13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- analyses of the composite medium. The transient thermal analyses of the FGM structure are carried out for three different material gradients. It is assumed that the composite medium is initially at a high processing temperature. Then, this structure is left in an environment which is at a low temperature. Due to the high temperature difference, thermal stresses are induced at the composite structure containing an inclined semi-elliptical surface crack. Mixed mode SIFs and energy release rates are calculated along the crack front. It is observed that as the inclination angle increases, the normalized modes stress intensity factors decrease. The normalized energy release rates also decrease as the inclination angle increases. It is seen that for all inclination angles the normalized temperature increases as the crack front angle increases. It is could be concluded that material gradation has considerable effect on mode-II and mode-III stress intensity factors also. Thus, it is concluded that the 3D elements can be applied to calculate mixed-mode cracks in FGMs accurately and efficiently without needing special meshes near the crack front and detailed post-processing of the finite element solution. References [1] Andrews EW, Kim KS. Threshold conditions for dynamic fragmentation of ceramic particles. Mech Mater1998; 29:161–80. [2] Barenblatt GI. The formation of equilibrium cracks during brittle fracture: general ideas and hypotheses, axially symmetric cracks. Appl Math Mech (PMM) 1959;23:622–36. [3] Dugdale DS. Yielding of steel sheets containing slits . J Mech Phys Solids 1960;8:100–8. [4] Willis JR . A comparison of the fracture criteria of Griffth and Barenblatt . J Mech Phys Solids 1967;15:151–62. [5] Needleman A. A continuum model for void nucleation by inclusion debonding . J Appl Mech 1987;54:525–31. [6] Larsson R.A generalized fictitious crack model based on plastic localization and discontinuous approximation. Int Journal Meth Eng.1995;38:3167–88. [7] XiaL , Shih FC.Ductile crack growth––I. A numerical study using computational cells with micro structurally based length scales.J Mech Phys Solids 1995;43:233–59. [8] Camacho GT, Ortiz M. Computational modeling of impact damage in brittle materials . Int J Solids Struct 1996;33:2899–938. [9] Xu XP, Needleman A. Numerical simulation of fast crack growth in brittle solids. J Mech Phys Solids 1994;42(9):1397–434. [10] Tvergaard V, Hutchinson JW. The relation between crack growth resistance and fracture process parameters in elastic–plastic solids. J Mech Phys Solids 1992;41:1377–97. [11] Tvergaard V, Hutchinson JW. The influence of plasticity on mixed mode interface toughness. J Mech Phys Solids 1993;41:1119–35. [12] Gullerud A, DoddsR.3-D modeling of ductile crack growth in thin sheet metals. Engng Fract Mech 1999;63:347–74. [13] Foulk JW , Allen DH, HelmsKLE. Formulation of a three dimensional cohesive zone model for application to a finite element algorithm. Comput Meth Appl Mech Engng 2000;183:51–66. [14] Gao H. A theory of local limiting speed in dynamic fracture . J Mech Phys Solids 1996;44:1453–74.
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