A Voronoi Finite Element Study of Fatigue Life Scatter in Rolling Contacts

Abstract

Microlevel material failure has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearing. Therefore, microlevel features of materials will be of significant importance to RCF investigation. At the microlevel, materials consist of randomly shaped and sized grains, which cannot be properly analyzed using the classical and commercially available finite element method. Hence, in this investigation, a Voronoi finite element method (VFEM) was developed to simulate the microstructure of bearing materials. The VFEM was then used to investigate the effects of microstructure randomness on rolling contact fatigue. Here two different types of randomness are considered: (i) randomness in the microstructure due to random shapes and sizes of the material grains, and (ii) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus. In this investigation, in order to determine the fatigue life, the model proposed by Raje et al. (“A Numerical Model for Life Scatter in Rolling Element Bearings,” ASME J. Tribol., 130, pp. 011011-1–011011-10), which is based on the Lundberg–Palmgren theory (“Dynamic Capacity of Rolling Bearings,” Acta Polytech. Scand., Mech. Eng. Ser., 1(3), pp. 7–53), is used. This model relates fatigue life to a critical stress quantity and its corresponding depth, but instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. We consider the maximum range of orthogonal shear stress and the maximum shear stress as the critical stress quantities. Forty domains are considered to study the effects of microstructure on the fatigue life of bearings. It is observed that the Weibull slope calculated for the obtained fatigue lives is in good agreement with previous experimental studies and analytical results. Introduction of inhomogeneous elastic modulus and initial flaws within the material domain increases the average critical stresses and decreases the Weibull slope.

Multiscale modeling and simulation of rolling contact fatigue

“…To overcome this limitation, a few models, including finite element models, were developed to take into account the micromechanical material behavior in the contact region. A so-called Voronoi finite element method (VFEM) was proposed by Jalalahmadi and Sadeghi [31]. With the implementation of a fatigue life criterion [32], VFEM can be used to study the effect of material micromechanical behavior on rolling contact fatigue.…”

Effect of non-metallic inclusions on butterfly wing initiation, crack formation, and spall geometry in bearing steels

“…They used Voronoi tessellations to capture the effect of microstructural randomness of the material in RCF. Jalalahmadi and Sadeghi [37], extended the approach to FEM. They, in particular, studied the effect of inclusions on fatigue crack initiation [1].…”

A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices

“…At microlevel, materials consist of grains which are random in size and shape. Ito and Fuller [25], Zavattieri and Espinosa [27], and Jalalahmadi and Sadeghi [33] showed that the Voronoi diagram can be used to simulate the topology of the material microstructure. Their reasoning for using the Voronoi diagram was that consider some random nucleation points in the crystallization process of a one-phase metal, if all grains start to grow simultaneously from these nucleation points at the same rate, microstructure produced will be in the form of a Voronoi diagram.…”

“…In VFEM, the strain energy method is used to extract the stiffness matrix for the triangular elements. For more detailed information about the VFEM, please refer to [33].…”

“…For this purpose, damage mechanics approach developed by Kachanov [29], Robotnov [30], Chaboche [31], Memon et al [32], and Slack et al [28] is incorporated into a Voronoi finite element model (VFEM) developed by Jalalahmadi and Sadeghi [33]. The model developed for this investigation relates the fatigue life to a damage parameter D which is a measure of the gradual material degradation under cyclic loading.…”