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arXiv 1404.0230cond-mat.mtrl-scicond-mat.mes-hall
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相似区位错模拟的标度性质

Scaling Properties of Dislocation Simulations in the Similitude Regime

Michael Zaiser, Stefan Sandfeld

摘要:

位错系统表现出众所周知的标度特性,例如流动应力和位错密度之间的泰勒关系,以及将流动应力与位错图案的特征波长联系起来的“相似律”。在这里,我们讨论了这些属性的起源,这可以涉及到一般的不变性属性的离散位错系统的演化方程,以及它们的影响广泛的一类模型的位错微观结构的演变。我们表明,在一定条件下进行不同的应力,位错密度和应变速率的位错模拟可以被认为是等效的,我们研究的变形条件(“相似制度”)的范围内,这种等效性可以预期举行。此外,我们讨论了所制定的不变性的性质为基础的密度,非局部或随机模型的位错微观结构的演变,位错模式和尺寸效应的限制。

英文摘要:

Dislocation systems exhibit well known scaling properties such as the Taylor relationship between flow stress and dislocation density, and the "law of similitude" linking the flow stress to the characteristic wavelength of dislocation patterns. Here we discuss the origin of these properties, which can be related to generic invariance properties of the equations of evolution of discrete dislocation systems, and their implications for a wide class of models of dislocation microstructure evolution. We demonstrate that under certain conditions dislocation simulations carried out at different stress, dislocation density, and strain rate can be considered as equivalent, and we study the range of deformation conditions ("similitude regime") over which this equivalence can be expected to hold. In addition, we discuss the restrictions imposed by the formulated invariance properties for density-based, nonlocal or stochastic models of dislocation microstructure evolution, and for dislocation patterns and size effects.

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