Using numerical simulations to compare the fracture toughness values for concrete from the size-effect, two-parameter and fictitious crack models

The size-effect, two-parameter, and fictitious crack models were developed to predict crack growth in materials like concrete that experience tension softening. The three models must predict the same response for infinitely large structures. Therefore, this study evaluates the differences in response for smaller structures. The metric used to compare response is the fracture toughness value required by the model to generate a particular load versus crack mouth opening displacement graph for a single edge specimen loaded in bending. The graphs, including unloading response, were generated numerically using the fictitious crack model and seventeen different sets of property values. The size-effect and two-parameter data reduction methods were then applied to the graphs to determine the associated fracture toughness values. Results of the evaluation indicate that the fracture toughness values for the size-effect and two-parameter models tend to be less than those of the fictitious crack model. However, there is a range of simulated materials for which the models are in reasonable agreement for structures on the scale of standard laboratory specimens.