无限大功能梯度材料反平面裂纹应力场

Stress Field of the Anti-plane Crack in an Infinite Orthotropic Functionally-graded Material

主要研究了无限大功能梯度正交各向异性材料的反平面裂纹问题。材料物性参数模型假定为三次幂函数模型。文中采用积分变换-对偶积分方程方法,通过数值求解对偶积分方程并考虑修正Bessel函数的渐进特性,推导出了裂纹尖端应力场及应力强度因子。利用数学软件分析了不均匀系数r以及裂纹长度a对无量纲应力强度因子ψ(1)的影响,结果显示ψ(1)随着r的增加而增加,随着a的增加而增加。

The problem of anti-plane crack in infinite orthotropic functionally-graded materials was studied in this paper. The shear modulus of the functionally graded material were assumed to vary proportionately in terms with power function, then the dual integral equations were numerically solved and the asymptotic behavior of Bessel function were considered to be revised, the local stress field and stress intensity factor around the crack tip were de- rived by using of integral transforms-dual integral equations. And the variation curves of the dimensionless stress in- tensity factorψ（ 1 ） with the nonhomogeneous coefficient r and the crack length a have been obtained by using the mathematical software. The results showed that the stress intensity factor ψ （ 1 ） increases with the increasing r and a.