A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin

被引:203
作者
Gurtin, ME [1 ]
机构
[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
关键词
strain-gradient plasticity;
D O I
10.1016/j.jmps.2004.04.010
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This study develops a gradient theory of small-deformation viscoplasticity based on: a system of microforces consistent with its peculiar balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that accounts for the Burgers vector through a free energy dependent on curl H-P, with H-P the plastic part of the elastic-plastic decomposition of the displacement gradient. The microforce balance and the constitutive equations, restricted by the second law, are shown to be together equivalent to a nonlocal flow rule in the form of a coupled pair of second-order partial differential equations. The first of these is an equation for the plastic strain-rate E-P in which the stress T plays a basic role; the second, which is independent of T, is an equation for the plastic spin W-P. A consequence of this second equation is that the plastic spin vanishes identically when the free energy is independent of curl H-P, but not generally otherwise. A formal discussion based on experience with other gradient theories suggests that sufficiently far from boundaries solutions should not differ appreciably from classical solutions, but close to microscopically bard boundaries, boundary layers characterized by a large Burgers vector and large plastic spin should form. Because of the nonlocal nature of the flow rule, the classical macroscopic boundary conditions need be supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a variational formulation of the flow rule is derived. Finally, we sketch a generalization of the theory that allows for isotropic hardening resulting from dissipative constitutive dependences on delE(P). (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2545 / 2568
页数:24
相关论文
共 15 条