A new approach for determination of material constants of internal state variable based plasticity models and their uncertainty quantification

Abstract

Physically-based plasticity models such as the BCJ model include internal state variables that represent the current state of the material and allow capturing strain rate and temperature history effects as well as the coupling of rate- and temperature-dependence with material hardening. However, the inclusion of internal state variables increases significantly the number of unknown material constants that need to be found through fitting of the model to experimental stress–strain data at different strain rates and temperatures. This makes the fitting process extremely challenging and increases the uncertainty in the material constants. The paper presents a physics-guided numerical fitting approach that reduces the associated difficulties and uncertainties involved in determining the material constants of the BCJ plasticity model. The approach uses experimental data from monotonic and reverse loading stress–strain curves at different temperatures and strain rates to determine the 18 material constants of the model. An evidential uncertainty quantification approach is used to determine uncertainties rooted in experimental data, selection of stress–strain curves at different loading conditions, variability of material properties, numerical aspects of the fitting method and mathematical formulations of the BCJ model. The represented uncertainty of the BCJ material constants based on mathematical tools of evidence theory is propagated through Taylor impact simulations of a 7075-T651 aluminum alloy cylinder. Uncertainty quantification results verify the presented numerical fitting approach for the BCJ model and its potential applicability to other similar material models.