The Higher Order Crack Tip Fields for FGMs Spherical Shell with Reissner’s Effect Yao Dai1, Xiao Chong1,*, Lei Zhang1 1 The department of mechanical engineering, the academy of armored force engineering, Beijing, 100072, China * chongxiao2005@163.com Abstract Based on the theory of shells considering the transverse shear deformation or Reissner’s effect, the crack tip fields are investigated for a cracked spherical shell made of isotropic functionally graded materials (FGMs). The elastic modulus and Poisson’s ratio of the FGMs are assumed to be the linear function of x and a constant, respectively. The governing equations, i.e. the system of the tenth order partial differential equations with variable coefficients are first derived. Then, the eigen-expansion method is employed to the system, and the higher order crack tip fields of the cracked spherical shell are obtained. As the in-homogeneity parameter approaches to zero, the solutions degenerate to the corresponding fields of isotropic homogeneous spherical shell with Reissner’s effect. Keywords crack tip fields, Reissner’s effect, spherical shell, FGMs 1. Introduction As the gradient can be tailored to meet specific needs and the macroscopic interfaces of traditional composites are eliminated, the functionally graded materials have been widely applied in engineering. However, due to the limitations of the manufacture technology, a large number of micro-cracks cannot be avoided in functionally graded plates and shells, which would seriously endanger the security of these structures. Therefore, the fracture analysis for functionally graded shells is necessary. It is well known that Kirchhoff classical theory does not consider the transverse shear deformation and has some limitations in the fracture analysis [1], so Reissner’s theory [2] is often adopted. Considering the effect of transverse shear, F.Delale[3] investigated the problem for spherical cap containing a through crack. For the plates and shells of homogeneous materials, the higher order crack tip fields are obtained based on Reissner’s theory by Liu Chuntu[4]. The corresponding field for FGMs shell has been given only for which the material gradient is along thickness direction [5]. In this paper, the crack tip fields are studied for functionally graded spherical shell with Reissner’s effect by the eigen-expansion method. 2. Basic equations The effect of Poisson’s ratio on stress intensity factor (SIF) is far less than that of elastic modules [6]. Therefore, Poisson’s ratio is assumed as a constant, and the elastic modules is assumed as the linear function of spatial coordinates xas 0 ( ) (1 ) E E x E xβ = = + ， const μ= (1)
RkJQdWJsaXNoZXIy MjM0NDE=