engleski

Recent advances in the development of rate- dependent cohesive-zone models based on fractional viscoelasticty

Rate dependence of crack propagation is important in many cases of great interest for engineering applications. A rate-dependent cohesive-zone model (CZM) which well captures rate-dependent crack growth along rubber interfaces has been developed in the framework of fractional-calculus based viscoelasticity [1]. Postulating the existence of a rate- independent rupture energy, associated with the rupture of bonds, a damage variable is introduced, which is assumed to evolve as a rate- independent function of part of the elastic energy. The overall rate-dependent response is retrieved by introducing additional internal variables associated with viscous dissipation. Excellent correlation between experimental and numerical results was found for the case of a double cantilever beam (DCB) made of two steel arms bonded along a rubber interface, for the entire range of the tested speeds, which spanned about 5 logarithmic decades. Further numerical simulations with the same interface parameters but over a much wider range of prescribed speeds showed that the work of separation for this case turns out to be a monotonically increasing function of the crack speed. In [2], thermodynamic and micro- mechanical arguments were used to extend the formulation to cases where the fracture energy does not increase monotonically with the crack speed, which is in better qualitative correlation with the behaviour of some glassy polymers. The identification of the 6 parameters of the fractional CZMs proposed in [1, 2] is not a trivial task and requires the solution of a large number of ‘forward’ problems, which can be time consuming. Therefore, we will discuss methods for the parameter identification which are based on the fast and accurate solution of DCB tests obtained by using an efficient code in which shear-deformable beam elements are used to model the DCB arms [3], with either linear or nonlinear kinematics. Furthermore, when the size of the cohesive zone is large relatively to the specimen dimensions, such as in the case studied in [1], the shape of the traction- separation law may have an influence on the structural response. It will be shown how such shape changes as the result of different damage evolution laws, and how the relevant parameters can be identified.

parameter identification ; damage evolution ; beam finite elements

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