Thermal dissipation as both the strength and weakness of matter. A material failure prediction by monitoring creep.

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, which 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 this macroscopic energy release rate of rupture, Ga, solely from monitoring slow creep, and we show that this reproduces the experimental values within 50% accuracy over twenty different materials, and over more than four decades of fracture energy.

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

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.

Verification of a Dynamic Scaling for the Pair Correlation Function during the Slow Drainage of a Porous Medium.

In this Letter we give experimental grounding for the remarkable observation made by Furuberg et al. [Phys. Rev. Lett. 61, 2117 (1988)PRLTAO0031-900710.1103/PhysRevLett.61.2117] of an unusual dynamic scaling for the pair correlation function N(r,t) during the slow drainage of a porous medium. Those authors use an invasion percolation algorithm to show numerically that the probability of invasion of a pore at a distance r away and after a time t from the invasion of another pore scales as N(r,t)∝r^{-1}f(r^{D}/t), where D is the fractal dimension of the invading cluster and the function f(u)∝u^{1.4}, for u≪1 and f(u)∝u^{-0.6}, for u≫1. Our experimental setup allows us to have full access to the spatiotemporal evolution of the invasion, which is used to directly verify this scaling. Additionally, we connect two important theoretical contributions from the literature to explain the functional dependency of N(r,t) and the scaling exponent for the short-time regime (t≪r^{D}). A new theoretical argument is developed to explain the long-time regime exponent (t≫r^{D}).

Frictional Fluid Dynamics and Plug Formation in Multiphase Millifluidic Flow.

We study experimentally the flow and patterning of a granular suspension displaced by air inside a narrow tube. The invading air-liquid interface accumulates a plug of granular material that clogs the tube due to friction with the confining walls. The gas percolates through the static plug once the gas pressure exceeds the pore capillary entry pressure of the packed grains, and a moving accumulation front is reestablished at the far side of the plug. The process repeats, such that the advancing interface leaves a trail of plugs in its wake. Further, we show that the system undergoes a fluidization transition-and complete evacuation of the granular suspension-when the liquid withdrawal rate increases beyond a critical value. An analytical model of the stability condition for the granular accumulation predicts the flow regime.

Interevent Correlations from Avalanches Hiding Below the Detection Threshold.

Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or clustered, evidenced by power-law-distributed waiting times separating two consecutive activity bursts. We show how such interevent correlations arise simply because of a finite detection threshold, created by the limited sensitivity of the measurement apparatus, or used to subtract background activity or noise from the activity signal. Data from crack-propagation experiments and numerical simulations of a nonequilibrium crack-line model demonstrate how thresholding leads to correlated bursts of activity by separating the avalanche events into subavalanches. The resulting temporal subavalanche correlations are well described by our general scaling description of thresholding-induced correlations in crackling noise.

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

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.

Non-Gaussian nature of fracture and the survival of fat-tail exponents.

We study the fluctuations of the global velocity V(l)(t), computed at various length scales l, during the intermittent mode-I propagation of a crack front. The statistics converge to a non-Gaussian distribution, with an asymmetric shape and a fat tail. This breakdown of the central limit theorem (CLT) is due to the diverging variance of the underlying local crack front velocity distribution, displaying a power law tail. Indeed, by the application of a generalized CLT, the full shape of our experimental velocity distribution at large scale is shown to follow the stable Levy distribution, which preserves the power law tail exponent under upscaling. This study aims to demonstrate in general for crackling noise systems how one can infer the complete scale dependence of the activity--and extreme event distributions--by measuring only at a global scale.

Frictional fluid instabilities shaped by viscous forces.

Multiphase flows involving granular materials are complex and prone to pattern formation caused by competing mechanical and hydrodynamic interactions. Here we study the interplay between granular bulldozing and the stabilising effect of viscous pressure gradients in the invading fluid. Injection of aqueous solutions into layers of dry, hydrophobic grains represent a viscously stable scenario where we observe a transition from growth of a single frictional finger to simultaneous growth of multiple fingers as viscous forces are increased. The pattern is made more compact by the internal viscous pressure gradient, ultimately resulting in a fully stabilised front of frictional fingers advancing as a radial spoke pattern.

Dynamics of Dendritic Ice Freezing in Confinement.

We use high-speed photography to observe the dendritic freezing of ice between two closely spaced parallel plates. Measuring the propagation speeds of dendrites, we investigate whether there is a confinement-induced thermal influence upon the speed beyond that provided by a single surface. Plates of thermally insulating plastic and moderately thermally conductive glass are used alone and in combination, at temperatures between -10.6 and -4.8 °C, with separations between 17 and 135 µm wide. No effect of confinement was detected for propagation on glass surfaces, but a possible slowing of propagation speed was seen between insulating plates. The pattern of dendritic growth was also studied, with a change from curving to straight dendrites being strongly associated with a switch from a glass to a plastic substrate.

Heat Emitting Damage in Skin: A Thermal Pathway for Mechanical Algesia.

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 responsible for 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°C 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, in which a role of the cutaneous thermal sensors has priorly 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.

Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces.

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 obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such an 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 an Arrhenius-like subcritical growth is particularly suitable for the description of creeping cracks.

Granular labyrinth structures in confined geometries.

Pattern forming processes are abundant in nature. Here, we report on a particular pattern forming process. Upon withdrawal of fluid from a particle-fluid dispersion in a Hele-Shaw cell, the particles are shown to be left behind in intriguing mazelike patterns. The particles, initially being uniformly spread out in a disc, are slowly pulled inwards and together by capillary and pressure forces. Invading air forms branching fingers, whereas the particles are compiled into comparably narrow branches. These branches are connected in a treelike structure, taking the form of a maze. The characteristic length scale within the structure is found to decrease with the volume fraction of the particles and increase with the plate separation in the Hele-Shaw cell. We present a simulator designed to simulate this phenomenon, which reproduces qualitatively and quantitatively the experiments, as well as a theory that can predict the observed wavelengths.

Experiments and simulations of a gravitational granular flow instability.

An instability is observed as a layer of dense granular material positioned above a layer of air falls in a gravitational field [Phys. Rev. Lett. 99, 048001 (2007)]. A characteristic pattern of fingers emerges along the interface defined by the grains, and a transient coarsening of the structure is caused by a coalescence of neighboring fingers. The coarsening is limited by the production of new fingers as the separation of the existing fingers reaches a certain distance. The experiments and simulations presented are shown to be comparable both qualitatively and quantitatively. The characteristic inverse length scale of the structures, obtained as the mean of the solid fraction power spectrum, relaxes toward a stable value shared by the numerical and experimental data. Further, the response of the numerical model to changes in various model parameters is investigated. These parameters include the density of the grains, the shape of the initial air-grain interface, and the dissipation of the granular phase. Also, the growth rates of the bulk solid fraction and the air-grain interface are obtained from Fourier power spectra of the numerical data. This analysis reveals that the instability is never in a linear regime, not even initially.

Statistics of fracture surfaces.

We analyze the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the distribution to an analysis based on the structure functions. For length scales delta larger than a characteristic scale Lambda that corresponds to a material heterogeneity size, we find that the distribution of the height increments Deltah=h(x+delta)-h(x) is Gaussian and monoaffine, i.e., the scaling of the standard deviation sigma is proportional to delta(zeta) with a unique roughness exponent. Below the scale Lambda we observe a deviation from a Gaussian distribution and a monoaffine behavior. We discuss for the latter, the relevance of a multiaffine analysis and the influences of the discreteness resulting from material microstructures or experimental sampling.

Note: Localization based on estimated source energy homogeneity.

Acoustic signal localization is a complex problem with a wide range of industrial and academic applications. Herein, we propose a localization method based on energy attenuation and inverted source amplitude comparison (termed estimated source energy homogeneity, or ESEH). This inversion is tested on both synthetic (numerical) data using a Lamb wave propagation model and experimental 2D plate data (recorded with 4 accelerometers sensitive up to 26 kHz). We compare the performance of this technique with classic source localization algorithms: arrival time localization, time reversal localization, and localization based on energy amplitude. Our technique is highly versatile and out-performs the conventional techniques in terms of error minimization and cost (both computational and financial).

Numerical approach to frictional fingers.

Experiments on confined two-phase flow systems, involving air and a dense suspension, have revealed a diverse set of flow morphologies. As the air displaces the suspension, the beads that make up the suspension can accumulate along the interface. The dynamics can generate "frictional fingers" of air coated by densely packed grains. We present here a simplified model for the dynamics together with a new numerical strategy for simulating the frictional finger behavior. The model is based on the yield stress criterion of the interface. The discretization scheme allows for simulating a larger range of structures than previous approaches. We further make theoretical predictions for the characteristic width associated with the frictional fingers, based on the yield stress criterion, and compare these to experimental results. The agreement between theory and experiments validates our model and allows us to estimate the unknown parameter in the yield stress criterion, which we use in the simulations.

Growth activity during fingering in a porous Hele-Shaw cell.

We present in this paper an experimental study of the invasion activity during unstable drainage in a two-dimensional random porous medium, when the (wetting) displaced fluid has a high viscosity with respect to that of the (nonwetting) displacing fluid, and for a range of almost two decades in capillary numbers corresponding to the transition between capillary and viscous fingering. We show that the invasion process takes place in an active zone within a characteristic screening length lambda from the tip of the most advanced finger. The invasion probability density is found to only depend on the distance z to the latter tip and to be independent of the value for the capillary number Ca. The mass density along the flow direction is related analytically to the invasion probability density, and the scaling with respect to the capillary number is consistent with a power law. Other quantities characteristic of the displacement process, such as the speed of the most advanced finger tip or the characteristic finger width, are also consistent with power laws of the capillary number. The link between the growth probability and the pressure field is studied analytically and an expression for the pressure in the defending fluid along the cluster is derived. The measured pressure is then compared with the corresponding simulated pressure field using this expression for the boundary condition on the cluster.

Interface scaling in a two-dimensional porous medium under combined viscous, gravity, and capillary effects.

We have investigated experimentally the competition between viscous, capillary, and gravity forces during drainage in a two-dimensional synthetic porous medium. The displacement of a mixture of glycerol and water by air at constant withdrawal rate has been studied. The setup can be tilted to tune gravity, and pressure is recorded at the outlet of the model. Viscous forces tend to destabilize the displacement front into narrow fingers against the stabilizing effect of gravity. Subsequently, a viscous instability is observed for sufficiently large withdrawal speeds or sufficiently low gravity components on the model. We predict the scaling of the front width for stable situations and characterize it experimentally through analyses of the invasion front geometry and pressure recordings. The front width under stable displacement and the threshold for the instability are shown, both experimentally and theoretically, to be controlled by a dimensionless number F which is defined as the ratio of the effective fluid pressure drop (i.e., average hydrostatic pressure drop minus viscous pressure drop) at pore scale to the width of the fluctuations in the threshold capillary pressures.

Flow paths in wetting unsaturated flow: experiments and simulations.

The flow paths and instabilities of gravity driven infiltration of a wetting fluid into a porous medium are studied. The model experiments and simulations independently represent techniques to study the unsaturated flow in porous media, and they produce a consistent picture of how the paths of fluid transport form and depend on the relative strength of the gravitational force. The experiments, which employ a transparent and quasi-two-dimensional model, reveal that the fluid pathways contain an internal link-blob structure and increase in width with decreasing gravity. The model, which couples the well established invasion percolation model for capillary governed flow with a model that describes the viscous film flow in partially filled pores, corroborates these experimental findings.

Direct velocity measurement of a turbulent shear flow in a planar Couette cell.

In a plane Couette cell a thin fluid layer consisting of water is sheared between the sides of a transparent band at Reynolds numbers ranging from 300 to 1400. The length of the cell's flow channel is large compared to the film separation. To extract the flow velocity in the experiments, a correlation image velocimetry method is used on pictures recorded with a high-speed camera. The flow is recorded at a resolution that allows us to analyze flow patterns similar in size to the film separation. The fluid flow is then studied by calculating flow velocity autocorrelation functions. The turbulent patterns that arise on this scale above a critical Reynolds number of Re=360 display characteristic patterns that are proven by use of the calculated velocity autocorrelation functions. The patterns are metastable and reappear at different positions and times throughout the experiments. Typically these patterns are turbulent rolls which are elongated in the stream direction, which is the direction in which the band is moving. Although the flow states are metastable they possess similarities to the steady Taylor vortices known to appear in circular Taylor Couette cells.