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We present a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces. To this end, we assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the hence obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that Arrhenius-like subcritical growth laws are particularly suitable for the description of creeping cracks., Comment: 22 pages, 14 figures, 5 appendices

We propose a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces [1]. We assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the obtained fracture dynamics to that from experimental cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that Arrhenius-like subcritical growth laws are particularly suitable for the description of creeping cracks.Reference:[1] Vincent-Dospital, T., Cochard, A., Santucci, S., Måløy, K.J., Toussaint, R., Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces. Sci Rep 11, 20418 (2021). https://doi.org/10.1038/s41598-021-98556-x

While of paramount importance in material science, the dynamics of cracks still lacks a complete physical explanation. The transition from their slow creep behavior to a fast propagation regime is a notable key, as it leads to full material failure if the size of a fast avalanche reaches that of the system. We here show that a simple thermodynamics approach can actually account for such complex crack dynamics, and in particular for the non-monotonic force-velocity curves commonly observed in mechanical tests on various materials. We consider a thermally activated failure process that is coupled with the production and the diffusion of heat at the fracture tip. In this framework, the rise in temperature only affects the sub-critical crack dynamics and not the mechanical properties of the material. We show that this description can quantitatively reproduce the rupture of two different polymeric materials (namely, the mode I opening of polymethylmethacrylate (PMMA) plates, and the peeling of pressure sensitive adhesive (PSA) tapes), from the very slow to the very fast fracturing regimes, over seven to nine decades of crack propagation velocities. In particular, the fastest regime is obtained with an increase of temperature of thousands of kelvins, on the molecular scale around the crack tip. Although surprising, such an extreme temperature is actually consistent with different experimental observations that accompany the fast propagation of cracks, namely, fractoluminescence (i.e., the emission of visible light during rupture) and a complex morphology of post-mortem fracture surfaces, which could be due to the sublimation of bubbles., Comment: 19 pages, 18 figures, including 4 appendices. Soft Matter, 2020

Mechanical pain (or mechanical algesia) can both be a vital mechanism warning us for dangers or an undesired medical symptom important to mitigate. Thus, a comprehensive understanding of the different mechanisms of this type of pain is paramount. In this work, we study the tearing of porcine skin in front of an infrared camera, and show that mechanical injuries in biological tissues can generate enough heat to stimulate the neural network. In particular, we report local temperature elevations of up to 24 degrees Celsius around fast cutaneous ruptures, which shall exceed the threshold of the neural nociceptors usually involved in thermal pain. Slower fractures exhibit lower temperature elevations, and we characterise such dependency to the damaging rate. Overall, we bring experimental evidence of a novel - thermal - pathway for direct mechanical algesia. In addition, the implications of this pathway are discussed for mechanical hyperalgesia as well, in which a role of the cutaneous thermal sensors has long been suspected. We also show that thermal dissipation shall actually account for a significant portion of the total skin's fracture energy, making temperature monitoring an efficient way to detect biological damages., 13 pages, 8 figures, 1 table

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

Mechanical algesia is an important process for the preservation of living organisms, allowing potentially life-saving reflexes or decisions when given body parts are stressed. Yet, its various underlying mechanisms remain to be fully unravelled. Here, we quantitatively discuss how the detection of painful mechanical stimuli by the human central nervous system may, partly, rely on thermal measurements. Indeed, most fractures in a body, including microscopic ones, release some heat, which diffuses in the surrounding tissues. Through this physical process, the thermo-sensitive TRP proteins, that translate abnormal temperatures into action potentials, shall be sensitive to damaging mechanical inputs. The implication of these polymodal receptors in mechanical algesia has been regularly reported, and we here provide a physical explanation for the coupling between thermal and mechanical pain. In particular, in the human skin, we show how the neighbouring neurites of a broken collagen fiber can undergo a sudden thermal elevation that ranges from a fraction to tens of degrees. As this theoretical temperature anomaly lies in the sensibility range of the TRPV3 and TRPV1 cation channels, known to trigger action potentials in the neural system, a degree of mechanical pain can hence be generated., 8 pages, 4 figures

In any domain involving some stressed solids, that is, from seismology to general engineering, the strength of matter is a paramount feature to understand. We here discuss the ability of a simple thermally activated sub-critical model, that includes the auto-induced thermal evolution of cracks tips, to predict the catastrophic failure of a vast range of materials. 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, G_a, solely from monitoring slow creep, and show that this reproduces the experimental values within 50% accuracy over twenty different materials, and over more than four decades of fracture energy., Comment: Supplementary Material (denoted as ESI in the manuscript) at the end of the file

The growth of fractures within mechanically loaded materials often shows two different behaviors. When loaded below a particular threshold in energy release rate, cracks tend indeed to creep at very slow velocities, while the rupture becomes catastrophic beyond this threshold, with propagation velocities approaching that of the material mechanical waves. Understanding according to which of these two behaviors a material is prone to break is of paramount importance, notably in engineering, where the brittle rupture of structures can lead to unpredicted disasters. It is also fundamental in Earth science, as damaging earthquakes are rather generated by abrupt ruptures in the crustal rocks than by their slow deformations. To explain both behaviors, we focus here on the thermal effects which are auto-induced by the growth of cracks. During their propagation, some of the system’s energy is indeed partly dissipated by Joule heating, which is arising from the friction in a damaged zone around the fracture fronts. The heat hence generated can in return have a significant impact on the physics of the propagation. For instance, the stability of faults is believed to be affected by the thermo-pressurization of their in situ fluids. Independently of this effect, we show, how statistical physics, as understood by an Arrhenius law that includes the dissipation and diffusion of heat around the fracture tip, can explain the full dynamics of cracks, from the slow creep to the fast rupture.We indeed show that such a model can successfully describe most of the experimentally reported fracture rheology, quantified in terms of velocity / energy release rate relations, in two different types of polymers, acrylic glasses and pressure sensitive adhesives, over eight decades of crack velocities. In these two cases, it is sufficient to assume that these polymers are homogeneous to model their failure. Yet, we in addition illustrate how the thermal disorder, from both the ambient temperature and the propagation induced heat, should interact with the matter typical quenched disorder in fracture energy. Numerical simulations of planar cracks in heterogeneous media indeed show that such quenched disorder helps to trigger hot avalanches in the propagation of cracks, making the overall toughness of a material highly dependent on both its heterogeneities, as it is often reported in the literature, and its thermal properties.

Anisotropic phenomena have long been studied in the vicinity of seismic faults. It has for instance been shown that both in situ pore fluids and seismic mechanical waves travel at different velocities along various directions of a fault zone. Yet, while more and more complexity and disorder in seismic models are introduced to better understand earthquakes, frictional anisotropy is only rarely regarded. In many other domains than geophysics, however, such anisotropy in solid friction is believed to be crucial. For instance, the tribology of rubber tires, skis or advanced adhesives is improved when those are designed to have a preferential frictional direction. But numerous natural systems also benefit from such anisotropy: is is notably essential in the motion of numerous animal skins and in the efficient hydration of some plants. In most cases, these frictional anisotropies derive from the existence of preferential topographic orientations on, at least, one of the contact surfaces, with scales for such structural directivity that can be multiple and various. Seismic faults also exhibit such preferential directions in their topography: unique rock crystals, such as antigorite, can already display some frictional anisotropy, fault zones are initiated by early fractures that often propagates through layered sediments, generating ramp-flat morphology in their surfaces and, finally, mature faults are marked by grooves of various wavelengths due to the slip induced erosion. In this work, we study how the morphology of faults affects their stability, as understood by their Coulomb static coefficient of friction. In particular we study its anisotropy with the slip direction. To do so, we make use of the 3D-printing technology and print actual fault surfaces, that were measured in the field. We perform friction experiments with gypsum casts of these 3D-printed faults, as mineral-like materials might deform differently under shear than plastic materials. With these experiments, we show that the friction coefficient along seismic faults is highly anisotropic, with slip motions that are easier in, but not limited to, the direction of the main grooves. This anisotropy could for instance be paramount to better predict the next direction of rupture along some faults under a varying stress state. In some cases, it could indeed not only be related to the orientation of the main regional stress, but also to the structural anisotropy, and depending on stress and friction anisotropy, along which orientation a rupture criterion will first be exceeded.

We present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which is described by an Arrhenius law. In this law, we take the thermal evolution of the crack front into account, assuming that a portion of the released mechanical energy is transformed into heat in a zone surrounding the tip. We show that such a model leads to a two-phase crack propagation: the first phase at low velocity in which the temperature elevation is of little effect and the propagation is mainly governed by the mechanical load and by the toughness of the medium, and the second phase in which the crack is thermally weakened and propagates at greater velocity. We illustrate, with numerical simulations of mode I cracks propagating in thin disordered media, how such a dual behavior can explain the usual stick-slip in brittle fracturing. In addition, we predict the existence of a limiting ambient temperature above which the weakened phase ceases to exist and we propose this critical phenomenon as a novel explanation for the brittle-ductile transition of solids.

International audience; Material failure is accompanied by important heat exchange, with extremely high temperature – thousands of degrees – reached at crack tips. Such 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 the 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. Monitoring the slow crack growth in paper sheets with an infrared camera, we measure a significant fraction α = 12% ± 4%. Besides, we show that (self-generated) heat accumulation could weaken our samples with microfibers combustion, and lead to a fast crack/dynamic failure/ regime.