Onuki Akira
Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Dec;68(6 Pt 1):061502. doi: 10.1103/PhysRevE.68.061502. Epub 2003 Dec 11.
A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field u and the lattice velocity v=delta(u)/delta(t). Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables the formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of +/-pi/4 with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to structurally disordered states, which are metastable due to the Peierls potential. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.
提出了二维固体塑性变形的含时金兹堡 - 朗道模型。基本动力学变量是位移场(u)和晶格速度(v = \frac{\partial u}{\partial t})。假设阻尼源于动量方程中的剪切粘度。弹性能密度是剪切应变和四方应变的周期函数，这使得在大应变下能够形成滑移。在这项工作中，我们忽略诸如空位、间隙原子或晶界等缺陷。最简单的滑移由两个具有相反柏氏矢量的刃型位错组成。如果滑移的取向在简单剪切变形中与流动方向平行或垂直，并且在单轴拉伸中相对于拉伸方向成(\pm\frac{\pi}{4})角，则滑移的形成能最小化。塑性流动中产生的高密度位错即使在流动停止后也不会消失。因此，大的外加应变会导致结构无序状态，由于派尔斯势，这种状态是亚稳的。我们将弹性能分为由于仿射变形产生的弹性部分和缺陷部分。后者代表无序程度，并且在循环应变下的塑性流动中几乎是恒定的。
