Reduced-Order Representations of Crystallographic Texture for Application to Surrogate Models of Material Behaviour

The mechanical behaviour of materials is influenced by processing and thermomechanical exposure. In safety-sensitive industries there is a need to make predictions on the envelope of safe use beyond proven constitutive equations. Microstructural simulations, such as crystal plasticity modelling, can model features like grain size, morphology and texture. However, they are computationally demanding and it can be hard to translate measured microstructures into meaningful or representative statistical distributions. Surrogate models incorporate machine learning regression and statistical methods to emulate the response of a complex model. As they are much faster, they can model the response over a wide range of material parameters, permitting sensitivity analysis and uncertainty quantification. Preferred orientation (texture) can be challenging to incorporate into surrogate models as accurate representations can require a lot of parameters. In this study, reduced-order representations of crystallographic texture are presented to represent the bulk response of a polycrystal volume element. These representations are used as inputs to a gaussian process regression (GPR) model that is used to predict the macroscopic stress-strain response of a polycrystal for different crystallographic textures. The GPR acts as a surrogate model of the underlying crystal plasticity model and allows an inherent quantification of the model epistemic uncertainty and the uncertainty related to unobserved effects not captured by the texture parameterization. Incorporation of the surrogate model into finite element coding will be used as an application of the method.