Multi-timescale analysis of fatigue crack growth on interfaces via cohesive-zone models

Abstract

The paper describes a new non-linear finite-element formulation to analyse fatigue debonding or delamination, along predefined interfaces, which is multi-scale in time. At the small timescale level, cyclic loading and the related oscillating response are considered in an explicit way, whereas at the large timescale level, both the real loading actions and the related response in terms of displacement and stress fields are replaced with ‘minimum’ and ‘maximum’ functions over the time of the analysis, which also implies doubling the degrees of freedom of the finite-element model. A cohesive-zone model capable of simulating sub-critical damage growth and hysteretic local response is used on the interface. With a conventional cycle-by-cycle incremental procedure, the analysis would require a number of increments significantly higher than the number of cycles, and would be therefore unfeasible for most industrial applications. Instead, with the developed multi-timescale method, the cycle-by-cycle time integration is transferred from the structural level to the local, integration-point level, whereby the time step can be, and in fact should better be, much larger than the period of the applied actions. The consequent significant saving in terms of computational cost largely offsets the shortcoming of having to double the degrees of freedom of the model and makes the analysis not only feasible but relatively inexpensive in many cases, while retaining excellent accuracy as showed by the presented numerical results.

Keywords:

• multi-scale methods
• cyclic loading
• interface elements
• hysteretic response
• sub-critical damage