13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- T-stress evaluation in nonhomogeneous materials under thermal loading by means of interaction energy integral method Fengnan Guo1, Licheng Guo1,*, Hongjun Yu2 1 Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001,China 2 Institute of Applied Mathematics, Harbin Institute of Technology, Harbin 150001, China * Corresponding author: guolc@hit.edu.cn Abstract This paper addresses finite element evaluation of the non-singular T-stress in nonhomogeneous materials under steady-state thermal loads by means of interaction energy integral method. The interaction energy integral method developed in this paper can solve the T-stress with high accuracy and efficiently in nonhomogeneous materials. The interaction energy integral method in conjunction with the extended FEM is used to solve several representative examples to show its validity. It can be found that the present method is efficiency to calculate the T-stress in nonhomogeneous materials. Keywords Interaction energy integral, T-stress, Interface, Nonhomogeneous materials 1. Introduction Stress intensity factors (SIFs) play a significant role in linear elastic fracture mechanics as they characterize the crack-tip stress and strain fields. Apart from the SIFs, the T-stress [1], which is the nonsingular term, has become another key parameter in fracture mechanics because it has been found the T-stress affects the crack growth direction, shape and size of the plastic zone, crack-tip constraint and fracture toughness greatly [2-4]. Many researchers evaluated T-stress when the material is subject to mechanic loading [5-8], however, there are few researches on T-stress when the material is subject to thermal loading. Sladek and Sladek [9] used the conservation integral method to evaluate the T-stress and the stress intensity factors in stationary thermoelasticity. Dag [10] used J integral to evaluate the mix-mode SIFs and the T-stress in FGMs under thermal loading. KC and Kim [11] and Kim and KC [12] have studied the SIFs and T-stress in FGMs under thermal loading using the interaction energy integral method. However, all of the above paper did not consider the situation that the materials contain interfaces. 2. Interaction energy integral formulation The traditional J-integral given by Rice [13] is 0 0 1 ,1 0 lim ( ) j ij i j J u n d δ σ Γ → Γ = − Γ ∫ W (1) where W is the strain energy density given by 1 1 ( ) 2 2 m t th ij ij ij ij ij σ ε σ ε ε = = − W (2) and j n is the outward normal vector to the contour 0Γ , as shown in Fig. 1, and ijδ is the Kronecker delta. In Eq. (2), mijε is the mechanical strain, t ijε denotes the total strain, th ij ij ε α θδ = Δ refers to thermal strain, α represents the thermal expansion coefficient and 0 θ θ θ Δ = − denotes temperature change with 0θ is the initial temperature.
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