反平面剪切作用下双材料滑动界面的细观力学模型

A Mesomechanics Model for Sliding Interface between Bimaterials under Antiplane Shear

非理想粘结界面对多相材料力学性能具有重要影响。对于双材料间含众多随机分布微裂纹的界面,宏观上可以等效为连续损伤的弱界面,其两侧的面力连续而位移有间断。只有切线方向的位移间断,而法线方向位移连续的弱界面称之为滑动界面。在反平面剪切的作用下,我们证明了对于含有随机分布微裂纹的弹性双材料界面在宏观上等效为线弹簧型滑动界面,并获得了滑动界面柔度的一般表达式。利用Mori-Tanaka方法和广义自洽方法,我们研究了滑动界面柔度系数和微裂纹密度的关系。对这两种方法所得的结果进行比较发现,Mori-Tanaka方法得到的界面柔度比广义自洽方法得到的界面柔度大。当裂纹密度比较小时,这两种方法求得的界面柔度很接近。两种方法的结果都表明,界面柔度随裂纹密度的增加而增加。Mori-Tanaka方法比广义自洽方法求解更为简便。

The imperfectly bonded interface has an important effect on the mechanical behavior of multiphase materials. The bimaterial interface can be treated as an imperfect interface when there exist many random distributed micro-cracks on the interface. The tractions are continuous while the displacements have a jump across the imperfect interface. The imperfect interface with a continuous normal displacement and a jumped tangential displacement is called a sliding interface. It is shown that the bimaterial interface with random distributed micro-cracks can be equivalent in macro scale to a linear spring type sliding interface. A general expression for the interfacial compliance of the sliding interface is obtained. By means of Mori-Tanaka method and generalized self-consistent method, we study the relation between the interfacial compliance and the crack density. Comparing the results of these two methods we found that the interfacial compliance obtained from Mori-Tanaka method is greater than that from generalized self-consistent method and these two methods give almost the same results when the crack density is small. The results also reveal that the interfacial compliance increases with the increase of the crack density. The Mori-Tanaka method is superior to generalized self-consistent method in that its solution procedure is more convenient.