Crack-Tip Fields For Inhomogeneous Materials

Functionally Graded Materials (FGMs) was developed due to the needs of the aeronautic and astronautic fields. Because of the influences of manufacture technology, working conditions and so on, cracks will appear in FGMs and cause the structure to fail. So the cracking problem of FGMs attracts the attention of many researchers and engineers. In this paper, an isoparametric graded finite element method is proposed to analysis the mechanical behaviors of FGMs. Some typical plane elasticity problems are calculated. The crack tip fields of FGMs are discussed in detail.Firstly, to simulate the spatial inhomogeneity of Young's modulus, a graded finite element is presented within the framework of a generalized isoparametric formulation and some plane elasticity problems involving inhomogeneous materials are studied. The results calculated are compared with these of conventional, homogeneous elements to show its advantage. The boundary value problems involving inhomogeneous materials are studied and the stress fields of structure are discussed in detail. Several engineering examples are presented to show that FGM lead to stress redistribution with a lower stress concentration factor.Secondly, the crack tip fields for finite size plate with single or double edge cracks subjected to common loading conditions are considered. The influence of dimensionless parameters representing the material inhomogeneity and the size of the crack and loading conditions to the stress intensity factors and crack open displacements are given.Lastly, the problem of a periodic array of parallel cracks in a functionally graded material is investigated. The influence of angle to stress intensity factors is discussed when there is certain angle between gradient and the crack. Numerical results and figures are obtained to illustrate the stress intensity factor as a function of the distance of adjacent cracks for different values of the material inhomogeneity.