On the three-dimensional spatial correlations of curved dislocation systems

Joseph Pierre Anderson, Anter El-Azab
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引用次数: 8

Abstract

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

Abstract Image

论弯曲位错体系的三维空间相关性
对结晶金属中位错运动的粗粒度描述固有地代表了有关位错-位错相互作用信息的丢失。在目前的工作中,我们考虑了一个能够通过位错-位错相关函数重新捕获这些相互作用的粗粒度框架。框架依赖于一个卷积长度来定义滑移系统特有的位错密度。根据这种粗粒化过程的统计定义,我们定义了一个空间相关函数,该函数将允许在两点上安排离散线系统,从而在短范围内重新捕获它们相互作用的强度,从而重新捕获到位错动力学的平均场描述中。通过统计同质性论证,我们提出了一种从离散位错动力学模拟中评估这种相关函数的方法。最后,以同一滑移系统上的位错密度的相关性形式表明了这一评价的结果。这些相关函数对塑性应变和位错密度的依赖性较弱,而对卷积长度的依赖性较强。讨论了这些相关函数在连续位错动力学方面的意义以及未来的研究方向。
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期刊介绍: Journal of Materials Science: Materials Theory publishes all areas of theoretical materials science and related computational methods. The scope covers mechanical, physical and chemical problems in metals and alloys, ceramics, polymers, functional and biological materials at all scales and addresses the structure, synthesis and properties of materials. Proposing novel theoretical concepts, models, and/or mathematical and computational formalisms to advance state-of-the-art technology is critical for submission to the Journal of Materials Science: Materials Theory. The journal highly encourages contributions focusing on data-driven research, materials informatics, and the integration of theory and data analysis as new ways to predict, design, and conceptualize materials behavior.
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