3. Contact fatigue strength of material

Any materials used in real application exist in the form of mechanical part. There is little mechanical part works under static stresses. For the time and space view, the amplitude of stresses may regularly or irregularly change with time. The fatigue is resulted from changes in the structure and properties of material led by the gradual accumulation of damage under the act of alternating stresses. Mechanically, the form of fatigue of material usually goes through the nucleation and growth of cracks, and ultimately leads to the volume fracture. This phenomenon occurring in the material of components working under contact load is often named pitting and wear.

The detail of the contact fatigue process may vary with the difference of material and load conditions, but in almost all cases, the process can be manifested as the initiation and propagation of cracks. Based on the actual application of different materials under different contact conditions, the initiation of cracks led by the accumulation of contact fatigue damage is from the surface or near-surface layer. The final manifested form of cracks, initiated from different sites of contact components, after propagation until a piece of material detaches itself, will form a pit or spall; while from the point of micro view, the wear is the accumulation process of pit or spall of asperities of contact surface due to contact load.

#### 3.1 Pit and spall

As mentioned before, pitting and spallling are the macro shown of material dropping from the contact surface due to damage accumulation with the cyclic of stresses.

Pitting is generally considered to be caused by the propagation of surfaceinitiated cracks. Figure 4 shows the typical form of pitting of a contact surface. The process also includes three stages: crack initiate, crack propagate and material drop from the surface [6].

In the first stage, the cracks will initiate from the site where the damage accumulation reached the damage capacity limit of material. In the second stage, the cracks will propagate under the comprehensive act of tensile stress result from surface friction and traction and squeezing effect of the lubricant into the crack. In the last stage, the material will rupture from the surface if the remaining section between part 1 and the parent surface cannot endure the comprehensive act of

Figure 4. Diagram for pitting form process.

Figure 5. Typical morphology of pitting.

stress. Due to the edge of pitting, it will further result in the increase of stress by stress concentration effect; more cracks will initiate around the generated pitting and finally form a pitting surface as shown in Figure 5. Usually, the pitting caused by contact fatigue will not result in the loss of function of mechanical components.

Sometimes the cracks initiating from contact surface or subsurface will first propagate along the path which is at an acute angle to the surface. Then it is propagated along the path parallel to the surface which will let the crack to propagate along a relatively long path and eventually leading to large chunks peeled off from the surface. The whole process can be described by the sketch shown in Figure 6 [7–9].

Figure 7 shows a typical spalling morphology of backup roll used in steel production. Based on the morphology of spalling of roll shown in Figure 7, it can be seen that the crack propagates along the peripheral direction of roll and causes extensive surface peeling. Usually, the spalling can cause the complete loss of function of mechanical components.

Contact Strength of Material DOI: http://dx.doi.org/10.5772/intechopen.90228

Figure 6. Spalling failure process of contact components [7].

Figure 7. Typical spalling of component result from contact fatigue.

#### 3.2 Wear

Wear is a common phenomenon for the mechanical components working under contact and having relative move. The wear resulted from contact fatigue is a more common phenomenon in components with good lubrication. As the machined

Figure 8.

Wear rate variation line in whole life.

surface of components such as gear, ball and ring of bearing and wheal/rail consists of asperities, the load of two surface contact is supported by contact of lots of asperities and lubricates in micro level [10, 11]. Usually, we considered that the pitting occurs at the surface contact under macro level. If we observe two contact surfaces in micro level, the contact of separate asperities is equivalent to that contact of two surfaces in macro level. The only difference between them is the relative radius of curvature.

So if we considered the contact of asperities as two components contact under micro level, the formation of wear is actually the accumulation of micro pitting between the contacted asperities, and the variation process of wear during the whole life of mechanical components can be described by the formation mechanism of macro pitting. As it is known, the process of wear of mechanical component in its whole life can be divided into three stages including run-in process, steady wear and rapid wear process as shown in Figure 8.

In the run-in stage, the contact of two macro surfaces is supported by contact of asperities, which will result in the micro contact fatigue of asperities. The fatigue damage accumulation due to contact of asperities will result in the pitting which occurs on the surface of asperities. The pitting of asperities leading to the equivalent radius of curvature of asperities increase and contact stress between the two asperities decrease, which will decrease the damage during later contact and the wear process enter into steady wear process and last long time. With the further increase of using time, the damage of whole surface will increase and the whole strength of surface will degrade. Then the occurrence of pitting of asperities will speed up and wear rate of surface will sharply increase, which means the arrival of rapid wear.

#### 4. New trend of contact fatigue strength research

With the development of material process technology, the contact strength of it is increased gradually. But the failure caused by contact fatigue and wear cannot be avoided. Lots of models, established based on fracture mechanics and damage accumulation theory, are established to assess the contact fatigue process of material. In these models, the most popular ones are Dang Van criterion and the critical plane method.

#### 4.1 Critical plane model

The critical plane method considered that the crack initiation plane may occur on a plane near the maximum normal stress range for medium to high strength

steels, and the model used for assess on the occurs of critical plane can be expressed as [12, 13]

$$FP = \frac{\Delta \varepsilon}{2} \sigma\_{\text{max}} + J \Delta \chi \Delta \tau \tag{9}$$

where Δε is the normal strain range, σmax is the maximum normal stress, Δγ is the shear strain range, Δτ is the shear stress range and J is material constant.

Based on the above equation, the relationship between the fatigue parameter and life is expressed as

$$(FP - FP\_0)^m N\_f = \text{constant} \tag{10}$$

where Nf is the fatigue life corresponding to fatigue parameter FP, and m, FP<sup>0</sup> and C are material fatigue properties determined from fatigue life experiments [13].

If the damage accumulates linearly, then the damage per loading cycle is [13]

$$\frac{dD\_f}{dN} = \frac{1}{N\_f} = \frac{(FP - FP\_0)^m}{C} \tag{11}$$

where Df is the fatigue damage equal or smaller than 1; and N represents the number of load cycles. If FP≤FP0, there is no damage resulted from the load cycle.

#### 4.2 Dang Van multi-axial fatigue criterion

Dang Van multi-axial fatigue criterion assumes there is elastic shakedown occurs before cracks initiation and considered two scales [14–16]. The first is that often used by engineers who used to analysis the fatigue of point that surrounded by an arbitrary elementary volume in macroscopic scale. The second one is used to subdivide the macroscopic scale element in mesoscopic scale.it thinks that macroscopic stress tension result in the mesoscopic one and the local inelastic deformation lead to the local residual stresses. Based on that assumptions, the model is expressed as an inequality of mesoscopic stresses at all instants t of the cycle to characterize the damage as below [14]:

$$\max\_{t} \left[ \pi(t) + a p(t) \right] \le b \tag{12}$$

Where τð Þt and p tð Þ are the instantaneous mesoscopic shear stress and hydrostatic stress, a and b are material constants which can be determined by classic bending and twisting fatigue test.

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51805355) and Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 201701D221136). The author is grateful to all the partners of College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, China.

Strength of Materials
