Comparative analytical study of the coupled criterion and the principle of minimum total energy with stress condition applied to linear elastic interfaces

Abstract

In the present work the Coupled Criterion of Finite Fracture Mechanics (CCFFM) is used to predict crack onset or growth by finite increments in a linear elastic interface. The predictions of the interface failure by two alternative approaches of the CCFFM applied to the Linear Elastic Brittle Interface Model (LEBIM): the widely used method based on looking for an intersection of stress and energy criteria curves and the novel Principle of Minimum Total Energy subjected to a Stress Condition (PMTE-SC), are studied and compared. For this purpose, two analytical studies, based on the stress and energy criteria curves and the PMTE-SC, are carefully explained, providing appropriate graphical representations, by considering the widely used Double Cantilever Beam (DCB) test as benchmark problem. For the sake of simplicity, the Euler–Bernoulli beam model including an elastic interface (the Winkler interface) to model the adhesive layer joint is used in this study. To the authors’ best knowledge, this is the first study showing, for both load and displacement control, that the PMTE-SC is equivalent to the classical formulation of the CCFFM, providing exactly the same analytical predictions for the crack onset and propagation. The fact that onset of a finite crack-advance typically predicted by CCFFM is associated to tunnelling the total energy barrier is also illustrated on the DCB test. The main advantages of the PMTE-SC are its versatility and possibility of applying it to complex configurations including multiple cracks and fracture mixed-mode behaviour.