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Extracting true stresses and strains from nominal stresses and strains in tensile testing
Strain ( IF 1.8 ) Pub Date : 2021-07-23 , DOI: 10.1111/str.12396
Rainer Schwab 1 , Anton Harter 1
Affiliation  

Seemingly a simple task, the extraction of the flow curve (true stress vs. true plastic strain) from nominal stresses and strains in standard tensile testing still has its unsolved points. This study addresses two of them: (i) in materials without yield point phenomenon (or generally in the region of homogeneous plastic deformation), the true stress is typically calculated assuming constant volume, ignoring the elastic volume changes. Here, we derive a set of exact analytical solutions for true stresses and strains with remarkable simplicity and beauty that fully account for the elastic volume changes. This set of exact solutions is cross-checked by finite element simulations as well as zeroth- and first-order approximations; perfect agreement has been found. (ii) In materials with a pronounced yield point phenomenon, a complicated three-dimensional stress state inevitably arises at the edge of the Lüders bands, which masks the real (or inherent) material behaviour. To determine the real material behaviour in the Lüders region, here we use a new macroscopic analytical approach characterised by a high true upper yield point, a typical strain hardening behaviour common for many materials, and the triaxiality of the stress state that inevitably develops at the edges of the Lüders bands and that determines the stress level at the observed lower yield point. This approach is verified by experiments (including video observations as well as digital image correlation (DIC) strain distribution measurements) and finite element simulations with very good agreement.

中文翻译:

从拉伸试验中的名义应力和应变中提取真实应力和应变

看似简单的任务,从标准拉伸试验中的名义应力和应变中提取流动曲线(真实应力与真实塑性应变)仍有未解决的问题。这项研究解决了其中两个问题:(i) 在没有屈服点现象的材料中(或通常在均匀塑性变形区域),真实应力通常是在假设体积不变的情况下计算的,忽略弹性体积的变化。在这里,我们推导出了一组针对真实应力和应变的精确解析解,非常简单和美观,充分考虑了弹性体积变化。这组精确解通过有限元模拟以及零阶和一阶近似进行交叉检查;找到了完美的一致。(ii) 在具有明显屈服点现象的材料中,在吕德斯带的边缘不可避免地会出现复杂的三维应力状态,它掩盖了真实(或固有)的材料行为。为了确定 Lüders 区域的真实材料行为,我们在这里使用了一种新的宏观分析方法,其特点是具有较高的真实上屈服点、许多材料常见的典型应变硬化行为以及在Lüders 带的边缘,这决定了观察到的较低屈服点的应力水平。这种方法通过实验(包括视频观察以及数字图像相关 (DIC) 应变分布测量)和有限元模拟得到了很好的验证。它掩盖了真实(或固有)的材料行为。为了确定 Lüders 区域的真实材料行为,我们在这里使用了一种新的宏观分析方法,其特点是具有较高的真实上屈服点、许多材料常见的典型应变硬化行为以及在Lüders 带的边缘,这决定了观察到的较低屈服点的应力水平。这种方法通过实验(包括视频观察以及数字图像相关 (DIC) 应变分布测量)和有限元模拟得到了很好的验证。它掩盖了真实(或固有)的材料行为。为了确定 Lüders 区域的真实材料行为,我们在这里使用了一种新的宏观分析方法,其特点是具有较高的真实上屈服点、许多材料常见的典型应变硬化行为以及在Lüders 带的边缘,这决定了观察到的较低屈服点的应力水平。这种方法通过实验(包括视频观察以及数字图像相关 (DIC) 应变分布测量)和有限元模拟得到了很好的验证。许多材料常见的典型应变硬化行为,以及在 Lüders 带边缘不可避免地产生的应力状态的三轴性,这决定了观察到的较低屈服点处的应力水平。这种方法通过实验(包括视频观察以及数字图像相关 (DIC) 应变分布测量)和有限元模拟得到了很好的验证。许多材料常见的典型应变硬化行为,以及在 Lüders 带边缘不可避免地产生的应力状态的三轴性,这决定了观察到的较低屈服点处的应力水平。这种方法通过实验(包括视频观察以及数字图像相关 (DIC) 应变分布测量)和有限元模拟得到了很好的验证。
更新日期:2021-07-23
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