Energy release rate for interlaminar cracks in graded laminates

In this study, the energy release rate for interlaminar cracks in a laminate beam, graded along the depth, has been derived using beam theory. The correction for accounting crack-tip flexibility, used for conventional composites, is incorporated into the derived expressions and the variation of the energy release rate as a function of crack location and elastic gradient is investigated for the load configurations of double cantilever beam (DCB), end notched flexure (ENF) and mixed mode bending (MMB). The results of the study indicate that the energy release rate calculated using the derived expressions is in very good agreement with that obtained through finite element analysis (FEA) whereas the mode partitioning calculated from the beam theory analysis was not in agreement with that obtained from FEA. As the position of the crack varies along the depth of the beam, there is a considerable change in the energy release rate and mode partitioning. Further, it is shown that by proper load configuration, pure mode (mode-I or mode-II) conditions can be achieved for crack located at any depth along the beam. The effect of the gradation type and its strength on the energy release rate and mode partitioning is also investigated. It was observed that the energy release rate is strongly sensitive to both the strength and type of gradation, whereas, the mode partitioning is influenced more by the gradation strength than by the gradation type.