New dynamical equation for cracks

Brittle fracture studied by ultra-high-speed synchrotron X-ray diffraction imaging

Crack propagation in a silicon single-crystal wafer is tracked in situ using synchrotron-based ultra-high speed X-ray diffraction imaging. The high spatio-temporal resolution reached in diffraction imaging mode allows for assessing different parameters such as crack velocity or post crack movements of the separated wafers.

In situ investigations of cracks propagating at up to 2.5 km s⁻¹ along an (001) plane of a silicon single crystal are reported, using X-ray diffraction megahertz imaging with intense and time-structured synchrotron radiation. The studied system is based on the Smart Cut process, where a buried layer in a material (typically Si) is weakened by microcracks and then used to drive a macroscopic crack (10⁻¹ m) in a plane parallel to the surface with minimal deviation (10⁻⁹ m). A direct confirmation that the shape of the crack front is not affected by the distribution of the microcracks is provided. Instantaneous crack velocities over the centimetre-wide field of view were measured and showed an effect of local heating by the X-ray beam. The post-crack movements of the separated wafer parts could also be observed and explained using pneumatics and elasticity. A comprehensive view of controlled fracture propagation in a crystalline material is provided, paving the way for the in situ measurement of ultra-fast strain field propagation.

Moving cracks in drying colloidal films

Drying colloidal films are encountered in many applications ranging from paints and coatings to ceramic and semiconductor processing. In many cases, shrinkage stresses are generated during drying, which can fracture the film. While much of the previous experimental and theoretical work has focused on cracking in static cracks, there are very few studies on the dynamics of cracks in colloidal coatings. Here, we derive an analytical solution for the stress, displacement, and pressure fields near the crack tip for a steadily moving crack. We consider first the two extreme cases, namely, the undrained limit where the crack motion is much faster than the Darcy flow rate and the opposite extreme of very slow crack propagation, the drained limit. Next, we consider the general case where the timescale for crack-tip motion is comparable to that for the interstitial flow. The results incorporate the micro-structural details of the system including the particle volume fraction and nature of packing, and the mechanical properties of the particles such as shear modulus and Poisson's ratio. While the predicted results are in line with those for brittle materials, the predicted crack speeds are at least an order of magnitude higher than those observed in experiments. We conclude with the possible reasons for the discrepancy.

How Supertough Gels Break

Fracture of highly stretched materials challenges our view of how things break. We directly visualize rupture of tough double-network gels at >50% strain. During fracture, crack tip shapes obey a x∼y^{1.6} power law, in contrast to the parabolic profile observed in low-strain cracks. A new length scale ℓ emerges from the power law; we show that ℓ scales directly with the stored elastic energy and diverges when the crack velocity approaches the shear wave speed. Our results show that double-network gels undergo brittle fracture and provide a testing ground for large-strain fracture mechanics.

On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One

The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith's criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

Brittle Fracture Theory Predicts the Equation of Motion of Frictional Rupture Fronts

We study rupture fronts propagating along the interface separating two bodies at the onset of frictional motion via high-temporal-resolution measurements of the real contact area and strain fields. The strain measurements provide the energy flux and dissipation at the rupture tips. We show that the classical equation of motion for brittle shear cracks, derived by balancing these quantities, well describes the velocity evolution of frictional ruptures. Our results demonstrate the extensive applicability of the dynamic brittle fracture theory to friction.

Origin of the microbranching instability in rapid cracks

The origin of the microbranching instability is a long-standing unresolved issue in the fracture of brittle amorphous materials. We investigate the onset of this instability by measuring the real-time dynamics and symmetries of the strain fields produced by rapid tensile cracks in brittle gels. We find that once a simple tensile crack is subjected to shear perturbations, cracks undergo the microbranching instability above a finite velocity-dependent threshold. We further reveal a distinct relation between the microbranching and the oscillatory instabilities of rapid cracks.

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.

Dynamic fracture in irregularly structured systems

Although commonly used materials are composed of irregular microstructures, most existing numerical methods for fracture dynamics are developed via regular discretizations. In the present Rapid Communication we investigate the dynamic fracture numerically by irregular domain discretizations. To explore the relationship between microscopic crack branching and the macroscopic instability of fracture dynamics, we simulate detailed diagrams for the crack branching and also calculate the crack speeds by varying the parameters of crack-tip cohesion. In particular, an equation to describe the relation between the crack speed and the fracture energy is proposed based on the simulation results. The present results indicate that the irregularities of mesoscopic structure contribute to the intrinsic instabilities of dynamic fracture and eventually to the crack speed. And the single-crack continuum theory should be at least carefully modified to describe the dynamic fracture governed by the complex branching and fluctuations.

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.

Acquisition of inertia by a moving crack

We experimentally investigate the dynamics of "simple" tensile cracks. Within an effectively infinite medium, a crack's dynamics perfectly correspond to inertialess behavior predicted by linear elastic fracture mechanics. Once a crack interacts with waves that it generated at earlier times, this description breaks down. Cracks then acquire inertia and sluggishly accelerate. Crack inertia increases with crack speed v and diverges as v approaches its limiting value. We show that these dynamics are in excellent accord with an equation of motion derived in the limit of an infinite strip [M. Marder, Phys. Rev. Lett. 66, 2484 (1991)].

A review of computational methods in materials science: examples from shock-wave and polymer physics

This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.

Unsteady crack motion and branching in a phase-field model of brittle fracture

Crack propagation is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability at a fraction of the wave speed.