Experimental and computational study of fracturing in an anisotropic brittle solid

Abstract

For isotropic materials, stress- and energy-based fracture criteria lead to fairly similar results. Theoretical studies show that the crack-path predictions made by these criteria are not identical in the presence of strong material anisotropy. Therefore, experiments are performed to ascertain which criterion may apply to anisotropic materials. Notched specimens made from sapphire, a microscopically homogeneous and brittle solid, are used for the experiments. An attempt is made to locate the notch on different crystallographic planes and thus to examine the fracture path along different cleavage planes. The experimental observations are compared with the numerical results of the maximum tensile stress and the maximum energy-release rate criteria. It is observed that most of the notched specimens are fractured where the tensile stress is maximum, whereas the energy criterion fails to predict the fracture path of most of the specimens. For the tensile-stress fracture criterion, a dimensionless parameter, A (n)= 2πR 0 σ nn / γ αE nn , is introduced, where σ nn and E nn , respectively, are the tensile stress and Young's modulus in the direction normal to the cleavage plane specified by the angle α (the fracture surface energy of this plane is γ α ) and R 0 is a characteristic length, e.g. the notch radius. Five out of six notched specimens which were tested, fractured at the point and along a cleavage plane where A (n) is maximum. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. It is suggested that for a specimen with a pre-existing crack, the maximum value of the parameter, A (c)= K nn / γ αE nn , should be used as the measure of the fracturing condition, where K nn is the hoop stress intensity factor in the direction normal to the cleavage plane. For the notched sapphire specimens, Laue-diffraction analysis, along with the considerations of the geometry of the unit cell of sapphire, shows that the weakest family of cleavage planes, { 1 ̄ 012 } and { 10 1 ̄ 0 }, are the fractured planes.