Abstract:
An important characteristic of the nonlinear fracture behavior of concrete is the presence of a fracture process zone at the crack front, which is significantly relative to the specimen dimensions and cannot be neglected. In this study, the displacement distribution along the fictitious crack in the concrete three-point bending beam is represented using a polynomial function. An analytical method is developed for fracture analysis of the beam. Analytical expressions describing the crack opening displacement and cohesive stress distribution throughout the crack propagation process are derived. Based on the analytical method, the distributions of crack opening displacement and cohesive stress during the fracture process are determined. The calculation results are compared with the experimental results and numerical analysis results. The distribution of crack opening displacement and cohesive stress during the propagation is analyzed, and the influences of specimen size and the initial crack length-to-depth ratio on the characteristics of the cohesive zone in concrete are investigated. The results show that the crack opening displacement curve exhibits a nonlinear distribution. As the specimen size increases, both the crack opening displacement and the length of critical fracture process zone gradually increase. With the increase of initial crack length-to-depth ratio, the critical crack opening displacement tends to increase gradually, while the cohesive stress tends to decrease gradually. Using the derived analytical expression for the crack opening displacement derived in this study, the crack opening displacement of three-point bending beams of different sizes at any stage during crack propagation can be calculated.