Flow curves can easily be obtained by uniaxial tensile tests, but strains are then limited by diffuse necking. For many applications, the flow stress must be known above this limit. The main objective of this paper is to obtain flow curves for material with low uniform elongation to relatively high strains compared to a uniaxial tensile test. A novel in-plane sheet bending experiment and stress evaluation procedure is presented. The developed bending device can be mounted in a tensile test machine and can produce very high bending curvatures compared to previously proposed pure bending setups. The bending angle and curvature are obtained by image processing and the bending moment is calculated directly from the force measured from the tensile test machine and the bending angle. The moment–curvature relation is used to determine the uniaxial stress–strain relation using an analytical approach, without presuming any hardening model. The bending process and the analytical procedure are validated by a numerical simulation as well as by experiments. The numerical validation shows good agreement between the stress–strain curve obtained from the bending process and that of the uniaxial input flow curve up to 12% strain. Experimentally the model is validated by comparing the stress–strain curve obtained from the bending test with the results directly obtained from a tensile test for mild steel. Good agreement is observed up to 12% strain. As an application example, bending tests were performed on a martensitic steel (MS) with low uniform strain (less than 3%). For this material, flow curves could be obtained up to relatively high strains (~12%), compared to a tensile test. This bending test setup allows to study materials with low uniform elongation up to significantly higher strains than are readily obtained in a tensile test.

中文翻译：

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一种新的平面内弯曲试验，用于确定低均匀伸长率材料的流动曲线

通过单轴拉伸试验可以很容易地获得流动曲线，但应变会受到扩散颈缩的限制。对于许多应用，必须知道高于此限制的流动应力。本文的主要目的是获得与单轴拉伸试验相比具有较低均匀伸长率至相对较高应变的材料的流动曲线。提出了一种新的平面内板材弯曲实验和应力评估程序。开发的弯曲装置可以安装在拉伸试验机中，与之前提出的纯弯曲设置相比，可以产生非常高的弯曲曲率。弯曲角度和曲率通过图像处理获得，弯曲力矩直接由拉伸试验机测得的力和弯曲角度计算得出。力矩-曲率关系用于使用分析方法确定单轴应力-应变关系，无需假设任何硬化模型。弯曲过程和分析程序通过数值模拟和实验进行验证。数值验证表明，从弯曲过程中获得的应力-应变曲线与高达 12% 应变的单轴输入流动曲线之间具有良好的一致性。通过将弯曲试验中获得的应力-应变曲线与低碳钢拉伸试验中直接获得的结果进行比较，对该模型进行了实验验证。观察到高达 12% 应变的良好一致性。作为一个应用示例，我们对均匀应变低（小于 3%）的马氏体钢 (MS) 进行了弯曲试验。对于这种材料，与拉伸试验相比，可以在相对较高的应变 (~12%) 下获得流动曲线。这种弯曲测试设置允许研究具有低均匀伸长率的材料，其应变比拉伸测试中容易获得的应变高得多。