复杂载荷下偏心穿透裂纹应力强度因子的计算方法

提出了三维矩形平板内偏心穿透裂纹承受复杂非线性载荷下,仅含有3个系数的通用权函数。采用有限元法获得了三维矩形平板裂纹体模型下的3组参考应力强度因子,结合二元拉格朗日插值法获得了通用权函数系数。进行了自洽性验证以及裂纹面上承受简单3次、5次、7次、复杂幂函数应力分布和残余应力分布下通用权函数的验证。结果表明,通用权函数的自洽性误差在0.9%以内；裂纹面上承受复杂幂函数应力分布时,通用权函数法的误差在4.5%以内；裂纹面承受残余应力分布载荷时,通用权函数法的误差在8.5%以内。说明所提出的通用权函数具有较高的计算精度,可以满足工程中高效、准确地计算偏心穿透裂纹承受任意复杂非线性载荷下的应力强度因子需求。 

Calculation method of stress intensity factors of eccentric through cracks subjected to complex loading

General weight functions only containning three coefficients for eccentric through cracks in a 3-D rectangular plate subjected to complex nonlinear loading were proposed. Three sets of reference stress intensity factors of 3-D rectangular cracked plate were obtained by the finite element method, and combining with binary Lagrange interpolation method, the three coefficients of each general weight function were also obtained. Self-consistency of general weight functions was verified and general weight functions were also validation when the crack surface was loaded by simple third-order, fifth-order, seventh-order, complex power law stress distributions and the residual stress distribution were conducted. Results showed that, the self-consistency error of general weight functions was smaller than 0.9%, when the crack surface was loaded by the complex power law stress distribution, error of the weight function method was smaller than 4.5%, when the crack surface was loaded by the residual stress distribution, error of the weight function method was smaller than 8.5%. This indicates that the proposed general weight functions has high computing accuracy, which could meet the challenge of calculating stress intensity factors of eccentric through cracks subjected to arbitrary complex nonlinear loading efficiently and correctly in engineering.