Comparison of calculations of energy release rates for DCB multi-directional laminate specimens

The double cantilever beam (DCB) specimen has been used extensively to measure the mode I fracture toughness of laminate composites. There are standards which were developed for testing unidirectional (UD) material. In addition, this specimen has been used extensively for multi-directional laminates. Typically, fracture resistance curves are presented. To this end, calculation of the energy release rate is required. For UD specimens, there are expressions for this parameter given in the standards. They depend upon the applied load, the crack opening displacement, specimen dimensions and the axial Young’s modulus or specimen compliance. For multi-directional composites, the specimen arms may not be symmetric. In this case, the arm heights differ, as well as their effective moduli. In this study, expressions are presented for all cases. That is, expressions for the energy release rate are presented in which the specimen arms are symmetric and in which their heights differ; these are found in the literature. In addition, new expressions for which the axial moduli also differ are developed. Calculations are made with these equations and compared to results obtained elsewhere using the finite element method and the conservative J-integral. It is seen that excellent agreement is achieved when both the different heights and moduli are accounted for, as well as a delamination length correction. The purpose of this investigation is to examine expressions for calculating the energy release rate in comparison to finite element analyses and to show that by taking into consideration the different specimen arm heights and stiffnesses, simple formulas may be used instead of the more complicated finite element analyses.