裂纹方向对剪切损伤模量的影响

The influence of crack direction on shear modulus of damage

损伤力学是研究含缺陷介质损伤演化及破坏的一门学科,研究方法主要分为2种:唯象的宏观损伤力学和细观损伤力学。其中,细观力学理论更容易描述损伤过程的力学本质。对于脆性和准脆性材料,可以利用弹性力学理论来分析细观损伤机理。模拟一个受组合载荷作用且中心含一条裂纹的单元体,裂纹的方向决定了所受载荷的组合方式,其中受压剪方式作用下的裂纹还考虑了裂纹面间的摩擦效应。利用弹性力学理论的复变函数法可以分析单元体边界的位移场和应力场,通过某种平均化的方法,可得到单元体的总体平均剪应变和总体平均剪应力,进而得到与裂纹方向有关的单元体的剪切损伤模量。计算结果表明,裂纹面间的摩擦效应对剪切损伤模量的影响不可忽视。此种方法还可用来分析其他与损伤相关的力学性能。

Damage mechanics is a subject that studies the evolution and failure of the medium containing defect.There are two main research methods：phenomenological macro damage mechanics and meso damage mechanics.Among them,the meso mechanics theory is more likely to describe the mechanical essence of the damage.The theory of elasticity can be used to analyze the meso-mechanism of the damage for brittle and quasi-brittle solids.A representative element with one micro crack under various loads is studied.In these combined loads,the frictional effect of crack surfaces is considered under compression and shearing.Based on the theory of elasticity,using the method of function of the complex variable,the displacement field and stress field of the boundary can be obtained.It can get the total average shear strain and the average shear stress by some averaging method,further can get the shear damage modulus of the element which related to the direction of the crack.The calculate results show that the effect of the shear damage modulus caused by friction can not be neglected.The method can also be used to analyze other mechanical properties related to damage.