Nonlinear fracture properties from size effect tests

The previously derived size effect law for blunt fracture is exploited for determining the parameters of the R-curve, of the crack band model, and of Hillerborg's fictitious crack model. No measurements of the crack length or of the unloading compliance are needed. It suffices to measure only the maximum load values for a set of geometrically similar specimens of different sizes. The parameters of the size effect law can then be identified by linear regression. The inverse slope of the regression line yields the fracture energy. The regression also has a twofold benefit: it smoothes statistically scattered data, and it extends the range of the data, so that one can do with fewer tests. From the experimentally calibrated size effect law, the R-curve may then be obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes. A simple algebraic formula for this envelope is presented. The size effect regression plot makes it also possible to determine crack band model parameters, particularly the fracture energy, the crack band width, and the strainsoftening modulus. The same is made possible for Hillerborg's model.