基于原子内聚力与表面能等效的内聚裂纹模型

A Surface-energy Equivalent Cohesive Crack Model Based on Atomic Cohesive Force

从非局部连续介质理论出发,采用一种新的理性力学方法对裂纹前缘内聚应力分布规律进行研究。首先,在内聚裂纹表面引入非局部应力边界条件,从而将内聚区内表面诱发张力(非局部表面残余)与内聚应力等价联系起来;然后,利用能量平衡关系,得到仅与表面能密度相关的I型裂纹内聚力新的本构方程。最后,在推导结果的基础上,计算一个具体的脆性断裂算例研究内聚区内表面能与内聚应力随裂纹张开位移(COD)变化的分布规律。由计算结果发现,裂纹尖端应力奇异性消除,且应力最大值不一定出现在裂纹尖端,而是发生在裂纹尖端周围的内聚区内。

Starting with the nonlocal continuum theory, a new rational mechanics method is applied to study logically the cohesive stress law of ahead of a crack tip. First, the equivalence between the cohesive stress and the surface-induced traction （nonlocal surface residual） within the cohesive zone is established by introducing nonlocal stress boundary conditions on the crack surface. Then, by means of the energy balance relation, a new cohesive stress law of Mode I crack is obtained which is only concerned with the surface energy density within the cohesive zone. On the basis of the results, a concrete example of brittle balance is calculated to investigate the distribution of surface energy and cohesive stress which changes with the variation of crack opening displacement （COD）. Finally, a summary of the study is provided and several conclusions are made. The results show that the stress singularity at the crack tip is removed, and the maximum stress may occur within the cohesive zone away from thc crack tip.