13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- ܧ ሺ ݔ ሻൌ ݁ܧ ఉ௫ 0൏ ݔ ൏ ݐ (Eq. 1) ݒ ሺ ݔ ሻൌ ݁ݒ ఉ௫ 0൏ ݔ ൏ ݐ (Eq. 2) ߙ ሺ ݔ ሻൌ ݁ߙ ఉ௫ 0൏ ݔ ൏ ݐ (Eq. 3) ݇ ሺ ݔ ሻൌ݇݁ ఉ௫ 0൏ ݔ ൏ ݐ (Eq. 4) ܿߩ ௧ሺ ݔ ሻൌ ܿߩ ௧݁ ఉ௫ 0൏ ݔ ൏ ݐ (Eq. 5) ߚ is material constant and ߚ ൌ 1 ݐ ൗ ݊ܮ ൭ ܧ ଶ ܧ ଵ ൗ ൱ (Eq. 6) Table 1 Table 1 Material Modulus Of Elasticity (GPa) Poisson’s ratio Coefficient of thermal expansion ( ͦ C-1) Coefficient of thermal conductivity (W/mK) thermal diffusivity (m2/s) Substrate (Ni) 175.8 0.25 13.91×10-6 7 2×10-6 Bond Coat (NiCrAIY) 137.9 0.27 15.16×10-6 25 8×10-6 Zirconia-Yttria 27.6 0.25 13.91×10-6 1 5×10-6 In this paper combined thermal-structural analysis is studied. In the thermal analysis, first transient heat conduction in the FGM structure is conducted and consequently temperature distribution within the structure is computed. Afterwards, this temperature distribution is utilized as an input for the structural problem. While performing the analyses, it is assumed that the crack surfaces are completely insulated and the medium is free of any mechanical constraints. Furthermore, coupling of the thermal and structural problems are assumed to be through the calculated temperature distribution only since the inertia effects are not taken into account. During the solution, minimum and maximum time step sizes are entered. In order to overcome oscillations in the distribution of temperature, minimum time step size is taken to be very small and maximum time step size is chosen as not to be very large. By imposing temperature of the environment and applying free and forced convection coefficients on related surfaces of the FGM structure in time steps the problem is solved and calculated at each node. Then after computing the mixed mode stress intensity factors at the crack front nodes by utilizing the displacement correlation technique, the procedure of solving is repeated for each required time until the end time is reached. 3. The Displacement Correlation Technique (DCT) Since the problem considered in this study is related to the inclined cracks (unsymmetrical), a complete crack model is needed to calculate the stress intensity factors. The figure below shows the full model which is to be used for mode I stress intensity factor calculation of an inclined crack.
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