Derivation of Constitutive Equation for Describing Cyclic Deformation in Terms of Dislocation Dynamics and Its Application to Fatigue under Multiaxial Stress Loading.

在本研究中，应力-应变场计算的裂纹尖端附近的退火通过厚度裂纹铜试样的弹塑性有限元法，其中的位错动力学的基础上推导出的本构方程的作者进行了修改，适用于循环加载分析与大变形。分析是在应力比R_ =-1的循环载荷下进行<sigma>的。然后，特别注意的应变和裂纹的启闭行为与循环硬化在前几个周期。同时，将计算结果与网格法测试结果进行了比较。所得主要结果概括如下。(1)循环硬化行为的定量表示的弹塑性有限元方法，使用的位错动力学的基础上推导出的本构方程修改适用于大变形。(2)从负载控制的循环试验，在裂纹尖端附近的循环应变范围趋于减少到稳定的恒定值与应力循环次数的增加。(3)计算得到的裂纹尖端局部化变形行为定量和定性地描述了试验结果。结果表明，该本构方程能有效地描述这些行为。(4)通过有限元分析，给出了位于裂纹尖端最小截面处的单元的应力-应变滞回线和应力应变分布的变化。这些结果可能与（3）中的实验结果一致。

In the present study, the stress-strain field was calculated in the vicinity of the crack tip by means of the elastic-plastic finite-element method in annealed through-thickness-cracked copper specimens, where the constitutive equation derived on the basis of dislocation dynamics by the authors was modified to apply to cyclic loading analysis with large deformation. The analysis was carried out under cyclic loading at stress ratio R_<sigma>=-1. Then special attention was given to the strain and crack opening-closing behaviors with the cyclic hardening during first a few cycles. At the same time, calculated behaviors were compared with the test result measured by means of the grid method. The main results obtained are summarized as follows.(1) The cyclic hardening behavior was expressed quantitatively by the elastic-plastic finite-element method, using the constitutive equation derived on the basis of dislocation dynamics modified to apply to the large deformation.(2) From the load-controlled cyclic test, a cyclic strain range in the vicinity of the crack tip tended to decrease to the stable constant value with an increase in the number of stress cycles.(3) The calculated localized deformation behavior in the vicinity of the crack tip quantitatively and qualitatively described the test results very well. It suggested that this constitutive equation is effective to describe these behaviors.(4) The stress-strain hysteresis loop of the element that is located at the minimum cross section ahead of crack tip and variation of stress/strain distribution was shown by means of F.E.M.analysis. These result were in probable agreement with those obtained experimentally in (3).