Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids
Displacement Fields and Self-Energies of Circular and Polygonal Dislocation Loops in Homogeneous and Layered Anisotropic Solids
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DOI：
10.1016/j.jmps.2015.06.008
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发表时间：
2015-10
影响因子：
5.3
通讯作者：
Yanfei Gao;B. Larson
中科院分区：
文献类型：
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作者：
Yanfei Gao;B. Larson
有一大类材料问题涉及弹性各向异性固体中位错环的应力、位移和应变能的解决方案，包括对辐照引起的缺陷簇的生成和演化的日益详细的研究，其尺寸范围从微观到介观长度尺度。基于适用于均匀和层状各向异性固体的二维傅里叶变换和斯特罗形式，我们开发了强大且计算高效的方法来计算圆形和多边形位错环的位移场。利用-1阶格林张量的齐次性质，我们证明了位错环的位移和应力场可以通过线积分的数值求积来获得。此外，还表明与环的应变能相关的六重积分可以用包含弹性各向异性效应的预因子与奇异且等于弹性各向同性情况的通用项的乘积来表示。此外，我们发现棱柱环的自能预因子与法向接触的有效模量相同，而剪切环的自能预因子与剪切中的有效压痕模量仅相差几个百分点。这些结果为检查位错反应的能量和有效程序提供了一种方便的方法，用于位错环局部位移和应力的数值计算，这两者在实验-理论联合研究中的定量缺陷分析中发挥着不可或缺的作用。
There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.