An improved model of refined zigzag theory with equivalent spring for mode II dominant strain energy release rate of a cracked sandwich beam

In this paper, an improved model, the refined zigzag theory with equivalent tangential spring (RZTES) in conjunction with the sub-laminate approach, for cracked sandwich beam (CSB) is developed. The kinematics of the refined zigzag theory (RZT) assumes that the axial displacements of a sandwich beam follow piecewise linear distribution across the thickness. This theory can accurately model the zigzag displacement in a sandwich beam without delamination. However, the kinematics of the RZT does not meet the deformations near the crack tip, which contain more complicated displacement distributions. It results in underestimations of both the compliance and mode II dominant strain energy release rate (SERR). The RZTES is developed to correct the inaccuracies due to this underestimation. In RZTES, an equivalent spring is inserted to decrease the local stiffness near the crack tip so that the compliance of the CSB is increased. Based on the procedure developed in this study, the equivalent spring constant can be determined according to the Young's modulus and shear modulus of the core. Then a gap determined from the equivalent spring constant can be determined and be used to re-formulate the continuity conditions at the crack tip of a CSB. In order to validate RZTES, the CSB is calculated by commercial finite element method (FEM) software ANSYS with two-dimensional elements. The compliances are also validated by experiments. The results show that the RZTES can increase both the compliance and strain energy release rate. The case studies with various ranges of geometric parameters and material properties of the CSB are solved by RZT, RZTES and ANSYS. For the case with soft core or thick beam thickness, the calculation results by RZT need more corrections. By comparing RZT, both the compliances and SERRs calculated by RZTES are more accurate.