Modelling of mixed mode debonding in externally FRP reinforced beams

In this paper a refined model able to analyze edge debonding problems in beams strengthened with externally bonded composite laminated plates, is presented. The structural system is viewed as composed by three physical different components: the base beam (made of steel or concrete), the adhesive layer and the bonded plate. Each component may be comprised by one or several mathematical layers which adopts the first-order shear deformation laminate theory. Bonding and continuity conditions between different layers are simulated by using the interface modelling technique. Strong and collapsed interface models are introduced in order to capture stress singularities and to reduce the complexity of the analysis, respectively. Governing equations for displacement fields complemented with boundary and continuity conditions, are obtained by a variational approach. According to a fracture mechanics approach, the analysis is carried out by evaluating the total and individual mode components of energy release rate (ERR).Applications for typical strengthened systems, carried out by numerical integration procedures, are proposed in which the energy release rates are evaluated by means of interface displacement jumps, leading to a very efficient numerical procedure. The approximations introduced in the model with respect to the adopted number of mathematical layers are analyzed and comparisons with existent models are given. For the simpler two-layer model of the structure, comparisons are given with the closed-form solutions obtained in [Greco F, Nevone Blasi P, Lonetti P. An analytical investigation of debonding problems in beams strengthened using composite plates. Eng Fract Mech 2006, in press]. The convergence to the results from continuum analysis is investigated when a refined assembly of layers is adopted, by means of comparisons with predictions from very careful FE solutions. Finally, the effect of different debonding modes on the overall behaviour of the structural system is analyzed. These results show the capability and the accuracy of the proposed approach to predict debonding failure behaviour in both steel and concrete strengthened beams. As a matter of fact, the proposed approach involves reduced computational cost with respect to FE solutions based on 2D continuum elements and the use of a multi-layer structural model leads to avoid some complexities related to the classical elasticity theory for bimaterial interface cracks.