Scaled cohesive zone models for fatigue crack propagation

A cohesive zone model is a phenomenological model of the fracture process, which straddles empiricism and material science and as such provides a pragmatic choice for fatigue analysis. Material separation in the cohesive zone is governed by a traction-separation law and consequently all cohesive models feature a size effect since they involve the explicit property separation. The application and assessment of cohesive zone models is focus of this paper for the design and analysis of scaled models. This is a subject area that is understandably scarce in the scientific literature in view of the changes that take place with scale, which make scaled models unrepresentative of full-scale behaviour. Recently however a new scaling theory has appeared in the open literature called finite similitude, which introduces new similitude rules that can in principle account for all scale dependencies. The similitude rule of interest here is the first-order rule involving two scaled experiments, which is shown to be sufficient in capturing modelled fatigue behaviour. The commercial finite element software Abaqus is employed to investigate the two-scaled experiment approach applied to both linear and non-linear materials. It is shown in the paper how large discrepancies between scaled and full-sized specimens with one scaled model are absent when two scaled models are combined according to the first-order finite similitude rule.