In polycrystalline materials, with the increase in grain size relative to the macrostructure, the collective behavior of crystal grains affects their macroscopic deformation field. To investigate the effect of relative size on the mechanical behavior of polycrystalline materials, the interaction between the microstructure-induced non-uniform deformation and the specimen shape-induced non-uniform deformation was evaluated based on experimental and numerical studies of uniaxial tensile tests of polycrystalline copper specimens with a curved gauge section. The effects of the macroscopic stress gradient and grain size on the strain field of the specimen were evaluated using specimens with different curvature radii obtained from different thermal treatment conditions. The development of strain distribution was measured using the digital image correlation method. A high strain concentration was observed at the minimum cross-section region in the specimen with smaller grains, whereas such strain concentration was relaxed in the specimen with larger grains because a random strain distribution occurred owing to the polycrystalline structure. A full-scale crystalline plasticity finite element method simulation, under conditions similar to those in the experiment, was then performed. Deformation concentrated zone, in which the length and width depended on the grain size, occurred in the polycrystalline specimen. The cross-section of the specimen was locally reduced when the deformation concentrated zone reached the free surface, and the tensile force became smaller for the specimen with larger grains. To discuss the relative specimen size effect, the plastic strain was divided into local and nonlocal plastic strains. Both the experimental and simulation results clarified that the nonlocal plastic strain gradient evaluated in the finite volume region increased with the region-averaged stress. From these results, we proposed a constitutive equation for the plastic strain as a function of local stress and finite volume averaged stress. The nonlocal plastic work for the evaluation region, which is estimated using the nonlocal strain gradient, increased with the stress during the strain-hardening stage in both the simulation and experimental results.

在多晶材料中，随着晶粒尺寸相对于宏观结构的增加，晶粒的集体行为会影响其宏观变形场。为了研究相对尺寸对多晶材料力学行为的影响，基于多晶单轴拉伸试验的实验和数值研究，评估了微观结构引起的非均匀变形和试样形状引起的非均匀变形之间的相互作用。具有弯曲规格截面的铜试样。使用从不同热处理条件获得的具有不同曲率半径的试样，评估宏观应力梯度和晶粒尺寸对试样应变场的影响。使用数字图像相关方法测量应变分布的发展。在晶粒较小的试样中，在最小截面区域观察到高应变浓度，而在晶粒较大的试样中，由于多晶结构出现随机应变分布，因此这种应变集中松弛。然后在与实验条件相似的条件下进行全尺寸结晶塑性有限元方法模拟。多晶试样出现变形集中区，其长度和宽度取决于晶粒尺寸。当变形集中区到达自由表面时，试样横截面局部减小，晶粒较大的试样拉力变小。为了讨论相对试样尺寸效应，塑性应变分为局部塑性应变和非局部塑性应变。实验和模拟结果都阐明了在有限体积区域中评估的非局部塑性应变梯度随着区域平均应力的增加而增加。根据这些结果，我们提出了塑性应变作为局部应力和有限体积平均应力的函数的本构方程。在模拟和实验结果中，评估区域的非局部塑性功（使用非局部应变梯度估计）随着应变硬化阶段的应力而增加。实验和模拟结果都阐明了在有限体积区域中评估的非局部塑性应变梯度随着区域平均应力的增加而增加。根据这些结果，我们提出了塑性应变作为局部应力和有限体积平均应力的函数的本构方程。在模拟和实验结果中，评估区域的非局部塑性功（使用非局部应变梯度估计）随着应变硬化阶段的应力而增加。实验和模拟结果都阐明了在有限体积区域中评估的非局部塑性应变梯度随着区域平均应力的增加而增加。根据这些结果，我们提出了塑性应变作为局部应力和有限体积平均应力的函数的本构方程。在模拟和实验结果中，评估区域的非局部塑性功（使用非局部应变梯度估计）随着应变硬化阶段的应力而增加。