13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Next, we consider material properties that vary along the y-direction as shown in Fig. 3(b). The material gradation parameter 1β is set to 0 and 2β is set as 0, 0.05 and 0.1. Since material properties vary along the y-direction, the material properties are the same at both crack tips. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Normalized KI & KII Normalized Time M-integral-KI (Song and Paulino 2006) M-integral-KII (Song and Paulino 2006) M-integral-KI (Present) M-integral-KII (Present) I-integral-KI (Present) I-integral-KII (Present) Fig. 4 Normalized DSIFs calculated by different methods 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ß2=0.10 ß2=0.05 ß2=0.0 ß1=0.0 Normalized KI (Right crack tip) Normalized Time Fig. 5 Normalized mode I DSIFs for different material gradations along the y-direction 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 ß2=0.0 ß2=0.05 ß2=0.10 Normalized KII (Right crack tip) Normalized Time ß1=0.0 Fig. 6 Normalized mode II DSIFs for different material gradations along the y-direction Fig. 5 and Fig. 6 show the mixed-mode DSIFs at the right crack tip. It is obvious that ( ) IK t is identical at both crack tips, while the magnitude of ( ) II K t at the left crack tip is equal in magnitude and opposite in sign to the value at the right crack tip. So we only list the results at the
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