When the dimension of a structure falls to the micro-/nanoscale, surface effect is significant and plays a key role in affecting the mechanical behavior. This article studies the influence of surface elasticity on the stress intensity factor of an antiplane shear crack embedded in an elastic strip made of functionally graded materials. Surface elasticity is applied on the strip surfaces and crack faces, and classic elasticity is invoked for the strip interior. An antiplane shear crack problem is solved for a symmetric FGM with a crack parallel to the strip surfaces. The associated problem is converted to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces through the Fourier transform and then to a singular integro-differential equation with Cauchy kernel. The Galerkin method is applied to expand the crack face displacement as a Chebyshev series, and the singular integro-differential equation reduces to a system of algebraic linear equations. Stress intensity factors at the crack tips and the out-of-plane displacement on the crack faces are calculated numerically. It is found that surface elasticity and gradient index strongly alter the bulk stress and its intensity factors near the crack tips. Positive surface shear modulus decreases the mode III stress intensity factors and negative surface shear modulus has an opposite behavior. The influence of the variation of material gradient on the mode III stress intensity factors is expounded in graph.

当结构的尺寸降到微米/纳米级时，表面效果会很显着，并且在影响机械性能方面起着关键作用。本文研究了表面弹性对嵌入功能梯度材料制成的弹性条中的反平面剪切裂纹的应力强度因子的影响。表面弹性作用在带材表面和裂纹面上，经典的弹性作用于带材内部。对于具有平行于带材表面的裂纹的对称FGM，解决了反平面剪切裂纹问题。相关的问题通过傅立叶变换转换为裂纹面上的平面外位移的超奇异积分微分方程，然后再转换为具有柯西核的奇异积分微分方程。应用Galerkin方法以Chebyshev级数的形式扩展裂纹面位移，并将奇异的积分微分方程简化为代数线性方程组。数值计算裂纹尖端的应力强度因子和裂纹面的平面外位移。发现表面弹性和梯度指数强烈改变了裂纹尖端附近的整体应力及其强度因子。正表面剪切模量会降低III型应力强度因子，负表面剪切模量会产生相反的行为。图中阐述了材料梯度变化对III型应力强度因子的影响。数值计算裂纹尖端的应力强度因子和裂纹面的平面外位移。发现表面弹性和梯度指数强烈改变了裂纹尖端附近的整体应力及其强度因子。正表面剪切模量会降低III型应力强度因子，负表面剪切模量会产生相反的行为。图中阐述了材料梯度变化对III型应力强度因子的影响。数值计算裂纹尖端的应力强度因子和裂纹面的平面外位移。发现表面弹性和梯度指数强烈改变了裂纹尖端附近的整体应力及其强度因子。正表面剪切模量会降低III型应力强度因子，负表面剪切模量会产生相反的行为。图中阐述了材料梯度变化对III型应力强度因子的影响。正表面剪切模量会降低III型应力强度因子，负表面剪切模量会产生相反的行为。图中阐述了材料梯度变化对III型应力强度因子的影响。正表面剪切模量会降低III型应力强度因子，负表面剪切模量会产生相反的行为。图中阐述了材料梯度变化对III型应力强度因子的影响。