含随机分布裂纹材料的剪切模量

Shear modulus of materials with randomly distributed cracks

材料内部的微裂纹会造成材料或结构的各项机械性能指标下降,其中包括剪切模量。随机分布的微裂纹对剪切模量的影响与其分布的规律有关,分析这种影响需要利用细观损伤力学理论,采用的方法有平均化方法和统计方法,同时还要结合弹性力学理论的复变函数法。分析一个受剪切载荷作用的薄板内部的一个代表性单元,其内含有按某种规律分布的随机微裂纹,先利用复变函数法和平均化法求出每一条微裂纹附近的局部剪应力和局部剪应变,再应用统计学方法推导出代表性单元的总体剪应力和剪应变,继而得到它的剪切模量。在分析过程中特别考虑了闭合裂纹面间的摩擦效应,使得模型更符合客观实际。针对微裂纹具体的一种分布进行了相关的数值计算,结果表明,薄板的剪切模量随微裂纹密度增加而下降的趋势符合预期。

Micro-cracks in materials will lead to the decline of various mechanical properties of materials or structures including shear modulus.The effect of randomly distributed micro-cracks on shear modulus is related to its distribution law.The analysis of this effect needs to use the meso-damage mechanics theory,including averaging method and statistical method,as well as the complex variable function method of the theory of elasticity.A representative element in a thin plate under shear load is analyzed,which contains random micro-cracks distributed according to a certain law.Firstly,the local shear stress and local shear strain near each micro-crack are calculated by using the complex variable function method and averaging method,and then the overall shear stress and shear strain of the representative element are deduced by using the statistical method.Then its shear modulus is obtained.In the analysis process,the friction effect between closed crack surfaces is specially considered,which makes the model more in line with the objective reality.The results show that the decreasing trend of shear modulus with the increase of micro-crack density is in line with the expectation.