刃型位错和圆弧形刚性线夹杂的干涉效应

Interaction Between an Edge Dislocation and Circular-arc Rigid Lines

位错和夹杂的干涉效应对于理解材料的强化和韧化机理具有十分重要的意义。文中研究了晶体材料中刃型位错和多条共圆弧刚性线夹杂的干涉作用。利用Riemann-Schwarz反照原理和复势函数的奇性主部分析技术,得到了问题的一般解答;对于只含一条刚性线夹杂的情况,给出了复势函数的封闭形式解。由Peach-Koe-hler公式求出了作用在刃型位错上的位错力,并讨论了圆弧形刚性线夹杂对位错力的影响规律,发现弧形刚性线对刃型位错有很强的排斥作用。本文解答不但可作为格林函数获得任意分布位错的相应解答,而且可以用于研究刚性线夹杂和任意形状裂纹的干涉效应问题。

The study of dislocations interacting with inhomogeneities is motivated by the need for a better understanding of the mechanism of strengthening and toughening of materials. The interaction of an edge dislocation with the cirular arc rigid line inclusions was studied. By using Riemann-Schwarz's reflection principle integrated with the analysis of singularity of the complex potentials, the general solution of the problem was derived explicitly. The closed form expressions of the holomorphic complex potentials and the stress fields were obtained for the case of single rigid line inclusion. The image force on the dilocation was then determined by means of the Peach-Koehle formula and the influence of the rigid line inclusion geometry on the image force was evaluated and discussed. It is shown that the circular arc rigid line has significant effect on the motion of edge dislocation. The closed form solutions of complex potentials can be used as Green's functions to obtain the corresponding solution for the case of arbitrary distribution dislocations and solve the problem of interaction between an interfacial rigid line and an arbitrary shape crack.