尺寸对无限长条功能梯度材料裂尖应力场影响

Influences of strip length on stresses at crack tip for functionally graded material

假设剪切摸量沿厚度方向连续且为指数形式模型,给出了含有限长裂纹的无限长条功能梯度材料在反平面剪应力载荷作用下的裂纹问题。利用非局部线弹性理论和积分变换方法,将混合边界值问题简化对偶积分方程,最后通过Schmidt方法对裂纹尖端的应力场和位移场进行了求解。与经典理论的解答不同,裂纹尖端应力为有限值,裂纹尖端应力幅值随长条高度的增加而降低。

This article provides a theoretical and numerical treatment of a finite crack subjected to an anti-plane shear loading in an infinite strip of functionally graded material （FGM）. It is assumed that the shear moduli varies continuously in the thickness direction and is of exponential form. The mixed boundary value problem is reduced to a dual integral equation by means of nonlocal linear elasticity theory and integral transform method The stress field and displacement field for an infinite strip of FGM are solved near the tip of a crack by using Schmidt＇s method. Unlike the classical elasticity solution, the magnitude of stress at the crack tip is finite, and it is found that the stress at the crack tip decreases in magnitude as the strip length is increased.