3D fracture and out-of-plane crack structures: the essential role of material disorder

In this pair of preprints (see also attached PDFs):

Quenched disorder and instability control dynamic fracture in three dimensions

Facet formation in slow three-dimensional fracture

we demonstrate that emerging out-of-plane crack structures in nominally mode-I, 3D fracture of amorphous materials – such as mist and hackle patterns, localized branches and step defects – are intrinsically nonlinear phenomena that require finite material disorder.

In the first, we show that quenched disorder – characterized by finite strength and correlation length – together with a high-speed 2D instability explain a wide range of experimental observations in 3D dynamic fracture. These include the onset of localized branching, the mirror-mist-hackle sequence of transitions, the transition to macroscopic branching/tip-splitting, the spontaneous renormalization of the fracture energy (in a way that resembles a critical point) and the existence of a limiting crack propagation velocity.

In the second, we show that quenched disorder – characterized by finite strength and correlation length – together with mesoscopic fluctuations in mode-I+III mixity explain the emergence of step defects in slow 3D fracture. We demonstrate the relations between small-scale surface roughness and step formation, and reveal the topology and geometry of steps, which involve interacting crack front segments along different, overlapping fracture planes. 

The two sets of results are obtained using a flexible 3D phase-field fracture approach, which allows to track the in silico real-time 3D spatiotemporal dynamics of cracks in a way that goes well beyond current experiments.