A machine learning model to predict yield surfaces from crystal simulations

We introduce a microstructurally informed machine learning model for predicting the anisotropic yield surfaces of polycrystalline materials. A full-field, spatially resolved crystal plasticity model is employed to generate a data set describing the yield response of an aluminum alloy, enabling the training of a neural network yield function and the calibration of 3D yield criteria of plastically anisotropic polycrystals. This novel formulation explores the flexibility of neural networks to describe complex-shaped yield loci and avoids common problems associated with conventional 3D yield functions, such as the non-trivial parameter identification and non -uniqueness of the anisotropy coefficients. Here, Bayesian optimization is applied to obtain an optimal neural network architecture and allows for an automated model design. The neural network yield function is able to learn intrinsic properties such as the convexity of the yield hull and tension-compression symmetry from a relatively small number of data points. The fully data-driven yield criterion can accurately reproduce multiaxial flow response and planar anisotropy despite of its material blind initial state. Stress gradients can also be computed from the neural network through automatic differentiation as derived quantities with good fidelity. This allows the calculation of r-values and provides a pathway for implementing the neural network yield model into finite element codes.