非均质材料与位错交互能的数值等效夹杂算法

工程结构中的夹杂物和位错会极大地影响材料的力学性能和服役寿命。以往的解析解主要关注特定形状(如圆形、椭圆形)夹杂物与位错之间的相互作用。当采用数值方法计算时，由于位错的奇异性，即使是商用有限元软件也会面临处理上的困难。该文基于数值等效夹杂算法并结合快速傅里叶变换，求解了无穷体内夹杂物与刃型位错的交互能，有效地规避了数值奇异性问题。相对误差的范数分析结果表明，在杂质附近所产生的应力扰动对最终结果具有较大影响。该文计算方法能够更加精确地确定应力扰动场，并显示出优越的数值收敛性和稳定性。在求解任意形状杂质与位错相互作用问题中，该文提供了一种便捷且有效的计算方案。

A NUMERICAL EQUIVALENT INCLUSION METHOD FOR DETERMINING THE INTERACTION ENERGY BETWEEN INHOMOGENEITIES AND DISLOCATIONS

The mechanical properties and service life of materials may be significantly influenced by the interaction between inhomogeneities and dislocations in engineering structures. Previous analytical studies on inhomogeneity-dislocation interactions have been concerned primarily on some special inhomogeneity shapes (e.g. circle and ellipse). On the other hand, the involved singularity issue in dislocation studies is challenging, even intractable for commercial finite element software. Using the numerical equivalent inclusion method (NEIM) in conjunction with the Fast Fourier Transforms technique, this work presents an effective computational scheme for evaluating the interaction energy between an edge dislocation and inhomogeneities. The proposed computational method may successfully circumvent the numerical singularity. The results of norm analyses on relative errors demonstrate that the stress disturbance field caused by the impurity has a great influence on the final solutions, especially when the dislocation is located in the neighborhood of the inhomogeneity. The proposed method in this work shows excellent numerical convergence and stability, and appears to be convenient and efficient for handling arbitrarily shaped inhomogeneities interacting with an edge dislocation.