Variational Bayesian Calibration of a PTW Material Strength Model for OFHC Copper

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Abstract The strength of materials at high strain rates is a challenging problem for model development and calibration. Such models can span a regime in strain rate from 1 × 10−3 s−1 to 1 × 1012 s−1 and a regime in temperature of 0K to up to the material’s melting temperature. The limits of these regimes can be difficult and expensive to access experimentally. There is interest in understanding how well calibrations made at moderate strain rates and temperature can perform when applied to more extreme regimes. Variational Bayesian techniques have been shown to be computationally inexpensive methods to both calibrate a model and understand the uncertainties in model parameters. This investigation will calibrate the parameters of a Peston-Tonks-Wallace (PTW) material strength model to low and moderate strain rate experiments from quasi-static, and Hopkinson bar experiments performed on fully annealed Oxygen Free High Conductivity (OFHC) copper. Bayesian methods will be used to quantify the correlated uncertainty in these parameters. These uncertainties will propagated forward to a simulation of a Richtmyer-Meshkov instability experiment which exercise a higher strain rate regime. The effects of the model uncertainties on the predictive ability of the simulation will be observed. This will demonstrate a strategy for Bayesian model calibration and uncertainty quantification for parametric models with applications to physics processes outside high strain rate plastic deformation.