A comparison of material flow strength models using Bayesian cross-validation

Abstract

Predicting material flow strength over a range of conditions, such as temperature and strain rate, is necessary for many engineering applications. This paper considers how to compare the predictiveness of several different strength models using a statistical technique called Bayesian cross-validation. Given a dataset of flow strength measurements obtained from mechanictesting experiments, the procedure consists of performing a Bayesian calibration of each strength model on a subset of the data and evaluating how well the trained models predict the remaining data. The predictiveness of a calibrated strength model is quantifiable probabilistically, which provides an interpretable metric for comparing the different models. As an illustrative example, we compare the Johnson-Cook (JC), Zerilli-Armstrong (ZA), Preston-Tonks-Wallace (PTW), and Mechanical Threshold Stress (MTS) flow strength models for the tantalum stress-strain curve data from Chen and Gray (1996). We show that prediction intervals for the four strength models cover the held-out data at most experimental conditions, but also that prediction interval coverage and prediction uncertainty varies by model and experimental condition. The analysis further allows us to identify experimental regimes for which one of the strength models predicts better than the other three.