Analysis of Crack Problems in Graded Halfspace Subject to Complex Loading

Abstract

In general, all solid materials can be considered as non-homogeneous because their properties can vary with location in the three-dimensional space. One special type of solid material is characterized by the variations of its physical and mechanical components, structures and properties along only one given coordinate; the material properties have very small or no variations in any other direction perpendicular to the given coordinate. These types of solid materials are called graded materials. The boundary element method (BEM) is now firmly established in many engineering disciplines and is increasingly used as an effective and accurate numerical tool. Fracture mechanics has been the most active, specialized area of research in BEM. In the past 15 years, we have used the fundamental solution of a mutlilayered elastic solid to develop a new type of BEM and analysed the fracture mechanics in layered and graded solids. In this paper, we examine the fracture mechanics problem of cracks embedded in a graded half-space. The half-space is subject to complex loading on the external surface. Two novel numerical methods and the superposition principle in fracture mechanics are employed for the analysis of the crack problem. The numerical methods are based on the fundamental solution of a multilayered elastic medium and are, respectively, applied to calculate the stress fields of a graded half-space without cracks and the discontinuous displacements of crack surfaces in a graded half-space. The stress intensity factor (SIF) values are calculated using discontinuous displacements and the influence of material properties and crack positions on the SIF values is analysed. Using the minimum strain energy density criterion and the SIF values, the minimum values of the strain energy density factor are calculated and the crack growth is analysed. Results show that the heterogeneity of graded media exerts an obvious influence on the fracture properties of cracked graded elastic solid. References: (1). Xiao HT, Yue ZQ, 2014. Fracture Mechanics in Layered and Graded Solids: Analysis Using Boundary Element Methods, De Gruyter & Higher Education Press, Berlin, Germany. (2). Xiao HT, Yue ZQ, 2011. A three-dimensional displacement discontinuity method for crack problems in layered rocks, Int. J. Rock Mech. Min. Sci., 48, 412-420. (3). Xiao HT, Yue ZQ, Zhao XM, 2012. A generalized Kelvin solution based method for analyzing elastic fields in heterogeneous rocks due to reservoir water impoundment, Computers & Geosciences, 43, 126-136. (4). Yue ZQ, Xiao HT, 2002. Generalized Kelvin solution based boundary element method for crack problems in multilayered solids, Eng. Anal. Bound. Elem., 26, 691-705.