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Crack 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 toughness increases between a value at very low speeds at a threshold toughness G0, to a very fast fracture value at Ginf, 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 toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.
In a simple and interesting theory of ultratough peeling of an elastic tape from a viscoelastic substrate, Afferrante and Carbone find that there are conditions for which the load for steady state peeling could be arbitrarily large in steady state peeling, at low angles of peeling - what they call "ultratough" peeling (Afferrante, L., Carbone, G., 2016, The ultratough peeling of elastic tapes from viscoelastic substrates, Journal of the Mechanics and Physics of Solids, 96, pp.223-234). Surprisingly, this seems to lead to toughness enhancement higher than the limit value observed in a very large crack in an infinite viscoelastic body, possibly even considering a limit on the stress transmitted. The Afferrante-Carbone theory seems to be a quite approximate, qualitative theory and many aspects and features of this "ultratough" peeling (e.g. conformity with the Rivlin result at low peel angles) are obtained also through other mechanisms (Begley, M.R., Collino, R.R., Israelachvili, J.N., McMeeking, R.M., 2013, Peeling of a tape with large deformations and frictional sliding, Journal of the Mechanics and Physics of Solids, 61(5), pp. 1265-1279) although not at “critical velocities”. Experimental and/or numerical verification would be most useful.