平板裂纹前缘三维效应区的弹性力学分析

AN ANALYSIS 0N THREE-DIMENSIONAL EFFECTS NEAR THE TIP OF A CRACK IN AN ELASTIC PLATE

本文利用Kane和Mindlin关于弹性乎板面内问题位移的基本假设及Fourier变换求解了无限大板的I型裂纹问题,得到了裂纹尖端应力位移场的渐近形式、应力强度因子随板厚的变化规律以及板厚对裂纹前缘三维效应区的影响.研究表明,对线性硬化材料,在塑性切线胰量不太小的情况下,线弹性分析的结果可近似适用于弹塑性材料.

An infinite plate containing a finite through crack under tensile loading is analysed by Fourier transform based on Kane-Mindlin kinematic assumptions for the uasi-three-dimensional deformation of plates in extension. The asymptotic expressions of stress and displacement fields near the crack tip, the variation of stress intensity factor with the plate-thickness and the three-dimensiodal deformation zone near the crack tip are investigated. The results of analysis show that, (a) the crack-tip stress and displacement fields accounting for the plate-thickness effects are different from the plane stress solutions and this is true even for extremely small parameter ε(=?). In a very small egion near the crack tip, plane strain solutions prevail; (b) the ratio of the stress intenity factor K_1 to the corresponding plane stress one K_1, K_1/K_1~0, approaches 1/(1-ν~2) as s tends to zero; (c) plane stress soiutions can give satisfactory results for points a distance from the crack tip greater than about three-fourths of the plate-thickness; (d) the linear elastic result for the zone of three-dimensional effects is approximately valid for an elasto-plastic material with linear strain-hardening when plastic tangential moudulas E_t is not very small.