3D cracks and crack stability
CECAM-HQ-EPFL, Lausanne, Switzerland
The fracture of solids has formed the cornerstone of engineering science since Galileo first posed the question of the maximum load before rupture of a beam subjected to tension. Our current understanding of the mechanics of fracture is formulated in the theory of linear elastic fracture mechanics, which predicts a singular stress at the crack tip, making the problem challenging on all levels. Experiments show that the mechanics and physics of brittle fracture are typically irregular, with the emergence of surface features and texture that are non-smooth. Even when a crack abides the over-all symmetry of planar loading conditions, characteristic fracture surface structures emerge with a strong velocity dependence, and can even persist at extremely low velocities. The emergent structures are indicative of non-linearities in the dynamics of a crack, and are the hallmarks of crack instability.
The long-standing paradigm in fracture mechanics, established from linear perturbation theory, is that any initial disturbance should decay or disperse, independent of its amplitude. Recent calculations challenge this paradigm[1-3], and instead suggest that due to non-linearities in the dynamics, the crack surface is susceptable to breaking planar symmetry for sufficiently large disturbances. Experiments support these calculations, as even quasi-static cracks exhibit structure and surface features that do not decay as the crack progresses. Indeed, such disturbances can have global consequences, as a rigid inclusion can completely arrest a propagating crack.
Recent numerical calculations using the phase-field method are capable of reproducing the texture and features of these dynamics, if at an altered threshold velocity for the onset of instability. A similar numerical method shows that a quasi-static crack subjected to mixed mode-I / mode-III loading will readily develop lances and a corrugated pattern. In both cases, the overall planar symmetry of the crack is broken, and a fully-3D stress state develops at the crack tip. This is significant, because such a stress state is extremely challenging to address analytically, and nearly impossible to characterize using existing experimental methods. While these numerical calculations led to advances in the methods available to the numericist to calculate the mechanics of more complex crack tip loading conditions, fundamental questions about the precise value of the threshold for the development of e.g. lances, or microbranches in the dynamic case, remain unanswered.
Experimental developments using a variety of materials are now positioned to inform numerical calculation on the most general loading cases, including fully 3D loading conditions, and mixed planar/ non-planar loading. Indeed, direct observations of crack tips in brittle hydrogels emphsize the sensitivity of a crack to mixed-mode loading conditions, and even the emergence of planar symmetry breaking. Method development, including direct microscopic measurement of crack tip opening displacement and deformation, or more sophisticated speckle-holography methods, stand to facilitate direct measurement of 3D deformation field, specifically for materials under high-strain near sharp geometries such as a crack tip.
Taken together, these advances suggest that the field will benefit from an opportunity to identify key outstanding questions, and discuss the best approaches to improve predictability of material failure in the most general 3D case.
Mokhtar Adda-Bedia (Laboratoire de Physique, Ecole Normale Supérieure de Lyon, Lyon) - Organiser & speaker
John Kolinski (Institute of Mechanical Engineering, School of Engineering, EPFL) - Organiser & speaker