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.Wepresentanovel,yetextremelysimple,derivationoftheclosed-formsolutionofthisproblemwhen thearmsaremodelledwithTimoshenkobeamtheory.Weremovetheassumptionthatthecrosssectionsofthe 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 section sareallowedtorotate,althoughthebeamaxisstaysundeformed.Thus,wecandeterminethecracktiprotationcausedbythedeformationofthebeaminfrontofthecracktipalsointheLEFMlimit.Asaresult, mostoftheinaccuraciesoftheSBTareeliminated,withouttheneedforacrack-length correction, use dinthe ‘corrected beam theory’(CBT).Inthisway,wecanderiveaveryaccuratedatareductionformulaforthecritical 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 compositeplates,inwhichsheardeformabilitycanplayasignificantrole.