计算平面Ⅰ、Ⅱ型复合应力强度因子的半权函数法

SEMI-WEIGHT FUNCTION METHOD ON COMPUTATION OF MIXED-MODE STRESS INTENSITY FACTORS

给出计算一般平面裂纹问题应力强度因子的半权函数方法。该方法引入两个满足裂纹面零应力条件、平衡方程以及裂尖位移具有r- 1 2 奇异性的虚拟位移与应力函数的解析表达式 ,即半权函数。从功能互等定理出发 ,结合从裂纹下缘到上缘绕裂尖任意路径的位移与应力的近似值 ,得到Ⅰ、Ⅱ复合型应力强度因子KⅠ 和KⅡ 积分形式的表达式。由于在积分中避开了裂尖的奇异性 ,因此即使采用较粗糙的模型或方法得到的近似值 ,也可以得到精度较高的KⅠ 、KⅡ 。相对于权函数法 ,本方法的限制条件较少 ,半权函数易于获得 ,实用性强 ;相对于有限元法计算量小 ,模型建立简便。

Semi-weight function method was used and developed to solve general plane fracture problems. Two sets of analytical expression of semi-weight functions were obtained. Integral expression of composite stress intensity factors, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. These semi-weight functions satisfy conditions of equilibrium equation, stress and strain relationship, special singularity of displacement near the crack tip and the traction free on the crack surface. The singularity of stress near crack tip is avoided. The approximate values can be calculated from numeric methods. FEA was used to calculate approximate values in this paper. There were no singular elements be used in modeling. With rough mesh size, the semi-weight function method can get more precision result than that from pure FEA with fine mesh size and singular elements on crack tip. The calculation results of applications show that among high precision calculation methods, compared with the weight function method, this method provides applicable analytical expressions of semi-weight functions and in less restrict conditions. Compared with finite element method, it needs fewer amounts of calculation and simple and convenient FEA model.