Multi-layer modeling of edge debonding in strengthened beams using interface stresses and fracture energies

The onset and propagation of edge debonding in beams strengthened with externally bonded fiber-reinforced composite plates, is here examined using an innovative multi-layer formulation. A novel mixed mode coupled criterion is adopted to predict debonding initiation accounting for both fracture energies and interfacial stresses and considering different debonding locations across the adhesive layer. The subsequent debonding propagation is studied by using a mixed mode fracture criterion. The beam system is assumed to be composed of three physical components, namely the beam, the adhesive layer and the bonded plate, each one being modeled by one or several first-order shear deformable layers. Both strong and weak interface constitutive relations are introduced to model the two physical interfaces (i.e. beam/adhesive and adhesive/plate), whereas a strong formulation is used to model the mathematical interfaces between layers inside each physical components. Results show that the proposed multilayer formulation, implemented by using a multivariable 1D finite element technique, enables to calculate interlaminar stresses and fracture energies in reasonable agreement with results obtained by using a continuum FE model, but with a significantly reduced computational cost. The numerical analyses, carried out also in a parametric form by varying both interfacial fracture toughness and strength, show that although the accuracy can be improved by using more layers for each components and adopting coupled strong/weak interface formulations, the use of few layers for each components of the strengthened system suffices to obtain an accurate prediction of debonding initiation and propagation