功能梯度材料裂纹尖端动态应力场

研究受反平面剪切作用的功能梯度材料动态裂纹问题，通过积分变换-对偶积分方程方法推出了裂纹尖端动态应力场，时间域内的动态应力强度因子由Laplace数值反演获得，研究结果表明功能梯度材料的梯度越大，相应的裂纹问题的动态应力强度因子值越低。

DYNAMIC STRESS FIELD AROUND THE CRACK TIP IN A FUNCTIONALLY GRADED MATERIAL

From the viewpoints of applied mechanics, Functionally Graded Materials (FGMs) are nonhomogeneous solids. The nonhomogeneity of FGMs has a great influence on their mechanical behavior. Recent years, significant attention has been paid to the fractural behavior of FGMs. However, the studies mainly concentrated on static problems. Report on dynamic fracture mechanics of FGMs is very few. In this paper, the problem of a Griffith crack in an unbounded FGM subjected to antiplane impact loading is considered. The main objective is to obtain the dynamic stress fields around the crack tip in FGMs and to investigate the effect of material nonhomogeneity on dynamic stress intensity factor. By using Laplace transform for the time variable and Fourier transform for the space variable, the problem is reduced to a pair of dual integral equations. The solution of the dual integral equations is expressed with a Fredholm integral equation of the second kind. The dynamic stress fields around the crack tip are obtained by considering the asymptotic behavior of Bessel function. The dynamic stress intensity factor in time domain is obtained by Laplace numerical inversion technique. The influence of material nonhomogeneity on the dynamic stress intensity factor is revealed graphically.