Application of a linear elastic - brittle interface model to the crack initiation and propagation at fibre-matrix interface under biaxial transverse loads

摘要

The crack onset and propagation at the fibre-matrix interface in a compositeunder tensile/compressive remote biaxial transverse loads is studied by a newlinear elastic - (perfectly) brittle interface model. In this model theinterface is represented by a continuous distribution of springs whichsimulates the presence of a thin elastic layer. The constitutive law for thecontinuous distribution of normal and tangential of initially linear elasticsprings takes into account possible frictionless elastic contact between fibreand matrix once a portion of the interface is broken. A brittle failurecriterion is employed for the distribution of springs, which enables the studyof crack onset and propagation. This interface failure criterion takes intoaccount the variation of the interface fracture toughness with the fracturemode mixity. The main advantages of the present interface model are itssimplicity, robustness and its computational efficiency when the so-calledsequentially linear analysis is applied. Moreover, in the present plane strainproblem of a single fibre embedded in a matrix subjected to uniform remotetransverse loads, this model can be used to obtain analytic predictions ofinterface crack onset. The numerical results provided by a 2D boundary elementanalysis show that a fibre-matrix interface failure initiates by onset of afinite debond in the neighbourhood of an interface point where the failurecriterion is reached first (under increasing proportional load), this debondfurther propagating along the interface in mixed mode or even, in someconfigurations, with the crack tip under compression. The analyticalpredictions of the debond onset position and associated critical load are usedfor checking the computational procedure implemented, an excellent agreementbeing obtained.