Dissipation During Crack Growth in a Viscoelastic Material from a Cohesive Model for a Finite Specimen

Abstract

Abstract In the present paper, we extend results recently given by Ciavarella, Zhang & McMeeking (2022, Journal of the Mechanics and Physics of Solids, 169, 105096) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, and we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant. Also, at intermediate rates dissipation can be orders of magnitude higher than work of fracture multiplied what is believed to be the “viscoelastic enhancement factor” at very large rates. Finally, the total work to break a specimen apart is found, in a realistic example, to be larger than this “limit”, and for quite a large range of realistic conditions at intermediate crack growth rates. This shows that the cohesive model of crack propagation in linear viscoelastic materials permits a more general understanding than models which assume steady state of energy fluxes and simplified energy balance of just the asymptotic singular stress field.