Fatigue and Corrosion in Metals

For centuries man has been aware that the repeated application of loads would lead to the early failure of materials. It came as something of a surprise, however, when he also found, almost two centuries ago, that failure could occur under stresses of relatively low amplitude, lower than the yield strength σ_y of the material.

We have seen, in Chapter 1 that the fatigue process develops through four fundamental steps that we called phases.

The purpose of this chapter is to provide some basic information about the morphological aspects associated with the various fatigue processes that take place in materials during cycling.

In Chap. 1, basic design S–N diagrams have been introduced that can be referred to as standard S–N or Wöhler curves for plain specimens. The present chapter is concerned with modifying these S–N curves to account for all those factors that may have an effect on fatigue life.

The role that the external surface exerts on the fatigue strength of materials will never be stressed enough. In high cycle fatigue and to a less extent also in low-cycle fatigue, the first and most effective barrier to the demolishing action of cyclic loads is provided by the surface. A really well-treated surface will make a workpiece last fatigue as expected while an inaccurate and odd surface will lead to an early as well unexpected fatigue failure.

If five specimens of the same material, size and surface finish were subjected to the same fatigue test, it is likely that there would be five different results. If the test pieces were ten, then it is likely that there would be ten different results. Increasing the number of specimens will not change this general outcome and new values, higher and lower, will be added. Therefore, also the spread between the maximum and the minimum value will increase, albeit most values will appear closely-spaced.

In Sect. 1.​2 we have introduced the Wöhler curve and the S–N curve. Generally, they are considered to be the same thing, but they are not. The difference is in the life domain they cover. The Wöhler curve describes the fatigue behavior of a generic material from ¼ of a cycle to the fatigue limit, σ_f, or, in case of no precise fatigue limit as for non-iron alloys (see Fig. 1.​11), up to 10⁸–10⁹ or more cycles. The Wöhler curve, therefore, spans the entire fatigue life from low-cycle fatigue to high-cycle fatigue and beyond (see Fig. 1.​10) covering all the three regions of fatigue. The S–N curve, instead, describes the fatigue behavior of materials in the elastic domain or Region II, where the plastic contribution to stresses and strains is negligible. We may say, then, that the Wöhler curve is typically an ε-N curve obtained under strain controlled conditions while the S–N curve relates the stress amplitude σ_a given by Eq. (1.​1), also indicated as S, to the number N of cycles to failure. When the stress amplitude is close to the fatigue limit, σ_f, or knee of the S–N curve the plastic component of deformation, ε_p, becomes negligible or even vanishes. Fatigue is driven by the elastic component of the strain amplitude that is proportional to the stress amplitude through the Young’s modulus of the material. Therefore, as we approach the fatigue limit of the material, σ_f, we can abandon strains as the controlling parameter and relate the fatigue life directly to the stress amplitude. The hysteresis loop disappears, as shown schematically in Fig. 1.​10, because the material behaves almost completely elastically. In this area of elastic or quasi-elastic behavior any analytical approach to fatigue is generally indicated as stress-life method. Historically, it has been the first approach to fatigue and has been the standard design method for almost 100 years. Stress-life methods are generally used when the designer pursues a target of infinite-life or safe-stress design. When the stress amplitude reaches the elastic limit and strains have a significant plastic component the S–N approach is no longer appropriate and a strain-based approach ε-N becomes necessary, as it will be described in the next section.

Three regions were identified in Sect. 1.​2 and shown in Fig. 1.​10 as Region I, II and III concerning the fatigue strength of materials. In Sect. 2.​5 Region III pertaining fatigue limit was analyzed. In that region the stress amplitude in not high enough to propagate a micro defect even though it may have been generated. In Chap. 5 we have been discussing of Region II, the region of high cycle fatigue where load levels are low and the main component of stress is elastic, when not totally elastic. In this chapter we will examine as last the first region or Region I of low cycle fatigue where strains and, in particular, plastic strains are the dominant factor. When load levels are low, stresses and strains are linearly related by Hooke’s law. Under such conditions they are fully interchangeable. But when the plastic component cannot be neglected anymore and, indeed, prevails, stresses are no longer uniquely determined and must be put aside. Although most engineering structures and components are design such that nominal loads remain elastic, stress concentrations can easily introduce a non-negligible plastic strain component.

The traditional subdivision of the Wöhler curve into the three regions of Fig. 1.​10, at least for ferrous alloys or, better, for BCC crystal lattice materials has been recently extended to include a new region beyond some 10⁷ or 10⁸ cycles. It is the region of the so called Very-High-Cycle-Fatigue or VHCF. The more demanding request for life from many technological applications has been the driving force to explore, also for BCC materials, the field of 10⁸ or even 10⁹ cycles. The pressure to know how these materials perform in the VHCF region, whether or not they really have a definite fatigue limit, has unveiled a new as well unexpected behavior that still remains argument of vigorous discussion among researchers. It is a fact that vast majority of the data so far collected since Wöhler first tests with fatigue specimens, are confined within 10⁷–10⁸ cycles.

At the base of fatigue design there is the Wöhler’s curve S–N that is obtained through fatigue tests. Giving a stress amplitude S or strain amplitude ε_a to a series of specimens it is possible to derive the corresponding cycles to failure N or life. Considering the importance of such a curve and, therefore, of laboratory tests in general, it is convenient to spend some arguments on the matter just to evidence the most important features and the limits that may be associated, too often forgotten.

It has been shown, in Chap. 2 in particular, that nucleation damage in fatigue is always a localized sub-microscopic damage either on persistent slip lines in some surface grain or in persistent grain boundaries somewhere in the material, depending on whether fatigue is acting in the high cycle or low cycle regime. It is evident that any factor producing a localized stress amplification favors the premature outbreaks of such a damage and the subsequent crack formation. This local stress amplification is generally caused by a component notch or discontinuity. William Rankine of England was probably the first to understand this effect studying axels failures and stating in 1842 (Rankine in Institution of Civil Engineers, Minutes of Proceedings, vol 2, pp105–108, London, 1842) “the fractures appear to have commenced with a smooth, regularly-formed, minute fissure, extending all-round the neck of the journal, and penetrating on an average to a depth of half an inch. … until the thickness of sound iron in the center became insufficient to support the shocks to which it was exposed”.

Loads so far considered had constant amplitude (CA), σ_a or S. This constitutes a particularity that rarely happens in real life. Usually, cyclic loads have variable amplitudes (VA) that are referred to as the load spectrum or time history. Even apparently simple operating conditions actually result in a more or less frequent variability of load amplitudes with time. Think about a pressure vessel that is heated up and cooled down every working day. During normal functioning at the nominal pressure the vessel can experience some pressure variations that depend on numerous factors, often aleatory. These pressure variations are generally small amplitude fluctuations, but they are applied to the vessel shell with high mean stress provided by the heat up and cool down cycle. In addition, from time to time there might be large temperature and pressure transients that results in major stress excursions that do not occur too often, but in a 20 or 30 years of expected life they can sum up to a consistent number.

So far it has been analyzed the phenomenology that precedes the macro-crack formation and studied all those factors, both mechanical and metallurgical, that have a role in the macro-crack formation that closes Stage I of fatigue (see Sect. 2.​7 and Fig. 2.​47). The next phase, Stage II, is that in which the macro-crack is directly opened by stresses normal to the crack plane and grows at each applied cycle.

It has been shown in the previous section that the fatigue crack propagation in metallic materials follows a trend that can be described by the Paris-Erdogan Eq. (10.​10). However, the Paris postulate is valid only under particular circumstances as constant load cycling in Region II of fatigue, long cracks and stress ratio R equal zero. If these circumstances are not met the Paris-Erdogan equation fails to represent the FCGR of the material.

More than half a century is passed from World War II when welding heavily entered into engineering practice and in the naval construction technique, in particular, often with catastrophic results. As in the development of any technological field it took its toll of failures and casualties before welding would become a discipline of its own and institutes, research centers, universities and industries would develop enough knowledge to provide good practices and standards.

Very few events, if any, have such a devastating effect from the point of view of structural, economical and human casualties as corrosion. Virtually any metallic material is subjected to corrosion even in a clean air environment. Structures are continuously attacked and sometime even completely demolished by corrosion. The damage caused in the world to metallic structures by corrosion can be assessed in terms of billions of Euro every year. Corrosion is certainly a very complex and many-sided phenomenon hardly tied to a single parameter theory. A first, generic classification divides corrosion into generalized or uniform and localized corrosion. Both are fundamentally electrochemical processes, but while the first affects almost uniformly the entire surface exposed to the corrosive agent, the second attacks the metal locally and selectively. Generalized corrosion is very common in carbon steel where it results in the formation of the so called rust which advances very slowly so that it is effectively dangerous only in very thin materials or very long terms. Localized corrosion, instead, initiates locally, unexpected and once started it proceeds very rapidly along intergranular or transgranular paths to go through the thickness of a work piece in matters of minutes or days, at most. Initiation may last years, but growth is fast. Localized corrosion is a subtle and continuous process in which stresses play a role, which is referred to as stress corrosion or SCC (stress corrosion cracking) or fatigue.

Even dough sensitization and hydrogen embrittlement failures can be classified as stress corrosion cracking, they are so distinctive and important a form of corrosion that deserve to be treated in a section of their own.

Stress corrosion cracking (SCC) is used as a generic term to describe any behavior in which a combination of a static load and an aggressive environment results in the generation and propagation of a crack by corrosion. Stress corrosion has been treated from the electrochemical point of view in Chap. 17 and with a chemical-metallurgical approach in Chap. 18 for the important cases of hydrogen embrittlement and sensitization embrittlement of metals. We shall now study SCC from a mechanical point of view showing how fracture mechanics, in particular, originally developed to treat brittle fracture of World War II ships and later used in the treatment of fatigue crack propagation (see Chap. 10) can be also applied to treat the mysterious world of stress corrosion. It has been said in Sect. 17 that the study of corrosion had evidenced the fundamental role played by the combination of a specific material with a specific environment.

It is rather difficult to establish a simple yet comprehensive picture of the combined effects of fatigue and environment. It is the author’s view that to fully understand corrosion fatigue it is necessary to proceed through fundamental steps starting with concepts that may seem elementary. As first, it must be said that any environment is potentially aggressive, even dry air.