Abstract

Magnesium alloys and metal matrix composites (MMCs) are attractive materials for biomedical application. Magnesium has a module of elasticity that is close to that of human bones and it is biocompatible with the human body. Human body fluids make a corrosive environment to magnesium. In addition, different body parts are subjected to cyclic loading reaching a magnitude of about 80 MPa and an estimated total of 106 cycles per year. Therefore, understanding the fatigue behavior of magnesium alloys and magnesium metal matrix composites (MMCs) is an essential aspect especially when they are used as load bearing components. Magnesium has a hexagonal closed-packed (HCP) lattice structure with a c/a ratio of 1.623, and it does not have enough independent slip systems to sustain large plastic deformation. Therefore, magnesium deforms plastically by two different mechanisms: slipping and twinning. Twinning-detwinning deformation is manifested in the cyclic stressstrain response of wrought magnesium alloys when loaded along the working direction. A significant stress asymmetry is usually observed resulting in the development of high mean stress. Research on magnesium and its alloys is rapidly increasing. This chapter presents different aspects of fatigue, in general, and on magnesium in particular, including experimental method, damage models and fatigue life equation.

Keywords: fatigue, cyclic behavior, life estimation, Mg alloys, magnesium metal matrix composites

### 1. Introduction

Magnesium has a hexagonal closed-packed (HCP) lattice structure with a c=a ratio of 1.623. According to von Mises [1], the ductility of the material, which depends on the its ability to withstand general homogeneous strain that involves changes in the shape of the crystal, is possible when five independent slip systems are activated. This condition is not met in HCP metals such as magnesium, therefore, deform plastically by two mechanisms: slip and twinning. Slip and twin planes for HCP metals are illustrated in Figures 1 and 2. Among these systems, the basal slip 0001 ð Þ and the 1012 tension twin are easiest to be activated due to their low critical resolved shear stresses (CRSS).

The American Society of Testing and Materials (ASTM) [3] defines fatigue as "the process of progressive localized permanent structural change occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a

1 mm in size. On the other hand, fatigue propagation approach is concerned about the relation between the applied cyclic loads and the growth of an existing crack to a

The initiation approach, which is commonly referred to as fatigue, is classified based on the damaging variable. There are three methods to analyzing fatigue: stress-, strain- and energy-based. If a damage model, stress-, strain- or energybased, is calculated on specific planes the used method is further classified as critical plane method. Stress-based methods use stresses, normal and/or shear, to quantify fatigue damage. Similarly, strain-based method use strains, normal and/or shear, to quantify fatigue damage. Lastly, energy-based methods use strain energy density to

All fatigue models require monotonic and/or cyclic properties of materials. Strain and energy-based cyclic properties can be obtained by performing series of tests under strain-controlled loading condition. On the other hand, stress-based cyclic tests properties can be obtained by performing series of tests under stresscontrolled loading condition. The well-known stress-life and strain-life curves can

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

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

size that causes catastrophic failure.

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

quantify fatigue damage.

be obtained from these tests.

2. Characterization of fatigue behavior

performed with frequencies higher than 20 Hz.

2.1 High cycle fatigue

47

Figure 1. Slip planes in HCP metals [2].

Figure 2. Twin planes in HCP metals [2].

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 necking are observed.

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 course, multiaxial loading can involve random loads.

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 impact on fatigue damage process and fatigue life.

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

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

1 mm in size. On the other hand, fatigue propagation approach is concerned about the relation between the applied cyclic loads and the growth of an existing crack to a size that causes catastrophic failure.

The initiation approach, which is commonly referred to as fatigue, is classified based on the damaging variable. There are three methods to analyzing fatigue: stress-, strain- and energy-based. If a damage model, stress-, strain- or energybased, is calculated on specific planes the used method is further classified as critical plane method. Stress-based methods use stresses, normal and/or shear, to quantify fatigue damage. Similarly, strain-based method use strains, normal and/or shear, to quantify fatigue damage. Lastly, energy-based methods use strain energy density to quantify fatigue damage.

All fatigue models require monotonic and/or cyclic properties of materials. Strain and energy-based cyclic properties can be obtained by performing series of tests under strain-controlled loading condition. On the other hand, stress-based cyclic tests properties can be obtained by performing series of tests under stresscontrolled loading condition. The well-known stress-life and strain-life curves can be obtained from these tests.
