The condition for plastic instability is a material characteristic and defines the onset of necking in tensile tests. In large deformation problems of ductile materials it is fundamental to determine the strain at which necking starts as well as the post-necking behaviour in the instability region properly. For verification purposes of material models, usually results of numerical analyses are compared to experimental outcomes. For tensile tests with ductile materials under dynamic loading, it is challenging to obtain comparable experimental and numerical results in terms of the onset of necking and the post-critical deformation behaviour. This paper focuses on the derivation of a theoretical criterion describing the plastic instability in rate-dependent materials based on the time variation of the strain gradient in a tensile specimen under isothermal conditions. We examine the influence of various constitutive equations on the theoretical stability condition predicted by different multiplicative as well as additive approaches. For multiplicative relations, the results indicate that the onset of necking is, in principle, independent of the strain rate, whereas for the considered additive relation, the dynamic necking strain must decrease with increasing strain rate. In conclusion, the theoretical stability condition is related to results from finite element simulations of dynamic tensile tests with various loading rates. It is shown that the simulated and the theoretical predicted onset of plastic instability agree reasonably.
Abstract: In this work, a conceptual framework is suggested for analyzing thermorheologically simple and complex behavior by using just one approach. Therefore, the linear relation between master time and real time which is required in terms of the time-temperature superposition principle was enhanced to a nonlinear equivalent relation. Furthermore, we evaluate whether there is any relation among well-known existing time-temperature equivalent formulations which makes it possible to generalize different existing formulations. For this purpose, as an example, the power law formulation was used for the definition of the master time. The method introduced here also contributes a further framework for a unification of established time-temperature equivalent formulations, for example the time-temperature superposition principle and time-temperature parameter models. Results show, with additional normalization conditions, most of the developed time-temperature parameter models can be treated as special cases of the new formulation. In the aspect of the arrow of time, the new defined master time is a bended arrow of time, which can help to understand the corresponding physical meaning of the suggested method.