In forming simulations, flow curves are cardinal inputs to predict features, such as forming forces and material flow. The laboratory-scale experiments to determine them, like compression or tensile tests, are affected by deformation heating, restricting direct flow curve determination. In principle, the current analytical and inverse methods determine flow curves from these tests, but while the analytical methods assume a simplified temperature profile, the inverse methods require a closed-form flow curve equation, which mostly cannot capture complex material behavior like multiple recrystallization cycles. Therefore, the inverse piecewise flow curve determination method “FepiM” previously developed and published by the current authors is extended by introducing a two-step procedure to obtain isothermal flow curves at elevated temperatures and different strain rates. Thereby, the flow curve is represented as tabular data instead of an equation to reproduce complex flow curve shapes while also compensating the effect of inhomogeneous temperature profiles on the flow stress. First, a flow curve at the highest temperature is determined. In the second step, using this first flow curve as a reference, the flow curves at lower temperatures are obtained via interpolation. Flow curves from conventional compression tests for aluminum and copper in the temperature range of 20–500 °C are predicted, and it is shown that these flow curves can reproduce the experimental forces with a maximum deviation of less than 1%. Therefore, the proposed new piecewise method accurately predicts isothermal flow curves for compression tests, and the method could be further extended to highly inhomogeneous methods in the future.

中文翻译：

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FepiM：确定热加工等温流动曲线的新型分段逆方法

在成形模拟中，流动曲线是预测特征（例如成形力和材料流动）的主要输入。用于确定它们的实验室规模实验（例如压缩或拉伸试验）受变形加热的影响，从而限制了直接流动曲线的确定。原则上，当前的分析方法和逆方法会从这些测试中确定流动曲线，但是尽管分析方法采用简化的温度曲线，但逆方法需要封闭形式的流动曲线方程，该方程通常无法捕获复杂的材料行为，如多次重结晶循环。所以，当前作者先前开发和发布的分段逆流曲线确定方法“ FepiM”通过引入两步法得到了扩展，从而获得了在高温和不同应变速率下的等温流动曲线。由此，流动曲线被表示为表格数据而不是方程式，以再现复杂的流动曲线形状，同时还补偿了不均匀的温度曲线对流动应力的影响。首先，确定最高温度下的流动曲线。在第二步中，以该第一流动曲线为参考，通过插值获得较低温度下的流动曲线。可以预测在20–500°C的温度范围内对铝和铜进行常规压缩测试的流量曲线，结果表明，这些流动曲线可以再现实验力，最大偏差小于1％。因此，所提出的新的分段方法可以准确地预测压缩试验的等温流动曲线，并且该方法可以在将来进一步扩展为高度不均匀的方法。