How cracks are hot and cool: a burning issue for paper

Abstract

Material failure is accompanied by important heat exchange, with extremely high temperature - thousands of degrees - reached at crack tips. Such a temperature may subsequently alter the mechanical properties of stressed solids, and finally facilitate their rupture. Thermal runaway weakening processes could indeed explain stick-slip motions and even be responsible for deep earthquakes. Therefore, to better understand catastrophic rupture events, it appears crucial to establish an accurate energy budget of fracture propagation from a clear measure of various energy dissipation sources. In this work, combining analytical calculations and numerical simulations, we directly relate the temperature field around a moving crack tip to the part α of mechanical energy converted into heat. By monitoring the slow crack growth in paper sheets using an infrared camera, we measure a significant fraction α = 12% ± 4%. Besides, we show that (self-generated) heat accumulation could weaken our samples by microfiber combustion, and lead to a fast crack/dynamic failure/regime.

How heat controls fracture: the thermodynamics of creeping and avalanching cracks

“…While the energy dissipation can be of several forms, ranging from the emission of mechanical waves 50 damped in the far field, to the nucleation of defaults in the matrix 51 (i.e., crazing 9,52 ), we here focus on the release of heat around the fracture tip. 27,40 We thus call f the percentage of G that is converted into some local rise in internal energy, and hence in temperature, and denote l the typical size over which this process occurs. As the heat, released on a production zone of area pl 2 close to the tip, is to diffuse in the whole bulk, the resulting temperature elevation DT can be modelled (e.g., ref.…”

“…16 Here we neglect any spatial variation of the fracture energy, but let the crack tip temperature vary as a function of the front velocity and of the applied mechanical load. Indeed, in a previous experimental and theoretical study of the tearing-induced heating in paper sheets, 27 we were able to relate the temperature field around moving cracks to a certain percentage of the mechanical energy which gets converted into heat as the tip advances. More recently, this rise in temperature was fed back into a sub-critical growth law and showed 28 that one can thus obtain a dynamics model holding numerous qualitative similarities with the observed behavior of cracks, namely, two stable phases of propagation and a critical point that is similar to a brittle-ductile transition (e.g., ref.…”

Predicting sample lifetimes in creep fracture of heterogeneous materials

“…In the experiments (material) at hand, typical fluctuations have a fairly large spatial scale compared to the sample size [24,26]. Also, the final crack is detectable using infrared thermography [41] only roughly 1 s before the sample failure (SM, Figs. S9 and S10).…”

Non-equilibrium cytoquake dynamics in cytoskeletal remodeling and stabilization

“…And since after an earthquake there are many local slow geological accommodations, much slower than the shock propagation itself, aftershocks are also clustered in time. In a similar fashion, the accumulation and sudden release of energy is widespread in other physical systems, such as snow avalanches, 14 particle gels, 15 catastrophic rupture events, 16 magnetism, 17 and in physiology, such as pressure volume instabilities, 18,19 and crackling lung sounds. 20,21 …”