Perspective Chapter: Fatigue of Materials

Abstract

This chapter deals with the fatigue fracture of the materials under cyclic loadings. Components of structures and machines may be subjected to cyclic loads and the resulting cyclic stress that can lead to microscopic physical damage and fracture of the materials involved. It has been seen at a stress well below the ultimate strength, this microscopic damage can accumulate under action of cyclic loadings until it develops into a crack that leads to final separation of the component. In addition, the material inherently has cracks and other microscopic defects that grow due to cyclic loads and lead to fracture of machine or structure parts. The failures are more often sudden, unpredictable and catastrophic which may occur after a short period of design life. The main objective in writing this chapter is to present scientific findings and relevant engineering practice involving materials fatigue failures.

1. Introduction

It has been found that a metal subjected to cyclic stress will fail at a stress level much lower than that of a single application load. Fractures occurring under cyclic loadings are known as fatigue fractures [1, 2]. Indeed, one of the main reasons for unpredictable and premature material failures in service is the application of cyclic loads and the occurrence of fatigue [3, 4, 5, 6, 7, 8].

Two event that caused a lot of human and financial losses due to fatigue were observed during the 1994 Northridge and 1995 Kobe earthquakes. Investigations have shown that cyclic loading of earthquakes alongside presents of high strain rates, notch and poor material properties were responsible for these premature failures in steel structures [9, 10, 11]. It should be noted that earthquake loads in the form of low cycle fatigue (LCF) and extremely low cycle fatigue (ELCF) caused the failure of steel structures [12, 13, 14, 15].

Machinery equipment’s such as compressors, turbines and pumps are more prone to this type of damage. Numerous destructions in these devices have been reported due to incorrect design or manufacturing defects and have caused loss of production and financial resources [16, 17, 18, 19]. Failure of a Ti6Al4V alloy compressor impeller used in a petrochemical plant is shown in Figure 1. Investigations revealed fatigue has been responsible in the failure of compressor impeller. Stress concentration in the blade root causes the formation of fatigue cracks and final failure of the part [16].

Figure 1.

Fracture of a gas compressor turbine blade [16].

Another practical example of fatigue failure is shown in Figure 2. This failure occurred in an AISI4140 steel material as a result of not considering the metallurgical parameters in the construction of U-bolts for a lift. Experience showed that surface modification technique is a suitable strategy for extending the life of U-bolts under cyclic loadings. The technique consisted of heating, quenching, tempering and transforming the initial ferritic/pearlitic microstructure to tempered martensite with a higher surface hardness. The idea was taken from the fact that surface hardening process produced a reduction in grain size, retained austenite level, compressive residual stress, and as a result significantly improves the fatigue limit of the low alloy steels [20, 21]. Thermo-chemical surface treatment such as carburizing and nitriding can also improve the fatigue properties of these steels [20, 22, 23, 24].

Figure 2.

Fatigue failure of U-bolt of an elevator.

This type of failure is insidious because it led the equipment’s to failure and plants to shut downs without any warning. Three main factors are necessary for this type of failure [2]:

1. Adequate tensile stress

2. Fluctuation of applied stress

3. Adequate cyclic loads

Other factors such as stress concentration, overload, temperature, metallurgical structure, surface finishing, and residual stresses accelerate the occurrence of these type of fractures [2, 16, 17, 25, 26, 27, 28, 29].

The purpose of this chapter is to present the fatigue failure of materials and the methods of minimizing such damages for safety, durability and reliability of the products. To achieve this, the mechanical aspects of fatigue are explained first. Then, fatigue damage mechanism and fatigue futures are discussed. In the next step, the author is placed a focus on the types of fatigue failure and their characteristics by stating several practical examples. Finally, it has been dealing with factors that affecting material fatigue properties. It should be noted that the material in this chapter is based on our interaction with fatigue damages of components in the industry as well as based on that were taught university.

2. Mechanical aspects of fatigue fracture

Analysis of stress and strains for cyclic loading is needed for dealing with engineering situation such as vibratory loading which lead the component to fatigue fracture. In some practical applications the material operates at a maximum and minimum stress levels that are constant. This is known as constant amplitude stressing and is shown in Figure 3.

Figure 3.

Various type of cyclic loadings. a) Completely reversed stressing, (b) nonzero mean stress, (c) zero to tension stressing.

The stress range is the difference between the maximum and minimum stress values, $∆\sigma ={\sigma }_{\mathit{max}}-{\sigma }_{\mathit{min}}$, the mean stress, ${\sigma }_m$ is the average of maximum and minimum of stress values that may be zero (Figure 3a). Half range is named stress amplitude. Mathematical expressions are as follows [1]:

$${\sigma }_a=\frac{{\sigma }_{\mathit{max}}-{\sigma }_{\mathit{min}}}{2}$$E1

$${\sigma }_m=\frac{{\sigma }_{\mathit{max}}+{\sigma }_{\mathit{min}}}{2}$$E2

The stress ratio R and amplitude ratio A is defined as:

$${\sigma }_a=\frac{{\sigma }_{\mathit{min}}}{{\sigma }_{\mathit{max}}}$$E3

$$A=\frac{{\sigma }_a}{{\sigma }_m}$$E4

2.1 S-N curves

Stresses (S) versus life (N) is an engineering representative of fatigue behavior of materials. When we do cyclic test on a sample at a stress level, S, the sample will be failed after N cycle. If the test repeated at higher stress level the cyclic to failure will be smaller. A typical plot of S-N curve in a rotating bending test of an aluminum alloy in logarithm scale is shown in Figure 4.

Figure 4.

S-N curve for specimens of steel. Fatigue limit can be seen at about Se = 414 MPa [30].

S-N data in Log–Log scale is usually in form of a straight line. An equation can be fitted on these data’s is [1]:

$${\sigma }_a=A{N}_f^B$$E5

It should be noted that Eq. 5 describes the linear part of the S-N curve and is known Baskin equation. The nonlinear part is called fatigue limit or endurance limit, Se which is seen in S-N curve of some materials like plain carbon and low alloy steels. This is a stress level that fatigue failure does not occur under ordinary conditions or the cycle number to failure is unlimited. It should be noted in practical applications irregular loads versus time histories are more commonly encountered [1]. Examples for these conditions are given in Figure 5.

Figure 5.

Loads for one flight of a fixed-wing aircraft (a), and a simplified form of this loading [31].

For such situations that the amplitude of loading is variable, the Palmgren-Miner rule predicts fatigue life of the component [2]:

$$\frac{n1}{N1}+\frac{n2}{N2}+\frac{n3}{N3}+\dots +\frac{\mathit{nk}}{\mathit{Nk}}=1$$E6

Where n1, n2, n3…and nk are the number of work cycles at each of the different stress levels and N2, N2, N3…and Nk are the life of the part at each similar stress levels.

According to this equation, the total life of the part is estimated from the sum of the percentage of lives spent by each stress cycle.

2.2 Fracture mechanic

The presence of cracks significantly reduces the strength and longevity of a component due to increasing the probability of occurring brittle fracture [32, 33, 34]. Cracks may be produced during the manufacturing process or other inherent flaws that convert to crack and grow until its rich critical sizes for brittle fracture. Paris equation describes the crack growth behavior of a material under cyclic loadings [1]:

$$\frac{\mathit{da}}{\mathit{dN}}=C{\left(∆K\right)}^m$$E7

$$∆K=F∆\sigma \sqrt{\mathit{\pi \alpha }}$$E8

$$∆\sigma ={\sigma }_{\mathit{max}}-{\sigma }_{\mathit{min}}$$E9

Where $\frac{\mathit{da}}{\mathit{dN}}$cyclic crack growth rate, ∆K stress intensity range, C and m are constants.

In fact this equation is log–log plot of $\frac{\mathit{da}}{\mathit{dN}}$ versus ∆K as shown in Figure 6. In this diagram there is a vertical part denoted $∆K_{\mathit{th}}$, which named the fatigue crack growth threshold. This quantity is a lower limiting value that below of that the crack growth does not occur. At high growth rate the curve again become steep due to rapid unstable crack growth [1].

Figure 6.

Fatigue crack growth rate for a ductile pressure vessel steel. (a)$$Threshold intensity factor, $∆K_{\mathit{th}}$, (b) intermediate region which shows with power equation, (c) rapid crack growth [35].

3. Fatigue damage mechanism

Fatigue is a damage processes of components caused by cyclic loads. The process involves four stages [1, 36]:

1. Crack nucleation 2. Short crack growth 3. Long crack growth 4. Final separation

The first step is crack nucleation. It has been observed that crack of fatigue damage starts at near high stress concentration sites such as slip bands, inclusions, porosities or other manufacturing discontinuity. Localized shear plans that usually occurs at surface or within grain boundaries is another location for nucleation of fatigue cracks. This stage of fatigue cracking may be relieved with proper annealing treatment.

The next step in fatigue damage process is the crack growth. This stage is the deepening of the initial crack on the planes with maximum shear stress and it is often called crack growth stage I. This stage is greatly affected by microstructure characteristic such as grain size, slip mode and stress level because the crack size is in the order of the microstructure.

Step 3 is the crack growth stage II. At this stage, the crack created in the previous stage grows in the direction perpendicular to the planes with high tensile stress. This stage is less affected by the microstructure because the plastic zone in crack tip is much larger than the material grain size.

Stage 4 is final separation. This stage is when the crack length reaches a critical value and the remaining cross-section cannot withstand the applied load.

Fatigue studies show that fatigue cracks usually start from a free surface. If these cracks start from the inside, the nucleation site of the crack is usually a carburized or similar surface layer [2].

4. Fatigue features

In macroscopic scale fatigue failure is seen with a brittle appearance and without any gross deformation in the failure. The fatigue failure surface usually consists of a smooth area due to crack growth and surface wear on each other, and a rough area formed when the load is unbearable [36]. Another characteristic of fatigue failure is the beach marks, fine and arch-shaped lines, that starts from the place of crack initiation and progresses to the area of ductile fracture as it is seen in Figure 7. They are also known as macroscopic striations.

Figure 7.

Beach marks on fractured surface. The arrow indicates the crack direction propagation [37].

It should be noted that striations are not always formed on the fracture surfaces. Inert environments, high strength materials for examples steels with hardness above 30 HRC, aqueous environments or high temperature air, creep fatigue condition, Low $∆K$ value for example stainless steel at $∆K<30\mathit{MPa}\sqrt{m}$ Mode II and III fracture [36]. Figure 8 shows a fatigue fracture of an AISI 316 L stainless steel in absence of striations.

Figure 8.

Surface fatigue failure of a duplex stainless steel due to high vibration in services.

The microscopic evaluation of fracture surface is generally carried out with a scanning electron microscopy (SEM). The most important characteristic of fatigue fracture that is manifested in failure fracture surface is the presence of striations. Seriations are small groves extended perpendicular to the crack growth direction as seen in Figure 9. In general, striations indicate the growth rate of cracks in microscopic scales where each striation correspond to one load cycle. It is important to note that striation in brittle materials are different from ductile materials [36]. In ductile state the striation profile is wavy and smooth while brittle striations are irregular or saw tooth-like as seen in Figure 9a, b.

Figure 9.

Microscopic striation in a fatigue fracture surface of a ductile material (a), brittle type of striations (b) [37].

5. Types of fatigue

Fatigue failure of parts and components can be categorized to high cyclic, low-cycle fatigue, extremely low cycle fatigue, corrosion fatigue, and thermal fatigue. Here the features and parameters that control each process are discussed:

5.1 High cycle fatigue

High cycle fatigue is characterized by high number of cycles to failure and little plastic deformation. This type of failure occurs with a brittle appearance. Figure 1 shows the occurrence of a typical high cycle fatigue failure in the stem of gas compressor turbine blade, due to high vibration and cyclic stress. In this case failure usually occurs at a stress concentration point such as a sharp corner or groove or a metallurgical stress concentration point such as an impurity [2].

The controlling parameter in this state is stress and this type of fatigue is called control stress fatigue. Failure evaluation of structures with this mechanism is done by testing the samples at different stress levels (N) and the number of cycles leading to failure (N) is obtained in this way.

In this case, the fatigue life of this type of fatigue can be approximated by the Baskin eq. [2]:

$${\sigma }_a=A{N}_f^B$$E10

Where ${\sigma }_a$ is the stress amplitude, N is the number of cycles to failure, A and B are the material constants.

5.2 Low cycle fatigue

Low-cycle fatigue is for situations where failure occurs in less than 10²–10⁴ cycles [13, 38]. This type of fatigue occurs at relatively high stresses and a small number of cycles. Steam reactors and power generators are more prone to this type of failure [39, 40, 41]. In these cases, cyclic stresses usually have a thermal origin and the material fails from fatigue due to thermal contraction and expansion. Special laboratory methods have been developed to study the cyclic behavior of materials [1]. Standard ASTM E 606 provides details of the study of the cyclic behavior of materials. These tests are usually performed in a constant strain range [42].

It is widely accepted that in this situations, generalized deformations, such as strain, displacement and rotation) are more representative than stress, force and moment. Figure 10 shows a stress–strain loop of a strain control cyclic test under a constant strain cycle in a fatigue test. The dimensions of this loop are described by its width, which indicates the amplitude of the strain $∆\mathrm{\epsilon }$, and its height, which is the amplitude of the stress $∆$σ. The strain amplitude consists of two components, elastic and plastic strain. The common method showing low fatigue cycle data is plotting of the plastic strain amplitude, $∆{\epsilon }_p$, in terms of cycle number $N$. This representation in log–log scale is in a form of straight line as it is seen in Figure 11. The relation that can be fitted to the data in this diagram is as follows [1]:

Figure 10.

Stable stress–strain hysteresis loop.

Figure 11.

Low cycle fatigue strength of a plain carbon steel and its weldment [14].

$$\frac{∆{\epsilon }_p}{2}={\epsilon }_f^{\prime }{\left(2N_f\right)}^c$$E11

where $\frac{∆{\epsilon }_p}{2}$ is the plastic strain amplitude, ${\epsilon }_f^{\prime }$ is the fatigue ductility coefficient, c is the fatigue ductility exponent and 2Nf is the number of reversals to failure. The relationship is often called Coffin-Manson [1].

Another classic example of LCF is the fracture of steel structures under earthquake loadings [12, 13, 43]. In these cases, as well structural deformation substitute in fatigue strength curve to establish the fatigue deformability curve of the structural connections. Figure 12 presents structural deformation of a beam to column steel structure during a seismic loading. Here $\phi$ is structural deformation parameter and somewhat represent the rotation intensity of the rigid connection. Drawing the logarithmic curve of changes $∆\phi$ in the number of cycles to failure $N_f$ is a straight line (Figure 13) that can be expressed by the following eq. (12):

Figure 12.

Schematic presentation of deformation of steel frame under horizontal earthquake loadings [12].

Figure 13.

Extremely low-cycle fatigue behavior of steel structures under earthquake loadings [12].

$$∆{\phi }^m{N}_f=K$$E12

Where m is the slope of the fatigue curve and K is constant.

5.3 Extremely low-cycle fatigue

Extremely low-cycle fatigue is a fatigue failure characterized by large plastic strains (several times of yield strains) and a number of cycles to failure less than 10² [14, 44]. This type of fatigue failure is observed under extreme seismic conditions, structural members, particularly those acting as dissipative elements [44]. A typical example of this failure mode is the failure of structures during the 1994 Northridge earthquake in USA and 1995 Kobe earthquakes in Japan. Extensive failures during these two events led to many casualties and financial losses [9, 45]. Since this type of failure in a large volume causes the destruction of industrial buildings and structures, we study specifically and discuss the governing relationships.

ELCF is quite different from conventional high cycle fatigue where stresses are below the yield strength or low cycle fatigue where strains are in the order of the yield strains. In this type of failure, the level of deformation is much greater than the yield stress and the so-called control strain fatigue conditions prevail. It has been shown that when the number of cycles to failure $N_f$ falls below approximately 200, estimation of fatigue life using the Coffin- Manson model will be associated with inaccuracy due to changes in the damage mechanism. As the strain amplitudes increases from LCF regime to the ELCF regime, the failure mode varies from fatigue fracture to accumulation of ductile damage, due to changes in damage mechanism. A series of modifications were made to the Coffin- Manson model by Tateishi et al. which also accounted the Ductile Damage. According to this model the total damage of material is the sum of the ductile damage fraction and fatigue damage fraction. Eq. 13 describes this mechanism [46]:

$$\frac{∆{\epsilon }_p}{2}={\epsilon }_f^{\prime }{\left(2N_f\right)}^c{C}_m$$E13

$$C_m=\left\{\begin{array}{c}\left(\frac{{\epsilon }_{f-}∆{\epsilon }_{\mathit{max}}}{{\epsilon }_{f-}{\epsilon }_u}\right)\mathit{\text{if}}∆{\epsilon }_{\mathit{max}}>{\epsilon }_u\\ 1.0\mathit{\text{if}}∆{\epsilon }_{\mathit{max}}\le {\epsilon }_u\end{array}\right.$$E14

Where ${\epsilon }_f^{\prime }$ and c are the Coffin- Manson constants. $∆{\epsilon }_{\mathit{max}}$maximum plastic strain range, ${\epsilon }_u$ ultimate strain in monotonic tensile test and $C_m$ a factor linked to the ductile damage fraction.

5.4 Corrosion fatigue

High reactivity of fracture surfaces along aggressive micro-environment in the crack cavity lead to strong interaction of the corrosion and cyclic plastic deformation and rupture of the material which is called corrosion fatigue [47, 48, 49]. When fatigue corrosion occurs, corrosion strongly accelerates the rate at which fatigue cracks spread. In corrosion fatigue fracture surfaces may contain brittle striations on large facets or surfaces similar to what we see in quasi-cleavage fracture. A typical corrosion fatigue fracture at the macroscopic and microscopic scales are shown in Figures 14 and 15, respectively [37].

Figure 14.

Macroscopic view of a typical corrosion-fatigue fracture surfaces.

Figure 15.

Microscopic view of a typical corrosion-fatigue fracture surfaces [37].

The fracture mechanism during a corrosion fatigue can be summarize as follow:

• Initiation of fatigue cracks due to mechanical stresses

• Penetration of the corrosive solution into the crack tip

• Reaction of solution with the material at the crack tip

• Passive layer rupture during cyclic strain at the crack tip

• Production of corrosion products that affect the effective stress factor

• This type of fatigue failure can occur in a high cycle or low cycle fatigue mode.

5.5 Thermal fatigue

Components may fail due to thermal stresses generated during cooling and heating at high temperatures. This is called thermal fatigue [50]. This type of failure can occur in a situation where no mechanical stress presents. In other words, the stresses that lead to the fracture of the part here have only a heat source. Thermal stresses occur when a constraint prevents dimensional changes due to variation in temperature. For a bar fixed on both sides, the heat stress due to $∆T$is calculated from the following equation [50, 51]:

$$\sigma =\mathit{\alpha E}∆T$$E15

Where $\alpha$ is thermal expansion coefficient and E is elastic modulus.

Thermal fatigue can be categorized in the low cycle fatigue state due to the low number of cycles; it causes the destruction of the part. Austenitic stainless steels are susceptible to this type of failure due to their low thermal conductivity and high thermal expansion [2].

6. Factors affecting material fatigue properties

The fatigue behavior of the material is very sensitive to design and structure. Three very important factors that affected fatigue properties are the stress concentration, the residual stresses and material selection.

6.1 Effects of microstructure and material properties

The microstructure significantly affects the fatigue properties [52]. It was found that any changes in the microstructure altering the fatigue behavior especially in the case of high cycle fatigues. Decreasing in grain sizes and increasing in density of dislocation also noticeably improved the fatigue lives. In brass alloys an increase in fatigue lives observed by cold working and increasing in the dislocation density [1, 2]. The analyses carried out after Northridge earthquake on material consumables showed that the fracture toughness levels of some of electrode materials were very poor and this has been a strong reason for the decrease in fatigue properties of metal structures during these events [53].

In metals, reducing the size of inclusions and impurities significantly increases the fatigue properties. It has been well accepted that second-phase particles in the microstructures play a major role in the fracture of steels and failure resistance can be improved through changes in the volume fraction and morphology of these particles [54, 55, 56, 57]. These particles are the centers of stress concentration and cause a decrease in the fatigue properties of the material [58]. Heat treatment is an effective factor in affecting the microstructure and improving fatigue properties.

6.2 Effects of surface

The source of all fatigue failures is the surface of the components. There is much evidence that fatigue properties are highly sensitive to surface conditions. Surface factors that affect the fatigue behavior consists of surface roughness, changes in the surface properties, and residual stress.

Surface roughness: Tests performed on metal samples have shown that the smoother the surface of the parts, the longer their fatigue life in the test [59]. This is due to the fact that local superficial scratches are the stress concentration points and the onset of fatigue cracking.

Surface properties: Because fatigue failure is highly dependent on surface conditions, any factor that affects the surface strength also affects its fatigue properties [60, 61]. For example, surface heat treatment of carbonation and nitration, which increase the surface hardness, improve the fatigue properties. On the other hand, carbonation operation, which reduces the surface hardness of the part, reduces the fatigue properties.

Surface residual stress: Residual stress is a type of stress that remain in a part after manufacturing processes even without supplementary thermal gradient and external loads. In welded parts due to local heating during welding, complex thermal stress produces during welding which led to residual stress and distortion in component [62, 63, 64]. Residual stresses are also created by deformation of formwork and fabrication. The residual stresses are combined with the applied stresses and in the tensile state reduce the fatigue life of the part during dynamic loadings [2]. It is important to note that these type of stresses in the compressed state can increase the fatigue life of components and structures. In fact, there are commercial methods such as ball bearing and surface rolling that produce compressive residual stress and are used to improve fatigue properties [65, 66, 67, 68, 69].

6.3 Notch effects

The manufacturing defects is a factor that produced stress concentration point and reducing the fatigue properties of a material [25, 70, 71]. Investigations on fracture of steel structures in Kobe and Northridge earthquakes have clarified the fatigue brittle fractures triggered by the crack-like defects in the weld metal [53]. In addition, device components usually have stress concentration areas such as fillets, grooves, keyways, and holes which called stress raisers. These areas generically termed notches for brevity and usually reduces the resistance of the equipment to fatigue failures. Figure 16 provides an example of a notch in a machinery equipment, in particular, the attachment of blade to shroud in a CO2 compressor. Despite carful design to minimize the severity of the notch, a fatigue crack led the equipment to premature failures. Another example is given in Figure 17. This is a fracture in beam to column steel structure under seismic loadings during Northridge earthquake where the source of fracture is a notch in welded part (lack of fusion) [72]. Stress raisers may also be due to metallurgical defects such as porosity, impurities, and defects due to crushing and surface decarbonization due to working at high temperatures [71, 73].

Figure 16.

Fatigue failure of impeller of a compressor due to presents of a notch.

Figure 17.

Effects of notch on fracture of steel structures under Northridge earthquake [72].

Stress intensity factor, $K_t$ is a parameter that characterizes the degree of severity of a notch or stress concentration point [1]:

$$K_t=\frac{\sigma }{S}$$E16

Where $\sigma$ is local notch stress and$S$ is the nominal stress.

On a plot of S versus life Nf, the fatigue life decreases in proportion to $K_t$ factor as presented in Figure 18.

Figure 18.

Effects of notch on S-N behavior of an aluminum alloy (Kt is estimate of fatigue life and Kf is data’s obtain by test) [74].

7. Conclusion

Cyclic loads may lead the machines and structural components to premature failure that is called fatigue. Concern about fatigue failure is due to the fact that it occurs at a stress level much lower than the ultimate strength and in a completely unpredictable way. Macroscopically fatigue failure is seen with a brittle appearance and without any gross deformation in the fracture area. Fatigue failure can be occurred in form of high cycle, low cycle, and extremely low cycle fatigue. There are metallurgical and mechanical parameters that affect the occurrence of fatigue failures. Hostile environment causes corrosion fatigue and decreases the operation life of the components. Presents of notch causes stress concentrations points and accelerated the fatigue failures. Residual stress in the tensile form reduces the fatigue life while in the form of compressive stress increases the life of components.