Damage-cluster distributions and size effect on strength in compressive failure

Research on the Impact Mechanical Properties of Real-Time High-Temperature Granite and a Coupled Thermal-Mechanical Constitutive Model

Studying the mechanical behavior of rocks under real-time high-temperature conditions is of great significance for the development of energy caverns, nuclear waste disposal projects, and tunneling engineering. In this study, a real-time high-temperature impact compression test was conducted on Sejila Mountain granite to explore the effects of temperature and external load on its mechanical properties. Based on the concepts of damage mechanics and statistics, a coupled thermal-mechanical (T-M) damage constitutive model was established, which considers the temperature effect and uses the double-shear unified strength as the yield criterion. The parameter expressions were clarified, and the accuracy and applicability of the model were verified by experimental data. The research results indicated that high temperatures had an obvious damaging and deteriorating effect on the strength of the granite, while an increase in impact velocity had an enhancing effect on the strength of the granite. The established constitutive model theoretical curve and test curve showed a high degree of agreement, indicating that the coupled T-M model can objectively represent the evolution process of damage in rocks and the physical meaning of its parameters is clear.

Crossover from mean-field compression to collective phenomena in low-density foam-formed fiber material

We study the compression of low-weight foam-formed materials made out of wood fibers. Initially the stress-strain behavior follows mean-field like response, related to the buckling of fiber segments as dictated by the random three-dimensional geometry. Our Acoustic Emission (AE) measurements correlate with the predicted number of segment bucklings for increasing strain. However, the experiments reveal a transition to collective phenomena as the strain increases sufficiently. This is also seen in the gradual failure of the theory to account for the stress-strain curves. The collective avalanches exhibit scale-free features both as regards the AE energy distribution and the AE waiting time distributions with both exponents having values close to 2. In cyclic compression tests, significant increases in the accumulated acoustic energy are found only when the compression exceeds the displacement of the previous cycle, which further confirms other sources of acoustic events than fiber bending.

Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness

By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point and when the rupture thresholds are small. However, irrespective of network and spring properties, a more brittle fracture is observed upon increasing system size. Differently from most of the fracture descriptors, the maximum stress drop, a proxy for brittleness, displays a universal nonmonotonic dependence on system size. Based on this uncommon trend it is possible to identify the characteristic system size L^{*} at which brittleness kicks in. The more the disorder in network connectivity or in spring thresholds, the larger L^{*}. Finally, we speculate how this size-induced brittleness is influenced by thermal fluctuations.

From plastic flow to brittle fracture: Role of microscopic friction in amorphous solids

Plasticity in soft amorphous materials typically involves collective deformation patterns that emerge on intense shearing. The microscopic basis of amorphous plasticity has been commonly established through the notion of "Eshelby"-type events, localized abrupt rearrangements that induce flow in the surrounding material via nonlocal elastic-type interactions. This universal mechanism in flowing disordered solids has been proposed despite their diversity in terms of scales, microscopic constituents, or interactions. Using a numerical particle-based study, we argue that the presence of frictional interactions in granular solids alters the dynamics of flow by nucleating micro shear cracks that continually coalesce to build up system-spanning fracturelike formations on approach to failure. The plastic-to-brittle failure transition is controlled by the degree of frictional resistance which is in essence similar to the role of heterogeneities that separate the abrupt and smooth yielding regimes in glassy structures.

Experimental Study on Mechanical Properties, Energy Dissipation Characteristics and Acoustic Emission Parameters of Compression Failure of Sandstone Specimens Containing En Echelon Flaws

To further understand the fracture behavior of rock materials containing en echelon flawsand determine precursor information for the final collapse of damaged mineral assemblies undercompression, a series of uniaxial compression experiments using a loading system, an acousticemission system and a video camera was conducted on sandstone specimens containing en echelonflaws. The mechanical properties, energy dissipation characteristics and acoustic emissionparameters of compression failure of selected specimens were successively analyzed. The resultsshowed that crack initiation was accompanied by a stress drop, step-like characteristics on theenergy consumption curve and increased crackling noises, which were used as early warningsignals before the final collapse happened. In addition, we used the histogram statistics methodand maximum likelihood method to analyze the distribution of acoustic emission energy anddetermined that the acoustic emission energy distributions of sandstone specimens containing enechelon flaws followed a power law. With the progress of the experiment, the optimum exponentschanged in different stages and gradually decreased as failure was approached, which could alsobe used as an early warning signal before the final collapse happened. This paper may providesome theoretical basis for monitoring and warning about the collapse and instability of engineeringrock masses containing en echelon flaws.

Compressive Failure as a Critical Transition: Experimental Evidence and Mapping onto the Universality Class of Depinning

Acoustic emission (AE) measurements performed during the compressive loading of concrete samples with three different microstructures (aggregate sizes and porosity) and four sample sizes revealed that failure is preceded by an acceleration of the rate of fracturing events, power law distributions of AE energies and durations near failure, and a divergence of the fracturing correlation length and time towards failure. This argues for an interpretation of compressive failure of disordered materials as a critical transition between an intact and a failed state. The associated critical exponents were found to be independent of sample size and microstructural disorder and close to mean-field depinning values. Although compressive failure differs from classical depinning in several respects, including the nature of the elastic redistribution kernel, an analogy between the two processes allows deriving (finite-) sizing effects on strength that match our extensive data set. This critical interpretation of failure may have also important consequences in terms of natural hazards forecasting, such as volcanic eruptions, landslides, or cliff collapses.

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO_{2}) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.

Damage cluster distributions in numerical concrete at the mesoscale

We investigate the size distribution of damage clusters in concrete under uniaxial tension loading conditions. Using the finite-element method, the concrete is modeled at the mesoscale by a random distribution of elastic spherical aggregates within an elastic mortar paste. The propagation and coalescence of damage zones are then simulated by means of dynamically inserted cohesive elements. Dynamic failure analysis shows that the size distribution of damage clusters follows a power law when a system-spanning cluster is first observed, with an exponent close to that of percolation theory. This is found for a range of selected mesostructural parameters, material defects, and applied strain rates. In all cases, the system-spanning cluster occurs prior to the onset of local decohesion, a regime of crack nucleation and propagation, and eventual material failure. The resulting fully damaged crack surfaces after failure are found to be only weakly correlated with the percolated damage region structures.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Avalanches in Wood Compression

Wood is a multiscale material exhibiting a complex viscoplastic response. We study avalanches in small wood samples in compression. "Woodquakes" measured by acoustic emission are surprisingly similar to earthquakes and crackling noise in rocks and laboratory tests on brittle materials. Both the distributions of event energies and of waiting (silent) times follow power laws. The stress-strain response exhibits clear signatures of localization of deformation to "weak spots" or softwood layers, as identified using digital image correlation. Even though material structure-dependent localization takes place, the avalanche behavior remains scale-free.

Avalanches in compressed porous SiO(2)-based materials

The failure dynamics in SiO(2)-based porous materials under compression, namely the synthetic glass Gelsil and three natural sandstones, has been studied for slowly increasing compressive uniaxial stress with rates between 0.2 and 2.8 kPa/s. The measured collapsed dynamics is similar to Vycor, which is another synthetic porous SiO(2) glass similar to Gelsil but with a different porous mesostructure. Compression occurs by jerks of strain release and a major collapse at the failure point. The acoustic emission and shrinking of the samples during jerks are measured and analyzed. The energy of acoustic emission events, its duration, and waiting times between events show that the failure process follows avalanche criticality with power law statistics over ca. 4 decades with a power law exponent ɛ≃ 1.4 for the energy distribution. This exponent is consistent with the mean-field value for the collapse of granular media. Besides the absence of length, energy, and time scales, we demonstrate the existence of aftershock correlations during the failure process.

Predicting failure: acoustic emission of berlinite under compression

Acoustic emission has been measured and statistical characteristics analyzed during the stress-induced collapse of porous berlinite, AlPO4, containing up to 50 vol% porosity. Stress collapse occurs in a series of individual events (avalanches), and each avalanche leads to a jerk in sample compression with corresponding acoustic emission (AE) signals. The distribution of AE avalanche energies can be approximately described by a power law p(E)dE = E(-ε)dE (ε ~ 1.8) over a large stress interval. We observed several collapse mechanisms whereby less porous minerals show the superposition of independent jerks, which were not related to the major collapse at the failure stress. In highly porous berlinite (40% and 50%) an increase of energy emission occurred near the failure point. In contrast, the less porous samples did not show such an increase in energy emission. Instead, in the near vicinity of the main failure point they showed a reduction in the energy exponent to ~ 1.4, which is consistent with the value reported for compressed porous systems displaying critical behavior. This suggests that a critical avalanche regime with a lack of precursor events occurs. In this case, all preceding large events were 'false alarms' and unrelated to the main failure event. Our results identify a method to use pico-seismicity detection of foreshocks to warn of mine collapse before the main failure (the collapse) occurs, which can be applied to highly porous materials only.

(Finite) statistical size effects on compressive strength

The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules.

Rupture cascades in a discrete element model of a porous sedimentary rock

We investigate the scaling properties of the sources of crackling noise in a fully dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly sized spherical particles that are then connected by breakable beams. Loading at a constant strain rate the cohesive elements fail, and the resulting stress transfer produces sudden bursts of correlated failures, directly analogous to the sources of acoustic emissions in real experiments. The source size, energy, and duration can all be quantified for an individual event, and the population can be analyzed for its scaling properties, including the distribution of waiting times between consecutive events. Despite the nonstationary loading, the results are all characterized by power-law distributions over a broad range of scales in agreement with experiments. As failure is approached, temporal correlation of events emerges accompanied by spatial clustering.

Crackling noise during failure of alumina under compression: the effect of porosity

We study acoustic emission avalanches during the process of failure of porous alumina samples (Al2O3) under compression. Specimens with different porosities ranging from 30% to 59% have been synthesized from a mixture of fine-grained alumina and graphite. The compressive strength as well as the characteristics of the acoustic activity have been determined. The statistical analysis of the recorded acoustic emission pulses reveals, for all porosities, a broad distribution of energies with a fat tail, compatible with the existence of an underlying critical point. In the region of 35%-55% porosity, the energy distributions of the acoustic emission signals are compatible with a power-law behaviour over two decades in energy with an exponent ϵ = 1.8 ± 0.1.

Natural time analysis of critical phenomena: the case of pre-fracture electromagnetic emissions

Criticality of complex systems reveals itself in various ways. One way to monitor a system at critical state is to analyze its observable manifestations using the recently introduced method of natural time. Pre-fracture electromagnetic (EM) emissions, in agreement to laboratory experiments, have been consistently detected in the MHz band prior to significant earthquakes. It has been proposed that these emissions stem from the fracture of the heterogeneous materials surrounding the strong entities (asperities) distributed along the fault, preventing the relative slipping. It has also been proposed that the fracture of heterogeneous material could be described in analogy to the critical phase transitions in statistical physics. In this work, the natural time analysis is for the first time applied to the pre-fracture MHz EM signals revealing their critical nature. Seismicity and pre-fracture EM emissions should be two sides of the same coin concerning the earthquake generation process. Therefore, we also examine the corresponding foreshock seismic activity, as another manifestation of the same complex system at critical state. We conclude that the foreshock seismicity data present criticality features as well.

Statistical similarity between the compression of a porous material and earthquakes

It has long been stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallels between these so separate phenomena. We study the acoustic emission events produced during the compression of Vycor (SiO(2)). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate.