Statistical study of mechanical responses of ordinary refractory ceramics under cold crushing condition with discrete element modelling

Abstract

Ordinary refractory ceramics are multi-phase materials, and their inhomogeneous microstructures induce the scatter of properties. The definition of a reasonable number of samples is important to obtain representative results from experiments and simulations, and this reasonable number might be property or microstructure relevant. Stochastic discrete element (DE) simulations of cold crushing tests with homogeneous interface properties were performed. Three minimum DE size ranges were used to represent matrix variation at different levels. Statistical methods, i.e., Kolmogorov–Smirnov (K–S) test, t-test, and correlation analysis, were utilized to study the influences of minimal number of samples on mechanical properties and crack density. It revealed that a relatively small number of samples are sufficient to obtain representative cold crushing strength (CCS) and Young’s modulus, whilst a large number of samples are favourable when the fracture energy and crack density under cold crushing conditions are of interest. The analysis also showed that the fracture energy under cold crushing condition generally correlates positively with CCS, and the static Young’s moduli determined from the stress–piston displacement curves with different definitions are divergent, caused by contact compliance and premature cracking. The data from the stress–strain curves recorded directly on the sample are required for the accurate static Young’s modulus calculation.