DEVELOPING A REDUCED-ORDER REPRESENTATION OF CRYSTALLOGRAPHIC TEXTURE FOR APPLICATION IN SURROGATE MODELLING AND UNCERTAINTY QUANTIFICATION OF CRYSTAL PLASTICITY MODELS

Crystal plasticity modelling is a powerful method for understanding the behaviour of materials at the mesoscale. These models allow prediction of behaviour including deformation, fatigue, damage and creep based on microstructural information about a material including crystallographic texture and grain morphology. This provides numerous opportunities for application in the structural integrity of nuclear plant components. However, the length scale of these models and the computational expense of individual simulations has limited incorporation into macroscopic level component assessment.<br/><br/>Reduced-order modelling is a useful tool which can incorporate machine learning regression algorithms and statistical methods to emulate the response of a complex model. Typically, these models are orders of magnitude faster than the complex models they emulate making tasks involving many model evaluations such as optimisation, sensitivity analysis and uncertainty quantification tractable.<br/><br/>In this study, two reduced-order representations of crystallographic texture are investigated to represent the bulk response of a polycrystal volume element using an approach based on the Taylor factor of a polycrystal and by using principal component analysis (PCA) on the orientation distribution function of the polycrystal. These representations are used as inputs to a Gaussian process regression (GPR) model which is used to predict the macroscopic stress-strain response of the 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.<br/><br/>The GPR model developed also allows uncertainties from the experimental measurement of texture to be propagated through the model which would be prohibitively computationally demanding for a crystal plasticity finite element model. The texture parameterisations investigated can additionally be incorporated into incremental finite element user subroutines providing a data driven tool for bridging material length scales and structure-property linkages