Analytical method for crack propagation process of lightly reinforced concrete beams considering bond-slip behaviour

Characterization of crack extension process is crucial for evaluating the fracture behaviour of reinforced concrete (RC) structures. Although extensive research has shown that cracking in RC members is generally influenced by the bond-slip behaviour between steel bars and the surrounding concrete, little attention has been paid to the crack growth process. Based on the principles of fracture mechanics, this paper presents an analytical method for predicting the crack extension process of lightly RC three-point bending beams with bond-slip behaviour. A closed-form solution is derived, with which the mode I crack growth process in concrete and the interfacial debonding evolution induced by the bond-slip between steel bars and concrete can be evaluated. The validity of the presented method is demonstrated through comparison with experimental data obtained from the literature. The effects of the bond-slip behaviour on the crack growth resistance curve and the evolution of fracture process zone (FPZ) length are examined with the method. The results show that the bond-slip behaviour exhibits a significant impact on the crack extension properties. At the initial loading stage, the crack growth resistance is primarily provided by the cohesive stress on the FPZ. When the crack approaches the beam top, the bridging force of steel bars is significantly strengthened and plays a dominant role against crack propagation. Since the tensile softening of concrete, the steel-concrete bond, and the yielding of steel have been taken into account, the presented method can be utilized as a simple tool to investigate the mechanical behaviour of lightly RC structures.