Scaled metal forming experiments: A transport equation approach

Abstract

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.

Zeroth-order finite similitude and scaling of complex geometries in biomechanical experimentation

“…An alternative scaling approach that has recently been developed has proved successful to a certain extent in the field of biomechanical experimentation [12,13]; the concept of finite similitude. The fundamental idea of finite similitude is the fact that the physics in general cannot be guaranteed to scale, but conservation (and some non-conservation) laws must hold over an extensive range of scales (where continuum mechanics is valid).…”

Scaling in biomechanical experimentation: a finite similitude approach

“…The underlying assumption of finite similitude is that the complete physics of a system is unlikely to scale but conservation laws must undoubtedly hold over a extensive range of length scales [5]. Thus, in continuum bio-mechanics, the laws of nature necessitate that volume, mass, momentum and energy must be conserved along with compliance of non-conservative laws for movement (for the description of displacement, see reference [6]) and entropy.…”

Experimental investigation into finite similitude for metal forming processes

“… and u  . Recall (see Davey et al (2017) and Section 2) that these parameters can be divided into independent (  ,   and h ) and dependent scaling parameters ( 1  , e  , v  and u  ). The scaling parameter values for full scale (Al 2024-T851) and trial scaled materials (Cu-C101, Al 6061-T651 and Al 2024-T851) are presented in Table 2.…”