The focus of this paper is on a method for the design of bespoke small-scale pilot, metalforming processes and models that accurately represent corresponding industrial-scale processes. Introducing new complex metal forming processes in industry commonly involves a trial and error approach to ensure that the final product requirements are met. Detailed process modelling, analysis and small-scale feasibility trials could be carried out instead. A fundamental concern of scaled experiments, however, is whether the results obtained can be guaranteed to be representative of the associated industrial processes. Presently, this is not the case with classical approaches founded on dimensional analysis providing little direction for the design of scaled metal-forming experiments. The difficulty is that classical approaches often focus predominantly on constitutive equations (which indirectly represent micro-structural behaviour) and thus focus on aspects that invariably cannot be scaled. This paper introduces a new approach founded on scaled transport equations that describe the physics involved on a finite domain. The transport approach however focuses on physical quantities that do scale and thus provides a platform on which bulk behaviour is accurately represented across the length scales. The new approach is trialled and compared against numerically obtained results to reveal a new powerful technique for scaled experimentation.

Applied in this paper is a new technique for scaling metal forming processes, founded on the idea that scaling can be achieved by scaling space itself. With this approach, the physics in two spaces is described using transport equations and are deemed to possess finite similitude if found to be proportional. Finite similitude can be shown to always exist in continuum mechanics for isotropic scaling and it is demonstrated here how the concept can be used to design experiments. Validation of the approach is achieved by means of scaled experimental, numerical and analytical solutions of scaled upsetting tests for cylindrical and ring samples. Three trial materials are tested and distinguished by the degree of strain softening, strain hardening and near perfect-plastic behaviour. Finite similitude results confirm that any discrepancies between the maximum loads are substantially reduced when the new scaling theory is applied. Best results are obtained when the same material is adopted for both full and small-scale experimentation.

Abstract. Scaled experimentation founded on dimensional analysis has a long history but has to-date achieved little success in complex metal-forming applications. This is particularly true for thermo-mechanical processes, where scaled experimentation is recognised to provide little insight. It is shown in this paper that current similarity approaches in continuum physics can be overly prescriptive. The concept of finite similitude is introduced, which is shown to be better suited to finite-element analysis for the design of scaled experiments.

No abstract

No abstract