Experimental investigation into finite similitude for metal forming processes

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.