Theoretical Model of Structural Phase Transitions in Al-Cu Solid Solutions under Dynamic Loading Using Machine Learning

The development of dynamic plasticity models with accounting of interplay between several plasticity mechanisms is an urgent problem for the theoretical description of the complex dynamic loading of materials. Here, we consider dynamic plastic relaxation by means of the combined action of dislocations and phase transitions using Al-Cu solid solutions as the model materials and uniaxial compression as the model loading. We propose a simple and robust theoretical model combining molecular dynamics (MD) data, theoretical framework and machine learning (ML) methods. MD simulations of uniaxial compression of Al, Cu and Al-Cu solid solutions reveal a relaxation of shear stresses due to a combination of dislocation plasticity and phase transformations with a complete suppression of the dislocation activity for Cu concentrations in the range of 30-80%. In particular, pure Al reveals an almost complete phase transition from the FCC (face-centered cubic) to the BCC (body-centered cubic) structure at a pressure of about 36 GPa, while pure copper does not reveal it at least till 110 GPa. A theoretical model of stress relaxation is developed, taking into account the dislocation activity and phase transformations, and is applied for the description of the MD results of an Al-Cu solid solution. Arrhenius-type equations are employed to describe the rates of phase transformation. The Bayesian method is applied to identify the model parameters with fitting to MD results as the reference data. Two forward-propagation artificial neural networks (ANNs) trained by MD data for uniaxial compression and tension are used to approximate the single-valued functions being parts of constitutive relation, such as the equation of state (EOS), elastic (shear and bulk) moduli and the nucleation strain distance function describing dislocation nucleation. The developed theoretical model with machine learning can be further used for the simulation of a shock-wave structure in metastable Al-Cu solid solutions, and the developed method can be applied to other metallic systems, including high-entropy alloys.