Scaled metal forming experiments: A transport equation approach

The focus of this paper is on a method for the design of bespoke small-scale pilot, metal-forming 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.