Interfacial fractures: thermal effects and material disorder -- PhD defense, Tom Vincent-Dospital

Abstract:

What are fractures if not a form of disorder?

During the rupture of a brittle elastic medium, a portion of the external mechanical load, provided to the matrix, is dissipated in a plastic zone at the fracture tip. The entropy rises. This irreversible dissipation, which can be characterized by a macroscopically measurable energy release rate, derives from various physical processes. In particular: the growth of the crack surfaces and the nucleation of new defects in the solid matrix, the emission of mechanical and electromagnetic waves propagating in the medium and dumped in the far field and, finally, a rise in temperature from the intermolecular friction, directly inside the plastic zone.

Such a rise in temperature, that is for instance observable by placing an infrared camera in front of a teared paper sheet, is often regarded as a mere consequence of the rupture. However, more than a marker for the damage, it could, backwardly, have a significant impact on the fracture dynamics. The growth of cracks can, indeed, be described as a thermally activated process, even when the heterogeneities of a material control the shape of crack fronts and the intermittency of their propagation. To understand the kinetics of rupture, it is then paramount to study the temperature field around progressing fractures, and to evaluate an accurate energy budget for this process.

This question is, of course, of importance in material sciences and in everyday engineering, to correctly grasp the toughness of matter and of structures. It is also rather central in geosciences, where the instability of some seismic faults is suspected to derive from the friction induced heat at their moving walls. In particular, the localized melting and deterioration of fault planes and the thermo-pressurization of their in situ fluids may lead to some slip-weakening and, thus, to brutal rock motions in the lithosphere.

The extremely slow growth of subcritical cracks can be accurately described by simple thermodynamics laws, such as an Arrhenius growth law. In this framework, the thermal agitation at the rupture tip allows to overcome the energy barriers that hold matter together. Thus, a rise in temperature at the tip can lead to an increase in the fracture velocity, as understood by statistical physics, and without requiring a phase change of the matrix or an overpressure of its pore fluids. In the present thesis, we study this possibility and propose an activation law in which the fracture induced heat is reintroduced. Such a heat is modeled by a standard Fourier diffusion law, and is proportional to the total energy release rate of the fracture. The hence described dynamics holds a positive feedback: the faster the crack, the hotter it is and the faster it becomes.

We then show that, from a specific mechanical load, which corresponds to a particular crack propagation velocity, this phenomenon can lead to so-called thermal avalanches. The facture shifts from a slow creep regime to a brutal, dynamical, one. Thus, we describe rupture as a first order phase transition, where the order parameter is the propagation velocity and where the external field is the mechanical load. This framework in particular explains the intermittent stick-slip propagation of cracks, which is typicallyobserved in brittle rupture, but also explains the brittle-ductile transition of matter, corresponding to a critical point (second order transition) in our phase transition problem. Indeed, when a material is hot enough. The thermal avalanches are inhibited as the temperature elevations become negligible compared to the thermal background, and the material is then ductile.

We then compare this model to some data sets from the literature, gathered during the rupture of two widely different polymers: polymethylmethacrylate (PMMA) and a pressure sensible adhesive (PSA), which is typical for the glue used to design standard roller tapes. We show that the dynamics of rupture of these two materials can be quantitatively reproduced by the model over more than six orders of magnitude of propagation velocities, using only physical parameters that are realistic. Thus, a high velocity fracturing can still be considered as subcritical (as understood by an Arrhenius law), but in an intense thermal bath. We indeed infer from this model comparison to experimental data that, during the rupture of PMMA and PSA, the fracture fronts can reach thousands of degrees, on the length scale of a few atoms and duringsmall time intervals. Although impressive, such high temperatures have long been theorized, and they thus explain the brittleness of matter. We, in particular, discuss how they are compatible with the fractoluminescence phenomenon, that is, the emission of visible light during rupture.

The experimental bench working is limited to a few polymers because only few studies report both the very slow and very fast velocities for given materials, mainly because measuring such a large range in the kinetics is challenging. However, slow creep has been characterized for many materials, from the weakest glasses to the toughest metals. We then compare these slow dynamics to our model features. We show that the intrinsic resistance of all solids is always comparable to a covalence energy, and that the actualmacroscopic tenacity of matter derives only from the length scale around the crack tips over which heat is released. The bigger this length, the lesser the tip stress and the stronger the material. We also show that the model allows, when monitoring creep, to approximately predict the critical load at which fractures will evolve to a fast stage. Thermal dissipation is thus both the strength and the weakness of matter.

Of course, a slow enough crack may, in theory, never experience a thermal avalanche. In this case, onecan neglect the fracture induced temperature elevations and approximate the tip temperature as constant. The model we present then allowed, in prior works, to successfully account for the mean dynamics of interfacial fronts in PMMA, with various loading conditions. When the rupture interfaces hold some disorder in their tenacity, the fracture fronts become rugous, and their propagation becomes intermittent. By adding to the model an elastic redistribution of the stress along the fronts, we show that many features of this intermittency can be reproduced. Namely, the local propagation velocity distribution and correlation functions, the growth law and the fracture morphology. These matches confirm that a thermodynamics description of rupture is particularly relevant, even whenthe cracks are slow enough for any thermal induced effect to be negligible. Finally, the velocity of a fracture likely derives from the interaction between the quenched disorder of the material where it propagates and the thermal disorder at its tip. The asperities of a solid can in particular help to trigger thermal avalanches.

In Earth sciences, accounting for the disorder along fault surfaces has gathered more and more interest, as it is suspected that this disorder plays an important role in the intermittency of earthquakes. The heterogeneity of friction along fault planes is often considered. However, the anisotropy of this friction, which arises from the anisotropy in the topography of the fault surfaces, is rarely studied. To characterize this frictional anisotropy, we present a novel experimental set-up, based on the 3D printing of actual faults, whose topography was measured in the field. We show that an earthquake along a direction other than the main tectonic stress direction is possible, notably because of the frictional anisotropy.

Finally, and as an illustration that the main topic of this thesis, heat dissipation in rupture, has not yet revealed all of its secrets, we propose a new theory to explain the perception of mechanical pain by the human body. Indeed, when our biological tissues are damaged, the related elevations in temperatures are likely to be captured by our neural thermo-sensors. Thus, the feeling of mechanical pain could, in part, arise from some thermal measurements.

Jointly supervised PhD, IPGS-EOST, University of Strasbourg, ED 413, and PoreLab, The Njord Center, Physics Dept, University of Oslo