A new voronoi finite element fatigue damage model

One of the most unavoidable modes of failure for mechanical components is fatigue. Fatigue mechanism in general consists of three stages: ( i) crack initiation, (ii) crack propagation and (iii) final catastrophic failure. Initial fatigue cracks occur at the microscale where the microstructural effects become more significant. Hence, in order to properly study the mechanical fatigue, the microstructure of materials needs to be taken into account. It has been recognized that the scatter in fatigue lives needs to be studied by considering the effect of material microstructure on early crack growth. For this purpose, this study presents modeling approaches developed to investigate fatigue. The new approaches deal with the fatigue problem from a different viewpoint, by considering the material microstructure consisting of randomly shaped, sized, and oriented grains and their effects on the fatigue lives. These modeling approaches have been used to investigate two special applications, rolling contact fatigue (RCF) and fatigue of the micro-electro-mechanical-systems (MEMS) devices. In order to achieve the objectives, a new Voronoi finite element model (VFEM) is developed using Voronoi tessellation. The VFEM developed was used to investigate the effects of the microstructure on the internal stress distribution and fatigue lives. Damage mechanics approach was then incorporated in the VFEM to model crack initiation and propagation in fatigue. It is found that the fatigue lives predicted for both applications are in good agreements with the experimental results available in the literature. It is seen that fatigue lives obtained for the various domains are different due to their different microstructural distribution. Moreover, four additional sources of randomness are considered in the model: (a) inhomogeneous elastic modulus, (b) inhomogeneous resistance stress, (c) initial flaws (internal voids), and (d) material inclusions. The Weibull statistics is employed to examine scatter of the fatigue lives due to different sources of randomness. It is concluded that both inhomogeneous elastic modulus and resistance stress reduces the fatigue lives and increase their scatter. In the case of initial flaws, decrease in the fatigue lives and increase in their scatter are even more significant. It is seen that larger and shallower inclusions reduce fatigue lives and their scatter more significantly. Also, a new statistical RCF life equation for bearing elements is developed which includes effects of the material inclusions