粘弹性结合材料界面端奇异场

Viscoelastic Singular Behavior Near an Interface Edge

在电子封装等结构中存在大量的粘弹性界面问题,其破坏一般均始于界面端,但目前尚无关于粘弹性界面端奇异场的解。粘弹性问题在拉普拉斯域内与弹性问题有对应关系,理论上可以利用对应性原理由弹性解经拉氏逆变换得到粘弹性问题的解。但是,对于粘弹性界面端,由于奇异场的奇异指数也是与时间有关的,因此进行严密的拉氏逆变换是非常困难的。本文借鉴弹性界面端奇异场,近似地给出了线性粘弹性体界面端奇异场的具体形式,并通过数值计算验证了近似理论解的有效性。

There is a great deal of viscoelastic interface problems in the electronic packaging structure, and the failure generally initiates from the interface edge. However, due to lacking of theoretical solution for viscoelastic interface edge problems, there is no theoretical foundation yet to set up the strength and life evaluation method for such a viscoelastic singular problem. Considering the principle of correspondence between elastic and viscoelastic problem, theoretically one can obtain the viscoelastic solutions by inversed Laplace transformation from the elastic ones in the Laplace field. However, as the singularities are also time-dependent, it is very difficult to process the inversed Laplace transformation exactly. An approximate solution of linear viscoelastic interface edge was deduced based on the theoretical solution of elastic interface edge. The validity of the approximate solution is proved by numerical analysis of viscoelastic interface edge problems.