Abstract

High temperature creep rupture in ceramics is characterized at the microstructure level by the nucleation and coalescence of voids. Replicated tests of any one ceramic at a constant applied stress and temperature show considerable scatter in the time-to-failure and in the strain at failure. Therefore the temporal process of nucleation and coalescence of voids is simulated in the plane to capture this variability. A domain is randomly discretized using a Poisson-Voronoi tessellation, with each Voronoi cell representing a superelement. A creep function corresponding to a three-parameter-solid linear viscoelastic model is prescribed for the material. Creep boundary conditions are imposed and the temporal evolution of strain is determined. Each cell is assigned a failure strain, sampled from a lognormal distribution. A cell is deleted when its effective strain equals its failure strain. The temporal increase in creep strains produces a sequential loss of cells (a model for void nucleation and growth) which in turn leads to failure. The simulation consists of performing analyses of a set of realizations of Poisson-Voronoi tessellations. Time-to-failure data are obtained and compared with existing uniaxial-tensile creep rupture data for a silicon nitride (SN88) ceramic. The objective is to calibrate the simulation so that it may be used to predict statistics of time-to-failure of ceramic components of arbitrary geometry and stress conditions.