Crack Extension Resistance Curve of Concrete Considering Variation of FPZ Length

Abstract

Owing to its importance in evaluating the fracture behavior of concrete, the crack extension resistance curve of concrete has been widely studied, both experimentally and theoretically. In this paper, a numerical approach is developed for the crack extension resistance curve of concrete by considering the variation of the fracture process zone (FPZ) length during the whole fracture process. In this approach, the FPZ length is determined by using the linear asymptotic superposition assumption. Dividing the whole fracture process into three different stages of the cohesive stress distribution within the FPZ, the crack extension resistance curve is formulated by superposition of the intrinsic fracture toughness of concrete and the fracture toughness caused by the cohesive stress within the FPZ. The developed numerical approach is applied to the tested and simulated standard three-point bending notched concrete beams. The effect of the variation of the FPZ length on the crack extension resistance curve is evaluated on the basis of the numerical results. The crack extension resistance first increases with an increase in ratio of the effective crack length to the beam depth and then reaches a plateau value when the FPZ is fully developed. When the effective crack length is normalized to the beam depth, the crack extension resistance is basically independent of the beam depth within the beam size range studied.