The analysis of mode II strain energy release rate in a cracked sandwich beam based on the refined zigzag theory

In this paper, the mode II strain energy release rates (SERR) of a cracked sandwich beam (CSB) subjected to a three-point loading are investigated. Due to the stiff face sheets and soft core, the displacements in the sandwich beam have the zigzag distribution through the thickness. A literature survey reveals that SERR of the CSB can be determined by the first-order shear deformation theory (FSDT). However, the accuracy of the results in FSDT is limited due to the lack of zigzag phenomenon. In this paper, we re-solve the CSB based on the refined zigzag theory (RZT), in which the kinematics of the displacements are assumed to have zigzag characteristic. The kinematic variables of the displacements can be determined from solving the governing equations of RZT in conjunction with the boundary conditions and continuity conditions of the CSB, and then SERR can be calculated by the compliance method. We show that for sandwich beams with slender aspect ratio (large L/h) or with thin face sheet (large r_h), the FSDT can provide a satisfactory results due to the insignificant zigzag displacements. Otherwise for small L/h or small r_h, the RZT should be used to take the significant zigzag displacements into consideration. For a given crack length, the FSDT give a result that the SERR is independent of the beam length. By using the RZT, it is found that the SERR depends on the beam length for a given crack length, especially for long crack length that a/L is ranged from 0.4 to 0.5. The material properties of the core materials on SERR are also investigated. By comparing with the finite element method (FEM), the deflections, compliances and SERRs in the CSB obtained by RZT are more accurate than those by FSDT. It is found that, for the cases of the core with very small shear modulus, the RZT gives correct results that are validated by FEM. For such cases, the FSDT gives incorrect calculations for SERR due to the lack of the zigzag model. The results arose in this study show the superior advantages of the use of the RZT in the SERR calculation of CSB specimen.