Stochastically forced dislocation density distribution in plastic deformation.
Stochastically forced dislocation density distribution in plastic deformation.
复制标题
塑性变形中随机受迫位错密度分布。
作者：
A. Chattopadhyay;E. Aifantis
金属塑性变形中位错的动态演化受外加载荷的确定性因素和内应力波动的随机效应的双重控制。这种类型的随机位错过程和相关的空间非均匀模式导致观测到的变形结构的随机性。以前的研究已经分析了随机性在这种纹理演化中的作用，但是这些模型都没有考虑到系统整体动力学中随机扰动的有限衰减时间（所有以前的模型都假设瞬时松弛，这是“非物理的”）的影响。本文通过在分析一类线性和非线性Wiener和Ornstein-Uhlenbeck过程中引入Ornstein-Uhlenbeck噪声形式的有色噪声来弥补这一知识差距，这些结构位错动力学可以映射到这些过程上。基于对相关Fokker-Planck模型的分析，我们的研究结果表明，线性维纳过程不受问题中第二个时间尺度的影响，但所有非线性过程，无论是维纳型还是Ornstein-Uhlenbeck型，尺度都是噪声衰减时间τ的函数。这些结果有望扩展现有的实验观察结果，并激发新的数值和实验室测试，以进一步了解在塑性变形样品建模中确定性效应和随机效应之间的竞争。
The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such types of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution, but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical") of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem, but all nonlinear processes, both the Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time τ. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples.