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To investigate, understanding and predicting dynamic fracture behavior of a cracked body, dynamic stress intensity factors (DSIFs) are important parameters. In the present work interaction integral method is presented to compute static and dynamic stress intensity factors for three-dimensional cracks contained in the functionally graded materials (FGMs), and is implemented in conjunction with the finite element method (FEM). By a suitable definition of the auxiliary fields, the interaction integral method which is not related to derivatives of material properties can be obtained. For the sake of comparison, center, edge and elliptical cracks in homogeneous and functionally graded materials under static and dynamic loading are considered. Then material gradation is introduced in an exponential form in the two directions in and normal to the crack plane. Then the influence of the graded modulus of elasticity on static and dynamic stress intensity factors is investigated. It has been shown that, material gradation has considerable reduce influence on DSIFs of functionally graded material in comparison with homogenous material. While, static stress intensity factors can decrease or increase, depend on the direction of gradation material property.

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This paper concerns the effect of auxiliary fields and distance of contours from the crack tip on the accuracy of stress intensity factors of Functionally Graded Materials (FGMs), using the interaction integral method. In the first step, defining auxiliary fields of displacement, strain, and stress appropriately, the interaction integral is derived which is independent of derivatives of properties of the materials. Actual and auxiliary fields of displacement, strain and stress are used to compute the interaction integral. Actual fields are obtained by isoparametric finite element method, while auxiliary fields are constructed by use of the crack tip properties on the basis of William’s solution. These auxiliary fields are not appropriate, except near the crack tip. Therefore, different non-equilibrium and incompatibility formulations are used to consider the changes in non-homogeneous material. Considering the changes in FGMs as an exponential function, the results will be obtained from these formulations and are compared with others recorded in the literature. Furthermore, considering different contours, the effect of distance of contours from the crack tip on the stress intensity factors of FGMs is examined. The results confirm that the solutions using the incompatibility and constant constitutive tensor are more accurate. In contrast the non-equilibrium method is not proper for contours which are placed far away from the crack tip and presents less accuracy.

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In this paper, the extended Finite Element Method (XFEM) is implemented to compute the Stress Intensity Factors (SIFs) for rectangular media subjected to a hygrothermal loading. In governing hygrothermoelasticity equations, the cross coupled of temperature and moisture fields and temperature-dependent diffusion in some cases are considered. Furthermore, an interaction integral for hygrothermal loading is developed to compute the stress intensity factors. The non uniform mesh of isoparametric eight-nod rectangular element is used in XFEM to decrease the absolute error in SIFs computations. In order to numerical results validation, the SIF of mode I is obtained analytically. The coupled governing equations are firstly decoupled in terms of new variables and then solved by the separation of variable method. According to the results, the moisture concentration gradient has a significant effect on the SIFs so should be considered in the model. Up to reaching temperature to its steady state, the cross coupled of temperature and moisture synchronies their time variation which affects on the time variation of SIF. At early time of thermal shock, the SIF for shorter cracks is not necessarily lesser than the longer ones. Also, the mode I SIF for longer and inclined cracks is smaller. On the other hand, considering the moisture concentration as a temperature function increases the time required to reach the moisture steady state.