塑性形变中随机受迫位错密度分布
Stochastically forced dislocation density distribution in plastic deformation
摘要：
塑性变形金属中位错的动力学演化既受外加载荷的确定性因素控制，又受内应力波动的随机性影响。这种类型的随机位错过程和相关的空间不均匀模式导致观察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系统的整体动态中的随机扰动的有限衰减时间（所有以前的模型假设瞬时松弛是“非物理的”）的影响。本文通过在一类线性和非线性维纳和Ornstein-Uhlenbeck过程的分析中引入Ornstein-Uhlenbeck噪声形式的有色噪声来弥合这一知识差距，这些结构位错动力学可以映射到这类噪声上。通过对相关Fokker-Planck模型的分析，我们的结果表明，线性Wiener过程不受第二时间尺度的影响，但所有非线性过程，包括Wiener型和Ornstein-Uhlenbeck型，都是噪声衰减时间$τ$的函数.预计这些结果将衍生现有的实验观察，并激发新的数值和实验室测试，以进一步了解建模塑性变形样品中确定性和随机效应之间的竞争。
英文摘要：
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 type 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 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.
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