Elastic-Plastic Finite Element Model For Rolling Contact Fatigue
The two most important failure mechanisms in RCF are sub-surface originated spalling and surface originated pitting. In this study, both of the above mentioned fatigue damage mechanisms are investigated using an elastic-plastic Voronoi finite element (EPVFE) model. In this approach, Voronoi tessellation is utilized to discretize the material domain. Next, each Voronoi polygon is subdivided into constant strain finite elements, forming the FEM mesh. Thus each grain consists of flexible elements and calculating deformation inside each individual grain becomes possible. The Voronoi finite element model (VFEM) is then coupled with the continuum damage mechanics framework in order to induce fatigue damage. The model assumes intergranular cracking and fatigue cracks are introduced in the material domain by employing a node release procedure.
Surface initiated fatigue is caused by the presence of surface defects such as dents, fretting wear etc. in elastohydrodynamic lubricated (EHL) contacts. Here, a line contact line EHL model is used to calculate the pressure distributions acting over the surface defects which are then employed by VFEM to determine sub-surface stresses. The model also takes into account the effects of residual stresses generated during the debris denting process. Using this methodology, the model is used to simulate micro-crack initiation, coalescence and propagation stages and finally a fatigue spall. The locations and patterns of dent initiated spalls are found to be consistent with experimental observations. A sample result is depicted in Fig. 1.
Figure 1: (a) Numerically obtained spall pattern in the presence of a surface dent (b) Experimentally observed spall pattern (Gao et al., 1999)
Subsurface spalling occurs due to the presence of an inclusion in the material domain. The EPVFE model coupled with damage mechanics approach is used to investigate the effects of material plasticity on RCF. Mises based plasticity model with kinematic hardening was employed to incorporate the effects of material plasticity. The results indicate that once a fatigue crack initiates within the domain, the fatigue damage induced due to the accumulated plastic strains around the crack tip drives the majority of the crack propagation stage. The results from this investigation reveal that depending on the contact pressure the crack propagation stage can constitute 15 to 40 percent of the total life. The spall shape, fatigue lives and Weibull slopes obtained from the EPVFE model correlate well with the experimental results (Refer Fig. 2).
Figure 2: (a) Numerically obtained spall pattern and accumulated plastic strain (b) Experimentally observed spall pattern (Jandeska et al., 2004)
The developed model is further extended to study the effects of plasticity induced residual stresses on RCF life. It is observed that there is an optimum level up to which the residual stresses are beneficial in improving the fatigue life of the bearing components. This optimum residual stress pattern is found to be a function of the materialâ€™s plastic response, yield limit and the bearing operating load.