Influence of the specimen geometry on R-curve behavior and roughening of fracture surfaces

Recently the R-curve behavior observed on quasi-brittle materials was proposed to be related to the roughness development of fracture surfaces. However, many experiments have shown that the R-curve behavior is not a material property but depends on the specimen shape. It is also expected that the roughening of fracture surfaces is influenced by the specimen geometry and so R-curve behaviors related to this roughening. From mode I fracture tests on wood specimens of three different shapes, R-curves are estimated and the morphology of the crack surfaces are analysed. We show that the scaling exponents of the anomalous scaling law used to describe accurately the roughness development of crack surfaces, are not influenced by the specimen geometry and appear as material dependent parameters. Nevertheless, the fracture surfaces exhibit a roughness growth region that reduces with the average stiffness of the specimens. Accordingly, the maximum roughness magnitude of fracture surfaces is a function of the initial stiffness: the higher the stiffness, the smaller the maximum magnitude of the roughness. We show that the analytical R-curves deduced from the roughnening of fracture surfaces provide good fits of the experimental macroscopic R-curves. However, if the scaling exponents obtained from the R-curve fits are close to those measured from the microscopic roughness analysis, the description of the experimental R-curves requires a magnification of the real area of the main crack. This magnification can be explained by the weakness of the assumption of an energy only dissipated by a single crack and not by a process zone. Finally, we argue that an approach where the energy is dissipated by a set of microcracks that follow the same anomalous scaling, could fully explain the experimental R-curves.