External work rate and dissipation during crack growth in a viscoelastic material

Abstract

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.