On the Role of Crack Orientation in Brittle Failure.

Many materials contain a large number of microcracks that can propagate under sufficiently high stress, but their stability is sensitive to crack orientation. We have explored this sensitivity using classical fracture mechanics with the added feature that interfacial friction is accounted for in the behavior of compression cracks. Our analysis shows that four types of unstable crack growth are possible for a penny-shaped crack under a general state of stress, depending on crack orientation: opening without shear, mixed opening and shear, pure shear without friction, and shear with interfacial friction. In addition, interfacial friction prevents crack growth at all stress intensities in a certain range of compressive stress. It will be shown that these analytic results are captured by the SCRAM brittle-failure algorithm, and that friction strongly affects the orientation of the most unstable shear crack as well as the range of unstable orientations. A second study examines the variations in material response as a function of the number of orientations represented. This is done by computing the dynamic response of an axisymmetric thick ring to internal pressure. With the traditional 9 crack orientations the fluctuation in porosity is about 28%, while with 480 orientations the fluctuation drops to just over 2%. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]