Machining Simulation for Ceramics Based on Continuum Damage Mechanics

Abstract

An abrasive machining process for ceramics is simulated with a nonlinear thermodynamic constitutive model based on the principle of continuum damage mechanics (CDM). The model consists of a set of parallel Maxwell-type elements arranged in series with a spring. It incorporates stochastic material microstructure through two sets of the newly introduced material parameters, spring-like constants Cr and damping-like coefficients arr=1,2,…,n. Damage is considered cumulative and related with current stress and damage state in a ceramic workpiece during loading, which constitutes damage evolution. A fourth-order isotropic damage tensor is introduced. This highly nonlinear CDM model is reduced to an incremental formulation and approximated by a 3D nonlinear finite element program based on the Newton-Raphson method. The stress-strain correlation calculated from the current model is presented for alumina, silicon carbide, and silicon nitride. The predicted results of damage versus the depth of cut for the three ceramics subjected to machining with single diamond grit are validated by the experiment. As one example, the development of damage with the movement of the abrasive grit in a silicon nitride workpiece is demonstrated by a contour plot. The final part of this paper presents the calculated distribution of residual stress in a silicon nitride sample and the factors contributing to the distribution are discussed.