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Register a new userForce-dependent bond dissociation explains the rate-dependent fracture of vitrimers
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We investigate the rate-dependent fracture of vitrimers by conducting a tear test. Based on the relationship between the frac-ture energy and the thickness of vitrimer films, we, for the first time, obtain the intrinsic fracture energy and bulk dissipation of vitrimers during crack extension. The intrinsic fracture energy strongly depends on tear speed, and such dependence can be well explained by Eyring theory. In contrast, the bulk dissipation only weakly depends on tear speed, which is drastically different from observations on traditional viscoelastic polymers. We ascribe such a weak rate-dependence to the strong force-sensitivity of the exchange reaction of the dynamic covalent bond in the vitrimer.
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We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles with a set of data points that encodes the fracture constitutive behavior of the material. The solution is found as the data point that best satisfies the meta-stability condition as given by the variational procedure and following a distance minimization approach based on closest-point-projection. The approach is tested on different setups adopting different types of rate-dependent fracture and fatigue models affected or not by white noise.
In this work, we investigate dissipative effects involved during the detachment of a smooth spherical glass probe from a viscoelastic silicone substrate patterned with micro-asperities. As a baseline, the pull-off of a single asperity, millimeter-sized contact between a glass lens and a smooth poly(dimethylsiloxane) (PDMS) rubber is first investigated as a function of the imposed detachment velocity. From a measurement of the contact radius a(t) and normal load during unloading, the dependence of the strain energy relase rate G on the velocity of the contact line vc = da/dt is determined under the assumption that viscoelastic dissipation is localized at the edge of the contact. These data are incorporated into Mullers model (V.M. Muller J Adh Sci Tech (1999) 13 999-1016) in order to predict the time-dependence of the contact size. Similar pull-off experiments are carried out with the same PDMS substrate patterned with spherical micro-asperities with a prescribed height distribution. From in situ optical measurements of the micro-contacts, scaling laws are identified for the contact radius a and the contact line velocity vc. On the basis of the observed similarity between macro and microscale contacts, a numerical solution is developed to predict the reduction of the contact radius during unloading.
The modelling of the adherence energy during peeling of Pressure Sensitive Adhesives (PSA) has received much attention since the 1950s, 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.
The yielding of concentrated cohesive suspensions can be deformation-rate dependent. One consquence of this is that a single suspension can present in one several different ways, depending upon how it is tested, or more generally, how it is caused to flow. We have seen variously Herschel-Bulkley flow, highly non-monotonic flow curves and highly erratic or chaotic yield, all in one suspension. In controlled-rate testing one sees a systematic effect of deformation rate. In controlled stress testing, matters are more subtle. Whereas step-stress creep testing will elicit reproducible behaviour, any attempt to determine a flow curve by, e.g. stepping up or sweeping stress at an inappropriate rate can lead to highly irreproducible behaviour.
An experimental system has been found recently, a coagulated CaCO3 suspension system, which shows very variable yield behaviour depending upon how it is tested and, specifically, at what rate it is sheared. At Peclet numbers Pe > 1 it behaves as a simple Herschel Bulkley liquid, whereas at Pe < 1 highly non-monotonic flow curves are seen. In controlled stress testing it shows hysteresis and shear banding and in the usual type of stress scan, used to measure flow curves in controlled stress mode routinely, it can show very erratic and irreproducible behaviour. All of these features will be attributed here to a dependence of the solid phase, or, yield stress, on the prevailing rate of shear at the yield point. Stress growth curves obtained from step strain-rate testing showed that this rate-dependence was a consequence of Peclet number dependent strain softening. At very low Pe, yield was cooperative and the yield strain was order-one, whereas as Pe approached unity, the yield strain reduced to that needed to break interparticle bonds, causing the yield stress to be greatly reduced. It is suspected that rate-dependent yield could well be the rule rather than the exception for cohesive suspensions more generally. If so, then the Herschel-Bulkley equation can usefully be generalized to read (in simple shear). The proposition that rate-dependent yield might be general for cohesive suspensions is amenable to critical experimental testing by a range of means and along lines suggested.
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