R-curve behavior and roughness development of fracture surfaces

We investigate the idea that the fractal geometry of fracture surfaces in quasibrittle materials such as concrete, rock, wood and various composites can be linked to the toughening mechanisms. Recently, the complete scaling analysis of fracture surfaces in quasibrittle materials has shown the anisotropy of the crack developments in longitudinal and transverse directions. The anomalous scaling law needed to describe accurately these particular crack developments emphasizes the insufficiency of the fractal dimension, usually used to characterize the morphology of fracture surfaces. It is shown that a fracture surface initiating from a straight notch, exhibits a first region where the amplitude of roughness increases as a function of the distance to the notch, and a second one where the roughness saturates at a value depending on the specimen size. Such a morphology is shown to be related to an R-curve behavior in the zone where the roughness develops. The post R-curve regime, associated with the saturation of the roughness, is characterized by a propagation at constant fracture resistance. Moreover, we show that the main consequence of this connection between anomalous roughening at the microscale and fracture characteristics at the macroscale is a material-dependent scaling law relative to the critical energy release rate. These results are confirmed by fracture experiments in Wood (Spruce and Pine).