An uncertainty quantification guided approach to modeling high-velocity impact into advanced ceramics

Abstract

Advanced ceramics are often used as components of protective structures for impact applications. Improving the impact performance of these materials is complicated, because the performance depends on multiple failure mechanisms operating at several time- and length-scales. The mechanisms involved can change with location with respect to the impact point and the time after impact, and include micro-cracking and subsequent degradation of elastic properties, as well as amorphization and/or lattice plasticity. In addition, the material may also be comminuted and experience granular flow in some regions. One approach to simulating the impact performance of advanced ceramics has been through mechanism-based models that incorporate the underlying physics. Such an approach provides guidance with respect to materials design for improved performance, but such models often involve large numbers of input parameters, can be hard to implement in computational solvers, and can be very expensive from a compute-viewpoint. In contrast, phenomenological models offer the advantages of simplicity and computational efficiency but require fitting parameters that are not tied to microstructure, and therefore are less effective from a materials design perspective. Further, the processing of advanced ceramic materials can introduce stochastic heterogeneities (lattice, grain scale and larger defects) which in turn, introduce variations in experimental results and associated uncertainty. In this study we first connect the physical input parameters of a mechanism-based model to the parameters of a phenomenological model, and quantify the uncertainty as it propagates across the parameters sets of the two models. Neural-network based surrogates of specific impact simulations are constructed to accomplish this. The uncertainty in an impact performance metric is then obtained from simulations-surrogates using the phenomenological model with uncertain parameters. As a result, we obtain sensitivity analysis of impact performance over the large parameter space of the mechanism-based model via the phenomenological parameters. Such analyses can prove useful in material selection and also guide processing methodologies for better material design.