Mechanics of Interfacial Debonding in FRP Strengthening Systems: Energy Limits and Characteristic Bond Lengths

This study examines the energy behavior of a strengthening system consisting of a Fiber Reinforced Polymer (FRP) plate bonded to a rigid substrate and subjected to tensile loading, where the adhesive interface is governed by a bilinear bond–slip law with a vertical descending branch. The investigation focuses on the interaction between the elastic energy stored in the FRP and the adhesive interface, as well as the characteristic lengths that control the debonding process. Analytical expressions for the strain energy stored in both the FRP plate and the adhesive interface are derived, enabling the identification and evaluation of two critical characteristic lengths as the bond stress at the loaded end approaches its maximum value lc, at which the elastic energies of the FRP and the adhesive interface converge, signaling energy saturation; and lmax, where the adhesive interface attains its peak energy absorption. Upon reaching the energy saturation state, the system undergoes failure through the sudden and complete debonding of the FRP from the substrate. The onset of unstable debonding is rigorously analyzed in terms of the first and second derivatives of the total potential energy with respect to the bond length. It is further demonstrated that abrupt debonding may also occur in cases where the length exceeds lc when the bond stress reaches its maximum, and the bond–slip law is characterized by a vertical branch. The findings provide significant insights into the energy balance and stability criteria governing the debonding failure mode in FRP-strengthened structures, highlighting the pivotal role of characteristic lengths in predicting both structural performance and failure mechanisms.