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

The growth dynamics of a single crack in a heterogeneous material under subcritical loading is an intermittent process; and many features of this dynamics have been shown to agree with simple models of thermally activated rupture. In order to better understand the role of material heterogeneities in this process, we study the subcritical propagation of a crack in a sheet of paper in the presence of a distribution of small defects such as holes. The experimental data obtained for two different distributions of holes are discussed in the light of models that predict the slowing down of crack growth when the disorder in the material is increased; however, in contradiction with these theoretical predictions, the experiments result in longer lasting cracks in a more ordered scenario. We argue that this effect is specific to subcritical crack dynamics and that the weakest zones between holes at close distance to each other are responsible both for the acceleration of the crack dynamics and the slightly different roughness of the crack path.Comment: 4 pages, 5 figures, accepted in Physical Review Letters (http://prl.aps.org

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

The cooperative effect of load and disorder in thermally activated rupture of a two-dimensional random fuse network

A random fuse network, or equivalently a two-dimensional spring network with quenched disorder, is subjected to a constant load and thermal noise, and studied by means of numerical simulations. Rupture is thermally activated and the lifetime follows an Arrhenius law where the energy barrier is reduced by disorder. Due to the non-homogeneous distribution of forces from the stress concentration at microcrack tips, spatial correlations between rupture events appear, but they do not affect the energy barrier's dependence on the disorder; they affect only the coupling between the disorder and the applied load

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

Imaging the stick-slip peeling of an adhesive tape under a constant load

Using a high speed camera, we study the peeling dynamics of an adhesive tape under a constant load with a special focus on the so-called stick-slip regime of the peeling. It is the first time that the very fast motion of the peeling point is imaged. The speed of the camera, up to 16000 fps, allows us to observe and quantify the details of the peeling point motion during the stick and slip phases: stick and slip velocities, durations and amplitudes. First, in contrast with previous observations, the stick-slip regime appears to be only transient in the force controlled peeling. Additionally, we discover that the stick and slip phases have similar durations and that at high mean peeling velocity, the slip phase actually lasts longer than the stick phase. Depending on the mean peeling velocity, we also observe that the velocity change between stick and slip phase ranges from a rather sudden to a smooth transition. These new observations can help to discriminate between the various assumptions used in theoretical models for describing the complex peeling of an adhesive tape. The present imaging technique opens the door for an extensive study of the velocity controlled stick-slip peeling of an adhesive tape that will allow to understand the statistical complexity of the stick-slip in a stationary case

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

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

A dynamical law for slow crack growth in polycarbonate films

We study experimentally the slow growth of a single crack in polycarbonate films submitted to uniaxial and constant imposed stress. For this visco-plastic material, we uncover a dynamical law that describes the dependence of the instantaneous crack velocity with experimental parameters. The law involves a Dugdale-Barenblatt static description of crack tip plastic zones associated to an Eyring's law and an empirical dependence with the crack length that may come from a residual elastic field

The effects of time correlations in subcritical fracture. An acoustic analysis

The fracture dynamics of heterogeneous materials is a rich subject with obvious practical interests, especially the subcritical fracture, where a material breaks through a series of successive, non-correlated and localized fracture events until the arriving to a critical situation where the whole material fails. Paper has been a common model material to study this phenomenon, and high-resolution and high-speed visualization are the usual ways to follow the dynamics of the process. However, visualization presents many limitations, especially for long experiences. That is one of the reasons why we are coupling acoustics to the measurements in an attempt to establish it as the main source of information. Acoustics presents a much better temporal resolution and captures a higher number of events than visualization. By thresholding the amplitude of the acoustic signal, it is possible to get similar activities in both measurements. The waiting times between events and the energy of the events are both distributed in power laws with exponents which are similar for the two different kind of measurements (visualization and acoustics), corroborating that the recorded acoustic data corresponds indeed to the fracture process

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.Peer reviewe