The roles of cohesive strength and toughness for crack growth in visco-elastic and creeping materials

A cohesive-zone analysis for crack propagation in a linear visco-elastic/creeping material is presented. The concept of a viscous fracture length is defined; this serves an analogous role to the elastic fracture length in determining the conditions under which fracture is controlled by the continuum crack-tip stress field. It is shown that there are two regimes for viscous crack growth. The first regime occurs in the limit of small viscous fracture lengths, when the crack-tip stress field has a region exhibiting the inverse square-root dependence expected from classical linear fracture mechanics. In this regime, the crack velocity is proportional to the fourth power of the stress-intensity factor. This is consistent with an existing analytical model developed for crack growth in linear polymers. The second regime occurs for large viscous fracture lengths, where classical fracture mechanics is not appropriate. In this regime, the crack velocity has a weaker dependence on the applied load, and can be modeled accurately by the solution to the problem of a viscous beam on an elastic foundation. At higher crack velocities, when the viscous fracture length exceeds the elastic fracture length, the expected transition to elastic fracture occurs.