Slow crack growth : models and experiments

The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.Comment: to be published in EPJ (European Physical Journal

Local waiting time fluctuations along a randomly pinned crack front

The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e. the local pinnings and depinnings of the crack front which trigger a rich burst activity, by measuring the local waiting time fluctuations along the crack front during its propagation. The local front line velocity distribution deduced from the waiting time analysis exhibits a power law behavior, $P(v) \propto v^{-\eta}$ with $\eta = 2.55 \pm 0.15$, for velocities $v$ larger than the average front speed $$. The burst size distribution is also a power law, $P(S)\propto S^{-\gamma}$ with $\gamma=1.7 \pm 0.1$. Above a characteristic length scale of disorder $L_d \sim 15 \mu m$, the avalanche clusters become anisotropic, and the scaling of the anisotropy ratio provides an estimate of the roughness exponent of the crack front line, $H=0.66$, in close agreement with previous independent estimates.Comment: Phys. Rev. Lett., accepte

Strong dynamical effects during stick-slip adhesive peeling

We consider the classical problem of the stick-slip dynamics observed when peeling a roller adhesive tape at a constant velocity. From fast imaging recordings, we extract the dependencies of the stick and slip phases durations with the imposed peeling velocity and peeled ribbon length. Predictions of Maugis and Barquins [in Adhesion 12, edited by K.W. Allen, Elsevier ASP, London, 1988, pp. 205--222] based on a quasistatic assumption succeed to describe quantitatively our measurements of the stick phase duration. Such model however fails to predict the full stick-slip cycle duration, revealing strong dynamical effects during the slip phase.Comment: Soft Matter 201

Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study

We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent poly(methyl methacrylate) (PMMA) block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a depinning regime of high velocity clusters defined as avalanches and a pinning regime of very low-velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behavior.Comment: Physical Review E (2011); 62.20.mt, 46.50.+a, 68.35.C

Intermittent stick-slip dynamics during the peeling of an adhesive tape from a roller

We study experimentally the fracture dynamics during the peeling at a constant velocity of a roller adhesive tape mounted on a freely rotating pulley. Thanks to a high speed camera, we measure, in an intermediate range of peeling velocities, high frequency oscillations between phases of slow and rapid propagation of the peeling fracture. This so-called stick-slip regime is well known as the consequence of a decreasing fracture energy of the adhesive in a certain range of peeling velocity coupled to the elasticity of the peeled tape. Simultaneously with stick-slip, we observe low frequency oscillations of the adhesive roller angular velocity which are the consequence of a pendular instability of the roller submitted to the peeling force. The stick-slip dynamics is shown to become intermittent due to these slow pendular oscillations which produce a quasi-static oscillation of the peeling angle while keeping constant the peeling fracture velocity (averaged over each stick-slip cycle). The observed correlation between the mean peeling angle and the stick-slip amplitude questions the validity of the usually admitted independence with the peeling angle of the fracture energy of adhesives.Comment: Forthcoming in Physical Review

Experimental study of stable imbibition displacements in a model open fracture. I. Local avalanche dynamics

We report the results of an experimental investigation of the spatiotemporal dynamics of stable imbibition fronts in a disordered medium, in the regime of capillary disorder, for a wide range of experimental conditions. We have used silicone oils of various viscosities μ and nearly identical oil-air surface tension and forced them to slowly invade a model open fracture at different constant flow rates v. In this first part of the study we have focused on the local dynamics at a scale below the size of the quenched disorder. Changing μ and v independently, we have found that the dynamics is not simply controlled by the capillary number Ca ∼ μv. Specifically, we have found that the wide statistical distributions of local front velocities, and their large spatial correlations along the front, are indeed controlled by the capillary number Ca. However, local velocities exhibit also very large temporal correlations, and these correlations depend more strongly on the mean imposed velocity v than on the viscosity μ of the invading fluid. Correlations between local velocities lead to a burstlike dynamics. Avalanches, defined as clusters of large local velocities, follow power-law distributions both in size and duration with exponential cutoffs that diverge as Ca → 0, the pinning-depinning transition of stable imbibition displacements. Large data sets have led to reliable statistics, from which we have derived accurate values of critical exponents of the relevant power-law distributions. We have investigated also the dependence of their cutoffs on μ and v and related them to the autocorrelations of local velocities in space and time

Physics of sub-critical crack growth in a fibrous material: experiments and model

Communication 4271 http://www.icf11.com/proceeding/EXTENDED/4721.pdfWe are interested in slow rupture processes observed when a material is submitted to a constant load below a critical rupture threshold. It is well known that the delay time (or lifetime) of the material before complete macroscopic rupture strongly depends on the applied stress. Thermodynamics has slowly emerged as a possible framework to describe delayed rupture of materials since early experiments have shown temperature dependence of lifetime with an Arrhenius law. On the other hand, efforts are made to describe slow rupture dynamics from rheological properties of the material such as viscoelasticity and plasticity. To shed light on this problem, it is important to compare experiments and models to distinguish between the different theoretical descriptions. For this purpose, we have studied experimentally the slow growth of a single crack in a fibrous material made of fax paper. Specifically, we have observed that the crack grows by steps of various sizes whose distribution is rather complex and evolves as a function of the crack length. In spite of this complexity, a statistical average of the growth dynamics reveals a very simple behaviour. We show that a model of thermally activated dynamics is able to reproduce many experimental observations. In particular, we show that the average dynamics is in good agreement with the experimental data. In addition, we find that the distribution of step sizes follows sub-critical point statistics with a power law and a stress-dependent exponential cut-off diverging at the critical rupture threshold. The exponent of the power law predicted by the model (3/2) seems to be slightly too large. Leaving the exponent as a free parameter gives a value 1.23+/-0.1. We stress that the material heterogeneity appears in the model only as a characteristic mesoscopic length scale. The fact that a simple model of thermally activated crack dynamics is able to reproduce with a good accuracy our experimental findings may open new perspectives in the description of slow rupture dynamics

Fracture Surfaces as Multiscaling Graphs

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.Comment: 4 pages, 5 figure

Disorder-induced capillary bursts control intermittency in slow imbibition

A multiscale analysis of the spatially averaged velocity of an imbibition front Vl measured at scale l reveals that the slow front dynamics is intermittent: the distributions of increments ΔVl(τ) evolve continuously through time scales τ, from heavy-tailed to Gaussian¿reached at a time lag τc set by the extent of the medium heterogeneities. Intermittency results from capillary bursts triggered from the smallest scale of the disorder up to the scale lc at which viscous dissipation becomes dominant. The effective number of degrees of freedom of the front l/lc controls its intensity