13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- right crack tip. The initiation time at both crack tips remains the same for all cases of material gradations because of the same definition of material properties. Values of ( ) II K t , induced by material gradients, are more sensitive with increasing β, whereas the maximum magnitude of ( ) IK t is relatively insensitive to β. However, the magnitude of ( ) II K t is relatively small compared to that of ( ) IK t . Acknowledgements This work is sponsored by the National Science Foundation of China under grant Nos. 11222216 and 11202058，the Fundamental Research Funds for the Central Universities under grant No. HIT. NSRIF. 2013082 and China Postdoctoral Science Foundation (20110491071) References [1] K. Kishimoto, S. Aoki, M. Sakata, Dynamic stress intensity factors using J-integral and finite element method. Eng Fract Mech, 13(1980) 387-394. [2] T. Nishioka, S.N. Atluri, On the computation of mixed-mode K-factors for a dynamically propagating crack using path-independent integrals. Eng Fract Mech, 20(1984) 193-208. [3] J.H. Kim, G.H. Paulino, The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors. Int J Solids Struct, 40(2003) 3967-4001. [4] S.H. Song, G.H. Paulino, Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method. Int J Solids Struct, 43(2006) 4830-4866. [5] J.H. Kim, G.H. Paulino, T-stress, mixed-mode stress intensity factors, and crack initiation angles in functionally graded materials: a unified approach using the interaction integral method. Comput Method Appl M, 192(2003) 1463-1494. [6] J.E. Dolbow, M. Gosz, On the computation of mixed-mode stress intensity factors in functionally graded materials. Int J Solids Struct, 39 (2002) 2557-2574. [7] J. Réthoré, A. Gravouil, A. Combescure, An energy-conserving scheme for dynamic crack growth using the extended finite element method. Int J Numer Meth Engng, 63(2005) 631-659. [8] J.W. Eischen, Fracture of non-homogeneous materials. Int J Fract, 34(1987) 3-22. [9] B. Moran, F.C. Shih, Crack tip and associated domain integrals from momentum and energy balance. Eng Fract Mech, 27(1987) 615-642. [10]Z.Y. Wang, L. Ma, L.Z. Wu, H.J. Yu, Numerical simulation of crack growth in brittle matrix of particle reinforced composites using the xfem technique. Acta Mech Solida Sin, 25(2012) 9-21.
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