A finite element analysis of fractured sandwich composite structures under small scale yielding

The fracture behavior in sandwich composite structures has been directed toward the understanding of crack propagation, and at the same time toward improving the durability of composites against fracture [1-4]. A crack flaw may be introduced during processing or subsequent service conditions. It may result from low velocity impact, from eccentricities in the structural load path, or from discontinuities in structures, which induce a significant out-of-plane stress. Generally for a state of plane stress the stresses normal to the plane of interest are negligibly small. On the other hand plane strain is assumed to occur where the strains to the normal plane are negligibly small. In our study both these cases will be studied. The sandwich beam considered is shown in Figure 1. Material properties and geometrical data are shown in Tables 1 & Tables 2 respectively. Additional information regarding material properties as shear and tensile strength, are given in Table 3. In this study combining the elastoplastic concepts approach with the step by step crack propagation inside the core of a sandwich beam very close to the upper skin interface, a numerical solution is proposed via the finite element analysis.1‒4 An initial crack length is assumed. Methods of evaluating the plastic zone under mixed mode loading conditions and small scale yielding ARE presented. In the presence of plastic zone at the crack tip the stiffness of the component decreases and the compliance increases. To incorporate the effect of plasticity in Fracture analysis the crack is mathematically modeled to be longer than the actual length. In the finite element model this is incorporated by taking into account the radius of singular elements around the crack tip. This radius is at the same order of magnitude with the crack tip plastic zone confronted in our analysis. The relations which relate the fracture parameters and the radius of the plastic as well as the direction of the propagation zone under the three point bending are presented. The extension of the plastic zone along the crack axis is succeeded by finding the point at which one of the yield criteria is satisfied. It is quite difficult to give a proper description of plastic zone shape and size. In all the models to simplify the analysis the material is assumed to be elastic-perfectly plastic. In this study considering that the plastic zones are created around the tips of the cracks under small scale yielding, the stress fields are determined in terms of the stress intensity factors using the asymptotic solutions.