Fatigue of Structures and Materials

Fatigue failures in metallic structures are a well-known technical problem. Already in the 19th century several serious fatigue failures were reported and the first laboratory investigations were carried out. Noteworthy research on fatigue was done by August Wöhler. He recognized that a single load application, far below the static strength of a structure, did not do any damage to the structure. But if the same load was repeated many times it could induce a complete failure. In the 19th century fatigue was thought to be a mysterious phenomenon in the material because fatigue damage could not be seen. Failure apparently occurred without any previous warning. In the 20th century, we have learned that repeated load applications can start a fatigue mechanism in the material leading to nucleation of a small crack, followed by crack growth, and ultimately to complete failure. The history of engineering structures until now has been marked by numerous fatigue failures of machinery, moving vehicles, welded structures, aircraft, etc. From time to time such failures have caused catastrophic accidents, such as an explosion of a pressure vessel, a collapse of a bridge, or another complete failure of a large structure. Many fatigue problems did not reach the headlines of the news papers but the economic impact of non-catastrophic fatigue failures has been tremendous. Fatigue of structures is now generally recognized as a significant problem.

The history of fatigue covering a time span from 1837 to 1994 was reviewed in an extensive paper by Walter Schütz [1]. Historical milestone papers were collected by Hanewinkel and Zenner [2] and Sanfor [3]. John Mann [4] compiled 21075 literature sources on fatigue problems covering the period from 1838 to 1969 in four books. Since that time the number of publications on fatigue has still considerably increased and it may be estimated to be around 100,000 in the year 2000. Fortunately, consulting the literature on specific topics can now be done with computerized literature retrieval systems.

In a specimen subjected to a cyclic load, a fatigue crack nucleus can be initiated on a microscopically small scale, followed by crack grows to a macroscopic size, and finally to specimen failure in the last cycle of the fatigue life. In the present chapter the fatigue phenomenon will be discussed as a mechanism occurring in metallic materials, first on a microscale and later on a macroscale.

Understanding of the fatigue mechanism is essential for considering various technical conditions which affect fatigue life and fatigue crack growth, such as the material surface quality, residual stress, and environmental influence. This knowledge is essential for the analysis of fatigue properties of an engineering structure. Fatigue prediction methods can only be evaluated if fatigue is understood as a crack initiation process followed by a crack growth period. For that reason, the present chapter is a prerequisite for most chapters of this book.

Calculations on the strength of structures are primarily based on the theory of elasticity. If the yield stress is exceeded plastic deformation occurs and the more complex theory of plasticity has to be used. Fatigue, however, and also stress corrosion, are phenomena which usually occur at relatively low stress levels, and elastic behavior may well be assumed to be applicable. The macroscopic elastic behavior of an isotropic material is characterized by three elastic constants, the elastic modulus or Young's modulus (E), shear modulus (G) and Poisson's ratio (ν). The well-known relation between the constants is E = 2G(1 + v).

In a structure, geometrical notches such as holes cannot be avoided. The notches are causing an inhomogeneous stress distribution, see Figure 3.1, with a stress concentration at the “root of the notch”. The (theoretical) stress concentration factor, K _t , ⁶ is defined as the ratio between the peak stress at the root of the notch and the nominal stress which would be present if a stress concentration did not occur.

The significance of residual stresses for fatigue is important in various practical problems. Unintentional tensile residual stress can have an adverse effect on the fatigue resistance, while compressive residual stress can significantly improve the fatigue behavior. The existence of residual stress and the introduction of such stresses in components are the subjects of the present chapter. It is restricted to basic aspects, while some specific topics will return in later chapters.

By definition, residual stress refers to a stress distribution, which is present in a structure, component, plate or sheet, while there is no external load applied. In view of the absence of an external load, the residual stresses are sometimes labeled as internal stresses. The background of the terminology “residual stress” is that a residual stress distribution in a material is often left as a residue of inhomogeneous plastic deformation.

Stress concentrations around notches were considered in Chapter 3 with the stress concentration factor K _t as an important parameter for characterizing the severity of the stress distribution around the notch. The crack initiation life is highly dependent on the K _t -value. The crack initiation period is followed by the fatigue crack growth period, recall Figure 2.1. For a crack, the K _t -value is no longer a meaningful concept to indicate the severity of the stress distribution around the crack tip. Because a crack is a notch with a zero tip radius, K _t would become infinite, and this would be true for any crack length. A new concept to describe the severity of the stress distribution around the crack tip is the so-called stress intensity factor K. This concept was originally developed through the work of Irwin [1]. The application of the stress intensity factor to present fatigue crack growth data and to predict fatigue crack growth is referred to as “linear elastic fracture mechanics”.

In the present chapter, fatigue properties of materials are described in terms of the fatigue limit, fatigue curves (S-N curves) and a fatigue diagram. The properties are restricted to results of constant-amplitude (CA) tests on unnotched specimens (K _t = 1.0) It is generally thought that the results of these tests reflect the basic fatigue behavior of a material. Mechanical properties of a material should include fatigue properties, but quite often reporting of fatigue properties is restricted to the fatigue limit on unnotched specimens obtained in rotating beam experiments (S _m = 0).

Material fatigue properties obtained on unnotched specimens were discussed in the previous chapter. However, an engineering structure is not an unnotched specimen. On the contrary, various “notched” elements can always be indicated in a structure. Fatigue tests on notched specimens are necessary for two major purposes:

The first topic is covered in the present chapter, while the second topic is addressed in Chapter 13.

In Chapter 2 the fatigue life until failure has been divided into two periods: (i) the crack initiation period, and (ii) crack growth period. Crack nucleation and microcrack growth in the first period are primarily phenomena occurring at the material surface. The second period starts when the fatigue crack penetrates into the subsurface material away from the material surface. The growth of the fatigue crack is then depending of the crack growth resistance of the material as a bulk property. The two previous chapters, Chapters 6 and 7, mainly deal with fatigue in the crack initiation period. The subject of the present chapter is fatigue crack growth in the second period. It could also be referred to as the growth of macro fatigue cracks.

Under which conditions is crack growth in the second period of practical interest? Obviously, the load spectrum should contain stress cycles above the fatigue limit in order to have a fatigue crack problem. Secondly, some macrocrack growth must be acceptable, but it should then be known how fast crack growth occurs. Two well-known examples are:

The fatigue loads on a structure in service are generally referred to as the load spectrum. The description of load spectra and methods to obtain load spectra are discussed in the present chapter. A survey of various aspects of fatigue of structures was presented as a flow diagram in introductory chapter (Chapter 1, Figure 1.2). A reduced diagram is presented here in Figure 9.1 to illustrate the significance of load spectra for fatigue design analysis of a structure. Without information on the anticipated load spectrum, the analysis of the fatigue performance of a structure is impossible. Furthermore, verification tests to support the analysis are often necessary for economic or safety reasons. The load spectrum must be consulted for planning such validation tests.

Sometimes the load spectrum is changed after a number of years by a modified use of the structure, which is different from the initial expectations. The load spectrum must then be considered again. Fatigue load spectra should also be reviewed if fatigue failures occur in service.

Constant-amplitude (CA) fatigue loading is defined as fatigue under cyclic loading with a constant amplitude and a constant mean load. Sinusoidal loading is a classical example of CA fatigue loads applied in many fatigue tests. In the previous chapter on fatigue loads, it has been pointed out that various structures in service are subjected to variable-amplitude (VA) loading, which can be a rather complex load-time history, see several figures in Chapter 9. Predictions on fatigue life and crack growth should obviously be more complex than predictions for CA loading. The latter problem was discussed in Chapter 7 (Fatigue Lives of Notched Elements) and Chapter 8 (Crack Growth). In Chapter 7, the best defined problem was the prediction of the fatigue limit of a notched element. The fatigue limit is a threshold value of the stress amplitude. Stress amplitudes below this level do not lead to failure, while stress amplitudes above the fatigue limit lead to crack initiation and crack growth to failure. Rational arguments could be adopted for the predictions of the fatigue limit, by comparing fatigue limits of a structure to fatigue limits of simple unnotched specimens, but certain problems had to be recognized associated with the notch effect, size effect, surface effect and environmental influences.

For structures subjected to VA load cycles in service, it may be desirable that fatigue failures should never occur. It implies that all load cycles of the load spectra should not exceed the fatigue limit. The prediction problems is then restricted to the prediction of the fatigue limit as discussed in Chapter 7. However, this requirement can lead to a heavy structure and it can be unnecessarily conservative, especially if the number of more severe load cycles above the fatigue limit is relatively small. Moreover, a complete avoidance of fatigue is not always required. Failures after a sufficiently long life can be acceptable from an economical point of view, the more so if safety issues are not involved. Fatigue under VA load conditions is the subject of the present chapter. Possibilities for fatigue life predictions under VA loading are discussed, while predictions on crack growth under VA loading are covered in the following chapter (Chapter 11).

Fatigue under Variable-Amplitude (VA) loading was discussed in the previous chapter. Key words of the discussion were: prediction of fatigue life until failures, the Miner rule and its shortcomings, fatigue damage of cycles with an amplitude below the fatigue limit, residual stress effects due to notch root plasticity, and service-simulation fatigue tests as an alternative to Miner rule predictions. The fatigue life was supposed to include the crack initiation period and the crack growth period until failure. It was tacitly assumed that the crack growth period was relatively short and could be disregarded. The present chapter is dealing with the growth of macrocracks under VA loading. The crack initiation period dealing with crack nucleation and microcrack growth is not addressed.

The propagation of macrocracks is a significant issue if fatigue cracks cannot be avoided, especially if safety or economy is involved. Dangerous situations can occur in pressure vessels, high-speed rotating masses (turbine disks, blades of wind turbines) and aircraft structures as some characteristic examples. Incidental cracks can be generated by a variety of conditions; such as surface damage, corrosion pits, material defects in welded joints, inferior production quality, etc. Furthermore, the fatigue life of a structure in service may cover many years. The occurrence of macrocracks can then be acceptable in order to avoid a low design stress level and a corresponding heavy structure.

Scatter is an inherent characteristic of mechanical properties of structures and materials. This also applies to fatigue properties. The fatigue lives of similar specimens or structures under the same fatigue load can be significantly different. Also, the fatigue limit of one and the same material is subjected to scatter. In the literature, statical aspects of fatigue of structures and materials are well recognized, but the implications for engineering problems are not always clear. In this chapter, various sources for scatter of fatigue are discussed first (Section 12.2). These sources can be essentially different for the crack initiation period and crack growth period. The description of the statistical variability is addressed in Section 12.3, including how to obtain experimental information about scatter. A special issue is scatter of the fatigue limit. Various engineering aspects of scatter are discussed in Section 12.4. The major topics of this chapter are recalled in Section 12.5.

Fatigue tests are carried out for different purposes. The engineering objectives are the determination of fatigue properties of materials, joints, structural elements, etc., including comparisons of different design options. Research objectives of fatigue tests are concerned with understanding of the fatigue phenomenon and its variables. Research objectives and engineering objectives may be complementary.

The variety of fatigue test programs reported in the literature is large, and the number of publication is steadily growing. Different types of fatigue loads, specimens, environments, and test equipment are used. Fatigue tests generally require significant experimental effort and time, which implies that these tests are more expensive than simple tests of several other mechanical properties. Experiments on fatigue problems are supposed to answer questions, while empirical answers are assumed to be more convincing than a theoretical analysis. The saying is: “Experiments never lie”. But, if an experiment is not correctly planned to answer the question under consideration, the result can be a right answer to a wrong question.

Fatigue cracks generally start at the free surface of a material. As a consequence, the conditions of the surface are most significant for the fatigue behavior of a structure. The importance of these conditions was recognized long ago, if not in the laboratory, it was by practical experience. Corrosion pits, fretting corrosion, nicks and dents became well-known sources of fatigue problems. Surface treatments to improve the fatigue resistance were also developed a long time ago.

As discussed in previous chapters, material surface conditions are important for fatigue crack nucleation, and thus affect the crack initiation period of the fatigue life. Major influences on the fatigue limit and fatigue strength under high-cycle fatigue are expected, see the discussion in Section 2.5.5. Aspects of surface conditions affecting the fatigue performance are briefly described in Section 14.2. It includes surface treatments, surface roughness and residual stress in surface layers. Some practical consequences are considered in Section 14.3. Topics of the present chapter are summarized in Section 14.4.

Fretting corrosion is primarily a surface damage phenomenon occurring as a result of small cyclic movements between two materials caused by cyclic loading. Fretting damage can occur in vacuum, although it then would be better to speak of fretting, rather than fretting corrosion. In normal air, corrosion plays an active role in causing fretting corrosion damage. The other contribution comes from rubbing between two material surfaces. Very small rubbing displacements are sufficient for initiating fretting corrosiondamage. Such displacements easily occur in joints; bolted joints, riveted joints, clamped joints, leaf springs, etc. It also occurs inside a bolt hole between the bolt and the wall of the hole. Fretting is even possible between two metallic parts where load transmission does not occur.

Fretting corrosion is a practical problem because it can cause significant reductions of fatigue properties of structural elements. In the present chapter, the fretting corrosion mechanism is discussed in Section 15.2. Important variables on fretting corrosion are discussed in Section 15.3. Methods to avoid fretting corrosion are the subject of Section 15.4. Some practical aspects, which will return in Chapter 18 on joints. Major topics of the present chapter are summarized in Section 15.5.

Corrosion fatigue by definition is fatigue in a corrosive environment. An aggressive environment can be harmful for the fatigue life of a structure, and protection against corrosion is necessary. Designers must consider corrosion in service, not only in view of fatigue. Corrosion is undesirable for reasons related to a safe and economic use of a structure during its service life. Corrosion can also be unacceptable in view of the appearance of a structure, i.e. for cosmetic reasons. Usually, corrosion prevention is considered to be a matter of selecting a corrosion resistant material or applying a suitable surface protection, such as paint or cadmium plating, etc. Unfortunately, these options do not guarantee good fatigue properties. Furthermore, several high-strength materials have a relatively poor corrosion resistance. Disastrous accidents have occurred due to fatigue cracks starting from corrosion damage, in several cases corrosion pits. Whenever corrosion damage can occur to the material surface of a dynamically loaded structure, corrosion fatigue can be a serious problem.

Corrosion fatigue should not be confused with stress corrosion, which is crack initiation and growth under a sustained load or residual stress. Usually, stress corrosion occurs along an intergranular crack growth path, whereas corrosion fatigue in many cases is still a transgranular crack growth phenomenon. Moreover, stress corrosion does not occur in many technical materials, whereas corrosion fatigue can occur in most materials. Corrosion fatigue is also not the same as fatigue of corroded material. Of course, corrosion damage can decrease the fatigue properties because it implies surface damage which will reduce the crack initiation life. The effect of the surface quality was discussed in Chapter 14. The problem considered in the present chapter is technically relevant if a corrosive environment is present during the entire life time of a structure. It implies that the crack initiation period and the crack growth period can be affected both.

Material properties are dependent on the temperature. The tensile strength, yield strength and modules of elasticity decrease with increasing temperature. It should be expected that fatigue properties are also affected by the temperature. The effect of a high temperature on mechanical properties can be associated with transformations of the material structure due to diffusion processes, aging, dislocation restructuring (softening), and recrystallization. In general, such processes imply that plastic deformation can occur more easily at an elevated temperature. This can lead to the well-known creep phenomenon defined as continued plastic deformation under sustained load. With respect to fatigue, it can imply that more plastic deformation and creep occur in the plastic zone of a fatigue crack which may apply to both microcracks and macrocracks. As a result, fatigue damage accumulation might be enhanced. Furthermore, other failure mechanisms are possible. During creep under sustained load, creep failures occur by grain boundary sliding, void formation (also often at grain boundaries), void growth and coalescence. In general, fatigue is not an intergranular but a transgranular failure mechanism. It thus is not obvious that fatigue and creep damage are simply additive. Actually, the different failure mechanisms of creep and fatigue suggest that a simple addition of damage contributions is physically not realistic. Furthermore, the combined action of cyclic load and an increased temperature should be expected to be different for different materials and different temperature ranges.

High-temperature fatigue combined with time-dependent temperature variations applies to specific structures. As an example, turbine blades are exposed to high combustion temperatures, high centrifugal forces and vibratory bending loads. In certain cases, the severe conditions of high-temperature fatigue have necessitated the development of new materials. Another aspect of the high-temperature fatigue problem is that the temperature will not be constant. In general, the temperature varies between a high operating temperature and a low non-operational ambient temperature. As a result of the temperature profile, cyclic thermal stresses can be introduced. High-temperature fatigue conditions imply that the fatigue load and temperature vary both as a function of time. In addition to the cyclic load, two more variables are time (t) and temperature (T). It then is easily recognized that the complexity of the problem scenario in practice can be considerable.

Fatigue failures in structures frequently occur in joints. Various catastrophic accidents due to fatigue have been reported in the literature. As a consequence joints are a major issue for designing against fatigue. The prime purpose of a joint is to transmit loads from one element of the structure to an other element. The variety of different joint configurations is very large. Some elementary types of joints are shown in Figure 18.1.

A significant difference between two categories of joints is associated with the question whether it should be possible to disassemble and reassemble a joint, or whether that is not necessary. The lug type joint and the bolted joint are in the first category. However, riveted lap joints, bonded lap joints and welded joint, including spot welded joints, are supposed to remain in the as-produced condition. Another noteworthy aspect of joints is associated with eccentricities in the joint. The bolted joint in Figure 18.1 is fully symmetric with respect to the line of the applied load. But that is not true for the two non-symmetric lap joints in Figure 18.1. As a result of the eccentricity in these joint, bending is introduced by the applied tensileload. The additional bending, referred to as secondary bending, will increase notch effects in these joints. Furthermore, fasteners in a simple lap joints are loaded in single shear whereas bolts in the symmetric joint are loaded in double shear which appears to be a more favorable situation. Still another complexity is the occurrence of fretting in lugs and bolted and riveted joints. Once again, the variety of joints is just large. Moreover, the number of design parameters for each type of joint also contributes to a broad spectrum of design questions. Variables included are associated with joint dimensions, production variables and selected materials.

Welding of metals is applied on a very wide scale, especially for building up structures by welding of steel plates and girders of different cross sections (I-beams, U-beams, angle beams). Welding provides many structural design options which cannot be simply realized with other production techniques. Major applications are found in bridges, cranes, ships, offshore structures, pressure vessels, buildings and various types of spatial frames.

Welding as a production technique is associated with various problems, which are characteristic for welding only. As a result, the subject “welding” became practically a discipline on its own as illustrated by the existence of welding institutes and organizations, standards and design codes, journals, and an extensive literature. Within the welding discipline, much attention has been paid to problems related to different welding techniques known under general names as: arc welding, gas welding, electron beam welding, laser welding, resistance spot welding, friction welding, and more recently stir friction welding. Welded joint designs and notch effects of welds are typical for welded structures. Welded joints are also known for a number of characteristic weld defects. These defects have created new issues for non-destructive inspections (NDI), which have stimulated developments of X-ray and ultrasonic equipment. Moreover, fatigue properties of welded joints can exhibit considerable scatter because of a variety of imperfections of these joints. As a consequence, fatigue of welded joints has always been a matter of concern, but good welding practice can be specified for fatigue critical structures including non-destructive inspections of all welds.s

The present chapter is a kind of a reflection on previous chapters. It starts with a brief survey of different types of structures and related prediction problems in Section 20.2, followed by a repetition of design tools in Section 20.3. Uncertainties of predictions and safety factors are addressed in Section 20.4. Some illustrative case histories of structural fatigue problems are presented in Section 20.5. The chapter is completed with summarizing conclusions.

The history of mankind has been characterized by an interesting development of materials originally used for tools, housing, weapons and other needs. Initially wood and clay were available materials, followed by stone (Stone Age) and much later, but still about 3000 years ago, by iron (Iron Age). Apart from the availability of building materials, the production and working processes were also decisive for the success of a material (which in fact is still true in the present time). In the past, material properties were related to strength, stiffness, and durability. It was recognized that stones could carry high-compression loads but not high-tension loads. Later, the engineering approach to new materials included the development of composite materials with the aim to combine favorable properties of different materials into a single composite material. Reinforced concrete is a well-known example and fiber-reinforced plastics another typical case. Several composite materials were designed for specific applications. Developing materials and designing composite materials for specific purposes is often essential for advanced applications. A noteworthy example is offered by modern ceramics for high-temperature applications with the space shuttle as an outstanding example.

The history of aircraft structures has seen a large variation of different materials. In the very beginning, the time of the Wright brothers, the materials of the aircraft structure were wood, steel and linen. In the first half of the 20th century, design criteria for materials used in aircraft structures were associated with low weight and sufficient strength. The introduction of aluminium alloys in the late 1920s was a kind of a revolution because it drastically changed structural design concepts. The efficiency of aircraft structures was significantly improved. Aluminium alloys also penetrated many other applications because of the low specific weight, e.g. in many household appliances.