13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 4. The theory of equivalent strain gradient Based on the analysis in the previous section, a damage evolution theory based on the equivalent strain gradient is suggested in this article. The suggested criterion states that: the initiation of the crack is occurred when the equivalent strain reaches its critical value. The propagation direction of the initiated crack is coincided with the direction where the equivalent strain decrease gradient reaches its maximum. The gradient of equivalent strain decrease with respect to the radial coordinate originating from the center point of the hole can be expressed as: 1 A A A A B A B A B B A C B A C B D A E C D FGH E A B C D MN MX X Y Z A=.090414 B=.267469 C=.444525 D=.62158 E=.798636 F=.975691 G=1.153 H=1.33 NODAL SOLUTION STEP=1 SUB =14 TIME=1 EPTOEQV (AVG) DMX =5.17 SMN =.001886 SMX =1.418 Fig.14, the equivalent strain distribution around the hole for α=0. 1 H F I G F G H I I H G I H G F H I E G I F H I G H F I E G H G F I I F G H I I H E I F G I I H F G H F F E G F H I I G I I H F E G F H I G F I H I E G F E I D E G H I I I F G I DE H FG D E H C HGF I ED H C D I E FG H I I I BC H DFG I HGF CBA E I D E I I I I F D I HG CB EF E G HI F D F H G H E AC D E F GD BC I HFE G D F E H I I H I H GFI H G FED HG EDFC FGHI CDE GFCA EDB F D E E FD C GHI F G D F E I H MN MX X Y Z A=264.619 B=373.484 C=482.349 D=591.214 E=700.079 F=808.943 G=917.808 H=1027 I=1136 NODAL SOLUTION STEP=1 SUB =16 TIME=1 SEQV (AVG) DMX =11.719 SMN =210.187 SMX =1190 Fig.13, the equivalent stress distribution around the hole for α=15.
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