裂纹尖端附近三维效应区的有限元分析

基于Kane-Mindlin关于弹性平板面内问题位移的运动学假设,本文首次推导了一种考虑板厚效应的平板面内问题的有限元格式。将Kane-Mindl.n假设推广到弹塑性问题,推导了相应的有限元方程.对双边及中心裂纹拉伸试件的计算结果表明,裂纹尖端附近的弹性三维效应区尺寸和板厚相当.对线性硬化弹塑性材料,当切线模量E_t和弹性模量E之比E_t/E大于0.2时,三维效应区在两倍板厚以内.

THE FINITE ELEMENT ANALYSIS FOR THREE-DIMENSIONAL EFFECTS NEAR CRACK TIPS

Based on the Kane-Mindlin kinematic assumptions for the quasi-threedimensional deformation of plates in extension, a new finite element formulation considering the effects of plate thickness is presented. The Kane-Mindlin assumptions are extended to elastic-plastic problems and the corresponding finite element formulation is also established. Computational results of double edge cracked panels and central cracked plates in tension show that, (a) the sizes of 3-D elastic deformation zones near the crack tips are close to the plate thickness, (b) in the case of plastic deformation, the 3-D zones increase with the decrease of plastic tangential modulus E_t and are confined within the extent of twice of the plate thickness near the crack tips when E_t/E is greater than 0.2.