13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Figure 1. An edge crack in a FG/homogeneous bimaterial plate height 0 1 3 h h w and crack-length 0.4 a w . An exponential material gradation with the gradient parameter g in the 2x -direction perpendicular to the crack-line of the FG coated structure is assumed as [8] 0 2 0 2 0 2 exp( ), exp( ), exp( ). g g g E E x k k x c c x (24) The mass density, the Poisson’s ratio and the linear thermal expansion coefficient are taken as ( ) 1 x ñ , ( ) 0.02 x and 0.25 , respectively. Plane-strain condition is assumed in the numerical calculations. The non-homogeneity of the FG layer induces a mixed mode crack-tip loading even though the cracked plate is subjected to a pure thermal loading on the top and the bottom side symmetric to the crack-faces, i.e., the mode-II dynamic SIF is also present along with the mode-I dynamic SIF. For convenience, the dynamic SIFs and the time are normalized as , , 0 0 0 ( ) ( ) / ( ) I II I II K t K t E a and 2 0 0 0 / ( ) t t k a c ñ . To test the accuracy of the proposed BEM, the numerical results are compared with those obtained by the FEM analysis, which show a good agreement [8, 9, 11]. The time variations of the normalized mode-I and mode-II SIFs for the three selected combinations of the gradient parameters 1 ln(2), ln(3), ln(5) gh and 1 ln(0.5), ln(0.333), ln(0.2) gh are presented in Figs. 2 and 3. The negative gradient parameters (Fig. 3) result in a reduction of the peak dynamic SIFs in comparison to that for positive gradient parameters (Fig. 2). The wave velocity in this case is also decreasing. Hence, the peak values of the dynamic SIFs are reached at larger time instants. The opposite tendency is observed in Fig. 2 with the increasing gradient parameters. Thus, the present results show that the gradient parameters may have significant influences on the dynamic SIFs. To investigate the influence of the thickness of the FG coating on the dynamic SIFs, four relative thickness values 0 1 / 5, 10, 15, 20 h h are selected for the gradient parameters 1 ln(2) gh and 1 ln(0.5) gh in the numerical analysis. The time variations of the normalized mode-I and mode-II dynamic SIFs for the selected thickness ratios are shown in Figs. 4 and 5. The peak of the SIFs decreases with decreasing thickness of the FG layer for both values of the material gradient parameter.
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