13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 2. Higher order displacement discontinuity (HODD) elements by quadratic elements To increase the accuracy in computing of the displacement discontinuities and stresses near original crack tips, the special crack tip elements are used. In previous works, usually, one or two special elements for crack tip were used, but in the present research, three special elements are used. Following equation can be used three elements, particularly for crack tip: () [ ()] () [ ()] () [ ()] () 3 3 2 2 1 1 D b D b D b D i T i T i T i (5) Figure 3. Quadratic element for the higher order displacement discontinuity variation 3. Verification of the semi-infinite displacement discontinuity method (using quadratic elements) Verification of this method is made through the solution of a simple example problem i.e. a center inclined micro crack in a semi-infinite body which is shown in Fig. 4. The tensile stress is acting parallel to the x axis at infinity. Considering a 30 degrees center inclined micro crack under uniform normal tension = 10 MPa, a half micro crack length b= 1 meter, fracture toughness KIC= 2 MPa y u 1 yD r θ v x 2 yD 3 yD ζ 2a1 2a2 2a3 2 1 Dj 3 Dj 1 ζ One displacement discontinuity element are divided into three Sub elements 2a 2c 2 2b 2a1 2a2 3 3 Dj 2 2a S3 ζ
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