Exact and inexact scaled models for hot forging

Davey, Keith and Bylya, Olga and Krishnamurthy, Bhaskaran (2020) Exact and inexact scaled models for hot forging. International Journal of Solids and Structures, 203. pp. 110-130. ISSN 0020-7683 (https://doi.org/10.1016/j.ijsolstr.2020.06.024)

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Scaled experimentation continues to play a significant role in process, product design and testing for metallic components and products but for hot forging in particular is recognized to suffer pronounced scale effects with physical behaviour changing with scale. This paper is concerned with an assessment of a new scaling approach called finite similitude that has appeared in the recent literature and a new methodology for exact and inexact-experimentation involving scaled experiments. Finite similitude is founded on the scaling of space itself and on a formulation that ensures that the governing physics (in transport form) remain invariant up to proportionality. Unfortunately proportionality breaks down with scale and to account for this careful experimental design is needed. A question of some importance, which is addressed in this paper, is whether it is possible that physically different materials can exhibit similar mechanical behaviour at certain conditions? These are termed “scaled-material twins” if they are able to match the required material response to some degree of accuracy for those ranges of temperature and strain rates that are representative of forging processes. Presented in the paper is a methodology for selecting scaled-material twins and the quantification of errors involved and its effect on scaled experimentation. Trials with hot disc forgings of different materials and sizes are performed to highlight the difficulties associated with scaling but also to demonstrate that scaled experimentation is possible and if correctly designed offers measurable advantages.