 研究文献发布相关信息

论文题目： Crystal Plasticity Finite Element Method for Slip Systems Evolution Analysis of α/β Duplex Titanium Alloys during Quasi-Static Tensile Testing

发表时间：Published: 3 November 2020

刊源：Appl. Sci. 2020, 10(21), 7782 [ 点击下载PDF ]

 研究文献内容展示

The model was developed from an EBSD image. The local area selected was 16.5 μm × 10.1 μm (see Figure 2a). The area consisted of 12 grains, including seven α-phase grains and five β-phase grains. The grains were numbered (i.e., ①, ② , ③ , and so on) and the excel file including crystal structure, centroid position, Euler angles (φ₁, Φ, φ₂) was output by channel5 software. Based on the RGB values of the image pixels, a 2D finite element model was developed. However, the 2D model used the plane strain or plane stress assumption, which may affect the accuracy of the simulation. Therefore, a unit thickness finite element model was established with 8-node 3D hexahedron solid elements, using the microstructure-based finite element model construction software developed by our group (see Figure 2b), so it is called a 2.5D finite element model, which can reduce the calculation time and well reflect the actual situation. Each grain was considered as a single crystal, with a uniform crystallographic orientation, and its Euler angle was determined by centroid result.

Figure 2. Process of developing the crystal plasticity finite element simulation method (CPFEM): (a) the Electron Backscatter Diffraction (EBSD) inverse pole figure (IPF) mapping, (b) 2.5D finite element model, (c) boundary condition, (d) displacement-time curve.

To further analyze the evolution of stress and strain, the Von Mises effective stress and effective strain field at macro strains of 0.1%, 0.7%, 1.2%, 4%, 7.8%, and 15.5% are shown in Fig. 7. Considering the needs of comparison and analysis, the figures were scaled to the same size. It can be found that the tendencies of Von Mises effective stress and effective strain are somewhat different. At the beginning, the initial stress and strain were relatively small. As the strain increases, the stress also increases. When entering the plastic stage, the stress value increases to a certain value and remains unchanged, while the accumulated strain continues to increase.

Figure 7. Stress and strain fields at macro strain = 0.1%, 0.7%, 1.2%, 4%, 7.8%, and 15.5%: (a–f) Von Mises effective stress field; (g–l) effective strain field.

Generally, a resolved shear stress is determined from the full Schmid tensors unless the stress state is uniaxial, what is unlikely for a local stress state. In this study, we analyze the major principal stress to verify the assumption and prove the influence of grain interactions on the SFs quantitatively For example, when the macro strain reached 0.7%， the prismatic slip systems of grain No. 3 and 11 were activated, while the SF of（0110 ）[2110] in grain No. 3 was 0. 136 and the SF of（0110）[2110] in grain No. 11 was 0. 321. It was found that the（0110 ）[2110] in grain No. 3 should not be the primary ip system. Therefore, as shown in Figure 12a, the macro deformation direction was parallel to X axis, and the direction of major principal stress δ₁ deviated from the X-axis and the deviation angle was e （ignoring the deviation angle between the direction of δ₁ and Z-axis）， which was used to fit with the Euler angle and recalculate the SFs. As shown in Figure 12b, the e of grain No. 3 was 30° and the e of grain No. 11 was close to 0°. After recalculation, the SF of（0110）[2110] in grain No. 3 was 0.233， which meant that the（0110 ）[2110] slip system was easily activated

Figure 12. (a) Schematic diagram of major principal stress; (b) ε = 0.7%; (c) ε = 2.4%; (d) ε = 7.8% effective strain increment fields in the local and the direction of major principal stress.