A data-driven approach to predicting the anisotropic mechanical behaviour of voided single crystals

Machine learning techniques are increasingly used to extract important physical information from a broad range of materials and to identify their processing-structure-property relationships. In this work, a neural network framework is coupled with a crystal plasticity finite element based approach to predict the deformation and ductile failure behaviour of porous FCC single crystals when subjected to multi-axial loading conditions. The work relies on 3D unit cells with a centrally located spherical void to represent the microstructure of the porous single crystal material, and on a crystallographic slip-based crystal plasticity constitutive model to describe its deformation behaviour. Stress-strain data generated by unit cell finite element simulations are relied upon to construct the neural network model. Different strategies for the neural network input and output variables and parameters are first explored so as to optimise performance and accuracy. Both proportional and non-proportional loading conditions resulting from a constant and a varying stress triaxiality during deformation, respectively, are considered. The optimum neural network strategy is shown to successfully predict the behaviour of the porous single crystal under both proportional and non-proportional loading, albeit with the void behaviour at high stress triaxialities better described than that at low triaxialities. The results also reveal that the use of tensorial quantities for both stresses and strains as input and output neural network quantities is more suitable as a form of data representation for multiaxial loading conditions than uniaxial equivalent stress and strain quantities. It was also found that the inclusion of prior knowledge as neural network input quantities in the form of reference stress-strain solutions for the void-free single crystal considerably improves the predictive capabilities of the proposed data-driven approach, even when only a very limited number of training cases was used.