弱界面异质球形夹杂本征应变问题的解析解

AN ANALYTICAL SOLUTION TO THE EIGENSTRAIN PROBLEM OF A SPHERICAL INHOMOGENEOUS INCLUSION WITH AN IMPERFECTLY BONDED INTERFACE

本文研究了具有线弹簧型弱界面的异质球形夹杂的本征应变问题。所采用的线弹簧型弱界面模型既能考虑界面的切线方向滑动,又能考虑界面的法线方向张开。根据叠加原理,原问题的弹性场可分成三部分:一部分由真实均匀本征应变所引起,另一部分由等效的非均匀本征应变所引起,最后一部分则由虚拟的Somigliana位错场所产生。本文求得了等效非均匀本征应变和虚拟位错场的Burger矢量的解析表达式,进而完全确定原问题的弹性场。

In this paper, the eigenstrain problem of a spherical inhomogeneous inclusion with an imperfectly bonded interface is studied. A linear spring model was adopted to consider both the interfacial shear sliding and the normal separation. According to the superposition principle, the elastic field induced by a real uniform eigenstrain given in the imperfectly bonded inhomogeneous inclusion was decomposed into three parts. The first part is prescribed as the real uniform eigenstrain distributed in a perfectly bonded inclusion. The second part is induced by an equivalent nonuniform eigenstrain given in a perfectly bonded inclusion which models the material mismatch between the inclusion and the matrix. And the third part is obtained from an imaginary Somigliana dislocation field which models the interfacial displacement discontinuities. The exact form of the equivalent nonuniform eigenstrain and the Burger's vector of the imaginary Somigliana dislocation field were fully determined and the elastic fields are then obtained.