Crack propagation in viscoelastic solids

Abstract

We study crack propagation in a viscoelastic solid. Using simple arguments, we derive equations for the velocity dependence of the crack-tip radius, a (v) , and for the energy per unit area to propagate the crack, G (v) . For a viscoelastic modulus E (omega) which increases as omega(1-s) (0< s< 1) in the transition region between the rubbery region and the glassy region, we find that a (v) approximately G (v) approximately v(alpha) with alpha= (1-s) / (2-s) . The theory is in good agreement with experiment.

Bulk Energy Dissipation Mechanism for the Fracture of Tough and Self-Healing Hydrogels

“…Therefore, the tearing energy obtained for a higher velocity at a given temperature has the same value as that measured at the lower velocity and low temperature according to the time-temperature equivalence. 27,28 Following this equivalence, we found that, as shown in Figure 3d, all the tearing energy data measured at different temperatures and crack velocities can be reduced to a nice master curve at a reference temperature (ܶ = 24 ℃) when the the same shift factors ܽ ் and ܾ ் determined from the linear dynamic measurement in Figure 1c and Figure 1d are used, respectively. The result indicates that the equivalence holds for the PA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 power law relation between the hysteresis energy and stretching strain rate, ܷ ௬௦ ~ ߝሶ .ଷଵ (Figure 2c).…”

“…Except for the points at high tearing velocity, all the observed crack velocities at various temperatures are slightly lower than the applied tearing velocities over a wide range, as shown in 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 velocity ܸ and temperature T, and ߁ is a threshold value of the polymer network below which no fracture occurs. 25,27,28,42,43 During crack propagation, the intrinsic fracture energy of a polymer network involves several complex processes, including chain breaking, cavitation formation, and so on, while the bulk viscoelastic energy dissipation only involves the viscoelastic deformation process around the crack tip.…”

“…For this purpose, let us first revisit the bulk energy dissipative model for the fracture of viscoelastic solid materials. 21,25,27,28 The model assumes that the viscoelastic solid is described by a single relaxation time τ, with two plateau moduli, ‫ܩ‬ and ‫ܩ‬ ஶ , at low frequency ( ωτ ≪ 1 ) and high frequency (ωτ ≫ 1), respectively. Given that the deformation rate at a distance ‫ݎ‬ from the crack tip is characterized by the angular frequency ߱ = ܸ ‫,ݎ/‬ the energy dissipation profile at the crack tip consists of three different zones depending on the distance ‫ݎ‬ from the crack tip, (Figure 4a).…”

Mode-mixity-dependent adhesive contact of a sphere on a plane surface

“…Maugis & Barquins 1978;Maugis 1987;Barthel & Roux 2000;Meitl et al 2006). Such models typically take the form of a powerlaw dependence upon velocity, and a theoretical basis for such phenomenological modelling has been developed by Greenwood & Johnson (1981), Hui et al (1992), de Gennes (1996, Muller (1996), Saulnier et al (2004) and Persson & Brener (2005), among others.…”

Hot Cracks in Rubber: Origin of the Giant Toughness of Rubberlike Materials

“…We calculate the crack propagation energy G v , which is an intrinsic material quantity that does not depend on the geometry of the sample, or how the system is loaded: in the following we focus on the simplest case of plane stress [6]. For plain stress, the crack propagation energy G is given by [7] G K 2 =E, where E is the elastic modulus.…”