13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A BEM for transient coupled thermoelastic crack analysis of homogeneous/functionally graded bimaterials Alexander Ekhlakov1,2*, Oksana Khay1,3, Chuanzeng Zhang1 1 Department of Civil Engineering, University of Siegen, Paul-Bonatz-Str. 9-11, D-57076 Siegen, Germany 2 Faculty of Architecture and Civil Engineering, RheinMain University of Applied Sciences, Kurt-Schumacher-Ring 18, D-65197 Wiesbaden, Germany 3 Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU, 3b Naukova Str., 79060 L’viv, Ukraine * Corresponding author: alexander.ekhlakov@hs-rm.de Abstract A transient coupled thermoelastic analysis of two-dimensional, isotropic and linear elastic bimaterials, which are composed of a functionally graded (FG) layer attached to a homogeneous substrate, subjected to thermal shock is investigated. For this purpose, a boundary element method (BEM) for linear coupled thermoelasticity is developed. The material properties of the FG layer are assumed to be continuous functions of the spatial coordinates. The boundary-domain integral equations are derived by using the fundamental solutions of linear coupled thermoelasticity for the corresponding isotropic, homogeneous and linear thermoelastic solids in the Laplace-transformed domain. For the numerical solution, a collocation method with piecewise quadratic approximation is implemented. Numerical results for the dynamic stress intensity factors are presented and discussed. Keywords Functionally graded materials, Homogeneous/functionally graded bimaterials, Transient linear coupled thermoelasticity, Boundary element method, Dynamic stress intensity factors 1. Introduction Functionally graded materials (FGMs) represent a new generation of high-performance composite materials formed by continuously variable composition of the constituents over volume [1]. They possess many superior mechanical, thermal, corrosion-resistant and wear-resistant properties in comparison to the conventional composite materials. Therefore, in recent years FGMs have received an increasing research interest in materials and engineering sciences. An important application area of FGMs is in the thermal barrier coating technology, where a functionally graded (FG) layer is deposited on a homogeneous substrate. Thermoelastic fracture analysis of FG coated materials and structures is of particular importance to their thermal and mechanical integrity, reliability and durability in novel engineering applications. Such analysis may provide a fundamental understanding of and a deep insight into the failure mechanisms of FG coated materials and structures, which may aid in their design, optimization and applications. Due to the high mathematical complexity of the corresponding dynamic thermoelastic problems for non-homogeneous FGMs, analytical methods can be obtained only for very simple geometry and loading conditions. In general cases, numerical and experimental methods have to be applied to fracture and fatigue analysis in FG coated materials and structures subjected to thermal shock loading conditions. In this paper, a boundary element method (BEM) for transient thermoelastic crack analysis in two-dimensional (2-D), isotropic and linear thermoelastic bimaterials consisting of an FG coating layer attached to a homogeneous substrate under thermal shock is developed. The FG/homogeneous bimaterials are modeled by using a sub-domain technique [2]. The bimaterial system is divided into a homogeneous and a non-homogeneous sub-domain along the interface. The equations of motion and the thermal balance equation constitute the governing equations of the transient linear coupled thermoelasticity. The Laplace-transform technique is applied to eliminate the time-dependence in the governing equations. A boundary-domain integral equation representation is derived from the generalized Betti’s reciprocal theorem for FGMs in conjunction with the fundamental solutions for
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