Reduced-order representations of crystallographic texture for application to surrogate modelling of austenitic stainless steel

Surrogate models are a useful tool in enabling efficient modelling and propagation of uncertainty through material process-structure-property linkages. One promising application is in the modelling the dependence of macroscopic material properties on the microstructure of polycrystalline materials. However, this requires parameterisation of complex microstructural features such as crystallographic texture.

This study compares two methods for parameterising texture for use in reduced-order models: a principal component analysis reduction of generalised spherical harmonics (GSH-PCA), and a simpler, scalar parameterisation using the Taylor factor. The effectiveness of each method is demonstrated by applying each to a Gaussian process (GP) regression surrogate of material deformation, trained on data from crystal plasticity simulation.

The GSH-PCA parameterisation reduces the number of variables required to capture texture to between 5-10 for cubic-orthorhombic symmetry and has the advantage of allowing reconstruction of the original texture from the GSH-PCA coefficients. In comparison, the Taylor factor offers a simpler surrogate model with a single input parameter, however this model has less overall predictive accuracy with more uncertainty in the input variable space. Despite this, the use of GP regression as the surrogate model with functional outputs allows the uncertainties from both texture parameterisations to be propagated through to the prediction of macroscopic mechanical behaviour.