Brittle-quasibrittle transition in dynamic fracture: an energetic signature

Effective Toughness of Heterogeneous Materials with Rate-Dependent Fracture Energy

We investigate the dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of the rate dependency of the fracture energy and the inertia of the medium, which allows the crack to cross a fracture energy discontinuity at a constant energy release rate. This discontinuous dynamics and the rate dependence cause higher effective toughness, which governs the coarse-grained behavior of these cracks.

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.

Modes of failure in disordered solids

The two principal ingredients determining the failure modes of disordered solids are the strength of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage-the two extreme natures of the failure modes. In this study, using the random fiber bundle model as a prototype for disordered solids, we classify all failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes. As the fiber bundle model is a long-standing model for interpreting various features of stressed disordered solids, the general phase diagram can serve as a guiding principle in anticipating the responses of disordered solids in general.

Nonlinear Focusing in Dynamic Crack Fronts and the Microbranching Transition

Cracks in brittle materials produce two types of generic surface structures: facets at low velocities and microbranches at higher ones. Here we observe a transition from faceting to microbranching in polyacrylamide gels that is characterized by nonlinear dynamic localization of crack fronts. To better understand this process we derive a first-principles nonlinear equation of motion for crack fronts in the context of scalar elasticity. Its solution shows that nonlinear focusing coupled to rate dependence of dissipation governs the transition to microbranching.

Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks

Using an elastodynamic boundary integral formulation coupled with a cohesive model, we study the problem of a dynamic rupture front propagating along an heterogeneous plane. We show that small-scale heterogeneities facilitate the supershear transition of a mode-II crack. The elastic pulses radiated during front accelerations explain how microscopic variations of fracture toughness change the macroscopic rupture dynamics. Perturbations of dynamic fronts are then systematically studied with different microstructures and loading conditions. The process zone size is the intrinsic length scale controlling heterogeneous dynamic rupture. The ratio of this length scale to asperity size is proposed as an indicator to transition from quasihomogeneous to heterogeneous fracture. Moreover, we discuss how the shortening of the process zone size with increasing crack speed brings the front to interact with smaller details of the microstructure. This study shines new light on recent experiments reporting perturbations of dynamic rupture fronts, which intensify with crack propagation speed.

Repulsion and Attraction between a Pair of Cracks in a Plastic Sheet

We study the interaction of two collinear cracks in polymer sheets slowly growing towards each other, when submitted to uniaxial stress at a constant loading velocity. Depending on the sample's geometry-specifically, the initial distances d between the two cracks' axes and L between the cracks' tips-we observe different crack paths with, in particular, a regime where the cracks repel each other prior to being attracted. We show that the angle θ characterizing the amplitude of the repulsion-and specifically its evolution with d-depends strongly on the microscopic behavior of the material. Our results highlight the crucial role of the fracture process zone. At interaction distances larger than the process zone size, crack repulsion is controlled by the microscopic shape of the process zone tip, while at shorter distances, the overall plastic process zone screens the repulsion interaction.

Crack front dynamics: the interplay of singular geometry and crack instabilities

When fast cracks become unstable to microscopic branching (microbranching), fracture no longer occurs in an effective 2D medium. We follow in-plane crack front dynamics via real-time measurements in brittle gels as microbranching unfolds and progresses. We first show that spatially local energy balance quantitatively describes crack dynamics, even when translational invariance is badly broken. Furthermore, our results explain microbranch dynamics; why microbranches form along spatially localized chains and how finite-time formation of cusps along the crack front leads to their death.

Fracturing across the multi-scales of diverse materials

Everyone has to deal with fracturing of materials at one level or another, beginning from normal household chores and extending to the largest scale of observations reported for catastrophic events occurring on a geological level or even expanded to events in outer space. Such wide perspective is introduced in the current introduction of this theme issue. The follow-on organization of technical articles provides a flavour of the range in size scales at which fracturing occurs in a wide diversity of materials-from 'fracking' oil extraction and earth moving to laboratory testing of rock material and extending to the cracking of tooth enamel. Of important scientific interest are observations made and analysed at the smallest dimensions corresponding to the mechanisms by which fracture is either enhanced or hindered by permanent deformation or other processes. Such events are irrevocably linked to the atomic structure in all engineering materials, a sampling of which is presented, including results for crystalline and amorphous materials. Hooray for the broad subject description that is hoped to be appealing to the interested reader.

Material grain size and crack size influences on cleavage fracturing

A review is given of the analogous dependence on reciprocal square root of grain size or crack size of fracture strength measurements reported for steel and other potentially brittle materials. The two dependencies have much in common. For onset of cleavage in steel, attention is focused on relationship of the essentially athermal fracture stress compared with a quite different viscoplastic yield stress behaviour. Both grain-size-dependent stresses are accounted for in terms of dislocation pile-up mechanics. Lowering of the cleavage stress occurs in steel because of carbide cracking. For crack size dependence, there is complication of localized crack tip plasticity in fracture mechanics measurements. Crack-size-dependent conventional and indentation fracture mechanics measurements are described also for results obtained on the diverse materials: polymethylmethacrylate, silicon crystals, alumina polycrystals and WC-Co (cermet) composites.

Effect of the porosity on the fracture surface roughness of sintered materials: from anisotropic to isotropic self-affine scaling

To unravel how the microstructure affects the fracture surface roughness in heterogeneous brittle solids like rocks or ceramics, we characterized the roughness statistics of postmortem fracture surfaces in homemade materials of adjustable microstructure length scale and porosity, obtained by sintering monodisperse polystyrene beads. Beyond the characteristic size of disorder, the roughness profiles are found to exhibit self-affine scaling features evolving with porosity. Starting from a null value and increasing the porosity, we quantitatively modify the self-affine scaling properties from anisotropic (at low porosity) to isotropic (for porosity >10%).

Fluctuations of global energy release and crackling in nominally brittle heterogeneous fracture

The temporal evolution of mechanical energy and spatially averaged crack speed are both monitored in slowly fracturing artificial rocks. Both signals display an irregular burstlike dynamics, with power-law distributed fluctuations spanning a broad range of scales. Yet, the elastic power released at each time step is proportional to the global velocity all along the process, which enables defining a material-constant fracture energy. We characterize the intermittent dynamics by computing the burst statistics. This latter displays the scale-free features signature of crackling dynamics, in qualitative but not quantitative agreement with the depinning interface models derived for fracture problems. The possible sources of discrepancies are pointed out and discussed.

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation-the dynamic process of fracture-couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the almost singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, namely linear elastic fracture mechanics (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined 'weakly nonlinear fracture mechanics', where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, ℓnl. These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of ℓnl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wavelength is determined by ℓnl. We conclude by delineating outstanding challenges in the field.

Fractographic aspects of crack branching instability using a phase-field model

A phase-field model of a crack front propagating in a three-dimensional brittle material is used to study the fractographic patterns induced by the branching instability. The numerical results of this model give rise to crack surfaces that are similar to those obtained in various experimental situations. Depending on applied loading configurations and initial conditions, we show that the branching instability is either restricted to a portion of the crack front or revealed through quasi-two-dimensional branches. For the former, the crack front leaves on the main broken surface either aligned or disordered parabolic marks. For the latter, fractography reveals the so called échelon cracks showing that branching instability can also induce crack front fragmentation.

Dynamic Initiation and Propagation of Multiple Cracks in Brittle Materials

Brittle materials such as rock and ceramic usually exhibit apparent increases of strength and toughness when subjected to dynamic loading. The reasons for this phenomenon are not yet well understood, although a number of hypotheses have been proposed. Based on dynamic fracture mechanics, the present work offers an alternate insight into the dynamic behaviors of brittle materials. Firstly, a single crack subjected to stress wave excitations is investigated to obtain the dynamic crack-tip stress field and the dynamic stress intensity factor. Second, based on the analysis of dynamic stress intensity factor, the fracture initiation sizes and crack size distribution under different loading rates are obtained, and the power law with the exponent of −2/3 is derived to describe the fracture initiation size. Third, with the help of the energy balance concept, the dynamic increase of material strength is directly derived based on the proposed multiple crack evolving criterion. Finally, the model prediction is compared with the dynamic impact experiments, and the model results agree well with the experimentally measured dynamic increasing factor (DIF).

Dynamic stability of crack fronts: out-of-plane corrugations

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids 45, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.

Intrinsic nonlinear scale governs oscillations in rapid fracture

When branching is suppressed, rapid cracks undergo a dynamic instability from a straight to an oscillatory path at a critical velocity v(c). In a systematic experimental study using a wide range of different brittle materials, we first show how the opening profiles of straight cracks scale with the size ℓ(nl) of the nonlinear zone surrounding a crack's tip. We then show, for all materials tested, that v(c) is both a fixed fraction of the shear speed and, moreover, that the instability wavelength is proportional to ℓ(nl). These findings directly verify recent theoretical predictions and suggest that the nonlinear zone is not passive, but rather is closely linked to rapid crack instabilities.

Understanding fast macroscale fracture from microcrack post mortem patterns

Dynamic crack propagation drives catastrophic solid failures. In many amorphous brittle materials, sufficiently fast crack growth involves small-scale, high-frequency microcracking damage localized near the crack tip. The ultrafast dynamics of microcrack nucleation, growth, and coalescence is inaccessible experimentally and fast crack propagation was therefore studied only as a macroscale average. Here, we overcome this limitation in polymethylmethacrylate, the archetype of brittle amorphous materials: We reconstruct the complete spatiotemporal microcracking dynamics, with micrometer/nanosecond resolution, through post mortem analysis of the fracture surfaces. We find that all individual microcracks propagate at the same low, load-independent velocity. Collectively, the main effect of microcracks is not to slow down fracture by increasing the energy required for crack propagation, as commonly believed, but on the contrary to boost the macroscale velocity through an acceleration factor selected on geometric grounds. Our results emphasize the key role of damage-related internal variables in the selection of macroscale fracture dynamics.

Stress concentration and size effect in fracture of notched heterogeneous material

We study theoretically and experimentally the effect of long-range correlations in the material microstructure on the stress concentration in the vicinity of the notch tip. We find that while in a fractal continuum the notch-tip displacements obey the classic asymptotic for a linear elastic continuum, the power-law decay of notch-tip stresses is controlled by the long-range density correlations. The corresponding notch-size effect on fracture strength is in good agreement with the experimental tests performed on notched sheets of different kinds of paper. In particular, we find that there is no stress concentration if the fractal dimension of the fiber network is D≤d-0.5, where d is the topological dimension of the paper sheet.