含夹杂复合材料宏观性能研究

STUDY OF OVERALL PROPERTIES OF COMPOSITES WITH INCLUSIONS

本文综述并评价了有关含夹杂复合材料的有效弹性模量研究的代表性工作，包括自洽理论，微分法，Ｅｓｈｅｌｂｙ－Ｍｏｒｉ－Ｔａｎａｋａ法，Ｈａｓｈｉｎ和Ｓｈｔｒｉｋｍａｎ的变分法等。指出上述理论由于没有充分考虑复合材料内部的微结构特征，如夹杂的形状、几何尺寸、分布和夹杂间的相互影响，在夹杂的体积份数较大，如大于０．３时已不能有效地预报复合材料的有效弹性模量，随后介绍了近来才发展起来的一种新方法─—相关函数积分法，理论与实验的结果的比较表明，该方法在夹杂体积份数较大时仍然有效。

This paper gives a review on the studies of the effective elastic moduli of composite materials with inclusions,which include the self-consistent theory,the differential method,Eshelby-Mori-Tanaka's method,and Hashin and Shtrikman's variational method etc.Since the microstructural characteristics of composites such as the shape,geometric size and distribution of inclusions and interaction between inclusions, have not been properly considered by the theories indicated above, the effective elastic moduli of composite materials are not successfully predicted when the volume fraction of inclusions is larger than 0.3. Subsequently, a new method which has recently been developed-the integral method of the related function-is introduced. As a comparison with experimental results, it is shown that the latter method is still effective when the volume fraction of inclusions is larger.