13th International Conference on Fracture June 16–21, 2013, Beijing, China 1 Elastodynamic analysis of a finite crack at an arbitrary angle in the functionally graded material under in-plane impact loading Sheng-Hu Ding*, Xing Li School of Mathematics and Computer Science, Ningxia University, Yinchuan, 750021, China *Corresponding author:Email:dshsjtu2009@163.com Abstract The plane problem for a infinite functionally graded material containing a finite crack subjected to the dynamic impact loads is investigated. The crack arbitrarily oriented with respect to the direction of property gradient is considered. Based on the use of Laplace and Fourier integral transforms, formulation of the transient crack problem is reduced to solving a system of Cauchy-type singular integral equation in the Laplace transform domain. The crack-tip response in the physical domain is recovered via the inverse Laplace transform and the values of dynamic stress intensity factors are obtained as a function of time. The effects come from the crack orientation and the nonhomogeneous material parameter on the dynamic stress intensity factors are discussed graphically. Keywords Functionally graded material, Arbitrarily oriented crack, Singular integral equations, Dynamic stress intensity factors 1. Introduction With the application of functionally gradient materials in engineering, most of the current researches [1-5] on the fracture analysis of the FGMs interface have been devoted to the FGMs interlayer and the interface between the functionally graded material (FGM) coating and the homogeneous substrate. However, to date, only a few articles were devoted to the dynamic fracture mechanics of FGMs. Among these limited work, Atkinson [6] first studied the crack propagation in media with spatially varying elastic properties. Li and Wen [7] investigated the dynamic stress intensity factor of a cylindrical interface crack located between two coaxial dissimilar homogeneous cylinders that are bonded with a functionally graded interlayer and subjected to a torsional impact loading. The transient response of a functionally graded coating-substrate system with an internal or edge crack perpendicular to the interface [8] has been studied under an in-plane impact load. Recently, the dynamic fracture problem of the weak-discontinuous interface between a FGM coating and a FGM substrate have been studied by Li and his coauthors [9]. Ding and Li [10] studied the dynamic stress intensity factor of collinear crack-tip fields in bonded functionally graded finite strips. For the arbitrarily oriented crack, Bogy [11] studied the problem of an arbitrarily oriented crack terminated at the bonded interface. For FGMs, till 1994 when Konda and Erdogan [12] considered the mixed mode crack problem in a nonhomogeneous elastic medium. Under the condition of antiplane shear impact, the corresponding dynamic stress intensity factors for a crack in a homogeneous material when a graded stip between dissimilar half-planes was evaluated by Choi [13]. The objective of the present paper is to provide a theoretical analysis of the dynamic behavior of a finite crack in the functionally graded material subjected to in-plane impact loading. To solve the proposed crack problem, the Fourier integral transform method is employed together with Laplace transform, leading to the derivation of a singular integral equation with a generalized Cauchy kernel. It is a simple and convenient method for solving this problem. In the numerical results, the values of mixed-mode stress intensity factors (SIFs) are provided as a function of crack orientation angle. The effects come from the crack orientation and the nonhomogeneous material parameter on the dynamic stress intensity factors (DSIFs) are discussed graphically.
RkJQdWJsaXNoZXIy MjM0NDE=