Crack tip higher order stress fields for functionally graded materials with generalized form of gradation  

作　　者：燕秀发 钱七虎 卢红标 王玮 孙翱 

机构地区：[1]Engineering Institute of Engineering Corps,People's Liberation Army University of Science and Technology [2]People's Liberation Army 91550 Unit

出　　处：《Journal of Central South University》2010年第6期1177-1184,共8页中南大学学报（英文版）

基　　金：Project(20080431344) supported by Postdoctoral Science Foundation of China;Project(51021001) supported by the National Natural Science Foundation of China

摘　　要：A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.A generalized form of material gradation applicable to a more broad range of functionally graded materials （FGMs） was presented. With the material model, analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis. Then, a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution. The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs. The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor, but also gives consistent estimates as the distance away from the crack tip increases Hence, the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.

关 键 词：functionally graded materials crack tip nonhomogeneity asymptotic analysis higher order stress field 

分 类 号：O346.1[理学—固体力学]