Delamination failure of RC beams strengthened with FRP strips a closed-form high-order and fracture mechanics approach

An analytical model for the prediction of the interfacial delamination failure of reinforced concrete (RC) beams strengthened with externally bonded fiber-reinforced plastic strips (FRPs) is presented. The analysis is conducted through a comprehensive stress analysis of the strengthened member and a failure criterion based on fracture mechanics concepts. The stress analysis follows the closed-form high-order approach for the analysis of deformations, stresses, and stress resultants in the multilayered structure. The model is based on equilibrium and compatibility requirements in and between all constituents of the strengthened beam, i.e., the concrete beam, the FRP strip, and the adhesive layer. The governing equations of the bonded and the delaminated regions are derived, and along with a unique set of boundary and continuity conditions that model the cracking of the RC beam, they are solved in a closed form. The results provide the basis for the fracture analysis stage in which a criterion for the initiation and stable or unstable growth of the interfacial delaminations is derived. This criterion is based on the fracture mechanics concept of the elastic energy release rate and replaces the classical stress-based criteria. The energy release rate is evaluated through the path independent J-integral over the stress, deformation, and energy fields determined by the stress analysis. Three numerical examples concerning interfacial delamination triggered by cracking of the concrete and by the stress concentration at the edge of the FRP strip are presented. The emphasis is put on the development of the internal stress resultants in the RC beam and the FRP strip, the stresses at the adhesive layer, and the energy release rate with the growth of the delamination. The paper is concluded with a summary and some recommendations for the design of such strengthened beams.