Propagation of a cohesive crack crossing a reinforcement layer

This paper analyzes the propagation of a cohesive crack through a reinforcement layer and gives a solution that can be used for any specimen and loading condition. Here it faces the case of a reinforced prismatic beam loaded at three points. Reinforcement is represented by means of a free-slip bar bridging the cracked section, anchored at both sides of the crack at a certain distance that is called the effective slip length. This length is obtained by making the free-slip bar mechanically equivalent to the actual adherent reinforcement. With this model, the crack development depends on three parameters (apart from those that represent the specimen geometry): the size of the specimen, the cover thickness of the layer and the reinforcement strength. The latter depends on the reinforcement ratio and its adherence to the matrix while the reinforcement is in the elastic regime; otherwise, on the reinforcement ratio and its yielding strength. The thickness of the reinforcement cover influences the first stages of the development of the cohesive crack, and thus it also affects the value of the load peak. The computed load-displacement curves display a noticeable size effect, as real cohesive materials do. Finally, the model is able to fit the available experimental results, and accurately reproduces the influence of size, amount of reinforcement and adherence variations in the tests.