Stored energy density solution for TSV-Cu structure deformation under thermal cyclic loading based on PINN

TSV-Cu is widely used for chip interconnects, where high testing costs and complex crystal plasticity finite element (CPFE) limit the research of its deep microplastic evolution process. Considering the stored energy density (SED) based on dislocation density and plastic work as a fatigue indicator factor (FIP), this paper proposes for the first time a physics-informed neural network (PINN) framework based on SED, which aims to achieve the solution of SED distributions quickly and efficiently to save computational time and cost. The grain orientation, geometrical compatibility factor, back stress, and effective plastic strain are taken into account as inputs to the PINN model. The total dislocation density is used as an indirect solution variable to construct the associated loss boundary terms, which results in the solution of the SED. The results of the two real EBSD tests show that the PINN model is able to accurately and sensitively predict the SED concentration distribution for different thermal cycle loadings, and maintains a high degree of agreement with the CPFE calculation results. Moreover, The superiority of PINN over other machine learning algorithms in terms of physical model interpretation and prediction accuracy is verified. These make it a reality for PINN to solve for the FIP distribution for the first time, and to accurately and quickly predict the location of crack initiation.