in the evening of 27 March 1980 more than 200 men were off duty in the accommodation on the Alexander L. Kielland. The wind was gusting to 40 knots with waves up to 12 m high. The rig had just been winched away from the Edda production platform. Minutes before 18:30 those on board felt a 'sharp crack' followed by 'some kind of trembling'. Suddenly the rig heeled over 30° and then stabilised. Five of the six anchor cables had broken, with one remaining cable preventing the rig from capsizing. The list continued to increase and at 18.53 the remaining anchor cable snapped and the rig turned upside down.

A year later in March 1981, the investigative report[35] concluded that the rig collapsed owing to a fatigue crack in one of its six bracings (bracing D-6), which connected the collapsed D-leg to the rest of the rig. This was traced to a small 6 mm fillet weld which joined a non-load-bearing flange plate to this D-6 bracing. This flange plate held a sonar device used during drilling operations. The poor profile of the fillet weld contributed to a reduction in its fatigue strength. Further, the investigation found considerable amounts of lamellar tearing in the flange plate and cold cracks in the butt weld. Cold cracks in the welds, increased stress concentrations due to the weakened flange plate, the poor weld profile, and cyclical stresses (which would be common in the North Sea), seemed to collectively play a role in the rig's collapse.


See also


  1. ^ Kim, W. H.; Laird, C. (1978). "Crack nucleation and stage I propagation in high strain fatigue—II. mechanism". Acta Metallurgica. 26 (5): 789–799. doi:10.1016/0001-6160(78)90029-9. 
  2. ^ Stephens, R. I.; Fuchs, H. O. (2001). Metal Fatigue in Engineering (2nd ed.). John Wiley & Sons. p. 69. ISBN 978-0-471-51059-8. 
  3. ^ Bathias, C. (1999). "There is no infinite fatigue life in metallic materials". Fatigue & Fracture of Engineering Materials & Structures. 22 (7): 559–565. doi:10.1046/j.1460-2695.1999.00183.x. 
  4. ^ Shigley, J. E.; Mischke, C. R.; Budynas, R. G. (2003). Mechanical Engineering Design (7th ed.). McGraw Hill Higher Education. ISBN 978-0-07-252036-1. 
  5. ^ Bäumel, A. Jr.; Seeger, T. (1990). Materials Data for Cyclic Loading, Supplement 1. Materials Science Monographs. 61. Elsevier. ISBN 978-0-444-88603-3. 
  6. ^ Korkmaz, S. (2010). Uniform Material Law: Extension to High-Strength Steels. VDM. ISBN 978-3-639-25625-3. 
  7. ^ Korkmaz, S. (2011). "A Methodology to Predict Fatigue Life of Cast Iron: Uniform Material Law for Cast Iron". International Journal of Iron and Steel Research. 18 (8): 42–45. doi:10.1016/S1006-706X(11)60102-7. 
  8. ^ Fleck, N. A.; Shin, C. S.; Smith, R.A. (1985). "Fatigue Crack Growth Under Compressive Loading". Engineering Fracture Mechanics. 21 (1): 173–185. doi:10.1016/0013-7944(85)90063-3. 
  9. ^ a b Schutz, W. (1996). "A history of fatigue". Engineering Fracture Mechanics. 54 (2): 263–300. doi:10.1016/0013-7944(95)00178-6. 
  10. ^ Rankine, W. J. M. (1843). "On the causes of the unexpected breakage of the journals of railway axles, and on the means of preventing such accidents by observing the law of continuity in their construction". Minutes of the Proceedings of the Institution of Civil Engineers. 2 (1843): 105–107. doi:10.1680/imotp.1843.24600. 
  11. ^ Braithwaite, F. (1854). "On the fatigue and consequent fracture of metals". Institution of Civil Engineers, Minutes of Proceedings. 13 (1854): 463–467. doi:10.1680/imotp.1854.23960. 
  12. ^ Basquin, O. H. (1910). "The exponential law of endurance test". Proceeding of the American Society for Testing and Materials. 10: 625–630. 
  13. ^ Cadwell, Sidney; Merrill; Sloman; Yost (1940). "Dynamic fatigue life of rubber". Rubber Chemistry and Technology. 13 (2): 304–315. doi:10.5254/1.3539515. 
  14. ^ Murray, W. M., ed. (1952). "The statistical aspect of fatigue failure and its consequences". Fatigue and Fracture of Metals. Technology Press of the Massachusetts Institute of Technology/Wiley. pp. 182–196. 
  15. ^ Matsuishi, M.; Endo, T. (1968). Fatigue of Metals Subjected to Varying Stress. Japan Society of Mechanical Engineers. 
  16. ^ Brown, M. W.; Miller, K. J. (1973). "A theory for fatigue failure under multiaxial stress-strain conditions". Proceedings of the Institution of Mechanical Engineers. 187 (1): 745–755. doi:10.1243/PIME_PROC_1973_187_161_02. 
  17. ^ Kawai, M.; Itoh, N. (2014). "A failure-mode based anisomorphic constant life diagram for a unidirectional carbon/epoxy laminate under off-axis fatigue loading at room temperature". Journal of Composite Materials. 48 (5): 571–592. doi:10.1177/0021998313476324. 
  18. ^ Eskandari, H.; Kim, H. S. (2017). "A theory for mathematical framework and fatigue damage function for S-N plane". In Wei, Z.; Nikbin, K.; McKeighan, P. C.; Harlow, G. D. Fatigue and Fracture Test Planning, Test Data Acquisitions and Analysis. ASTM Selected Technical Papers. 1598. pp. 299–336. doi:10.1520/STP159820150099. 
  19. ^ Kim, H. S. (2016). Mechanics of Solids and Fracture (2nd ed.). Ventus Publishing. ISBN 978-87-403-1395-6. 
  20. ^ Beardmore, R. (13 January 2013). "Fatigue Stress Action Types". Roymechx. 
  21. ^ Paris, P. C.; Gomez, M. P.; Anderson, W. E. (1961). "A rational analytic theory of fatigue" (PDF). The Trend in Engineering. 13: 9–14. 
  22. ^ Kim, S. T.; Tadjiev, D.; Yang, H. T. (2006). "Fatigue Life Prediction under Random Loading Conditions in 7475-T7351 Aluminum Alloy using the RMS Model". International Journal of Damage Mechanics. 15 (1): 89–102. doi:10.1177/1056789506058605. 
  23. ^ Courtney, T. H. (2005). Mechanical Behavior of Materials. Waveland Press. pp. 578–581. ISBN 978-1-57766-425-3. 
  24. ^ Coffin, L. F. Jr. (1954). "A study of the effects of cyclic thermal stresses on a ductile metal". Transactions of the ASME. 76: 931–950. 
  25. ^ Manson, S. S. (1953). "Behavior of materials under conditions of thermal stress" (PDF). National Advisory Committee for Aeronautics. NACA TN-2933. 
  26. ^ O'Donnell, W. J.; Langer, B. F. (1964). "Fatigue Design Basis for Zircaloy Components". Nuclear Science and Engineering. 20 (1): 1–12. doi:10.13182/NSE64-A1926. 
  27. ^ Udomphol, T. (2007). "Fatigue of metals" (PDF). Suranaree University of Technology. p. 54. 
  28. ^ "Material Technologies, Inc. Completes EFS Inspection of Bridge in New Jersey" (Press release). Material Technologies. 17 April 2007. 
  29. ^ Hoffer, W. (June 1989). "Horrors in the Skies". Popular Mechanics. 166 (6): 67–70, 115–117. 
  30. ^ "Research (Laser Peening)". LAMPL. 
  31. ^ Can Yildirim, H.; Marquis, G. B. (2012). "Fatigue strength improvement factors for high strength steel welded joints treated by high frequency mechanical impact". International Journal of Fatigue. 44: 168–176. doi:10.1016/j.ijfatigue.2012.05.002. 
  32. ^ Can Yildirim, H.; Marquis, G. B.; Barsoum, Z. (2013). "Fatigue assessment of High Frequency Mechanical Impact (HFMI)-improved fillet welds by local approaches". International Journal of Fatigue. 52: 57–67. doi:10.1016/j.ijfatigue.2013.02.014. 
  33. ^ "Search Results for 'fatigue'". Cryogenic Treatment Database. 
  34. ^ "ObjectWiki: Fuselage of de Havilland Comet Airliner G-ALYP". Science Museum. 24 September 2009. Archived from the original on 7 January 2009. Retrieved 9 October 2009. 
  35. ^ The Alexander L. Kielland accident, Report of a Norwegian public commission appointed by royal decree of March 28, 1980, presented to the Ministry of Justice and Police March. Norwegian Public Reports 1981:11. Norwegian Ministry of Justice and Public Security. 1981. ASIN B0000ED27N. 
  36. ^ Ansberry, C. (5 February 2001). "In Firestone Tire Study, Expert Finds Vehicle Weight Was Key in Failure". Wall Street Journal. Retrieved 6 September 2016. 

Further reading

  • PDL Staff (1995). Fatigue and Tribological Properties of Plastics and Elastomers. Plastics Design Library. ISBN 978-1-884207-15-0. 
  • Leary, M.; Burvill, C. (2009). "Applicability of published data for fatigue-limited design". Quality and Reliability Engineering International. 25 (8): 921–932. doi:10.1002/qre.1010. 
  • Dieter, G. E. (2013). Mechanical Metallurgy. McGraw-Hill. ISBN 978-1259064791. 
  • Little, R.E.; Jebe, E.H. (1975). Statistical Design of Fatigue Experiments. John Wiley & Sons. ISBN 0-470-54115-6. 
  • Palmgren, A. G. (1924). "Die Lebensdauer von Kugellagern" [Life Length of Roller Bearings]. Zeitschrift des Vereines Deutscher Ingenieure (in German). 68 (14): 339–341. 
  • Schijve, J. (2009). Fatigue of Structures and Materials. Springer. ISBN 978-1-4020-6807-2. 
  • Lalanne, C. (2009). Fatigue Damage. ISTE - Wiley. ISBN 978-1-84821-125-4. 
  • Pook, L. (2007). Metal Fatigue, What it is, Why it matters. Springer. ISBN 978-1-4020-5596-6. 
  • Draper, J. (2008). Modern Metal Fatigue Analysis. EMAS. ISBN 0-947817-79-4. 
  • Suresh, S. (2004). Fatigue of Materials. Cambridge University Press. ISBN 0-521-57046-8. 

External links

Creep (deformation)

Creep (deformation)

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods, and generally increases as they near their melting point.

The rate of deformation is a function of the material properties, exposure time, exposure temperature and the applied structural load. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function — for example creep of a turbine blade will cause the blade to contact the casing, resulting in the failure of the blade. Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures. Creep is a deformation mechanism that may or may not constitute a failure mode. For example, moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking.

Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long-term stress. Therefore, creep is a "time-dependent" deformation.

Temperature dependence

The temperature range in which creep deformation may occur differs in various materials. For example, tungsten requires a temperature in the thousands of degrees before creep deformation can occur, while ice will creep at temperatures near 0 °C (32 °F).[1] As a general guideline, the effects of creep deformation generally become noticeable at approximately 35% of the melting point (as measured on a thermodynamic temperature scale such as Kelvin or Rankine) for metals, and at 45% of melting point for ceramics.[2] Virtually any material will creep upon approaching its melting temperature. Since the creep minimum temperature is related to the melting point, creep can be seen at relatively low temperatures for some materials. Plastics and low-melting-temperature metals, including many solders, can begin to creep at room temperature, as can be seen markedly in old lead hot-water pipes. Glacier flow is an example of creep processes in ice.[3]

Stages of creep

Strain as a function of time due to constant stress over an extended period for a viscoelastic material.

In the initial stage, or primary creep, or transient creep, the strain rate is relatively high, but decreases with increasing time and strain due to a process analogous to work hardening at lower temperatures. For instance, the dislocation density increases and, in many materials, a dislocation subgrain structure is formed and the cell size decreases with strain.[4] The strain rate diminishes to a minimum and becomes near constant as the secondary stage begins. This is due to the balance between work hardening and annealing (thermal softening). The secondary stage, referred to as "steady-state creep", is the most understood. The microstructure is invariant during this stage, which means that recovery effects are concurrent with deformation. No material strength is lost during these first two stages of creep.

The characterized "creep strain rate" typically refers to the constant rate in this secondary stage. Stress dependence of this rate depends on the creep mechanism. In tertiary creep, the strain rate exponentially increases with stress because of necking phenomena or internal cracks or voids decreases the effective area of the specimen. Strength is quickly lost in this stage while the material's shape is permanently changed. The acceleration of creep deformation in the tertiary stage eventually leads to material fracture.[5]

Mechanisms of creep

The mechanism of creep depends on temperature and stress. Under the conditions of different temperature and applied stress, dislocation glide, dislocation climb, or diffusional-flow mechanisms may dominate creep deformation. Some mechanisms of creep, especially those involving dislocations, have not been verified by direct microstructural examination yet.[4] However, processes just like the mechanisms conjectured should happen during creep deformation. 

Various mechanisms are:

  • Bulk diffusion (Nabarro-Herring creep)
  • Climb — here the strain is actually accomplished by climb
  • Climb-assisted glide — here the climb is an enabling mechanism, allowing dislocations to get around obstacles
  • Grain boundary diffusion (Coble creep)
  • Thermally activated glide — e.g., via cross-slip

General creep equation

where is the creep strain, C is a constant dependent on the material and the particular creep mechanism, m and b are exponents dependent on the creep mechanism, Q is the activation energy of the creep mechanism, σ is the applied stress, d is the grain size of the material, k is Boltzmann's constant, and T is the absolute temperature.[6]

Dislocation creep

At high stresses (relative to the shear modulus), creep is controlled by the movement of dislocations. For dislocation creep, Q = Q(self diffusion), m = 4–6, and b = 0. Therefore, dislocation creep has a strong dependence on the applied stress and the intrinsic activation energy, but no grain size dependence.

Some alloys exhibit a very large stress exponent (n > 10), and this has typically been explained by introducing a "threshold stress," σth, below which creep can't be measured. The modified power law equation then becomes:

where A, Q and n can all be explained by conventional mechanisms (so 3 ≤ n ≤ 10). The creep increases with increasing applied stress, since the applied stress tends to drive the dislocation past the barrier, and make the dislocation get into a lower energy state after bypassing the obstacle, which means that the dislocation is inclined to pass the obstacle. In other words, part of the work required to overcome the energy barrier of passing an obstacle is provided by the applied stress and the remainder by thermal energy. 

Nabarro–Herring creep

A diagram showing the diffusion of atoms and vacancies under Nabarro–Herring Creep.

Nabarro–Herring (NH) creep is a form of diffusion creep, while dislocation glide creep does not involve atomic diffusion. Nabarro-Herring creep dominates at high temperatures and low stresses. As shown in the figure on the right, the lateral sides of the crystal are subjected to a tensile stress, and the horizontal sides to a compressive stress. The atomic volume is altered by applied stress: it increases in regions under tension and decreases in regions under compression. So the activation energy for vacancy formation is changed by ±, where is the atomic volume, the "" sign is for compressive regions and "" sign is for tensile regions. Since the fractional vacancy concentration is proportional to , where is the vacancy-formation energy, the vacancy concentration is higher in tensile regions than in compressive regions, leading to a net flow of vacancies from the regions under tension to the regions under compression, and this is equivalent to a net atom diffusion in the opposite direction, which causes the creep deformation: the grain elongates in the tensile stress axis and contracts in the compressive stress axis.

In Nabarro–Herring creep, k is related to the diffusion coefficient of atoms through the lattice, Q = Q (self diffusion), m = 1, and b = 2. Therefore, Nabarro–Herring creep has a weak stress dependence and a moderate grain size dependence, with the creep rate decreasing as grain size is increased.

Nabarro–Herring creep is strongly temperature dependent. For lattice diffusion of atoms to occur in a material, neighboring lattice sites or interstitial sites in the crystal structure must be free. A given atom must also overcome the energy barrier to move from its current site (it lies in an energetically favorable potential well) to the nearby vacant site (another potential well). The general form of the diffusion equation is D = D0exp(E/KT) where D0 has a dependence on both the attempted jump frequency and the number of nearest neighbor sites and the probability of the sites being vacant. Thus there is a double dependence upon temperature. At higher temperatures the diffusivity increases due to the direct temperature dependence of the equation, the increase in vacancies through Schottky defect formation, and an increase in the average energy of atoms in the material. Nabarro–Herring creep dominates at very high temperatures relative to a material's melting temperature.

Coble creep

Coble creep is a second form of diffusion controlled creep. In Coble creep the atoms diffuse along grain boundaries to elongate the grains along the stress axis. This causes Coble creep to have a stronger grain size dependence than Nabarro–Herring creep, thus, Coble creep will be more important in materials composed of very fine grains. For Coble creep k is related to the diffusion coefficient of atoms along the grain boundary, Q = Q(grain boundary diffusion), m = 1, and b = 3. Because Q(grain boundary diffusion) < Q(self diffusion), Coble creep occurs at lower temperatures than Nabarro–Herring creep. Coble creep is still temperature dependent, as the temperature increases so does the grain boundary diffusion. However, since the number of nearest neighbors is effectively limited along the interface of the grains, and thermal generation of vacancies along the boundaries is less prevalent, the temperature dependence is not as strong as in Nabarro–Herring creep. It also exhibits the same linear dependence on stress as Nabarro–Herring creep. Generally, the diffusional creep rate should be the sum of Nabarro–Herring creep rate and Coble creep rate. Diffusional creep leads to grain-boundary separation, that is, voids or cracks form between the grains. To heal this, grain-boundary sliding occurs. The diffusional creep rate and the grain boundary sliding rate must be balanced if there are no voids or cracks remain. When grain-boundary sliding couldn't accommodate the incompatibility, grain-boundary voids are generated, which is related to the initiation of creep fracture. 

Solute drag creep

Solute drag creep is one kind of mechanisms for power law creep (PLC), involving both dislocation and diffusional flow. Solute drag creep is observed in certain metallic alloys. Their creep rate increases during the first stage of creep before a steady-state, which can be explained by a model associated with solid-solution strengthening. The size misfit between solute atoms and edge dislocations could restrict dislocation motion. The flow stress required for dislocations to move is increased at low temperatures due to immobility of the solute atoms. But solute atoms are mobile at higher temperatures, so the solute atoms could move along with edge dislocations as a "drag" on their motion, if the dislocation motion or the creep rate is not too high. The solute drag creep rate is:

where C is a constant, is the solute diffusivity, is the solute concentration, and is the misfit parameter, is the applied stress. So it could be seen from the equation above, m is 3 for solute drag creep. Solute drag creep shows a special phenomenon, which is called the Portevin-Le Chatelier effect. When the applied stress becomes sufficiently large, the dislocations will break away from the solute atoms since dislocation velocity increases with the stress. After breakaway, the stress decreases and the dislocation velocity also decreases, which allows the solute atoms to approach and reach the previously departed dislocations again, leading to a stress increase. The process repeats itself when the next local stress maximum is obtained. So repetitive local stress maxima and minima could be detected during solute drag creep.

Dislocation climb-glide creep

Dislocation climb-glide creep is observed in materials at high temperature. The initial creep rate is larger than the steady-state creep rate. Climb-glide creep could be illustrated as follows: when the applied stress is not enough to for a moving dislocation to overcome the obstacle on its way via dislocation glide alone, the dislocation could climb to a parallel slip plane by diffusional processes, and the dislocation can glide on the new plane. This process repeats itself each time when the dislocation encounters an obstacle. The creep rate could be written as:

where ACG includes details of the dislocation loop geometry, DL is the lattice diffusivity, M is the number of dislocation sources per unit volume,  is the applied stress, and is the atomic volume. The exponent m for dislocation climb-glide creep is 4.5 if M is independent of stress and this value of m is consistent with results from considerable experimental studies. 

Harper–Dorn creep

Harper–Dorn creep is a climb-controlled dislocation mechanism at low stresses that has been observed in aluminum, lead, and tin systems, in addition to nonmetal systems such as ceramics and ice. It is characterized by two principal phenomena: a linear relationship between the steady-state strain rate and applied stress at a constant temperature, and an independent relationship between the steady-state strain rate and grain size for a provided temperature and applied stress. The latter observation implies that Harper–Dorn creep is controlled by dislocation movement; namely, since creep can occur by vacancy diffusion (Nabarro–Herring creep, Coble creep), grain boundary sliding, and/or dislocation movement, and since the first two mechanisms are grain-size dependent, Harper–Dorn creep must therefore be dislocation-motion dependent.[7]

However, Harper–Dorn creep is typically overwhelmed by other creep mechanisms in most situations, and is therefore not observed in most systems. The phenomenological equation which describes Harper–Dorn creep is:

where: is dislocation density (constant for Harper–Dorn creep), is the diffusivity through the volume of the material, is the shear modulus, is the Burger's vector, is the applied stress, is Boltzmann's constant, and is temperature.

The volumetric activation energy indicates that the rate of Harper–Dorn creep is controlled by vacancy diffusion to and from dislocations, resulting in climb-controlled dislocation motion.[8][9] Unlike in other creep mechanisms, the dislocation density here is constant and independent of the applied stress.[7] Moreover, the dislocation density must be low for Harper–Dorn creep to dominate. The density has been proposed to increase as dislocations move via cross-slip from one slip-plane to another, thereby increasing the dislocation length per unit volume. Cross-slip can also result in jogs along the length of the dislocation, which, if large enough, can act as single-ended dislocation sources.[10]


Creep of polymers

a) Applied stress and b) induced strain as functions of time over a short period for a viscoelastic material.

Creep can occur in polymers and metals which are considered viscoelastic materials. When a polymeric material is subjected to an abrupt force, the response can be modeled using the Kelvin-Voigt model. In this model, the material is represented by a Hookean spring and a Newtonian dashpot in parallel. The creep strain is given by the following convolution integral:


  • σ = applied stress
  • C0 = instantaneous creep compliance
  • C = creep compliance coefficient
  • = retardation time
  • = distribution of retardation times

When subjected to a step constant stress, viscoelastic materials experience a time-dependent increase in strain. This phenomenon is known as viscoelastic creep.

At a time t0, a viscoelastic material is loaded with a constant stress that is maintained for a sufficiently long time period. The material responds to the stress with a strain that increases until the material ultimately fails. When the stress is maintained for a shorter time period, the material undergoes an initial strain until a time t1 at which the stress is relieved, at which time the strain immediately decreases (discontinuity) then continues decreasing gradually to a residual strain.

Viscoelastic creep data can be presented in one of two ways. Total strain can be plotted as a function of time for a given temperature or temperatures. Below a critical value of applied stress, a material may exhibit linear viscoelasticity. Above this critical stress, the creep rate grows disproportionately faster. The second way of graphically presenting viscoelastic creep in a material is by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time.[11] Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material's critical stress value.

Additionally, the molecular weight of the polymer of interest is known to affect its creep behavior. The effect of increasing molecular weight tends to promote secondary bonding between polymer chains and thus make the polymer more creep resistant. Similarly, aromatic polymers are even more creep resistant due to the added stiffness from the rings. Both molecular weight and aromatic rings add to polymers' thermal stability, increasing the creep resistance of a polymer.[12]

Both polymers and metals can creep. Polymers experience significant creep at temperatures above ca. –200 °C; however, there are three main differences between polymeric and metallic creep.[13]

Polymers show creep basically in two different ways. At typical work loads (5 up to 50%) ultra high molecular weight polyethylene (Spectra, Dyneema) will show time-linear creep, whereas polyester or aramids (Twaron, Kevlar) will show a time-logarithmic creep.

Creep of concrete

The creep of concrete, which originates from the calcium silicate hydrates (C-S-H) in the hardened Portland cement paste (which is the binder of mineral aggregates), is fundamentally different from the creep of metals as well as polymers. Unlike the creep of metals, it occurs at all stress levels and, within the service stress range, is linearly dependent on the stress if the pore water content is constant. Unlike the creep of polymers and metals, it exhibits multi-months aging, caused by chemical hardening due to hydration which stiffens the microstructure, and multi-year aging, caused by long-term relaxation of self-equilibrated micro-stresses in the nano-porous microstructure of the C-S-H. If concrete is fully dried it does not creep, though it is difficult to dry concrete fully without severe cracking.


Creep on the underside of a cardboard box: a largely empty box was placed on a smaller box, and more boxes were placed on top of it. Due to the weight, the portions of the empty box not upheld by the lower support gradually deflected downward.

Though mostly due to the reduced yield strength at higher temperatures, the collapse of the World Trade Center was due in part to creep from increased temperature operation.[14]

The creep rate of hot pressure-loaded components in a nuclear reactor at power can be a significant design constraint, since the creep rate is enhanced by the flux of energetic particles.

Creep in epoxy anchor adhesive was blamed for the Big Dig tunnel ceiling collapse in Boston, Massachusetts that occurred in July 2006.[15]

The design of tungsten light bulb filaments attempts to reduce creep deformation. Sagging of the filament coil between its supports increases with time due to the weight of the filament itself. If too much deformation occurs, the adjacent turns of the coil touch one another, causing an electrical short and local overheating, which quickly leads to failure of the filament. The coil geometry and supports are therefore designed to limit the stresses caused by the weight of the filament, and a special tungsten alloy with small amounts of oxygen trapped in the crystallite grain boundaries is used to slow the rate of Coble creep.

Creep can cause gradual cut-through of wire insulation, especially when stress is concentrated by pressing insulated wire against a sharp edge or corner. Special creep-resistant insulations such as Kynar (polyvinylidene fluoride) are used in wirewrap applications to resist cut-through due to the sharp corners of wire wrap terminals. Teflon insulation is resistant to elevated temperatures and has other desirable properties, but is notoriously vulnerable to cold-flow cut-through failures caused by creep.

In steam turbine power plants, pipes carry steam at high temperatures (566 °C (1,051 °F)) and pressures (above 24.1 MPa or 3500 psi). In jet engines, temperatures can reach up to 1,400 °C (2,550 °F) and initiate creep deformation in even advanced-design coated turbine blades. Hence, it is crucial for correct functionality to understand the creep deformation behavior of materials.

Creep deformation is important not only in systems where high temperatures are endured such as nuclear power plants, jet engines and heat exchangers, but also in the design of many everyday objects. For example, metal paper clips are stronger than plastic ones because plastics creep at room temperatures. Aging glass windows are often erroneously used as an example of this phenomenon: measurable creep would only occur at temperatures above the glass transition temperature around 500 °C (932 °F). While glass does exhibit creep under the right conditions, apparent sagging in old windows may instead be a consequence of obsolete manufacturing processes, such as that used to create crown glass, which resulted in inconsistent thickness.[16][17]

Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media.[18]

Nimonic 75 has been certified by the European Union as a standard creep reference material.[19]

Preventing creep

There are three general ways to prevent creep in metal. One way is to use higher melting temperature metals. The second way is to use materials with greater grain size. The third way is to use alloying.

Creep of superalloys

Materials operating at high temperatures, such as this nickel superalloy jet engine (RB199) turbine blade, must be able to withstand the significant creep present at these temperatures.

Materials operating in high-performance systems, such as jet engines, often reach extreme temperatures surpassing 1200 °C, which causes creep to be a serious issue. Superalloys based on Co, Ni, and Fe are capable of being engineered to be highly resistant to creep, and have thus arisen as an ideal material in high-temperature environments. As an example, Ni-base alloys modeled after the Ni-Al system, known as γ-γ’ alloys are even resistant to dislocation creep. The γ is the main fcc matrix, while the γ’ is the precipitate-phase of Ni3(Al, Ti), which adds particle strengthening. Solute elements added, e.g., Ta, W, Mo, Fe, Cr, and Co, contribute solid-solution hardening, and are often reacted with carbon to form carbide particles that deposit at grain boundaries, and thus inhibit grain boundary sliding.[4] 

See also


  1. ^ "Rheology of Ice". Archived from the original on 2007-06-17. Retrieved 2008-10-16. 
  2. ^ Ashy, Michael (2014). Materials. Oxford: Elsevier. p. 336. ISBN 978-0-08-097773-7. 
  3. ^ "Deformation & Flow | Mechanics". Encyclopedia Britannica. Retrieved 2017-03-29. 
  4. ^ a b c H., Courtney, Thomas (2005). Mechanical behavior of materials. Waveland Press. ISBN 9781577664253. OCLC 894800884. 
  5. ^ "Thermal Creep". NADCA Design. Retrieved 2017-03-29. 
  6. ^ "Creep and Stress Rupture" (PDF). NC State University. 2017-03-29. 
  7. ^ a b Mohamed, F. A.; Murty, K. L.; Morris, J. W. (April 1973). "Harper–dorn creep in al, pb, and sn". Metallurgical Transactions. 4 (4): 935–940. doi:10.1007/BF02645593. 
  8. ^ Kassner, M.E; Pérez-Prado, M.-T (January 2000). "Five-power-law creep in single phase metals and alloys". Progress in Materials Science. 45 (1): 1–102. doi:10.1016/S0079-6425(99)00006-7. 
  9. ^ Paufler, P. (October 1986). "J.-P. Poirier. Creep of crystals. High-temperature deformation processes in metals, ceramics and minerals. Cambridge University Press. Cambridge – London – New York – New Rochelle – Melbourne – Sydney 1985. 145 figs., XII + 260 p., price £ 10.95 (paperback). ISBN 0-521-27851-1". Crystal Research and Technology. 21 (10): 1338–1338. doi:10.1002/crat.2170211021. 
  10. ^ Mohamed, Farghalli A.; Ginter, Timothy J. (October 1982). "On the nature and origin of Harper–Dorn creep". Acta Metallurgica. 30 (10): 1869–1881. doi:10.1016/0001-6160(82)90027-X. 
  11. ^ Rosato, D. V. et al. (2001) Plastics Design Handbook. Kluwer Academic Publishers. pp. 63–64. ISBN 0792379802.
  12. ^ M. A. Meyers; K. K. Chawla (1999). Mechanical Behavior of Materials. Cambridge University Press. p. 573. ISBN 978-0-521-86675-0. 
  13. ^ McCrum, N.G, Buckley, C.P; Bucknall, C.B (2003). Principles of Polymer Engineering. Oxford Science Publications. ISBN 0-19-856526-7. 
  14. ^ Zdeněk Bažant and Yong Zhu, "Why Did the World Trade Center Collapse?—Simple Analysis", Journal of Engineering Mechanics, January 2002
  15. ^ "Ceiling Collapse in the Interstate 90 Connector Tunnel". National Transportation Safety Board. Washington, D.C.: NTSB. July 10, 2007. Retrieved 2 December 2016. 
  16. ^ Lakes, Roderic S. (1999). Viscoelastic Solids. p. 476. ISBN 0-8493-9658-1. 
  17. ^ "Is glass liquid or solid?". University of California, Riverside. Retrieved 2008-10-15. 
  18. ^ Osama Abuzeid, Anas Al-Rabadi, Hashem Alkhaldi . Recent advancements in fractal geometric-based nonlinear time series solutions to the micro-quasistatic thermoviscoelastic creep for rough surfaces in contact, Mathematical Problems in Engineering, Volume 2011, Article ID 691270
  19. ^

Further reading

  • Ashby, Michael F.; Jones, David R. H. (1980). Engineering Materials 1: An Introduction to their Properties and Applications. Pergamon Press. ISBN 0-08-026138-8. 
  • Frost, Harold J.; Ashby, Michael F. (1982). Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics. Pergamon Press. ISBN 0-08-029337-9. 
  • Turner, S (2001). Creep of Polymeric Materials. Oxford: Elsevier Science Ltd. pp. 1813–1817. ISBN 0-08-043152-6. 

External links

Cyclic corrosion testing

Cyclic corrosion testing

Example of a Cyclic corrosion test chamber.

Cyclic Corrosion Testing (CCT) has evolved in recent years, largely within the automotive industry, as a way of accelerating real-world corrosion failures, under laboratory controlled conditions. As the name implies, the test comprises different climates which are cycled automatically so the samples under test undergo the same sort of changing environment that would be encountered in the natural world. The intention being to bring about the type of failure that might occur naturally, but more quickly i.e. accelerated. By doing this manufacturers and suppliers can predict, more accurately, the service life expectancy of their products.

Until the development of Cyclic Corrosion Testing, the traditional Salt spray test was virtually all that manufacturers could use for this purpose. However, this test was never intended for this purpose. Because the test conditions specified for salt spray testing are not typical of a naturally occurring environment, this type of test cannot be used as a reliable means of predicting the ‘real world’ service life expectancy for the samples under test. The sole purpose of the salt spray test is to compare and contrast results with previous experience to perform a quality audit. So, for example, a spray test can be used to ‘police’ a production process and forewarn of potential manufacturing problems or defects, which might affect corrosion resistance. .[1]

To recreate these different environments within an environmental chamber requires much more flexible testing procedures than are available in a standard salt spray chamber.

The lack of correlation between results obtained from traditional salt spray testing[2] and the ‘real world’ atmospheric corrosion of vehicles, left the automotive industry without a reliable test method for predicting the service life expectancy of their products. This was and remains of particular concern in an industry where anti-corrosion warranties have been gradually increasing and now run to several years for new vehicles.

With ever increasing consumer pressure for improved vehicle corrosion resistance and a few ‘high profile’ corrosion failures amongst some vehicle manufactures – with disastrous commercial consequences, the automotive industry recognized the need for a different type of corrosion test.

Such a test would need to simulate the types of conditions a vehicle might encounter naturally, but recreate and accelerate these conditions, with good repeatability, within the convenience of the laboratory.[3] CCT is effective for evaluating a variety of corrosion types, including galvanic corrosion and crevice corrosion.

Graph showing the temperature & humidity steps required during cyclic corrosion test VDA 621-415

Test Stages

Taking results gathered largely from ‘real world’ exposure sites, automotive companies, led originally by the Japanese automobile industry, developed their own Cyclic Corrosion Tests. These have evolved in different ways for different vehicle manufacturers, and such tests still remain largely industry specific, with no truly international CCT standard. However, they all generally require most of the following conditions to be created, in a repeating sequence or ‘cycle’, though not necessarily in the following order:[2]

• A salt spray ‘pollution’ phase. This may be similar to the traditional salt spray test although in some cases direct impingement by the salt solution on the test specimens, or even complete immersion in salt water, is required. However, this ‘pollution’ phase is generally shorter in duration than a traditional salt spray test.

Graph showing the temperature & humidity steps required during cyclic corrosion test D17 2028 ECC1

• An air drying phase. Depending on the test, this may be conducted at ambient temperature, or at an elevated temperature, with or without control over the relative humidity and usually by introducing a continuous supply of relatively fresh air around the test samples at the same time. It is generally required that the samples under test should be visibly ‘dry’ at the end of this test phase.

Graph showing the temperature & humidity steps required during cyclic corrosion test CETP 00.00-L-467

• A condensation humidity ‘wetting’ phase. This is usually conducted at an elevated temperature and generally a high humidity of 95-100%RH. The purpose of this phase is to promote the formation of condensation on the surfaces of the samples under test.

• A controlled humidity/humidity cycling phase. This requires the tests samples to be exposed to a controlled temperature and controlled humidity climate, which can either be constant or cycling between different levels. When cycling between different levels, the rate of change may also be specified.

The above list is not exhaustive, since some automotive companies may also require other climates to be created in sequence as well, for example; sub-zero refrigeration, but it does list the most common requirements.[2]

Tests Standards

The below list is not exhaustive, but here are some examples of popular cyclic corrosion test standards,

See also

Further reading

  • Cyclic Cabinet Corrosion Testing - Gardner S.Haynes - 1995
  • ASTM American Society for Testing of Materials. ASTM B 117-11 Standard Practice for Operating Salt Spray (Fog) Apparatus, 2011
  • Corrosion Testing and Evaluation, Issue 1000 - Robert Baboian, S. W. Dean - ATM International - 1990
  • Laboratory Corrosion Tests and Standards: A Symposium by ASTM Committee G-1 on Corrosion of Metals - Gardner S. Haynes, Robert Baboian - 1985
  • Corrosion Basics, An Introduction, L.S. Van Delinder, ed. (Houston, TX: NACE, 1984).
  • Laboratory Corrosion Tests and Standards, Haynes GS, Baboian R, 1985


  1. ^ Palmer, J (1978). "Automotive Corrosion Testing". SAE Technical Paper 780910. doi:10.4271/780910. 
  2. ^ a b c N. LeBozec, N. Blandin and D. Thierry (2008). "Materials & Corrosion". Accelerated corrosion tests in the automotive industry: A comparison of the performance towards cosmetic corrosion. No.11 (59): 889–893. doi:10.1002/maco.200804168. 
  3. ^ Baboian, Robert (2005). "Corrosion Tests and Standards: Application and Interpretation". Automotive: 673–679. 
  4. ^ SAE J2334, Laboratory Cyclic Corrosion Test.



Rust, the most familiar example of corrosion
Volcanic gases have accelerated the extensive corrosion of this abandoned mining machinery, rendering it almost unrecognizable
Corrosion on exposed metal, including a bolt and nut

Corrosion is a natural process, which converts a refined metal to a more chemically-stable form, such as its oxide, hydroxide, or sulfide. It is the gradual destruction of materials (usually metals) by chemical and/or electrochemical reaction with their environment. Corrosion engineering is the field dedicated to controlling and stopping corrosion.

In the most common use of the word, this means electrochemical oxidation of metal in reaction with an oxidant such as oxygen or sulfur. Rusting, the formation of iron oxides, is a well-known example of electrochemical corrosion. This type of damage typically produces oxide(s) or salt(s) of the original metal, and results in a distinctive orange colouration. Corrosion can also occur in materials other than metals, such as ceramics or polymers, although in this context, the term "degradation" is more common. Corrosion degrades the useful properties of materials and structures including strength, appearance and permeability to liquids and gases.

Many structural alloys corrode merely from exposure to moisture in air, but the process can be strongly affected by exposure to certain substances. Corrosion can be concentrated locally to form a pit or crack, or it can extend across a wide area more or less uniformly corroding the surface. Because corrosion is a diffusion-controlled process, it occurs on exposed surfaces. As a result, methods to reduce the activity of the exposed surface, such as passivation and chromate conversion, can increase a material's corrosion resistance. However, some corrosion mechanisms are less visible and less predictable.

Galvanic corrosion

Galvanic corrosion of aluminium. A 5-mm-thick aluminium alloy plate is physically (and hence, electrically) connected to a 10-mm-thick mild steel structural support. Galvanic corrosion occurred on the aluminium plate along the joint with the steel. Perforation of aluminium plate occurred within 2 years.[1]

Galvanic corrosion occurs when two different metals have physical or electrical contact with each other and are immersed in a common electrolyte, or when the same metal is exposed to electrolyte with different concentrations. In a galvanic couple, the more active metal (the anode) corrodes at an accelerated rate and the more noble metal (the cathode) corrodes at a slower rate. When immersed separately, each metal corrodes at its own rate. What type of metal(s) to use is readily determined by following the galvanic series. For example, zinc is often used as a sacrificial anode for steel structures. Galvanic corrosion is of major interest to the marine industry and also anywhere water (containing salts) contacts pipes or metal structures.

Factors such as relative size of anode, types of metal, and operating conditions (temperature, humidity, salinity, etc.) affect galvanic corrosion. The surface area ratio of the anode and cathode directly affects the corrosion rates of the materials. Galvanic corrosion is often prevented by the use of sacrificial anodes.

Galvanic series

In any given environment (one standard medium is aerated, room-temperature seawater), one metal will be either more noble or more active than others, based on how strongly its ions are bound to the surface. Two metals in electrical contact share the same electrons, so that the "tug-of-war" at each surface is analogous to competition for free electrons between the two materials. Using the electrolyte as a host for the flow of ions in the same direction, the noble metal will take electrons from the active one. The resulting mass flow or electric current can be measured to establish a hierarchy of materials in the medium of interest. This hierarchy is called a galvanic series and is useful in predicting and understanding corrosion.

Corrosion removal

Often it is possible to chemically remove the products of corrosion. For example, phosphoric acid in the form of naval jelly is often applied to ferrous tools or surfaces to remove rust. Corrosion removal should not be confused with electropolishing, which removes some layers of the underlying metal to make a smooth surface. For example, phosphoric acid may also be used to electropolish copper but it does this by removing copper, not the products of copper corrosion.

Resistance to corrosion

Some metals are more intrinsically resistant to corrosion than others (for some examples, see galvanic series). There are various ways of protecting metals from corrosion (oxidation) including painting, hot dip galvanizing, and combinations of these.[2]

Intrinsic chemistry

Gold nuggets do not naturally corrode, even on a geological time scale.

The materials most resistant to corrosion are those for which corrosion is thermodynamically unfavorable. Any corrosion products of gold or platinum tend to decompose spontaneously into pure metal, which is why these elements can be found in metallic form on Earth and have long been valued. More common "base" metals can only be protected by more temporary means.

Some metals have naturally slow reaction kinetics, even though their corrosion is thermodynamically favorable. These include such metals as zinc, magnesium, and cadmium. While corrosion of these metals is continuous and ongoing, it happens at an acceptably slow rate. An extreme example is graphite, which releases large amounts of energy upon oxidation, but has such slow kinetics that it is effectively immune to electrochemical corrosion under normal conditions.


Passivation refers to the spontaneous formation of an ultrathin film of corrosion products, known as a passive film, on the metal's surface that act as a barrier to further oxidation. The chemical composition and microstructure of a passive film are different from the underlying metal. Typical passive film thickness on aluminium, stainless steels, and alloys is within 10 nanometers. The passive film is different from oxide layers that are formed upon heating and are in the micrometer thickness range – the passive film recovers if removed or damaged whereas the oxide layer does not. Passivation in natural environments such as air, water and soil at moderate pH is seen in such materials as aluminium, stainless steel, titanium, and silicon.

Passivation is primarily determined by metallurgical and environmental factors. The effect of pH is summarized using Pourbaix diagrams, but many other factors are influential. Some conditions that inhibit passivation include high pH for aluminium and zinc, low pH or the presence of chloride ions for stainless steel, high temperature for titanium (in which case the oxide dissolves into the metal, rather than the electrolyte) and fluoride ions for silicon. On the other hand, unusual conditions may result in passivation of materials that are normally unprotected, as the alkaline environment of concrete does for steel rebar. Exposure to a liquid metal such as mercury or hot solder can often circumvent passivation mechanisms.

Corrosion in passivated materials

Passivation is extremely useful in mitigating corrosion damage, however even a high-quality alloy will corrode if its ability to form a passivating film is hindered. Proper selection of the right grade of material for the specific environment is important for the long-lasting performance of this group of materials. If breakdown occurs in the passive film due to chemical or mechanical factors, the resulting major modes of corrosion may include pitting corrosion, crevice corrosion, and stress corrosion cracking.

Pitting corrosion

Diagram showing cross-section of pitting corrosion

Certain conditions, such as low concentrations of oxygen or high concentrations of species such as chloride which complete as anions, can interfere with a given alloy's ability to re-form a passivating film. In the worst case, almost all of the surface will remain protected, but tiny local fluctuations will degrade the oxide film in a few critical points. Corrosion at these points will be greatly amplified, and can cause corrosion pits of several types, depending upon conditions. While the corrosion pits only nucleate under fairly extreme circumstances, they can continue to grow even when conditions return to normal, since the interior of a pit is naturally deprived of oxygen and locally the pH decreases to very low values and the corrosion rate increases due to an autocatalytic process. In extreme cases, the sharp tips of extremely long and narrow corrosion pits can cause stress concentration to the point that otherwise tough alloys can shatter; a thin film pierced by an invisibly small hole can hide a thumb sized pit from view. These problems are especially dangerous because they are difficult to detect before a part or structure fails. Pitting remains among the most common and damaging forms of corrosion in passivated alloys[citation needed], but it can be prevented by control of the alloy's environment.

Pitting results when a small hole, or cavity, forms in the metal, usually as a result of de-passivation of a small area. This area becomes anodic, while part of the remaining metal becomes cathodic, producing a localized galvanic reaction. The deterioration of this small area penetrates the metal and can lead to failure. This form of corrosion is often difficult to detect due to the fact that it is usually relatively small and may be covered and hidden by corrosion-produced compounds.

Weld decay and knifeline attack

Normal microstructure of Type 304 stainless steel surface
Sensitized metallic microstructure, showing wider intergranular boundaries

Stainless steel can pose special corrosion challenges, since its passivating behavior relies on the presence of a major alloying component (chromium, at least 11.5%). Because of the elevated temperatures of welding and heat treatment, chromium carbides can form in the grain boundaries of stainless alloys. This chemical reaction robs the material of chromium in the zone near the grain boundary, making those areas much less resistant to corrosion. This creates a galvanic couple with the well-protected alloy nearby, which leads to "weld decay" (corrosion of the grain boundaries in the heat affected zones) in highly corrosive environments. This process can seriously reduce the mechanical strength of welded joints over time.

A stainless steel is said to be "sensitized" if chromium carbides are formed in the microstructure. A typical microstructure of a normalized type 304 stainless steel shows no signs of sensitization, while a heavily sensitized steel shows the presence of grain boundary precipitates. The dark lines in the sensitized microstructure are networks of chromium carbides formed along the grain boundaries.[3]

Special alloys, either with low carbon content or with added carbon "getters" such as titanium and niobium (in types 321 and 347, respectively), can prevent this effect, but the latter require special heat treatment after welding to prevent the similar phenomenon of "knifeline attack". As its name implies, corrosion is limited to a very narrow zone adjacent to the weld, often only a few micrometers across, making it even less noticeable.

Crevice corrosion

Corrosion in the crevice between the tube and tube sheet (both made of type 316 stainless steel) of a heat exchanger in a seawater desalination plant[4]

Crevice corrosion is a localized form of corrosion occurring in confined spaces (crevices), to which the access of the working fluid from the environment is limited. Formation of a differential aeration cell leads to corrosion inside the crevices. Examples of crevices are gaps and contact areas between parts, under gaskets or seals, inside cracks and seams, spaces filled with deposits and under sludge piles.

Crevice corrosion is influenced by the crevice type (metal-metal, metal-nonmetal), crevice geometry (size, surface finish), and metallurgical and environmental factors. The susceptibility to crevice corrosion can be evaluated with ASTM standard procedures. A critical crevice corrosion temperature is commonly used to rank a material's resistance to crevice corrosion.

Microbial corrosion

Microbial corrosion, or commonly known as microbiologically influenced corrosion (MIC), is a corrosion caused or promoted by microorganisms, usually chemoautotrophs. It can apply to both metallic and non-metallic materials, in the presence or absence of oxygen. Sulfate-reducing bacteria are active in the absence of oxygen (anaerobic); they produce hydrogen sulfide, causing sulfide stress cracking. In the presence of oxygen (aerobic), some bacteria may directly oxidize iron to iron oxides and hydroxides, other bacteria oxidize sulfur and produce sulfuric acid causing biogenic sulfide corrosion. Concentration cells can form in the deposits of corrosion products, leading to localized corrosion.

Accelerated low-water corrosion (ALWC) is a particularly aggressive form of MIC that affects steel piles in seawater near the low water tide mark. It is characterized by an orange sludge, which smells of hydrogen sulfide when treated with acid. Corrosion rates can be very high and design corrosion allowances can soon be exceeded leading to premature failure of the steel pile.[5] Piles that have been coated and have cathodic protection installed at the time of construction are not susceptible to ALWC. For unprotected piles, sacrificial anodes can be installed locally to the affected areas to inhibit the corrosion or a complete retrofitted sacrificial anode system can be installed. Affected areas can also be treated using cathodic protection, using either sacrificial anodes or applying current to an inert anode to produce a calcareous deposit, which will help shield the metal from further attack.

High-temperature corrosion

High-temperature corrosion is chemical deterioration of a material (typically a metal) as a result of heating. This non-galvanic form of corrosion can occur when a metal is subjected to a hot atmosphere containing oxygen, sulfur, or other compounds capable of oxidizing (or assisting the oxidation of) the material concerned. For example, materials used in aerospace, power generation and even in car engines have to resist sustained periods at high temperature in which they may be exposed to an atmosphere containing potentially highly corrosive products of combustion.

The products of high-temperature corrosion can potentially be turned to the advantage of the engineer. The formation of oxides on stainless steels, for example, can provide a protective layer preventing further atmospheric attack, allowing for a material to be used for sustained periods at both room and high temperatures in hostile conditions. Such high-temperature corrosion products, in the form of compacted oxide layer glazes, prevent or reduce wear during high-temperature sliding contact of metallic (or metallic and ceramic) surfaces.

Metal dusting

Metal dusting is a catastrophic form of corrosion that occurs when susceptible materials are exposed to environments with high carbon activities, such as synthesis gas and other high-CO environments. The corrosion manifests itself as a break-up of bulk metal to metal powder. The suspected mechanism is firstly the deposition of a graphite layer on the surface of the metal, usually from carbon monoxide (CO) in the vapor phase. This graphite layer is then thought to form metastable M3C species (where M is the metal), which migrate away from the metal surface. However, in some regimes no M3C species is observed indicating a direct transfer of metal atoms into the graphite layer.

Protection from corrosion

The US military shrink wraps equipment such as helicopters to protect them from corrosion and thus save millions of dollars

Various treatments are used to slow corrosion damage to metallic objects which are exposed to the weather, salt water, acids, or other hostile environments. Some unprotected metallic alloys are extremely vulnerable to corrosion, such as those used in neodymium magnets, which can spall or crumble into powder even in dry, temperature-stable indoor environments unless properly treated to discourage corrosion.

Surface treatments

When surface treatments are used to retard corrosion, great care must be taken to ensure complete coverage, without gaps, cracks, or pinhole defects. Small defects can act as an "Achilles' heel", allowing corrosion to penetrate the interior and causing extensive damage even while the outer protective layer remains apparently intact for a period of time.

Applied coatings

Galvanized surface

Plating, painting, and the application of enamel are the most common anti-corrosion treatments. They work by providing a barrier of corrosion-resistant material between the damaging environment and the structural material. Aside from cosmetic and manufacturing issues, there may be tradeoffs in mechanical flexibility versus resistance to abrasion and high temperature. Platings usually fail only in small sections, but if the plating is more noble than the substrate (for example, chromium on steel), a galvanic couple will cause any exposed area to corrode much more rapidly than an unplated surface would. For this reason, it is often wise to plate with active metal such as zinc or cadmium.

Painting either by roller or brush is more desirable for tight spaces; spray would be better for larger coating areas such as steel decks and waterfront applications. Flexible polyurethane coatings, like Durabak-M26 for example, can provide an anti-corrosive seal with a highly durable slip resistant membrane. Painted coatings are relatively easy to apply and have fast drying times although temperature and humidity may cause dry times to vary.

Reactive coatings

If the environment is controlled (especially in recirculating systems), corrosion inhibitors can often be added to it. These chemicals form an electrically insulating or chemically impermeable coating on exposed metal surfaces, to suppress electrochemical reactions. Such methods make the system less sensitive to scratches or defects in the coating, since extra inhibitors can be made available wherever metal becomes exposed. Chemicals that inhibit corrosion include some of the salts in hard water (Roman water systems are famous for their mineral deposits), chromates, phosphates, polyaniline, other conducting polymers and a wide range of specially-designed chemicals that resemble surfactants (i.e. long-chain organic molecules with ionic end groups).


This climbing descender is anodized with a yellow finish.

Aluminium alloys often undergo a surface treatment. Electrochemical conditions in the bath are carefully adjusted so that uniform pores, several nanometers wide, appear in the metal's oxide film. These pores allow the oxide to grow much thicker than passivating conditions would allow. At the end of the treatment, the pores are allowed to seal, forming a harder-than-usual surface layer. If this coating is scratched, normal passivation processes take over to protect the damaged area.

Anodizing is very resilient to weathering and corrosion, so it is commonly used for building facades and other areas where the surface will come into regular contact with the elements. While being resilient, it must be cleaned frequently. If left without cleaning, panel edge staining will naturally occur. Anodization is the process of converting an anode into cathode by bringing a more active anode in contact with it.

Biofilm coatings

A new form of protection has been developed by applying certain species of bacterial films to the surface of metals in highly corrosive environments. This process increases the corrosion resistance substantially. Alternatively, antimicrobial-producing biofilms can be used to inhibit mild steel corrosion from sulfate-reducing bacteria.[6]

Controlled permeability formwork

Controlled permeability formwork (CPF) is a method of preventing the corrosion of reinforcement by naturally enhancing the durability of the cover during concrete placement. CPF has been used in environments to combat the effects of carbonation, chlorides, frost and abrasion.

Cathodic protection

Cathodic protection (CP) is a technique to control the corrosion of a metal surface by making that surface the cathode of an electrochemical cell. Cathodic protection systems are most commonly used to protect steel, and pipelines and tanks; steel pier piles, ships, and offshore oil platforms.

Sacrificial anode protection

Sacrificial anode attached to the hull of a ship

For effective CP, the potential of the steel surface is polarized (pushed) more negative until the metal surface has a uniform potential. With a uniform potential, the driving force for the corrosion reaction is halted. For galvanic CP systems, the anode material corrodes under the influence of the steel, and eventually it must be replaced. The polarization is caused by the current flow from the anode to the cathode, driven by the difference in electrode potential between the anode and the cathode.

Impressed current cathodic protection

For larger structures, galvanic anodes cannot economically deliver enough current to provide complete protection. Impressed current cathodic protection (ICCP) systems use anodes connected to a DC power source (such as a cathodic protection rectifier). Anodes for ICCP systems are tubular and solid rod shapes of various specialized materials. These include high silicon cast iron, graphite, mixed metal oxide or platinum coated titanium or niobium coated rod and wires.

Anodic protection

Anodic protection impresses anodic current on the structure to be protected (opposite to the cathodic protection). It is appropriate for metals that exhibit passivity (e.g. stainless steel) and suitably small passive current over a wide range of potentials. It is used in aggressive environments, such as solutions of sulfuric acid.

Rate of corrosion

These neodymium magnets corroded extremely rapidly after only 5 months of outside exposure

A simple test for measuring corrosion is the weight loss method.[7] The method involves exposing a clean weighed piece of the metal or alloy to the corrosive environment for a specified time followed by cleaning to remove corrosion products and weighing the piece to determine the loss of weight. The rate of corrosion (R) is calculated as

where k is a constant, W is the weight loss of the metal in time t, A is the surface area of the metal exposed, and ρ is the density of the metal (in g/cm³).

Other common expressions for the corrosion rate is penetration depth and change of mechanical properties.

Economic impact

The collapsed Silver Bridge, as seen from the Ohio side

In 2002, the US Federal Highway Administration released a study titled "Corrosion Costs and Preventive Strategies in the United States" on the direct costs associated with metallic corrosion in the US industry. In 1998, the total annual direct cost of corrosion in the U.S. was ca. $276 billion (ca. 3.2% of the US gross domestic product).[8] Broken down into five specific industries, the economic losses are $22.6 billion in infrastructure; $17.6 billion in production and manufacturing; $29.7 billion in transportation; $20.1 billion in government; and $47.9 billion in utilities.[9]

Rust is one of the most common causes of bridge accidents. As rust has a much higher volume than the originating mass of iron, its build-up can also cause failure by forcing apart adjacent parts. It was the cause of the collapse of the Mianus river bridge in 1983, when the bearings rusted internally and pushed one corner of the road slab off its support. Three drivers on the roadway at the time died as the slab fell into the river below. The following NTSB investigation showed that a drain in the road had been blocked for road re-surfacing, and had not been unblocked; as a result, runoff water penetrated the support hangers. Rust was also an important factor in the Silver Bridge disaster of 1967 in West Virginia, when a steel suspension bridge collapsed within a minute, killing 46 drivers and passengers on the bridge at the time.

Similarly, corrosion of concrete-covered steel and iron can cause the concrete to spall, creating severe structural problems. It is one of the most common failure modes of reinforced concrete bridges. Measuring instruments based on the half-cell potential can detect the potential corrosion spots before total failure of the concrete structure is reached.

Until 20–30 years ago, galvanized steel pipe was used extensively in the potable water systems for single and multi-family residents as well as commercial and public construction. Today, these systems have long ago consumed the protective zinc and are corroding internally resulting in poor water quality and pipe failures.[10] The economic impact on homeowners, condo dwellers, and the public infrastructure is estimated at 22 billion dollars as the insurance industry braces for a wave of claims due to pipe failures.

Corrosion in nonmetals

Most ceramic materials are almost entirely immune to corrosion. The strong chemical bonds that hold them together leave very little free chemical energy in the structure; they can be thought of as already corroded. When corrosion does occur, it is almost always a simple dissolution of the material or chemical reaction, rather than an electrochemical process. A common example of corrosion protection in ceramics is the lime added to soda-lime glass to reduce its solubility in water; though it is not nearly as soluble as pure sodium silicate, normal glass does form sub-microscopic flaws when exposed to moisture. Due to its brittleness, such flaws cause a dramatic reduction in the strength of a glass object during its first few hours at room temperature.

Corrosion of polymers

Polymer degradation involves several complex and often poorly understood physiochemical processes. These are strikingly different from the other processes discussed here, and so the term "corrosion" is only applied to them in a loose sense of the word. Because of their large molecular weight, very little entropy can be gained by mixing a given mass of polymer with another substance, making them generally quite difficult to dissolve. While dissolution is a problem in some polymer applications, it is relatively simple to design against.

A more common and related problem is "swelling", where small molecules infiltrate the structure, reducing strength and stiffness and causing a volume change. Conversely, many polymers (notably flexible vinyl) are intentionally swelled with plasticizers, which can be leached out of the structure, causing brittleness or other undesirable changes.

The most common form of degradation, however, is a decrease in polymer chain length. Mechanisms which break polymer chains are familiar to biologists because of their effect on DNA: ionizing radiation (most commonly ultraviolet light), free radicals, and oxidizers such as oxygen, ozone, and chlorine. Ozone cracking is a well-known problem affecting natural rubber for example. Plastic additives can slow these process very effectively, and can be as simple as a UV-absorbing pigment (e.g. titanium dioxide or carbon black). Plastic shopping bags often do not include these additives so that they break down more easily as ultrafine particles of litter.

Corrosion of glasses

Glass corrosion

Glass is characterized by a high degree of corrosion-resistance. Because of its high water-resistance it is often used as primary packaging material in the pharma industry since most medicines are preserved in a watery solution.[11] Besides its water-resistance, glass is also very robust when being exposed to chemically aggressive liquids or gases. While other materials like metal or plastics quickly reach their limits, special glass-types can easily hold up.

Glass disease is the corrosion of silicate glasses in aqueous solutions. It is governed by two mechanisms: diffusion-controlled leaching (ion exchange) and hydrolytic dissolution of the glass network.[12] Both mechanisms strongly depend on the pH of contacting solution: the rate of ion exchange decreases with pH as 10−0.5pH whereas the rate of hydrolytic dissolution increases with pH as 100.5pH.[13]

Mathematically, corrosion rates of glasses are characterized by normalized corrosion rates of elements NRi (g/cm2·d) which are determined as the ratio of total amount of released species into the water Mi (g) to the water-contacting surface area S (cm2), time of contact t (days) and weight fraction content of the element in the glass fi:


The overall corrosion rate is a sum of contributions from both mechanisms (leaching + dissolution) NRi=NRxi+NRh. Diffusion-controlled leaching (ion exchange) is characteristic of the initial phase of corrosion and involves replacement of alkali ions in the glass by a hydronium (H3O+) ion from the solution. It causes an ion-selective depletion of near surface layers of glasses and gives an inverse square root dependence of corrosion rate with exposure time. The diffusion-controlled normalized leaching rate of cations from glasses (g/cm2·d) is given by:


where t is time, Di is the i-th cation effective diffusion coefficient (cm2/d), which depends on pH of contacting water as Di = Di0·10–pH, and ρ is the density of the glass (g/cm3).

Glass network dissolution is characteristic of the later phases of corrosion and causes a congruent release of ions into the water solution at a time-independent rate in dilute solutions (g/cm2·d):


where rh is the stationary hydrolysis (dissolution) rate of the glass (cm/d). In closed systems the consumption of protons from the aqueous phase increases the pH and causes a fast transition to hydrolysis.[14] However, a further saturation of solution with silica impedes hydrolysis and causes the glass to return to an ion-exchange, e.g. diffusion-controlled regime of corrosion.

In typical natural conditions normalized corrosion rates of silicate glasses are very low and are of the order of 10−7–10−5 g/(cm2·d). The very high durability of silicate glasses in water makes them suitable for hazardous and nuclear waste immobilisation.

Glass corrosion tests

Effect of addition of a certain glass component on the chemical durability against water corrosion of a specific base glass (corrosion test ISO 719).[15]

There exist numerous standardized procedures for measuring the corrosion (also called chemical durability) of glasses in neutral, basic, and acidic environments, under simulated environmental conditions, in simulated body fluid, at high temperature and pressure,[16] and under other conditions.

The standard procedure ISO 719[17] describes a test of the extraction of water-soluble basic compounds under neutral conditions: 2 g of glass, particle size 300–500 μm, is kept for 60 min in 50 ml de-ionized water of grade 2 at 98 °C; 25 ml of the obtained solution is titrated against 0.01 mol/l HCl solution. The volume of HCl required for neutralization is classified according to the table below.

Amount of 0.01M HCl needed to neutralize extracted basic oxides, ml Extracted Na2O
equivalent, μg
< 0.1 < 31 1
0.1-0.2 31-62 2
0.2-0.85 62-264 3
0.85-2.0 264-620 4
2.0-3.5 620-1085 5
> 3.5 > 1085 > 5

The standardized test ISO 719 is not suitable for glasses with poor or not extractable alkaline components, but which are still attacked by water, e.g. quartz glass, B2O3 glass or P2O5 glass.

Usual glasses are differentiated into the following classes:

Hydrolytic class 1 (Type I):

This class, which is also called neutral glass, includes borosilicate glasses (e.g. Duran, Pyrex, Fiolax).

Glass of this class contains essential quantities of boron oxides, aluminium oxides and alkaline earth oxides. Through its composition neutral glass has a high resistance against temperature shocks and the highest hydrolytic resistance. Against acid and neutral solutions it shows high chemical resistance, because of its poor alkali content against alkaline solutions.

Hydrolytic class 2 (Type II):

This class usually contains sodium silicate glasses with a high hydrolytic resistance through surface finishing. Sodium silicate glass is a silicate glass, which contains alkali- and alkaline earth oxide and primarily sodium oxide and Calcium oxide.

Hydrolytic class 3 (Type III):

Glass of the 3rd hydrolytic class usually contains sodium silicate glasses and has a mean hydrolytic resistance, which is two times poorer than of type 1 glasses.

Acid class DIN 12116 and alkali class DIN 52322 (ISO 695) are to be distinguished from the hydrolytic class DIN 12111 (ISO 719).

See also


  1. ^ Galvanic Corrosion. Retrieved on 2012-07-15.
  2. ^ Methods of Protecting Against Corrosion Piping Technology & Products, (retrieved January 2012)
  3. ^ Intergranular Corrosion. Retrieved on 2012-07-15.
  4. ^ Crevice Corrosion. Retrieved on 2012-07-15.
  5. ^ JE Breakell, M Siegwart, K Foster, D Marshall, M Hodgson, R Cottis, S Lyon (2005). Management of Accelerated Low Water Corrosion in Steel Maritime Structures, Volume 634 of CIRIA Series, ISBN 0-86017-634-7
  6. ^ R. Zuo; D. Örnek; B.C. Syrett; R.M. Green; C.-H. Hsu; F.B. Mansfeld; T.K. Wood (2004). "Inhibiting mild steel corrosion from sulfate-reducing bacteria using antimicrobial-producing biofilms in Three-Mile-Island process water". Appl. Microbiol. Biotechnol. 64 (2): 275–283. doi:10.1007/s00253-003-1403-7. 
  7. ^ [Fundamentals of corrosion – Mechanisms, Causes and Preventative Methods]. Philip A. Schweitzer, Taylor and Francis Group, LLC (2010) ISBN 978-1-4200-6770-5, p. 25.
  8. ^ Gerhardus H. Koch, Michiel P.H.Brongers, Neil G. Thompson, Y. Paul Virmani and Joe H. Payer. CORROSION COSTS AND PREVENTIVE STRATEGIES IN THE UNITED STATES – report by CC Technologies Laboratories, Inc. to Federal Highway Administration (FHWA), September 2001.
  9. ^ "NACE Corrosion Costs Study". NACE. Retrieved 16 June 2014. 
  10. ^ Daniel Robles. "Potable Water Pipe Condition Assessment For a High Rise Condominium in The Pacific Northwest". GSG Group, Inc. Dan Robles, PE. Retrieved 10 December 2012. 
  11. ^ Bettine Boltres (2015) When Glass Meets Pharma: Insights about Glass as Primary Packaging Material. Editio Cantor. ISBN 978-3-87193-432-2
  12. ^ A.K. Varshneya (1994). Fundamentals of inorganic glasses. Gulf Professional Publishing. ISBN 0127149708.
  13. ^ M.I. Ojovan, W.E. Lee. New Developments in Glassy Nuclear Wasteforms. Nova Science Publishers, New York (2007) ISBN 1600217834 pp. 100 ff.
  14. ^ Corrosion of Glass, Ceramics and Ceramic Superconductors. D.E. Clark, B.K. Zoitos (eds.), William Andrew Publishing/Noyes (1992) ISBN 081551283X.
  15. ^ Calculation of the Chemical Durability (Hydrolytic Class) of Glasses. Retrieved on 2012-07-15.
  16. ^ Vapor Hydration Testing (VHT) Archived December 14, 2007, at the Wayback Machine.. Retrieved on 2012-07-15.
  17. ^ International Organization for Standardization, Procedure 719 (1985). (2011-01-21). Retrieved on 2012-07-15.

Further reading

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