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.

1D charge density wave in the hidden order state of URu2Si2

Single crystals of URu2Si2 show below 17.5 K a transition into an ordered state with a significantly reduced entropy. The low temperature phase is called the hidden order (HO) state, because its microscopic origin is still unknown—there are no charge, structural or magnetic transitions associated to HO. Here we report a one-dimensional (1D) charge modulation within the HO state of URu2Si2. We perform detailed Scanning Tunneling Microscopy (STM) experiments with high resolution on many atomically flat surfaces of URu2Si2 obtained by fracturing single crystals at cryogenic temperatures and find a 1D charge density wave with a large wavevector. We show that the 1D modulation is connected to the dynamical magnetic excitations of the HO through a moiré construction and appears as a consequence of excitations quenched through the interaction between the travelling fracture front and the dynamic modes of the crystal. The combination of fracture dynamics and the dynamics of the solid provides a method to create ground states and shows that charge interactions are among the most relevant features competing with HO in URu2Si2.

Thermal jet drilling of granite rock: a numerical 3D finite-element study

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Fracture mechanics of rate-and-state faults and fluid injection induced slip

Propagation of a slip transient on a fault with rate- and state-dependent friction resembles a fracture whose near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy G c , dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity v r . This opens a possibility to model slip transients on rate-and-state faults as singular cracks characterized by approximately steady-state frictional resistance in the fracture bulk, and by a stress singularity with the intensity defined in terms of G c ( v r ) at the crack tip. In pursuing this route, we develop and use an analytical equation of motion to study 1-D slip driven by a combination of uniform background stress and a localized perturbation of the fault strength with the net Coulomb force Δ T . In the context of fluid injection, Δ T is a proxy for the injection volume V inj . We then show that, for ongoing fluid injection, the propagation speed of a transient induced on a frictionally stable fault is bounded by a large-time limiting value proportional to the injection rate dV inj /d t , while, for stopped injection, the maximum slip run-out distance is proportional to V inj , total 2 . This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Pre-P gravity signals from dynamic earthquake rupture: modelling and observations

Dynamic earthquake rupture is one of the most extensive and devastating fracture phenomena on the Earth. It causes a sudden crustal deformation around a fault and generates seismic waves that induce bulk density variations propagating with them. Both processes constitute rock-mass redistribution, which is expected to induce simultaneous transient gravity perturbations at all distances before the arrival of P-waves. Interest in such pre-P gravity signals has increased both in terms of modelling and observations because of their potential for earthquake early warning. A simple forward model has pioneered the search for the so-called prompt elasto-gravity signals, which led to the first report of a signal from the 2011 M w 9.0 Tohoku-Oki earthquake using a single superconducting gravimeter record. The second report followed using hundreds of broadband seismometers with critical modification of the previous model to consider the pre-P ground acceleration in the measurement of gravity. Post-event analyses have identified prompt elasto-gravity signals from several large earthquakes, and state-of-the-art instruments are now being developed for real-time signal detection. This paper reviews recent progress in the cutting-edge subject of prompt elasto-gravity signals owing to large-scale earthquake rupture. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Molecular dynamics study on atomic elastic stiffness at mode I crack along bi-metal interface

Propagation of mode I crack along bi-metal (001) interfaces of Fe/W, Fe/Ni, Fe/Co and Ti/Mg is simulated by molecular dynamics and discussed with the eigenvalue/vector of the atomic elastic stiffness, B i j a = Δ σ i a / Δ ε j , and surface energy. The crack does not propagate at the interface but in the adjacent phase of smaller surface energy, except in Fe/Ni. The 1st eigenvalue η a (1) , or the solution of B i j a Δ ε j = η a Δ ε i of each atom, clarifies the difference of ‘soft/hard’ of both phases at the onset of crack propagation. In the case of Fe/Ni, the η a (1) of Ni atoms remarkably decreases in the Fe/Ni bi-metal structure, even though Ni has higher η a (1) than Fe at no-load perfect lattices. Thus the rupture occurs in the Ni side even though the Ni has slightly higher (001) surface energy than Fe. Deformation modes at the crack propagation are also visualized by the eigenvector of η a (1) < 0 unstable atoms. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Complexities of underground mining seismic sources

This paper presents a numerical investigation on the influence of the mining environment on seismic sources, with a focus on pillar failure mechanisms in tabular mining. We investigate the influence of the mining stope (underground excavation or void) on seismic inversions for the scalar moment, corner frequency, source radius, stress drop and moment tensor using synthetic events created within elastodynamic numerical modelling software, WAVE3D. The main objective is to determine whether the source parameters calculated from the recorded waveforms are due to a combination of the stope source and the pillar sources, rather than being related only to crushing of the pillar or shearing in the pillar footwall. The main finding is that the presence of stopes, and types of pillars, have a significant impact on the seismic moment and other source parameters. This is important since the moment is viewed as a robust parameter on which seismic magnitude is often based; however, this study indicates that moments calculated for pillar failure in a tabular stoping environments are less representative of the shearing or crushing source than originally thought. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Fracture asperity evolution during the transition from stick slip to stable sliding

Fracture asperities interlock or break during stick slip and ride over each other during stable sliding. The evolution of fracture asperities during the transition between stick slip and stable sliding has attracted less attention, but is important to predict fracture behaviour. Here, we conduct a series of direct shear experiments on simulated fractures in homogeneous polycarbonate to examine the evolution of fracture asperities in the transition stage. Our results show that the transition stage occurs between the stick slip and stable sliding stages during the progressive reduction in normal stress on the smooth and rough fractures. Both the fractures exhibit the alternative occurrence of small and large shear stress drops followed by the deterministic chaos in the transition stage. Our data indicate that the asperity radius of curvature correlates linearly with the dimensionless contact area under a given normal stress. For the rough fracture, a bifurcation of acoustic energy release appears when the dimensionless contact area decreases in the transition stage. The evolution of fracture asperities is stress-dependent and velocity-dependent. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Micro-mechanical fracture dynamics and damage modelling in brittle materials

This study explores the interplay between wave propagation and damage in brittle materials. The damage models, based on micro-mechanical fracture dynamics, capture any possible unstable growth of micro-cracks, introducing a macroscopic loss of stability. After stating the non-dimensional mathematical problem describing the wave propagation with damage, we introduce a non-dimensional number, called the microscopic evolution index, which links the micro and macro scales and discriminates the microscopic scale behaviour. For large values of microscopic evolution index, corresponding to a microscopic quasi-static process coupled with a macroscopic dynamic one, the macroscopic dynamic system could lose its hyperbolicity or become very stiff and generate shock waves. A semi-analytical solution to the one-dimensional wave propagation problem with damage, which could be very useful in the accuracy evaluation of the numerical schemes, was constructed. Concerning the asymptotic behaviour of the dynamic exact solution on the microscopic evolution index (or on the strain rate), an important strain rate sensitivity was found: the pulse loses its amplitude for decreasing strain rate and, starting with a critical value, the micro-scale model is rate independent. A possible regularization technique to smooth the shock waves at low and moderate strain rates is discussed. Finally, some numerical results analyse the role played by the the friction on the micro-cracks in the damage modelling of blast wave propagation. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.