Rate-dependent elastic and elasto-plastic cohesive zone models for dynamic crack propagation

Abstract

To overcome deficiencies with existing approaches a new cohesive zone model is introduced and trialled in this paper. The focus is on rate-dependent cohesive zone models which have appeared in the recent literature but can be shown to suffer unrealistic behaviour. Different combinations of material response are examined with rate effects appearing either in the bulk material or localised to the cohesive zone or in both. A benefit of using a cohesive-zone approach is the ability to capture plasticity and rate effects locally. Introduced is a categorisation of bulk-material responses and cohesive zone models with particular prominence to the role of rate and plasticity. The shape of the traction separation curve is shown to have an effect and captured in this paper with application of a trapezoidal cohesive zone model. Rate dependency for the cohesive zone model is introduced in terms of a rate-dependent dashpot models applied either in parallel and/or in series. Traditionally, two possible methods are adopted to incorporate rate dependency, which are either via a temporal critical stress or a temporal critical separation. Applied singularly, tests reveal unrealistic crack behaviour at high loading rates. The new rate-dependent cohesive model introduced here couples the temporal responses of critical stress and critical displacement and is shown to provide for a stable realistic solution to dynamic fracture. Dynamic trials are performed on a cracked specimen to demonstrate the capability of the new approach.