**5. Types of fatigue**

Fatigue failure of parts and components can be categorized to high cyclic, lowcycle 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]:

$$
\sigma\_a = \mathbf{A} \mathbf{N}\_f^{\mathcal{B}} \tag{10}
$$

Where *σ<sup>a</sup>* 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 –10<sup>4</sup> 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 [39–41]. 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 Δε, and its height, which is the amplitude of the stress Δσ. 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, Δ*εp*, 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]:

$$\frac{\Delta \varepsilon\_p}{2} = \varepsilon\_f'(2\mathbf{N}\_f)^\circ \tag{11}$$

where <sup>Δ</sup>*ε<sup>p</sup>* <sup>2</sup> is the plastic strain amplitude, *ε*<sup>0</sup> *<sup>f</sup>* 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 *φ* is structural deformation parameter and somewhat represent the rotation intensity of the rigid connection. Drawing the

**Figure 10.** *Stable stress–strain hysteresis loop.*

**Figure 11.** *Low cycle fatigue strength of a plain carbon steel and its weldment [14].*

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

*Perspective Chapter: Fatigue of Materials DOI: http://dx.doi.org/10.5772/intechopen.107400*

**Figure 13.** *Extremely low-cycle fatigue behavior of steel structures under earthquake loadings [12].*

logarithmic curve of changes Δ*φ* in the number of cycles to failure *Nf* is a straight line (**Figure 13**) that can be expressed by the following eq. (12):

$$
\Delta \rho^m N\_f = K \tag{12}
$$

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 10<sup>2</sup> [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 *Nf* 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]:

$$\frac{\Delta \varepsilon\_p}{2} = \varepsilon\_f' \left( 2 \mathbf{N}\_f \right)^c \mathbf{C}\_m \tag{13}$$

$$C\_m = \left\{ \begin{array}{c} \left( \frac{\varepsilon\_f - \Delta \varepsilon\_{\max}}{\varepsilon\_f - \varepsilon\_u} \right) \text{ if } \Delta \varepsilon\_{\max} > \varepsilon\_u \\\\ \mathbf{1.0} \text{ if } \Delta \varepsilon\_{\max} \le \varepsilon\_u \end{array} \right. \tag{14}$$

Where *ε*<sup>0</sup> *<sup>f</sup>* and c are the Coffin- Manson constants. Δ*ε max* maximum plastic strain range, *ε<sup>u</sup>* ultimate strain in monotonic tensile test and *Cm* 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 [47–49]. 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].

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


**Figure 14.** *Macroscopic view of a typical corrosion-fatigue fracture surfaces.*

*Perspective Chapter: Fatigue of Materials DOI: http://dx.doi.org/10.5772/intechopen.107400*

**Figure 15.** *Microscopic view of a typical corrosion-fatigue fracture surfaces [37].*


#### **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 Δ*T* is calculated from the following equation [50, 51]:

$$
\sigma = aE\Delta T \tag{15}
$$

Where *α* 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].
