Luminescent and sustainable d10 coinage metal thiolate coordination polymers for high-temperature optical sensing.

The d10 coinage metal coordination polymers (CPs) are known to display photophysical properties which can be tuned depending on the functionality of the ligand. Three new CPs made of d10 coinage metals and methyl thiosalicylate, [M(o-SPhCO2Me)]n (M = Cu, Ag, Au), are reported. They are all constructed from one-dimensional metal-sulfur networks, in which Cu and Ag are three-coordinated to sulfur atoms, whereas Au is only two-coordinated. It results that both Cu(I) and Ag(I) CPs show orange photoemission at room temperature, and the Au(I) one exhibits near-infrared emission at low temperatures. The intense orange-emissive Ag(I) CP and the blue-emissive coumarin 120 have been mixed in an organic matrix, the polyvinylidene fluoride (PVDF), to form a dual luminescent flexible composite film. This film, evaluated for thermometry, shows great sensitivity for temperatures up to 100°C, a temperature never reached with non-lanthanide-based CPs.

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.

Interacting Cracks Obey a Multiscale Attractive to Repulsive Transition.

The observed repulsive behavior of two initially collinear cracks growing towards each other and leading to a hook-shaped path questioned recently the validity of the principle of local symmetry within linear elastic fracture mechanics theory. Our theoretical and numerical work solves this dilemma, providing the precise geometric conditions for the existence of this repulsive phase. We moreover reveal a multiscale behavior of the repulsive-attractive transition, explaining its ubiquitous occurrence, but also the difficulty to predict the final cracks' paths.

Inertial and stick-slip regimes of unstable adhesive tape peeling.

We present an experimental characterization of the detachment front unstable dynamics observed during the peeling of pressure sensitive adhesives. We use an experimental set-up specifically designed to control the peeling angle θ and the peeled tape length L, while peeling an adhesive tape from a flat substrate at a constant driving velocity V. High-speed imaging allows us to report the evolution of the period and amplitude of the front oscillations, as well as the relative durations of their fast and slow phases, as a function of the control parameters V, L and θ. Our study shows that, as the driving velocity or the peeling angle increases, the oscillations of the peeling front progressively evolve from genuine "stick-slip" oscillations, made of alternating long stick phases and very brief slip phases, to sinusoidal oscillations of amplitude twice the peeling velocity. We propose a model which, taking into account the peeling angle-dependent kinetic energy cost to accelerate and decelerate the peeled tape, explains the transition from the "stick-slip" to the "inertial" regime of the dynamical instability. Using independent direct measurements of the effective fracture energy of the adhesive-substrate joint, we show that our model quantitatively accounts for the two regimes of the unstable dynamics.

Multiscale Stick-Slip Dynamics of Adhesive Tape Peeling.

Using a high-speed camera, we follow the propagation of the detachment front during the peeling of an adhesive tape from a flat surface. In a given range of peeling velocity, this front displays a multiscale unstable dynamics, entangling two well-separated spatiotemporal scales, which correspond to microscopic and macroscopic dynamical stick-slip instabilities. While the periodic release of the stretch energy of the whole peeled ribbon drives the classical macro-stick-slip, we show that the micro-stick-slip, due to the regular propagation of transverse dynamic fractures discovered by Thoroddsen et al. [Phys. Rev. E 82, 046107 (2010)], is related to a high-frequency periodic release of the elastic bending energy of the adhesive ribbon concentrated in the vicinity of the peeling front.

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.

Rate-dependent elastic hysteresis during the peeling of pressure sensitive adhesives.

The modelling of the adherence energy during peeling of Pressure Sensitive Adhesives (PSA) has received much attention since the 1950's, uncovering several factors that aim at explaining their high adherence on most substrates, such as the softness and strong viscoelastic behaviour of the adhesive, the low thickness of the adhesive layer and its confinement by a rigid backing. The more recent investigation of adhesives by probe-tack methods also revealed the importance of cavitation and stringing mechanisms during debonding, underlining the influence of large deformations and of the related non-linear response of the material, which also intervenes during peeling. Although a global modelling of the complex coupling of all these ingredients remains a formidable issue, we report here some key experiments and modelling arguments that should constitute an important step forward. We first measure a non-trivial dependence of the adherence energy on the loading geometry, namely through the influence of the peeling angle, which is found to be separable from the peeling velocity dependence. This is the first time to our knowledge that such adherence energy dependence on the peeling angle is systematically investigated and unambiguously demonstrated. Secondly, we reveal an independent strong influence of the large strain rheology of the adhesives on the adherence energy. We complete both measurements with a microscopic investigation of the debonding region. We discuss existing modellings in light of these measurements and of recent soft material mechanics arguments, to show that the adherence energy during peeling of PSA should not be associated to the propagation of an interfacial stress singularity. The relevant deformation mechanisms are actually located over the whole adhesive thickness, and the adherence energy during peeling of PSA should rather be associated to the energy loss by viscous friction and by rate-dependent elastic hysteresis.

Peeling-angle dependence of the stick-slip instability during adhesive tape peeling.

The influence of peeling angle on the dynamics observed during the stick-slip peeling of an adhesive tape has been investigated. This study relies on a new experimental setup for peeling at a constant driving velocity while keeping constant the peeling angle and peeled tape length. The thresholds of the instability are shown to be associated with a subcritical bifurcation and bistability of the system. The velocity onset of the instability is moreover revealed to strongly depend on the peeling angle. This could be the consequence of peeling angle dependance of either the fracture energy of the adhesive-substrate joint or the effective stiffness at play between the peeling front and the point at which the peeling is enforced. The shape of the peeling front velocity fluctuations is finally shown to progressively change from typical stick-slip relaxation oscillations to nearly sinusoidal oscillations as the peeling angle is increased. We suggest that this transition might be controlled by inertial effects possibly associated with the propagation of the peeling force fluctuations through elongation waves in the peeled tape.

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 dependence of the stick and slip phase durations on 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 a model however fails to predict the full stick-slip cycle duration, revealing strong dynamical effects during the slip phase.

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 quasistatic 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.

Softening induced instability of a stretched cohesive granular layer.

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such a type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.

Statistics of fracture surfaces.

We analyze the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the distribution to an analysis based on the structure functions. For length scales delta larger than a characteristic scale Lambda that corresponds to a material heterogeneity size, we find that the distribution of the height increments Deltah=h(x+delta)-h(x) is Gaussian and monoaffine, i.e., the scaling of the standard deviation sigma is proportional to delta(zeta) with a unique roughness exponent. Below the scale Lambda we observe a deviation from a Gaussian distribution and a monoaffine behavior. We discuss for the latter, the relevance of a multiaffine analysis and the influences of the discreteness resulting from material microstructures or experimental sampling.

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 viscoplastic 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.

Fracture surfaces as multiscaling graphs.

Fracture paths in quasi-two-dimensional (2D) media (e.g., thin layers of materials or 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 nth order moments of the height fluctuations across any distance l 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 quasistatic fracture passes this test.

Subcritical statistics in rupture of fibrous materials: experiments and model.

We study experimentally the slow growth of a single crack in a fibrous material and observe stepwise growth dynamics. We model the material as a lattice where the crack is pinned by elastic traps and grows due to thermally activated stress fluctuations. In agreement with experimental data we find that the distribution of step sizes follows subcritical point statistics with a power law (exponent 3/2) and a stress-dependent exponential cutoff diverging at the critical rupture threshold.