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| 基于有限元-虚场法的I型应力强度因子表征方法研究 |
| Research on Characterizing the Mode I Stress Intensity Factors using the Finite Element-based Virtual Fields Method |
| 投稿时间：2023-06-27 修订日期：2023-08-13 |
| DOI： |
| 中文关键词: 虚场法 反问题 应力强度因子；数字图像相关方法 |
| 英文关键词:virtual fields method inverse problems stress intensity factors digital image correlation |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 虚场法（Virtual Fields Method, VFM）是求解力学反问题的一种重要方法，目前虚场法在材料的本构参数表征方面发展迅速并得到了广泛应用。为了提高虚场法的参数表征能力，本文研究了基于虚场法的应力强度因子表征方法。在该方法中，以裂尖为中心选择扇形分析区域，在此基础上通过Williams应力公式及虚功原理建立了表征应力强度因子的控制方程。进一步地，通过数值模拟实验分析了两种不同虚场选择策略下的抗噪性。基于数字图像相关方法（Digital Image Correlation, DIC）及单边缺口拉伸实验，利用虚场法表征了激光修复GH4169试样的I型应力强度因子，并与基于Williams位移公式的最小二乘法结果进行了比较。结果表明，在小范围屈服条件下，基于虚场法的应力强度因子表征值与载荷之间存在明显的线性关系，并且虚场法的表征误差要小于最小二乘法的表征误差。上述研究结果表明了虚场法在断裂力学领域具有广阔的发展前景。 |
| 英文摘要: |
| The virtual fields method (VFM) is an important method for solving mechanical inverse problems. Recently, VFM has been rapidly developed and widely used for characterizing the constitutive parameters of materials. To improve the parameter characterization capability of VFM, a strategy for identifying the stress intensity factors (SIFs) based on the VFM is investigated in this study. For this method, the sector area is selected for analysis with the crack tip as the center, and the governing equations characterizing the stress intensity factor are established on this basis by Williams’ series expansions in stress form and the principle of virtual work. Furthermore, the noise immunity under two different strategies for selecting the virtual fields is analyzed by numerical experiments. Based on the digital image correlation (DIC) and single edge notched tensile (SENT) tests, mode I SIFs of the laser-repaired GH4169 specimens are characterized using VFM, and the results are compared with those of the least-squares method (LSM) which is based on the Williams’ series expansions in displacement form. The results of this study show that there is an obvious linear relationship between the SIFs by VFM and the external loads under the small-scale yielding (SCY) conditions. Moreover, the relative errors of VFM are smaller than those of LSM. The above research results demonstrate that the VFM has a promising development in the field of fracture mechanics. |
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