A crystal plasticity model that incorporates stresses and strains due to slip gradients
A crystal plasticity model that incorporates stresses and strains due to slip gradients
复制标题
包含滑移梯度引起的应力和应变的晶体塑性模型
DOI：
10.1016/j.jmps.2007.07.012
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发表时间：
2008
影响因子：
5.3
通讯作者：
P. Dawson
中科院分区：
文献类型：
--
作者：
J. M. Gerken;P. Dawson
本工作是关于将多余位错的运动学和应力效应纳入晶体材料弹塑性行为的本构模型。该模型的基础是变形梯度的三项乘法分解，其中包括塑性和弹性变形的两个经典项沿着由于过量位错的集体效应引起的长程应变的附加项。长程应变是从假设的沃尔泰拉刃位错密度得到的，并与滑移梯度直接相关。一个新的材料参数出现，这是一个连续点附近的区域的大小，有助于长程应变。使用胡克弹性，在一个点上的应力是线性相关的总和的弹性加上长期应变场。然而，滑移的驱动力被假定为仅是由于弹性应力，使得长程应力在塑性变形的本构关系中是背应力。总变形速率与三种变形机制的一致平衡导致一组微分方程，可以求解弹性应力、旋转和压力，然后隐含地定义材料状态和平衡应力。从一个锥形拉伸试样的模拟结果表明，本构模型具有各向同性和运动型硬化效应，以及塑性变形和颈缩的模式相比，没有滑移梯度效应的材料的变化。
This work is concerned with incorporating the kinematic and stress effects of excess dislocations in a constitutive model for the elastoplastic behavior of crystalline materials. The foundation of the model is a three term multiplicative decomposition of the deformation gradient in which the two classical terms of plastic and elastic deformation are included along with an additional term for long range strain due to the collective effects of excess dislocations. The long range strain is obtained from an assumed density of Volterra edge dislocations and is directly related to gradients in slip. A new material parameter emerges which is the size the region about a continuum point that contributes to long range strains. Using Hookean elasticity, the stress at a point is linearly related to the sum of the elastic plus the long range strain fields. However, the driving force for slip is postulated to be due only to the elastic stress so that the long range stress is a back stress in the constitutive relationship for plastic deformation. A consistent balance of the total deformation rate with the three proposed mechanisms of deformation leads to a set of differential equations that can be solved for the elastic stress, rotation and pressure which then implicitly defines the material state and equilibrium stress. Results from the simulation of a tapered tensile specimen demonstrate that the constitutive model exhibits isotropic and kinematic type hardening effects as well as changes in the pattern of plastic deformation and necking when compared to a material without slip gradient effects.