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Three-dimensional formulation of dislocation climb

机译：错位爬升的三维公式

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摘要

We derive a Green's function formulation for the climb of curved dislocations and multiple dislocations in three-dimensions. In this new dislocation climb formulation, the dislocation climb velocity is determined from the Peach-Koehler force on dislocations through vacancy diffusion in a non-local manner. The long-range contribution to the dislocation climb velocity is associated with vacancy diffusion rather than from the climb component of the well-known, long-range elastic effects captured in the Peach-Koehler force. Both long-range effects are important in determining the climb velocity of dislocations. Analytical and numerical examples show that the widely used local climb formula, based on straight infinite dislocations, is not generally applicable, except for a small set of special cases. We also present a numerical discretization method of this Green's function formulation appropriate for implementation in discrete dislocation dynamics (DDD) simulations. In DDD implementations, the long-range Peach-Koehler force is calculated as is commonly done, then a linear system is solved for the climb velocity using these forces. This is also done within the same order of computational cost as existing discrete dislocation dynamics methods.
机译：我们为弯曲位错和多维位错的三维爬升推导了格林函数公式。在这种新的位错爬升公式中，位错爬升速度是由Peach-Koehler通过非局部方式通过空位扩散对位错施加的力来确定的。对位错爬升速度的远距离贡献与空位扩散相关，而不是与在Peach-Koehler力中捕获的众所周知的远距离弹性效应的爬升分量有关。两种远程效应对于确定位错的爬升速度都很重要。分析和数值示例表明，除了少数特殊情况外，基于直线无限位错的广泛使用的局部爬升公式通常不适用。我们还提出了一种适用于离散位错动力学（DDD）模拟的格林函数公式的数值离散方法。在DDD实现中，通常会计算远距离Peach-Koehler力，然后使用这些力为爬升速度求解线性系统。这也以与现有离散位错动力学方法相同的计算成本顺序进行。

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  • 来源
    《Journal of the Mechanics and Physics of Solids》 |2015年第10期|319-337|共19页
  • 作者

    Yejun Gu; Yang Xiang; Siu Sin Quek; David J. Srolovitz;

  • 作者单位

    Nano Science and Technology Program, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;

    Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;

    Institute of High Performance Computing, 1 Fusionopolis Way, #16-16, Connexis, Singapore 138632, Singapore;

    Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA,Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Dislocation climb; Green's function; Long-range effect; Dislocation dynamics;

    机译：脱位爬升;格林函数;远距离效果;脱位动力学;

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