FGM受冲击载荷作用下裂纹尖端应力的数值分析  

Numerical analysis of crack-tip stress fields in FGMs under impact loading

作　　者：毕贤顺[1] 陈华艳[1] 

机构地区：[1]福建工程学院土木工程系,福建福州350108

出　　处：《辽宁工程技术大学学报（自然科学版）》2011年第4期522-525,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：福建省科技厅资助省属高校基金资助项目(2008F5005)

摘　　要：为了解决梯度参数和特征尺寸对裂纹尖端应力场的影响,根据非局部理论对含裂纹无限大板在反平面冲击载荷作用下的问题进行研究,假设材料的剪切模量和密度为指数形式模型,泊松比为常数,利用拉普拉斯和傅立叶变换将混合边界值问题简化为对偶积分方程。通过Jacobi多项式和Schmidt方法求解对偶积分方程,获得裂纹尖端应力场。结果表明:裂纹尖端应力无奇异性,裂纹尖端应力随着时间的增加先增大而后降低并随着梯度参数和特征尺寸的增加而降低。In order to investigate the influence of the grade parameters and the characteristic dimension on the crack-tip stress fields in Functionally Graded Materials（FGMs）,a crack in an infinite plate of FGMs subject to anti-plane shear impact loading is analyzed using non-local theory.The shear modulus and mass density of FGMs are assumed to be of exponential form and the Poisson＇s ratio is assumed to be constant.The mixed boundary value problem is reduced to dual integral equation through the use of Laplace and Fourier integral transform method.The crack-tip stress fields in FGMs are obtained by solving the dual integral equations using Jacobi＇s polynomials and Schmidt＇s method.The numerical results show that no stress singularity is presented at the crack-tip and the stress near the crack tip tends to increase with time at early stage and then decrease in amplitude.At the same time,the stress at crack tip decreases with the increase of the grade parameters and the characteristic dimension.

关 键 词：功能梯度材料 裂纹 应力场 积分变换 非局部理论 对偶积分方程 裂纹尖端应力场 混合边界值问题 

分 类 号：O346[理学—固体力学]