Li Huashu, Cheng Yang, Wang Zheheng, Wang Xiaogui
College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310032, China.
Materials (Basel). 2025 Jul 28;18(15):3532. doi: 10.3390/ma18153532.
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.
梯度纳米结构（GS）316L不锈钢中具有不同特征尺度的结构单元协同作用，以实现强度和塑性的匹配，并充分展现了纳米级和超细晶粒的本征塑性。通过对微试样进行拉伸或压缩试验，可以直接测量GS表层中每个材料单元的宏观应力-应变响应。然而，基于微试样的实验结果既没有反映出非均匀变形引起的非凡强化效果，也没有反映出纳米级和超细晶粒的本征塑性。本文提出了一种构建GS材料深度相关本构关系的方法，该方法将应变硬化参数（硬度）与物理信息神经网络（PINNs）相结合。首先，在拉伸至不同应变后测量试样横截面上的显微硬度分布，并使用硬度-应变-力测试数据构建真实应变-硬度关系的深度相关PINNs模型（PINNs_εH）。使用具有均匀粗晶粒的试样的硬度-应变-力测试数据对硬度和真实应力的PINNs模型（PINNs_Hσ）进行预训练，在此基础上通过迁移学习构建GS材料的深度相关PINNs_Hσ模型。然后，以硬度为中间变量构建表征GS材料深度相关本构关系的PINNs_εσ模型。最后，通过三点弯曲试验和有限元模拟验证了PINNs_εσ模型的准确性和有效性。本研究提出的建模方法可用于确定异质材料的位置相关本构关系。
