考虑应变梯度效应的低碳钢试样单向拉伸尺寸效应理论研究

采用二阶应变梯度塑性理论，得出伸长率、峰值应力后工程应力应变曲线和真应力应变曲线的解析解，结果表明三者均具有尺寸效应。将低碳钢试样的单轴拉伸简化为轴向的一维问题。采用拉伸过程中体积不变假设及平衡条件，将应变梯度引入屈服函数，得到伸长率、平均应变及真应变的解析式。理论结果完全反映伸长率与标定长度呈反比的客观事实。工程应力应变曲线尺寸效应可以在数值结果中找到佐证。拉应变局部化是三者尺寸效应的本质原因。

ANALYSIS OF SIZE EFFECT IN UNIAXIAL TENSION FOR LOW-CARBON STEEL SPECIMEN CONSIDERING STRAIN GRADIENT EFFECT

Analytical solutions of scale law for the engineering stress-engineering strain curve, true stress-true strain curve and percentage elongation were proposed based on gradient-dependent plasticity. Low-Carbon steel specimen uniaxial tension was simplified as a one-dimensional problem. The assumption that plastic volumetric strain was zero in the process of localized deformation was adopted and stress equilibrium in the direction of tension was considered. The strain gradient term was introduced into the yield function to obtain distributed plastic strain. The theoretical solution of relation between percentage elongation and scale length coincides with many experimental results that percentage elongation is inverse proportional to scale length. The present size effect law for the engineering stress-engineering strain curve is also agreement with earlier numerical results. The reasons for size effect are localized deformations.