功能梯度板条Ⅲ型运动裂纹问题研究  

Moving Mode Ⅲ Crack in Functionally Graded Strip

作　　者：程站起[1] 仲政[2] 

机构地区：[1]郑州大学,郑州450001 [2]同济大学,上海200092

出　　处：《应用力学学报》2008年第1期62-65,182,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金重点项目(10432030);国家杰出青年科学基金(10125209)

摘　　要：现存文献关于梯度材料断裂问题的研究大都是假设材料参数为坐标的指数函数或幂函数,而其它函数形式较少采用。本文假设功能梯度材料剪切模量和密度的倒数均为坐标的线性函数,而泊松比为常量,研究功能梯度板条的反平面运动裂纹问题。利用Fourier积分变换技术和传递矩阵法将混合边值问题化为一对奇异积分方程,通过数值求解奇异积分方程获得板条运动裂纹在反平面载荷作用下的动态应力强度因子,并讨论了裂纹运动速度、裂纹相对尺寸、以及材料非均匀性对动态应力强度因子的影响,结果证明梯度参数、裂纹速度和几何尺寸对材料动态断裂行为有显著影响。In the existing papers, most researchers assume that the material properties of functionally graded material get in accordance with the exponential function or power function. The problem of a moving anti-plane crack in a functionally graded strip is investigated provided the reciprocals of the shear modulus and the density are both linear functions of the coordinate, while Possion ratio keeps constant. With the Fourier integral transform technique and the transfer matrix method, the mixed boundary problem is reduced to acouple of singular integral equations. The mode III dynamic stress intensity factor is obtained by solving the singular integral equations numerically. The influences of the velocity and the size of the moving crack and the material graded parameter on the stress intensity factors is discussed. The numerical results show that the graded parameter, geometrical parameters and velocity of the moving crack exert significant effects on the dynamic fracture behavior.

关 键 词：功能梯度材料 运动裂纹 应力强度因子 板条 

分 类 号：O344.3[理学—固体力学]