随机分布共线微裂纹的强相互作用

STRONG INTERACTION AMONG RANDOMLY DISTRIBUTED COLLINEAR MICROCRACKS

微裂纹串接为宏观灾难性裂纹的过程取决于相邻微裂纹的强相互作用。微裂纹的分布规律影响材料的强度和韧性。本文研究简单的共线微裂纹构型,确定由于微裂纹长度和韧度尺寸的统计分布所产生的影响。研究结果预计了脆性材料的尺度效应,即对于相同密度的微裂纹分布,大尺寸构件的强度比小尺寸构件要低。计算还表明脆性体的强度随微裂纹分布函数标准方差的增加而减小。

The linking process form microcracks to a fatal macroscopic crack is dominated by the strong interaction among neighboring microcracks. The distribution of microcracks modifies the strength and toughness of a material. The present paper focuses on the simple case of collinear microcracks, and quantifies the influence by the statistical distribution of crack lengths and ligament sizes. We predict the scale dependency of the brittle materials. A specimen of large size would have lower strength than a small specimen with the same microcrack density. Furthermore, the strength of a brittle solid decreases as the standard deviation of those distribution increase.