任意裂纹面荷载作用下界面断裂分析

Analysis of interface crack with arbitrary crack tractions

摘要:

为研究裂纹面上作用的荷载对裂纹稳定性的影响，本文基于比例边界有限元方法提出裂纹面作用有任意方向、任意大小面荷载的界面应力强度因子求解模型.界面裂纹具有复数形式的应力奇异性指数，在任意裂纹面荷载作用下其奇异应力场更为复杂.应用本模型，径向的位移和应力可解析求解，无需网格细分即可自动反映裂尖的应力奇异性.裂纹面上的任意荷载首先可分解成平行于裂纹面以及垂直于裂纹面的分量，并进一步分解成有限项幂函数的和.对每个幂函数荷载解析求解，基于线性叠加原理获得结构在全部荷载作用下的解.该模型对各向同性材料和各向异性材料均适用.文中通过板承受裂缝面荷载时的应力强度因子求解的多个算例对该模型进行了验证和应用，对板的几何尺寸和双材料参数进行了敏感性分析，并应用于重力坝坝踵界面裂缝在水压力作用下的应力强度因子求解.

Abstract:

This paper presents a model for solving interface crack with arbitrary crack traction based on the Scaled boundary finite element method to study the significant influence of the traction acting on the crack faces on the stability of a crack. The order of stress singularity is complex for an interface crack. With the existence of crack traction, the stress singularity is more complicated. Base on the proposed model, stress and displacement are solved analytically in the radial direction, and the stress singularity at crack tip is obtained with high precision without refined mesh. The arbitrary crack traction is firstly decomposed to one component parallel to the crack and the other one perpendicular to the crack, then both the two components are expressed as the sum of a limited number of power functions respectively. The effect of each power function is solved analytically. According to the Linear superposition principle, the solution of a structure with arbitrary crack traction can be obtained. The proposed model is effective for both anisotropic and isotropic materials. The model is verified by several plates with crack tractions, in which stress intensity factors are calculated. Sensitivity analysis is also performed concerning the plate geometry and material properties. Finally the model is applied to solve the stress intensity factors of an interface crack of a gravity dam filled with water.