An analytical investigation of debonding problems in beams strengthened using composite plates

This work deals with an enhanced analytical model for the analysis of typical edge debonding problems in concrete or steel beams strengthened/repaired with externally bonded composite laminated plates induced by beam/adhesive interface fracture phenomena. The strengthened system is viewed as composed by three physical different layers: the strengthened beam, the adhesive layer and the bonded plate. On the other hand, the structural model consists of two shear deformable mathematical layers, the upper one representing the beam and the lower one incorporating the adhesive layer and the bonded plate. Bonding conditions between layers are simulated by using the Lagrangian multipliers method and governing equations are obtained by a variational approach. In the context of a fracture mechanics approach, analytical solutions for both total and mode components of energy release rate are obtained by using stress resultant and strain discontinuities across at the crack tip. Closed form solutions are obtained for specific loading conditions and geometric configurations. Comparisons with predictions from very careful FE investigations point out the effectiveness of the proposed results which may form the basis for a design process taking into account properly of debonding failure modes triggered by interface fracture at the edge of the repairing composite plate. Finally, the significance of the paper relies in the analytical approach to the problem, which avoids the complexities commonly shared by FE-based methodologies, related to stress singularities and differences in length scales and in mechanical properties of the single components of the system.