A model of multiaxial cyclic plasticity describing yield-point phenomena and nonhomogeneous plastic deformation and its applications

在本研究中，为了描述金属的屈服点现象和非均匀塑性变形，提出了一个循环粘塑性模型。该模型是在基于双曲面建模的超应力理论框架内建立的。该模型已在本研究人员开发的有限元程序中实现。利用该有限元程序对几种循环变形(不同变形速度的单轴拉伸、循环应变和棘轮)进行了数值模拟，并与软钢的相应实验数据进行了比较。本文的研究结果如下：(1)在位错快速增殖和位错速度与应力相关的前提下，该模型较好地描述了单轴拉伸下的急剧屈服点和随后的突然屈服下降现象。对强塑性应变局部化以及Luders带传播进行了数值模拟。两种Luders带的传播，即只有一个Luders波阵面和两个Luders波阵面，可以通过给定不同程度的试件几何缺陷来数值再现。(2)材料的应变范围相关循环硬化行为由应力空间中定义的非各向同性硬化区的概念来表示。(3)棘轮的数值模拟结果与实验观测结果一致，如应变率的影响和棘轮的安定。描述应力-应变滞后环闭合的运动硬化规则对于精确模拟棘轮过程至关重要。

In the present research, a model of cyclic viscoplasticity has been presented in order to describe the yield-point phenomena and nonhomogeneous plastic deformation of metals. This model has been constructed within a framework of the overstress theory based on the two-surface modeling. The model has been implemented to a finite element code originally developed by the present researchers. Using this FE code, the numerical simulation of some cyclic deformations (uniaxial tension with various deformation speeds, cyclic straining and ratchetting) were conducted, and the results were compared to the corresponding experimental data on mild steel. The results obtained in the present work are summarized as follows.(1) The phenomena of sharp yield point and the subsequent abrupt yield drop under uniaxial tension are well described by the model which is proposed on the premise that result from rapid dislocation multiplication and the stress-dependence of dislocation velocity. Strong plastic strain localization, as well as the Luders-band propagation, is numerically simulated. Two types of Luders-band propagation, i.e., one has only one Luders front, and the other has two fronts, can be numerically reproduced by giving different levels of geometrical imperfections of the specimen.(2) The strain-range dependent cyclic hardening behavior of materials is expressed by the concept of non-isotropic hardening region defined in the stress space.(3) The results of numerical simulation for ratchetting show good agreement with the experimental observations, such as the effect of strain rate and the shakedown of ratchetting. The kinematic hardening rule which describes the closure of the stress-strain hysteresis loop is of vital importance for accurate simulation of ratchetting.