Wang Zhenda, Fu Xiuli, Xu Nianwei, Pan Yongzhi, Zhang Yijia
Department of Mechanical Engineering, University of Jinan, Jinan 250022, China.
Materials (Basel). 2022 Aug 30;15(17):5998. doi: 10.3390/ma15175998.
The mechanical properties of anisotropic materials are generally characterized based on the orthotropy or transverse isotropy. However, the two-dimensional plane stress problems cannot comprehensively characterize the anisotropy of materials. In this study, based on the theory of elasticity and the transformation of the three-dimensional space coordinate system, combined with the projection relationship of the Cauchy stress tensor of an arbitrary section, the transformation relationship of the elastic modulus, shear modulus, and stress-strain between the orthogonal and load coordinate systems are obtained. The orthotropic Johnson-Cook (JC) constitutive model of AA7050-T7451 aluminum alloy is modified by fitting, and the constitutive relationship at any spatial angle is theoretically calculated by combining the obtained spatial coordinate transformation matrix. The generated spatial constitutive model is verified and modified through experiments. The results demonstrate that the theoretical mechanical properties and the modified spatial constitutive model can accurately reflect the effect of the spatial angle on the material stress distribution.
各向异性材料的力学性能通常基于正交各向异性或横向各向同性来表征。然而，二维平面应力问题无法全面表征材料的各向异性。在本研究中，基于弹性理论和三维空间坐标系的变换，结合任意截面的柯西应力张量的投影关系，得到了正交坐标系与载荷坐标系之间弹性模量、剪切模量以及应力 - 应变的变换关系。通过拟合对AA7050 - T7451铝合金的正交各向异性约翰逊 - 库克（JC）本构模型进行修正，并结合所得到的空间坐标变换矩阵从理论上计算任意空间角度下的本构关系。通过实验对所生成的空间本构模型进行验证和修正。结果表明，理论力学性能和修正后的空间本构模型能够准确反映空间角度对材料应力分布的影响。
