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Nanoscale Elastic Properties of Dislocations and Disclinations

机译:位错和错位的纳米级弹性

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A correct description of the behavior of defects in thin-film and nanostructured systems needs to take into account both the strong influence of outer and inner interphase boundaries and the fact that the size of a defect core, where classical solutions are signular and incorrect, occurs in the same order as the characteristic length of the system (film thickness, grain size, etc.). To take into account the influence of itnerphase boundaries, many solutions of boundary value problems for defects have been obtained in the framework of the classical theory of elasticity (see [1-5] for a review). To solve the second problem, some approaches have been proposed which have been aimed at dispensing with classical singularity of elastic fields within defect cores (see [6,7] for a review). The present paper represents a brief description of our recent results [6-10] dealing with nanoscale elastic fields within and near cores of disclinations [6,7] and dislocations [6-10] in the framework of gradient elasticity. The main result shown there was an elimination of displacement, strain, stress and energy singularities at the defect line. It is worth noting, that previous continuum models for such kind of defects which have taken into account couple stresses or non-locality (see [6,7] for a review), do not dispense with the singularity in the displacement or strai nfield, even though some of them {11-13] claim elimination of stress singularity.
机译:正确描述薄膜和纳米结构系统中的缺陷行为时,必须考虑到外部和内部相界边界的强烈影响以及缺陷核心的尺寸(在经典解决方案中是有符号的和不正确的)的发生这一事实以与系统特征长度相同的顺序(薄膜厚度,晶粒尺寸等)。考虑到中间相边界的影响,在经典的弹性理论的框架内已经获得了许多缺陷边界值问题的解决方案(参见[1-5])。为了解决第二个问题,已经提出了一些旨在消除缺陷核心内弹性场的经典奇异性的方法(有关综述,请参见[6,7])。本文是对我们最近的结果[6-10]的简要描述,该结果涉及梯度弹性框架内旋错[6,7]和位错[6-10]的核心内和附近的纳米级弹性场。主要结果表明,消除了缺陷线上的位移,应变,应力和能量奇异性。值得注意的是,先前针对此类缺陷的连续模型已经考虑了耦合应力或非局部性(请参见[6,7]进行回顾),并没有放弃位移或应变场中的奇异性,即使其中一些人[11-13]声称消除了应力奇异性。

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