13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Figure 1. Crack propagation in the core of a sandwich beam under flexural loading 3. Crack Kinking Analysis. The cracked sandwich beam is analyzed using the finite element method. Because of high stress gradients around the interface, fairly fine mesh consisting of two dimensional plane strain elements was used. The assumption of plane strain is justified throughout. The finite element analysis is performed with the use of the general purpose finite element programs. The 6 node and 8 node two-dimensional plane strain triangular elements (plane 6) were used in order to model the beam. The frictionless contact area at the crack surfaces is modeled with 2-node linear contact elements, in order to prevent one surface from entering into the other. Singular elements (mid-side nodes at ¼) were used at the two crack tips. In order to analyze the first damage event, a small crack is considered at about1.5mm below the interface under the central load introduction and parallel to the beam axis. This small crack is considered propagating under the interface. For the different crack lengths the stress intensity factors, max min max min 1 , , I I II II II K K K K K K ∆ ∆ = − = − (1) are calculated automatically from the finite element analysis for the left and right crack tip. The Ι ∆Κ and II ∆Κ ratios are given in Fig. 2, considering the lower stress level 0.70 r = and for the load P to be taken equal to ultimate 0.7P ( ) 943.46N = , where ultimate P the static failure load of the beam.
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