无限大板功能梯度材料反平面裂纹问题的研究

Study on Anti-plane Crack of Functionally Graded Material in Infinite Plates

对功能梯度材料在无限大板上的静态反平面裂纹问题作出了探究。材料物性模型按负指数幂的特定形式变化。利用积分变换—对偶积分方程法且考虑修正贝塞尔函数的渐进性,通过解析法将方程进行相应的转化,求得裂纹尖端应力强度因子的解析式。考查了不均匀系数、裂纹长度、梯度参数对应力强度因子的影响。结果显示,不均匀系数r与应力强度因子正相关;裂纹长度a与应力强度因子正相关;梯度参数c与应力强度因子负相关。

The static antiplane crack of functionally graded materials on infinite plates is discussed.The material physical properties model varies according to the specific form of negative exponential power.By using the integral transformation dual integral equation method and considering the asymptotic behavior of the modified Bessel function,the corresponding transformation of the equation is carried out by the analytical method,and the analytical expression of the stress intensity factor at the crack tip is obtained.The effects of inhomogeneity coefficient,crack length and gradient parameters on stress intensity factor were investigated.The results show that the inhomogeneity coefficient r is positively correlated with the stress intensity factor,the crack length a is positively correlated with the dimensionless stress intensity factor,and the gradient parameter c is negatively correlated with the stress intensity factor.