含平行币状裂纹复合材料的强度准则

对于含平行币状裂纹材料表现出来的横观各向同性, 引入Walpole’s基来表示和计算。通过构造能量密度支函数来定义复合材料的宏观应力, 在非线性均质化方案中采用了基于能量原理的修正割线法, 考虑了静水压力对偏应变的影响。研究了含微裂纹材料弹性刚度张量的三种解法: 稀疏解法、 MT法和PCW法, 获得了含平行币状裂纹材料具有Drucker-Prager型式的宏观强度准则, 研究结果表明, 材料的弹性模量比和宏观摩擦系数随着裂纹的体积分数增加而减小, 并且裂纹外形比越小, 稀疏解法、 MT法和PCW法对材料的弹性模量比和宏观摩擦系数预测曲线差异越大。

Strength criterion of the composite with a set of parallel penny-shaped cracks

The materials with a set of penny-shaped cracks exhibited transversely radically isotropic. The Walpole’s base was introduced for tensorial represtation and calculation. The macroscopic stress states of the composites were defined by introducing the energy density supporting function. In order to capture the local deviatoric effects induced by a hydrostatic loading, the modified secant method based on energy approach was adopted in non-linear homogenized. Three schemes of macroscopic elastic moduli for microcracks materials were considered, i.e. dilute scheme, MT scheme and PCW scheme. It can be found from the research result that the elastic modulus ratios and the macroscopic friction coefficient tend to decrease with the increase of the crack volume fraction. The smaller the crack aspect ratio is, the larger of the difference is between the predictions by the dilute scheme, MT scheme and PCW scheme.