Rabiei Marzieh, Palevicius Arvydas, Dashti Amir, Nasiri Sohrab, Monshi Ahmad, Vilkauskas Andrius, Janusas Giedrius
Faculty of Mechanical Engineering and Design, Kaunas University of Technology, LT-51424 Kaunas, Lithuania.
Department of Materials Science and Engineering, Sharif University of Technology, Tehran 11365-9466, Iran.
Materials (Basel). 2020 Oct 1;13(19):4380. doi: 10.3390/ma13194380.
Young's modulus (E) is one of the most important parameters in the mechanical properties of solid materials. Young's modulus is proportional to the stress and strain values. There are several experimental and theoretical methods for gaining Young's modulus values, such as stress-strain curves in compression and tensile tests, electromagnetic-acoustic resonance, ultrasonic pulse echo and density functional theory (DFT) in different basis sets. Apparently, preparing specimens for measuring Young's modulus through the experimental methods is not convenient and it is time-consuming. In addition, for calculating Young's modulus values by software, presumptions of data and structures are needed. Therefore, this new method for gaining the Young's modulus values of crystalline materials is presented. Herein, the new method for calculating Young's modulus of crystalline materials is extracted by X-ray diffraction. In this study, Young's modulus values were gained through the arbitrary planes such as random (hkl) in the research. In this study, calculation of Young's modulus through the relationship between elastic compliances, geometry of the crystal lattice and the planar density of each plane is obtained by X-ray diffraction. Sodium chloride (NaCl) with crystal lattices of FCC was selected as the example. The X-ray diffraction, elastic stiffness constant and elastic compliances values have been chosen by the X'Pert software, literature and experimental measurements, respectively. The elastic stiffness constant and Young's modulus of NaCl were measured by the ultrasonic technique and, finally, the results were in good agreement with the new method of this study. The aim of the modified Williamson-Hall (W-H) method in the uniform stress deformation model (USDM) utilized in this paper is to provide a new approach of using the W-H equation, so that a least squares technique can be applied to minimize the sources of errors.
杨氏模量（E）是固体材料力学性能中最重要的参数之一。杨氏模量与应力和应变值成正比。有几种获取杨氏模量值的实验和理论方法，例如压缩和拉伸试验中的应力 - 应变曲线、电磁 - 声共振、超声脉冲回波以及不同基组下的密度泛函理论（DFT）。显然，通过实验方法制备用于测量杨氏模量的试样既不方便又耗时。此外，使用软件计算杨氏模量值时，需要对数据和结构进行假设。因此，提出了这种获取晶体材料杨氏模量值的新方法。在此，通过X射线衍射提取了计算晶体材料杨氏模量的新方法。在本研究中，通过研究中的任意平面（如随机（hkl）平面）获得了杨氏模量值。在本研究中，通过X射线衍射，根据弹性柔顺性、晶格几何形状和每个平面的面密度之间的关系计算杨氏模量。选择具有面心立方（FCC）晶格的氯化钠（NaCl）作为示例。分别通过X'Pert软件、文献和实验测量选取了X射线衍射、弹性刚度常数和弹性柔顺性值。通过超声技术测量了NaCl的弹性刚度常数和杨氏模量，最终结果与本研究的新方法吻合良好。本文在均匀应力变形模型（USDM）中采用的修正威廉姆森 - 霍尔（W - H）方法的目的是提供一种使用W - H方程的新方法，以便可以应用最小二乘法来最小化误差来源。
