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Item type:Publication, Access status: without files , External work rate and dissipation during crack growth in a viscoelastic material(2022-12); ; We analyse crack growth in viscoelastic material by use of a correspondence principle that allows elasticity solutions for traction boundary value problems in plane strain to be converted to viscoelasticity solutions. We consider an edge cracked strip in tension and assess 2 limiting cases of the geometry. In one case, we allow the component to become a geometry that is an infinite body with a semi-infinite crack, or a large body with a long crack. In the other case, we consider a component of finite width with a remaining ligament that is very small compared to the width of the strip. In these geometries we compute the work done by the applied load per unit area of crack growth and a measure that we consider to represent the dissipation per unit area of crack growth. We do so for a standard viscoelastic material with a single retardation time and for a Maxwell material with a single viscous element. In the latter case, our computation of the dissipation per unit area of crack growth is definite. We consider various aspects of the behaviour of the work done per unit area of viscoelastic crack propagation and the dissipation per unit area of crack advance. These include the extent to which these parameters depend on the rate of crack propagation, the extent to which these parameters are independent or dependant on component geometry, and the extent to which these parameters exhibit transient behaviour during crack growth at a steady rate under a constant applied stress intensity factor. A motivation is the common insight that a parameter is probably more useful as a measure of material behaviour if it is relatively insensitive to component geometry and if, during steady state response in terms of crack growth rate and applied stress intensity factor, the parameter also exhibits a steady state. We find outcomes that vary quite considerably depending on the case that we consider. We provide our results for the reader to use when considering the various models that have been proposed in the literature for viscoelastic crack propagation. We observe, however, that crack propagation models based on a rupture process zone interacting with material viscoelasticity are much simpler to implement in bodies with finite geometry than those based on quantifying the dissipation per unit area of crack growth. In this regard, we conclude that viscoelastic crack growth models that are based on quantifying the dissipation per unit area of crack growth are, by themselves, not a promising concept as we see no obvious way to extend them to provide unique results in components having a finite geometry. We further conclude that a reliable viscoelastic crack growth model should include a crack tip rupture process zone at the crack tip.Publicationtype: Journal Article14 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Transient and steady state viscoelastic crack propagation in a double cantilever beam specimen(2022-09-01); ; Crack growth in viscoelastic materials is understood with the use of cohesive models, or steady state theories which focus on viscoelastic dissipation. We consider a double cantilever beam (DCB) specimen under a remote constant pure moment, which is initially suddenly applied to the beams. It is shown that the response to the applied moment rapidly reaches a steady state in terms of crack propagation speed. In contrast, it is shown that the external work rate, contributing to fracture energy, stored elastic energy and viscous dissipation, has a transient that possibly lasts a significantly longer time. The dissipation rate increases with speed for a standard material, reaching a limit governed by the ratio of instantaneous to relaxed modulus. However, the initial dissipation rate at low crack propagation speeds can be orders of magnitude larger than the latter limit, and depends on the ratio between the initial crack size and the fracture process zone size, a regime which we define ultratough. For thin beams, we do not find any evidence, even in the steady state, of the dissipation-based theories’ suggestion of a reduced maximum load and then of an unstable regime of decreasing load with speed.Publicationtype: Journal Article18 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A comparison of crack propagation theories in viscoelastic materialsCrack propagation in viscoelastic materials cannot be understood with the use of classical fracture mechanics, which predicts no dependence on the speed of propagation, unless cohesive models like Barenblatt or Dugdale are introduced, as done by Knauss & Schapery first in the 1970s. However, there is another approach, suggested qualitatively by de Gennes in 1996, and quantitatively by Persson and Brener in 2005, which attempts an energy (power) balance by considering viscoelastic dissipation in the bulk of the material. Here, we revisit the main results of the two theories and show that they lead to approximately the same scaling laws not just for the standard material, but also for power law materials (which have a continuous spectrum of relaxation times). Recent findings by Schapery have concluded that the shape of the cohesive law results essentially in a shift in velocity which depends both on cohesive law shape and viscoelastic properties. Therefore, the Persson-Brener cutoff radius in the integral of dissipation can be chosen to fit approximately the cohesive model results to match the shift of the reference velocity.Publicationtype: Journal Article39 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Crack propagation at the interface between viscoelastic and elastic materialsCrack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970’s. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the “apparent” toughness in a semi-infinite crack increases between a value at very low speeds at a threshold toughness w0, to a very fast fracture value at w∞, and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli. Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum “effective” toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.Publicationtype: Journal Article74 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , The Interaction of Frictional Slip and Adhesion for a Stiff Sphere on a Compliant Substrate(2020-03-01); ; ; How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson-Kendall-Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A simple model for the interaction of friction and adhesion is utilized, in which some of the work done against frictional resistance is assumed to be stored reversibly. This behavior is considered to arise from surface microstructures associated with frictional slip such as interface dislocations, where these microstructures store some elastic strain energy in a reversible manner. When it is assumed that a fixed fraction of the work done against friction is stored reversibly, we obtain good agreement with data.Publicationtype: Journal Article24