Experimental study of the effect of disorder on subcritical crack growth dynamics

Record statistics of fracture in the random spring network model

We study the role of record statistics of damage avalanches in predicting the fracture of a heterogeneous material under tensile loading. The material is modeled using a two-dimensional random spring network where disorder is introduced through randomness in the breakage threshold strains of the springs. It is shown that the waiting strain interval between successive records of avalanches has a maximum for moderate disorder, thus showing an acceleration in occurrence of records when approaching final fracture. Such a signature is absent for low disorder when the fracture is nucleation-dominated, as well as for high disorder when the fracture is percolation type. We examine the correlation between the record with the maximum waiting strain interval and the crossover record at which the avalanche statistics change from off-critical to critical. Compared to the avalanche exponent crossover based prediction for failure, we show that the record statistics have the advantage of both being real-time as well as being a precursor significantly prior to final fracture. We also find that in the avalanche-dominated regime, the failure strain is at best weakly correlated with the strain at the maximum waiting strain interval. A stronger correlation is observed between the index of the largest record and the index of the record at the maximum waiting strain interval.

Critical crack length during fracture

Through controlled numerical simulations in a one-dimensional fiber bundle model with local stress concentration, we established an inverse correlation between the strength of the material and the cracks which grow inside it-both the maximum crack and the one that sets in instability within the system, defined to be the critical crack. Through the Pearson correlation function as well as probabilistic study of individual configurations, we found that the maximum and the critical crack often differ from each other unless the disorder strength is extremely low. A phase diagram on the plane of disorder vs system size demarcates between the regions where the largest crack is the most vulnerable one and where they differ from each other but still show moderate correlation.

Unified scenario for the morphology of crack paths in two-dimensional disordered solids

A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent ζ≈0.6-0.7 as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent ζ=0.50±0.05, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with ζ≈0.6-0.7 observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.

Impact-induced transition from damage to perforation

We investigate the impact-induced damage and fracture of a bar-shaped specimen of heterogeneous materials focusing on how the system approaches perforation as the impact energy is gradually increased. A simple model is constructed which represents the bar as two rigid blocks coupled by a breakable interface with disordered local strength. The bar is clamped at the two ends, and the fracture process is initiated by an impactor hitting the bar in the middle. Our calculations revealed that depending on the imparted energy, the system has two phases: at low impact energies the bar suffers damage but keeps its integrity, while at sufficiently high energies, complete perforation occurs. We demonstrate that the transition from damage to perforation occurs analogous to continuous phase transitions. Approaching the critical point from below, the intact fraction of the interface goes to zero, while the deformation rate of the bar diverges according to power laws as function of the distance from the critical energy. As the degree of disorder increases, farther from the transition point the critical exponents agree with their zero disorder counterparts; however, close to the critical point a crossover occurs to a higher exponent.

Record statistics of bursts signals the onset of acceleration towards failure

Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast methods predict the lifetime of the system based on the time-to-failure power law of observables describing the final acceleration towards failure. We show that the statistics of records of the event series of breaking bursts, accompanying the failure process, provides a powerful tool to detect the onset of acceleration, as an early warning of the impending catastrophe. We focus on the fracture of heterogeneous materials using a fiber bundle model, which exhibits transitions between perfectly brittle, quasi-brittle, and ductile behaviors as the amount of disorder is increased. Analyzing the lifetime of record size bursts, we demonstrate that the acceleration starts at a characteristic record rank, below which record breaking slows down due to the dominance of disorder in fracturing, while above it stress redistribution gives rise to an enhanced triggering of bursts and acceleration of the dynamics. The emergence of this signal depends on the degree of disorder making both highly brittle fracture of low disorder materials, and ductile fracture of strongly disordered ones, unpredictable.

System-size-dependent avalanche statistics in the limit of high disorder

We investigate the effect of the amount of disorder on the statistics of breaking bursts during the quasistatic fracture of heterogeneous materials. We consider a fiber bundle model where the strength of single fibers is sampled from a power-law distribution over a finite range, so that the amount of materials' disorder can be controlled by varying the power-law exponent and the upper cutoff of fibers' strength. Analytical calculations and computer simulations, performed in the limit of equal load sharing, revealed that depending on the disorder parameters the mechanical response of the bundle is either perfectly brittle where the first fiber breaking triggers a catastrophic avalanche, or it is quasibrittle where macroscopic failure is preceded by a sequence of bursts. In the quasibrittle phase, the statistics of avalanche sizes is found to show a high degree of complexity. In particular, we demonstrate that the functional form of the size distribution of bursts depends on the system size: for large upper cutoffs of fibers' strength, in small systems the sequence of bursts has a high degree of stationarity characterized by a power-law size distribution with a universal exponent. However, for sufficiently large bundles the breaking process accelerates towards the critical point of failure, which gives rise to a crossover between two power laws. The transition between the two regimes occurs at a characteristic system size which depends on the disorder parameters.

Effect of disorder on the spatial structure of damage in slowly compressed porous rocks

Faults and damage zone properties control a range of important phenomena, from the hydraulic properties of underground reservoirs to the physics of earthquakes on a larger scale. Here, we investigate the effect of disorder of porous rocks on the spatial structure of damage emerging under compression. Model rock samples are numerically generated by sedimenting particles where the amount of disorder is controlled by the particle size distribution. To obtain damage bands with a sufficiently large length along axis, we performed simulations of 'Brazilian'-type compression tests of cylindrical samples. As failure is approached, damage localization leads to the formation of two conjugate shear bands. The orientation angle of bands to the loading direction increases with disorder, implying a decrease in the internal coefficient of friction. The width of the damage band scales as a power law of the degree of disorder. Inside the damage band, the sample is crushed into a large number of pieces with a power law mass distribution. The shape of fragments undergoes a crossover at a disorder-dependent size from the isotropy of small pieces to the anisotropic flattened form of the large ones. The results provide important constraints in understanding the role of disorder in geological fractures.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Seismic and experimental insights into eruption precursors at Volcán de Colima

We combine geophysical and experimental observations to interpret preeruptive unrest at Volcán de Colima in 1998. 17,893 volcanic earthquakes were detected between 1 October and 31 December 1998, including 504 clusters. Using seismic ambient noise interferometry, we observe a drop in velocity prior to the eruption linked to damage accumulation during magma ascent. This is supported by experimental observations where static stress causes a velocity decrease prior to failure. Furthermore, we observe acoustic emission clusters during the experiments, with lower porosity samples producing higher numbers of repeaters. This behavior introduces tensile failure as an additional viable mechanism for clusters during magma ascent. The findings suggest that preeruptive magma ascent may be monitored to variable degrees of accuracy via descriptions of damage accumulation and associated seismic velocity changes.

Blending stiffness and strength disorder can stabilize fracture

Quasibrittle behavior, where macroscopic failure is preceded by stable damaging and intensive cracking activity, is a desired feature of materials because it makes fracture predictable. Based on a fiber-bundle model with global load sharing we show that blending strength and stiffness disorder of material elements leads to the stabilization of fracture, i.e., samples that are brittle when one source of disorder is present become quasibrittle as a consequence of blending. We derive a condition of quasibrittle behavior in terms of the joint distribution of the two sources of disorder. Breaking bursts have a power-law size distribution of exponent 5/2 without any crossover to a lower exponent when the amount of disorder is gradually decreased. The results have practical relevance for the design of materials to increase the safety of constructions.

Heterogeneity: The key to failure forecasting

Elastic waves are generated when brittle materials are subjected to increasing strain. Their number and energy increase non-linearly, ending in a system-sized catastrophic failure event. Accelerating rates of geophysical signals (e.g., seismicity and deformation) preceding large-scale dynamic failure can serve as proxies for damage accumulation in the Failure Forecast Method (FFM). Here we test the hypothesis that the style and mechanisms of deformation, and the accuracy of the FFM, are both tightly controlled by the degree of microstructural heterogeneity of the material under stress. We generate a suite of synthetic samples with variable heterogeneity, controlled by the gas volume fraction. We experimentally demonstrate that the accuracy of failure prediction increases drastically with the degree of material heterogeneity. These results have significant implications in a broad range of material-based disciplines for which failure forecasting is of central importance. In particular, the FFM has been used with only variable success to forecast failure scenarios both in the field (volcanic eruptions and landslides) and in the laboratory (rock and magma failure). Our results show that this variability may be explained, and the reliability and accuracy of forecast quantified significantly improved, by accounting for material heterogeneity as a first-order control on forecasting power.

High frequency monitoring reveals aftershocks in subcritical crack growth

By combining direct imaging and acoustic emission measurements, the subcritical propagation of a crack in a heterogeneous material is analyzed. Both methods show that the fracture proceeds through a succession of discrete events. However, the macroscopic opening of the fracture captured by the images results from the accumulation of more-elementary events detected by the acoustics. When the acoustic energy is cumulated over large time scales corresponding to the image acquisition rate, a similar statistics is recovered. High frequency acoustic monitoring reveals aftershocks responsible for a time scale dependent exponent of the power law energy distributions. On the contrary, direct imaging, which is unable to resolve these aftershocks, delivers a misleading exponent value.

Creep rupture as a non-homogeneous Poissonian process

Creep rupture of heterogeneous materials occurring under constant sub-critical external loads is responsible for the collapse of engineering constructions and for natural catastrophes. Acoustic monitoring of crackling bursts provides microscopic insight into the failure process. Based on a fiber bundle model, we show that the accelerating bursting activity when approaching failure can be described by the Omori law. For long range load redistribution the time series of bursts proved to be a non-homogeneous Poissonian process with power law distributed burst sizes and waiting times. We demonstrate that limitations of experiments such as finite detection threshold and time resolution have striking effects on the characteristic exponents, which have to be taken into account when comparing model calculations with experiments. Recording events solely within the Omori time to failure the size distribution of bursts has a crossover to a lower exponent which is promising for forecasting the imminent catastrophic failure.