13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 2 , , 2 2 2 , , 1 o I o II om o II o I δ δ β δ δ β δ + = + (16) The mixed-mode damage propagation is simulated considering the linear fracture energetic criterion: 1 I II Ic IIc G G G G + = (17) The released energy in each model at complete failure can be obtained from the area of the triangle: , , 1 2 i um i um i G σ δ = (18) being , ( , ) um i i I II δ = , the relative displacement in each direction for which complete failure occurs. From Equations (8), (11), (13), (14), (17) and (18), the mixed mode relative displacement leading to total failure ( ) umδ can be obtained: 2 2 2(1 ) 1 [ ] um om Ic IIc e G G β β δ δ + = + (12) The values of eδ, omδ and umδ are introduced into Eq. (10), instead of iδ, ,o i δ and ,u i δ , thus setting the damage parameter under mixed mode. The mixed mode model proposed is general and it can be applied under any combination of modes. The same sandwich beam considered in section 3 under three point bending with a crack parallel to the beam axis very close to the upper skin interface (Figure 1), is solved numerically. But in this case we adjust the model according to the demands of the previous analysis. Different models with different cohesive parameters, different crack lengths, different crack positions and orientations, may be confronted. The element type used in this analysis is the four-node two dimensional plane strain elements CPE4 [16]. Different mesh configurations were used in the vicinity of the crack tip and the cohesive layer in order the convergence of the solution to be succeeded. The cohesive layer is placed over the entire plane of crack propagation (Figure 3) by implementing the procedure given in Abaqus [15].
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