Stochastic finite element analysis of the diametral compression test of powder compacts and porous materials

Abstract

Abstract This paper presents a stochastic finite element approach for modeling the mechanical behavior of powder compacts and porous materials under diametral compression test conditions. The main goal is assessing the validity of the diametral compression test as an indirect technique to estimate tensile strengths of brittle or quasi-brittle materials exhibiting porosity heterogeneity. Thus, the study seeks to predict the influence of porosity randomness on stress distributions and the spatial location of the highest tensile stress on thin disc-shaped specimens. The proposed formulation uses a stochastic framework that couples a random spatial field to the finite element analysis to include non-deterministic features. Two case studies consider comparable targets for the mean porosity but different coefficients of variations. For each case study, a total of 1000 realizations are conducted under identical loading and boundary conditions. The predicted stress distributions are compared to the ones from homogenous closed-form solutions from the literature. Then, the expected magnitude and location of the maximum tensile stress are evaluated by statistical means. Findings from the stochastic model show that porosity randomness induces stress concentration around less dense volumes and location deviation of the maximum tensile stress from the center of the discs. Likewise, porosity heterogeneity could affect the accuracy of experimental diametral compression tests even for small variance cases; and so, the reliability of the mechanical properties derived from models based exclusively on the classic assumption of material homogeneity.