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本文应用GMC方法计算了纤维在规则排列和随机排列时单向纤维加强复合材料的总体弹性系数。结果表明,在一定纤维体积比范围内,虽然纵向弹性模量不受纤维排列方式的影响,但是复合材料的横向弹性模量和横向剪切模量受纤维排列方式的影响较大。所以,在考察复合材料的横向弹性常数时,应该考虑纤维排列方式的影响。在相同纤维比的情况下,正方形排列和正方形对角排列所得的弹性常数是上下界,而六角形排列和随机排列的结果位于以上两者之间。当纤维比较小时(小于20％),纤维的排列方式对各弹性常数均无明显影响。本文的结果在工程应用中有指导意义。
In this paper, the overall elastic modulus of unidirectional fiber-reinforced composites is calculated by GMC method when the fibers are arranged regularly and randomly. The results show that the transverse elastic modulus and transverse shear modulus of the composites are greatly affected by the fiber arrangement, although the elastic modulus in the longitudinal direction is not affected by the arrangement of fibers at a certain fiber volume ratio. Therefore, in examining the transverse elastic constants of composite materials, the effect of fiber arrangement should be considered. In the case of the same fiber ratio, the elastic constants obtained by the diagonal arrangement of the square and the square are the upper and lower bounds, and the hexagonal arrangement and the random arrangement result lie between the two. When the fiber is relatively small (less than 20%), the fiber arrangement has no significant effect on the elastic constants. The result of this paper is instructive in engineering application.