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纤维增强复合材料中某根纤维断裂后,断口作为裂纹向何处发展?它可以向纤维和基体的界面发展形成界面脱粘,也可向基体发展,造成基体开裂,从而殃及邻近纤维。另外,一根纤维的断裂会在其邻近纤维中造成应力集中。本文采取轴对称边界无法对这些问题进行仔细研究。本文假定纤维在基体中成六角形分布,即每根纤维周围有六根纤维,均匀地分布在以该纤维为中心的圆周上。为应用轴对称边界元,在具体计算时又把这六根纤维近似地等价为一个与所论纤维同心的圆筒。在这圆筒外面与这圆筒相邻的十二根纤维构成第二层圆筒。如此等等。对裂纹发展方向的判定则采用能量释放率准则。本文还对于纤维基体模量比、摩擦力和纤维体积比对裂纹发展和裂口周围纤维中的应力集中的影响作了系统的研究。
When a certain fiber in a fiber-reinforced composite material is broken, where does the fracture develop as a crack? It can develop interface debonding to the interface between the fiber and the matrix, and can also develop to the matrix, causing the matrix to crack, thus affecting adjacent fibers. In addition, the rupture of one fiber can cause stress concentrations in its adjacent fibers. In this paper, the use of axisymmetric boundaries can not be studied carefully on these issues. This paper assumes that the fibers have a hexagonal distribution in the matrix, that is, six fibers per fiber, uniformly distributed over the circumference centered on the fiber. In order to apply the axisymmetric boundary element, in the concrete calculation, the six fibers are approximately equivalent to a cylinder concentric with the fiber in question. Twelve fibers outside the cylinder adjacent to the cylinder make up the second cylinder. And so on. The determination of the direction of crack development uses the energy release rate criterion. The effects of fiber matrix ratio, friction and fiber volume ratio on the development of cracks and the stress concentration in the fibers around the gap were systematically studied.