Abstract 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.

中文翻译：

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用于热锻的精确和不精确的比例模型

摘要 规模实验在金属部件和产品的工艺、产品设计和测试中继续发挥重要作用，但特别是热锻被认为会遭受显着的规模效应，物理行为随规模变化。本文涉及对最近文献中出现的一种称为有限相似的新标度方法的评估，以及一种用于涉及标度实验的精确和不精确实验的新方法。有限相似性建立在空间本身的缩放比例和确保控制物理（以传输形式）保持不变的公式上，直到成比例。不幸的是，比例会随着规模的扩大而失效，需要考虑到这种仔细的实验​​设计。一个很重要的问题，在本文中讨论的是，物理上不同的材料是否有可能在某些条件下表现出相似的机械行为？如果它们能够在代表锻造工艺的温度和应变率范围内以某种程度的精度匹配所需的材料响应，则它们被称为“缩放材料孪晶”。论文中介绍了一种选择缩放材料孪生体的方法，以及所涉及的误差的量化及其对缩放实验的影响。对不同材料和尺寸的热盘锻件进行试验，以突出与缩放相关的困难，但也证明缩放实验是可能的，如果设计正确，则可提供可衡量的优势。物理上不同的材料是否有可能在某些条件下表现出相似的机械性能？如果它们能够在代表锻造工艺的温度和应变率范围内以某种程度的精度匹配所需的材料响应，则它们被称为“缩放材料孪晶”。论文中介绍了一种选择缩放材料孪生体的方法，以及所涉及的误差的量化及其对缩放实验的影响。对不同材料和尺寸的热盘锻件进行试验，以突出与缩放相关的困难，但也证明缩放实验是可能的，如果设计正确，则可提供可衡量的优势。物理上不同的材料是否有可能在某些条件下表现出相似的机械性能？如果它们能够在代表锻造工艺的温度和应变率范围内以某种程度的精度匹配所需的材料响应，则它们被称为“缩放材料孪晶”。论文中介绍了一种选择缩放材料孪生体的方法，以及所涉及的误差的量化及其对缩放实验的影响。对不同材料和尺寸的热盘锻件进行试验，以突出与缩放相关的困难，但也证明缩放实验是可能的，如果设计正确，则可提供可衡量的优势。