13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- The mode I and Mode II stress intensity factors Ik and II k can be estimated based on LEFM theory as the opening and sliding displacements [23]: ( ) 2 4(1 ) (), and 2 4(1 ) 2 1 2 1 D c c K D c c K x II y I (6) 3. Verification of DDM with quadratic elements A simple problem for verifying the numerical results and the proposed code is presented in this paper. This problem is the center slant micro crack in an infinite specimen shown in Fig. 3. The slant angle ψ, changes counter clock wise from the x (horizontal) axis, and the tensile stress = 10 MPa is acting. Half of the micro crack length, b= 1 meter, modulus of elasticity E=10 GPa, Poisson’s ratio 0.2 , fracture toughness KIC= 1.8MPa m1/2 are assumed. Figure 3. A center slant micro crack in an infinite body under uniform tension (parallel to the x axis) The center slant micro crack problem has been solved by different researchers e.g. Guo et.al [20] to get a simple analysis, also these researchers used the constant element displacement discontinuity with a special crack tip element for angles 30, 40, 50,60,70,80 degrees. To evaluate the micro crack initiation angle 0, they used two initiation criteria: Maximum tangential tensile stress criterion ( -criterion), and Minimum strain energy density criterion (S-criterion), and compared their results with the results from other models. Fig. 4 compares the numerical results for the wing crack initiation directions 0 (obtained by HDDMCR2D code) and the results given by Guo et. al [20]. X σ∞=10Mpa σ∞=10M pa 2b Y
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