2. Characterization of fatigue behavior

A common classification in fatigue initiation analysis is based on fatigue life [4]. The term "low cycle fatigue, LCF" refers to fatigue failure that occurs between 10<sup>3</sup> and 105 cycles. On the other hand, the term "high cycle fatigue, HCF" refers to fatigue failure that occurs between 10<sup>5</sup> and 10<sup>7</sup> cycles. The last class is called "very high cycle fatigue, VHCF" that refers to fatigue failure that occurs after 10<sup>7</sup> cycles. Because it is easier to control the stress at low load levels than strain, HCF and VHCF tests are usually performed under stress-controlled condition. However, strain-controlled tests can be performed with wide strain levels that cover lives less than 10<sup>3</sup> and up to 10<sup>7</sup> cycles. Because strain-controlled tests are usually performed at high strain levels and significant plasticity resulting in low number of cycles to failure, heating of the sample due to internal friction becomes a concern. Therefore, tests that are expected to last for few hundred or thousand cycles shall be performed with frequencies that shall not exceed few Hertz, if not less 1 Hz. Yet, a common practice in strain-controlled testing is to switch the control mode to stress when a test exceeds 104 cycles. This allows for increasing the frequency to reduce the time required to finish the test. On the contrary, HCF and VHCF tests are usually performed with frequencies higher than 20 Hz.

#### 2.1 High cycle fatigue

The high cycle fatigue behavior of materials can be characterized for a mode of stress, i.e., normal or shear, by performing stress-controlled experiments. ASTM standard for conducting force controlled constant amplitude axial fatigue tests of metallic materials [5] can be followed in tests performed using cyclic axial machine. Similarly, the standard by International Organization for Standardization [6] can be followed in tests performed using four-point rotating bending machine. Unlike cyclic axial or rotating bending tests that are usually performed on solid specimens, cyclic torsion test is usually performed on tubular specimen because shear stress across tubular specimens that satisfy thin-walled tube condition can be assumed constant. Of course, a machine with dynamic torsional load cell is required to perform cyclic torsional experiment. There is no particular standard for performing

sufficient number of fluctuations". Fatigue failure can occur even if the generated stress is below the yield limit. Therefore, in a macro-scale viewpoint fatigue failure is similar to brittle fracture where no signs of severe plastic deformation such as

Magnesium - The Wonder Element for Engineering/Biomedical Applications

Cyclic loading is very common. It can occurs because of operational condition such as increase and decrease of loads or due to the motion of loaded parts. Cyclic loads can be classified into constant and random loads. Constant load can be represented by an amplitude and a mean. A cycle in a constant amplitude loading is clearly defined. However, the definition of a cycle in random loading case is not as clear as in constant amplitude loading. Therefore, a count method is required to quantify the number of cycles in random loading situation. Applied cyclic loading can either be uniaxial or multiaxial. In a constant multiaxial cyclic loading, amplitudes, means, phases and frequencies of the applied loads can be different. Of

The classifications explained before were merely based on mechanical loads such as forces, moments and torques. However, fatigue damage might result from the application of cyclic thermal loads. In addition, fatigue damage process can get complex due to interactions between applied cyclic loads, mechanical or thermal, and other damaging phenomenon such as creep. Effect of environmental attacks, residual stress, coating, surface finish, geometrical irregularities have significant

There are two approaches to study fatigue of materials: initiation and propagation of cracks. Fatigue initiation approach is concerned about relation between the applied cyclic loads and the initiation of small cracks that generally do not exceed

course, multiaxial loading can involve random loads.

impact on fatigue damage process and fatigue life.

necking are observed.

Twin planes in HCP metals [2].

Figure 1.

Figure 2.

46

Slip planes in HCP metals [2].

#### Magnesium - The Wonder Element for Engineering/Biomedical Applications

cyclic torsional tests, however, the ASTM standard for strain-controlled axialtorsional fatigue testing with thin-walled tubular specimens [7] can be used.

The stress-life (S � N) curve, which is also known as the Wöhler curve, is usually used to represent the relation between applied stress amplitude, σ<sup>a</sup> or τ<sup>a</sup> and fatigue life Nf in a log-log scale. A typical S � N curve shows a linear curve in the finite life region as shown in Figure 3.

Understanding that a linear curve in a log-log scale indicates that the relation between the stress amplitude and fatigue life is of a power-type, Basquin [8] was the first to model this curve as

$$
\sigma\_a = \sigma\_f' \left(2N\_f\right)^b \tag{1}
$$

does not exist. Run-out tests are usually marked with an arrow symbol. Stress-life curves for six different magnesium alloys are presented in Figure 4. This figure clearly shows the difference between die-cast and extruded alloys with the former having less fatigue strength due to the existence of pores and cavity resulting from

Similar to the HCF, the low cycle fatigue (LCF) behavior of materials can be characterized for a mode of strain, i.e., normal or shear, by performing straincontrolled experiments. ASTM standard for conducting strain controlled fatigue tests of materials [14] can be followed in tests performed using cyclic axial machine. While controlling the strain, using strain measurement device such as an extensometer, the load signal is also acquired. This allows calculating both the stress and strain that can be represented for a given cycle by a hysteresis loop as shown in

Wrought alloys that are produced by extrusion, rolling or forging processes develop strong texture. This texture is characterized by alignment of the basal plane with the working direction with the c-axis perpendicular to it. The two plastic deformation mechanisms, slipping or twinning, can be activated depending on the loading orientation with respect to the basal plane. An extension along the c-axis activates the tension twins and a subsequent contraction causes detwinning of the lattice. During cyclic loading, twinning occurs in the compression reversal leading to low stress yielding. Detwinning starts as the load is reversed, i.e., during the tension reversal. However, as the tension load increases the hard pyramidal slip

is activated in order to accommodate additional strain. This change from

AZ31B, AZ61A and ZK60 magnesium extrusions are presented in Figure 7.

detwinning to slip is reflected on the cyclic hysteresis as an inflection point and a concave upward hardening behavior. A representative cyclic hysteresis loop for different magnesium extrusion loaded along the extrusion direction is shown

The strain-life (ε N) curve is usually used to represent the relation between applied strain amplitude, ε and fatigue life Nf in a log-log scale. Strain life curves for

the casting process.

Figure 5.

in Figure 6.

Figure 5.

49

A typical cyclic hysteresis loop [2].

2.2 Low cycle fatigue

Fatigue of Magnesium-Based Materials DOI: http://dx.doi.org/10.5772/intechopen.85226

where σ<sup>0</sup> <sup>f</sup> is the axial fatigue strength coefficient and b is the axial fatigue strength exponent.

Some materials such as steel and magnesium alloys show a distinct plateau commonly called the "fatigue limit". This limit is usually observed between 10<sup>6</sup> and 10<sup>7</sup> cycles. Tests that exceed 107 cycles are usually stopped and are called run-out. This limit used to be called the "endurance limit" that is a stress amplitude below which no failure will occur. However, it has been shown if the testing is continued specimens eventually fail. Therefore, it is recently accepted that endurance limit

Figure 3. A typical stress life curve.

Figure 4. Stress life curve for different Mg-alloys [9–13].

does not exist. Run-out tests are usually marked with an arrow symbol. Stress-life curves for six different magnesium alloys are presented in Figure 4. This figure clearly shows the difference between die-cast and extruded alloys with the former having less fatigue strength due to the existence of pores and cavity resulting from the casting process.
