13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Fig. 2 Computing method of DSIF: interaction integral technique. This method introduced by Sih et al [11], combines with the actual field an auxiliary field satisfying the boundary conditions of the problem. In this case, The J integral is given as follows: . J J J M aux act (5) Where act J , aux J are the J integrals in the actual and auxiliary fields, respectively, and M is the interaction integral that we are interested in, defined by : aux II II aux I I A i i M x aux u x u ij K K K K E d x q W M i ij aux i ' 1 2 1 1 . (6) With /2 ij aux ij aux ij ij MW is the strain energy of interaction and E E ' in plane stress and ) /(1 2 ' E E in plane strain. Therefore, the stress intensity factors in mode I and II take the form: . 2 ' M E K (7) We take 0 1, aux II aux I K K in mode I and 1 0, aux II aux I K K in mode II. The computing procedure of M is based on the Gauss technique, the integration points are within the elements describing the area A of the J domain (see Fig 2). 4. Applications We consider a plate of size 2w × 2h = 30mm × 40 mm containing an internal crack of initial length 2l = 4.8 mm and an inclusion of diameter d = 4 mm as shown in Fig. 3. The plate is subjected to a uniaxial Heaviside step tension loading σ(t) or a triangular blast loading with t1 = 2 μs and t2 = 8 μs. The inclusion is eccentrically positioned relatively to the crack center as shown Fig 3. The material properties for the plate and the inclusion are respectively: E = 260 GPa and 640 GPa, υ = 0.08 and 0.01, and ρ = 3.220 kg/m3 and 3.515 kg/m3. The DSIFs evaluated at crack tip A, and normalized with respect to the SIF of a similar situation in infinite plate under a uniaxial tension σ0 without inclusion. The normalized DSIFs for this problem are defined as: a K K I I 0 a K K II II 0 (8)
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