A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations
A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations
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DOI：
10.1016/s0022-5096(01)00104-1
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发表时间：
2002
影响因子：
5.3
通讯作者：
M. Gurtin
中科院分区：
文献类型：
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作者：
M. Gurtin
这项研究发展了单晶塑性梯度理论，占几何必要的位错。该理论基于经典晶体运动学;经典宏观力;每个滑动系统的微观力与微观力平衡一致;第二定律的机械版本，包括通过微观力在滑动期间执行的功;率无关本构理论，包括对几何必要位错的张量测量的依赖性。微力平衡被证明是相当于非局部屈服条件的个人滑移系统。场方程由与标准宏观力平衡相耦合的屈服条件组成;这些条件由经典宏观边界条件和与滑移相关的非标准边界条件补充。作为一种辅助解决方案，弱（虚功率）制定的非局部屈服条件。为了与经典的位错理论接触，所示的微观应力表示对应的Peach-Koehler力在一个单一的位错。
This study develops a gradient theory of single-crystal plasticity that accounts for geometrically necessary dislocations. The theory is based on classical crystalline kinematics; classical macroforces; microforces for each slip system consistent with a microforce balance; a mechanical version of the second law that includes, via the microforces, work performed during slip; a rate-independent constitutive theory that includes dependences on a tensorial measure of geometrically necessary dislocations. The microforce balances are shown to be equivalent to nonlocal yield conditions for the individual slip systems. The field equations consist of the yield conditions coupled to the standard macroscopic force balance; these are supplemented by classical macroscopic boundary conditions in conjunction with nonstandard boundary conditions associated with slip. As an aid to solution, a weak (virtual power) formulation of the nonlocal yield conditions is derived. To make contact with classical dislocation theory, the microstresses are shown to represent counterparts of the Peach–Koehler force on a single dislocation.