Determination of the bridging law for mode I delamination via elastic restraint beam model and equivalent crack method. (1st March 2020) - Liu, Weiling; Chen, Puhui
Highlights: Closed-form solution of the DCB has been derived based on a novel 'Elastic Restrained Beam Model'. The proposed procedure does not require the measurement of the crack length and crack tip separation. Only load-displacement curve is needed to determine the bridging law. The simulation can reproduce the loading history of the test via derived bridging law. Abstract: This article presented a simple procedure to determine the Mode I bridging law for both unidirectional and multidirectional composite laminates. It was based on an 'Elastic Restrained Beam Model' which assumed that the boundary conditions at the end of the cracked arms of the double cantilever beam (DCB) are elastically restrained by torsion springs. In this way, the closed-form solution of the DCB has been derived, without the need for a crack-length correction used in the corrected beam theory (CBT). We also derived very accurate data reduction formulas for the energy release rate ( GI ) and the opening displacement at the pre-crack tip ( δ *). Then, the bridging law was obtained by numerical differentiation of GI with respect to δ * using the J -integral approach. Two major advantages of the proposed procedure are that it does not require the measurement of the crack length and separation δ * during the test. The derived bridging laws were implemented into the cohesive zone model (CZM) for numerical simulations and the results were proved to have a great agreement with experimental results, which validated that the proposed procedure is suitable for the determination of Mode I bridging law.