Is breaking through matter a hot matter? How to predict material failure by monitoring creep

In any domain involving some stressed solids, that is, from seismology to rock physics or general engineering, the strength of matter is a paramount feature to understand.  The global failure of a mechanically loaded solid is usually dictated by the growth of its internal micro-cracks and dislocations. When this growth is rather smooth and distributed, the solid is considered to be in ductile condition. Alternatively, an abrupt propagation of localized defects leads to a brittle rupture of the full matrix.
It is then critical to understand what the physics and dynamics of isolated cracks are, when their tips are loaded at a given stress level. While the general elasticity theory predicts such stress to diverge, it is  acknowledged that some area around the crack fronts is rather plastic. In other words, some dissipation of mechanical energy, in a so-called process zone around a crack tip, prevents the - unphysical - stress divergence and shields the fronts from excessive load levels.

In this work, we focus on the local Joule heating, that significantly contributes to the energy dissipation. Analysing experimental data of the rupture of many materials, we indeed show that the scale for the thermal release around crack tips explains why the toughness of different media spans over orders of magnitude (we analysed materials spanning over 5 decades of energy release rate), whereas the covalent energy to separate two atoms does not.

We here discuss the ability of this simple thermally activated sub-critical model, which includes the auto-induced thermal evolution of crack stips [1], to predict the catastrophic failure of a vast range of materials [2]. It is in particular shown that the intrinsic surface energy barrier, for breaking the atomic bonds of many solids, can be easily deduced from the slow creeping dynamics of a crack. This intrinsic barrier is however higher than the macroscopic load threshold at which brittle matter brutally fails, possibly as a result of thermal activation and of a thermal weakening mechanism. We propose a novel method to compute the macroscopic critical energy release rate of rupture, Gc macroscopic, solely from monitoring slow creep, and show that this reproduces the experimental values within 50% accuracy over twenty different materials (such as glass, rocks, polymers, metals), and over more than four decades of fracture energy. We also infer the characteristic energy of rupturing bonds, and the size of an intense heat source zone around crack tips, and show that it scales as the classic process zone size, but is significantly (10⁵ to 10⁷ times) smaller.

References:

[1] Vincent-Dospital, T., Toussaint, R., Santucci, S., Vanel, L., Bonamy, D., Hattali, L., Cochard,  A, Flekkøy, E.G. and Måløy, K.J. (2020). How heat controls fracture: the thermodynamics of creeping and avalanching cracks. Soft Matter, 2020, 16, 9590-9602. DOI: 10.1039/D0SM01062F

 

[2] Vincent-Dospital, T., Toussaint, R., Cochard, A., Flekkøy, E. G., & Måløy, K. J. (2020). Is breaking through matter a hot matter? A material failure prediction by monitoring creep. arXiv preprint arXiv:2007.04866.  https://arxiv.org/abs/2007.04866