| 朱宝,孙豪,刘玥.基于参变量变分原理的纳米孪晶结构的各向异性Cosserat理论建模[J].计算力学学报,2025,42(2):196~204 |
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| 基于参变量变分原理的纳米孪晶结构的各向异性Cosserat理论建模 |
| Anisotropic Cosserat theoretical modeling of nano twin structure based on parametric Variational principle |
| 投稿时间：2023-09-16 修订日期：2023-12-06 |
| DOI：10.7511/jslx20230916005 |
| 中文关键词: 参数量变分原理 各向异性 Cosserat 二次规划算法 纳米孪晶铜 |
| 英文关键词:variational principle of parameter quantity anisotropy Cosserat sequential quadratic program-ming nano-twinned copper |
| 基金项目:国家自然科学基金(52375170)资助项目. |
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| 摘要点击次数: 16 |
| 全文下载次数: 15 |
| 中文摘要: |
| 纳米孪晶结构金属不仅得到实验证明具有优异的强度,而且具有良好的延展性,是改善金属强度-塑韧性倒置关系的重要途径,体现出巨大的工程应用价值。本文基于参变量变分原理,发展了三维各向异性Cosserat弹塑性分析的参数二次规划算法,并且将该算法应用于纳米孪晶铜的数值建模模拟。通过引入孪晶与基体之间的特殊取向关系,建立了纳米孪晶铜的各向异性Cosserat连续介质模型。考虑到晶体取向不同而产生的各向异性效应以及孪晶与基体之间的不均匀变形产生的应变梯度效应,得到的模型结果与不同实验研究所得的纳米孪晶铜的应力-应变曲线吻合良好。基于该模型,系统地研究了平均孪晶厚度对纳米孪晶铜屈服强度、弹性模量等力学性能的影响。结果表明,各向异性效应主要影响弹性模量和屈服强度,应变梯度效应影响屈服强度和应变硬化率。 |
| 英文摘要: |
| Nanotwin structured metals have not only been experimentally proven to have excellent strength,but also good ductility,which is an important way to improve the inverse relationship between metal strength and ductility,demonstrating enormous engineering application value.In this paper,based on the parametric variational principle,a parametric quadratic programming algorithm for three-dimensional anisotropic Cosserat elasto-plastic analysis is developed and applied to the numerical modeling and simulation of nano-twinned copper.An anisotropic Cosserat continuum model for nano-twinned copper is established by introducing a special orientation relationship between the twin and the matrix.Considering the anisotropic effect caused by different crystal orientations and the strain gradient effect caused by uneven deformation between the twin and the matrix,the model results obtained are in good agreement with the stress-strain curve of nano-twinned copper obtained from different experimental studies.Based on this model,the influence of average twin thickness on the mechanical properties such as yield strength and Young’s modulus of nano-twinned copper is systematically studied.The results indicate that the anisotropic effect mainly affects the Young’s modulus and yield strength,while the strain gradient effect affects the yield strength and strain-hardening rate. |
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