Fracture analysis of FRP-plated notched concrete beams subjected to three-point bending

Three-point bending tests of fiber-reinforced polymer (FRP) plated notched concrete beams have great potential to become a standard test method for evaluating the shear bond performance of FRP-to-concrete interfaces. This paper presents an analytical approach to predict the full-range response of FRP-plated notched concrete beams. The focus of the analysis is to simulate the interactions between Mode II debonding of the FRP-to-concrete interface and Mode I fracture at the crack tip of the concrete beam. In analyzing the FRP-to-concrete interface, the slip is selected as the unknown function to derive a second-order ordinary differential equation, and the analytical relationship between the pull force of the FRP laminate and the interfacial slip at its loaded end is formulated. Crack propagation in concrete is modeled using the weight function method. The stress intensity factors induced by various external loads and internal forces are all given in an analytical manner. Finally, a global equation with one single unknown is established. The equation can be solved easily and good convergence is assured. The derived analytical solutions are verified with experimental results obtained from the literature. Further parametric studies reveal quantitatively the effects of various factors on the load-crack mouth opening displacement (CMOD) curve of the FRP-plated concrete beam, which is found to be characterized by two peak loads. The first and second peak loads increase with the increase in the strength of concrete, the thickness of the FRP laminate, and the interfacial bond strength. It is also found that increasing the initial crack length decreases the first peak load but exerts no effect on the second peak load.