Enhanced simple beam theory for characterising mode-I fracture resistance via a double cantilever beam test

Abstract

We study a double-cantilever beam (DCB), in which either the crack-mouth opening displacement or the end rotations are prescribed, in the linear-elastic-fracture-mechanics (LEFM) limit of an infinitely stiff and brittle interface. We present a novel, yet extremely simple, derivation of the closed-form solution of this problem when the arms are modelled with Timoshenko beam theory. We remove the assumption that the cross sections of the DCB arms are assumed not to rotate (i.e. that they are clamped) at the crack tip, which is made in so-called ‘simple beam theory’ (SBT). Therefore, with our ‘enhanced simple beam theory’ (ESBT), in front of the crack tip, cross sections are allowed to rotate, although the beam axis stays undeformed. Thus, we can determine the crack-tip rotation caused by the deformation of the beam in front of the crack tip also in the LEFM limit. As a result, most of the inaccuracies of the SBT are eliminated, without the need for a crack-length correction, used in the ‘corrected beam theory’ (CBT). In this way, we can derive a very accurate data reduction formula for the critical energy release rate, Gc, which does not require the measurement of the crack length, unlike CBT. In our numerical results we show that, compared to the most effective data reduction methods currently available (including CBT), our formula is either as accurate or more accurate for the case of brittle delamination of thick composite plates, in which shear deformability can play a significant role.