Computational extreme value statistics of strength for WC-Co composites at small specimens

Abstract

The mechanical behavior of ceramic–metal (WC-Co) composites at small specimen level is subject to significant uncertainty due to the random assembly of (1) its constituent phases, (2) the crystal orientation of the WC grains, (3) the intrinsic residual stresses, and (4) the variable level of confinement of the metallic binder, within the contiguous network of much stiffer WC grains. In the existing literature, a Weibull distribution of strength is typically assumed at large specimen level. However, it is unknown whether this assumption can be carried over to small samples. Thus, the aim of this study is to shed light into the randomness in the mechanical strength of WC-Co composites, by using Monte Carlo simulations employing Latin Hypercube Sampling. The marginal distribution of the model parameters is assumed to be a grafted zero-threshold Weibull-Gaussian probability distribution, applied individually to the ceramic particles and the metallic binder using autocorrelation fields. The deterministic models are the recently calibrated microplane models M7WC and MPJ2 for the ceramic phase (WC) and the metallic matrix (Co) respectively. Test data in the form of strength histograms, gathered from literature on tensile tests conducted on nanowires of WC-Co composites, are used to calibrate the Weibull and Gaussian parameters, the grafting point locations and the autocorrelation lengths. The deterministic models M7WC and MPJ2 are assumed to be predictive in this study, as they were already calibrated in a previously published work by the authors. The finite element meshes used in the Monte Carlo simulations are generated using real tomography images, which easily captures the Gaussian part of the probability density function (pdf) without any random variables. This approach is shown to account successfully for the randomness observed in the strength of these ceramic–metal composites. Predictions are made for the strength distribution of differently sized nanowire specimens in tension.