Physics-Informed Neural Networks for Depth-Dependent Constitutive Relationships of Gradient Nanostructured 316L Stainless Steel.

The structural units with different characteristic scales in gradient nanostructured (GS) 316L stainless steel act synergistically to achieve the matching of strength and plasticity, and the intrinsic plasticity of nanoscale and ultrafine grains is fully demonstrated. The macroscopic stress-strain responses of each material unit in the GS surface layer can be measured directly by tension or compression tests on microspecimens. However, the experimental results based on microspecimens do not reflect either the extraordinary strengthening effect caused by non-uniform deformation or the intrinsic plasticity of nanoscale and ultrafine grains. In this paper, a method for constructing depth-dependent constitutive relationships of GS materials was proposed, which combines strain hardening parameter (hardness) with physics-informed neural networks (PINNs). First, the microhardness distribution on the specimen cross-sections was measured after stretching to different strains, and the hardness-strain-force test data were used to construct the depth-dependent PINNs model for the true strain-hardness relationship (PINNs_εH). Hardness-strain-force test data from specimens with uniform coarse grains were used to pre-train the PINNs model for hardness and true stress (PINNs_Hσ), on the basis of which the depth-dependent PINNs_Hσ model for GS materials was constructed by transfer learning. The PINNs_εσ model, which characterizes the depth-dependent constitutive relationships of GS materials, was then constructed using hardness as an intermediate variable. Finally, the accuracy and validation of the PINNs_εσ model were verified by a three-point flexure test and finite element simulation. The modeling method proposed in this study can be used to determine the position-dependent constitutive relationships of heterogeneous materials.