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基于高阶应变梯度塑性理论的受限薄层剪切问题研究

华奋飞,罗彤,雷剑,刘大彪

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华奋飞, 罗彤, 雷剑, 刘大彪. 基于高阶应变梯度塑性理论的受限薄层剪切问题研究. 力学学报, 2024, 56(1): 59-68 doi: 10.6052/0459-1879-23-318
引用本文: 华奋飞, 罗彤, 雷剑, 刘大彪. 基于高阶应变梯度塑性理论的受限薄层剪切问题研究. 力学学报, 2024, 56(1): 59-68doi:10.6052/0459-1879-23-318
Hua Fenfei, Luo Tong, Lei Jian, Liu Dabiao. Study of confined layer plasticity based on higher-order strain gradient plasticity theory. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(1): 59-68 doi: 10.6052/0459-1879-23-318
Citation: Hua Fenfei, Luo Tong, Lei Jian, Liu Dabiao. Study of confined layer plasticity based on higher-order strain gradient plasticity theory.Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(1): 59-68doi:10.6052/0459-1879-23-318

基于高阶应变梯度塑性理论的受限薄层剪切问题研究

doi:10.6052/0459-1879-23-318
基金项目:国家自然科学基金 (12002129, 11702103)和湖北省自然科学基金 (2022CFB288)资助项目
详细信息
    通讯作者:

    刘大彪, 教授, 主要研究方向为实验固体力学、微尺度塑性力学. E-mail:dbliu@hust.edu.cn

  • 中图分类号:O343

STUDY OF CONFINED LAYER PLASTICITY BASED ON HIGHER-ORDER STRAIN GRADIENT PLASTICITY THEORY

  • 摘要:针对受限金属薄层在剪切塑性变形时出现明显尺度效应这一问题, 现有理论分析多采用纯剪切假设和传统钝化边界条件, 其理论预测与实验结果不符. 文章采用黏弹塑性本构模型, 对Gudmundson高阶应变梯度塑性理论进行了有限元实现, 深入研究了金属薄层受限剪切的塑性变形机理. 考虑因界面倾斜引起的附加压应力, 采用自定义平面单元对材料的压缩−剪切组合变形进行了有限元模拟. 根据表面解锁的物理机制, 引入“软−硬”中间态的边界条件. 结果表明, 在压缩−剪切组合变形条件下, 受限薄层的剪切流动应力明显低于纯剪切条件下的流动应力, 而压应力的存在降低了剪切屈服强度. 利用周期性钝化边界条件, 能够定量描述界面处几何必需位错饱和引起的边界条件变化, 理论预测与实验结果吻合. 相关研究揭示了加载方式和高阶边界条件在受限薄层剪切尺度效应问题中的重要作用.

  • 图 1自然坐标系下的二次单元

    Figure 1.A quadratic element in natural coordinate system

    图 2压缩和剪切组合作用下的金属薄层

    Figure 2.Thin metallic layer under combined compressive and shear loads

    图 3压缩−剪切组合作用下归一化的切应力−位移关系

    Figure 3.Normalized shear stress-displacement relation under combined compression and shear

    图 4${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时塑性切应变$ {\gamma _{\text{P}}} $的分布云图

    Figure 4.Contours of the plastic shear strain $ {\gamma _{\text{P}}} $ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$

    图 5SGP理论预测结果与受限薄层剪切实验结果[11]的比较

    Figure 5.Comparison between SGP predictions and experimental results of shear deformation of confined layer[11]

    图 6周期矩形边界条件

    Figure 6.Periodic rectangular boundary condition

    图 7不同周期下归一化切应力与位移的变化关系

    Figure 7.Normalized shear stress-displacement relation under different periods

    图 8${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时不同周期下塑性切应变$ {\gamma _{\text{P}}} $分布云图

    Figure 8.Contours of the plastic shear strain $ {\gamma _{\text{P}}} $ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$ under different periods

    图 9${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时不同周期下储能高阶应力$\tau _{122}^{\text{E}}$分布云图

    Figure 9.Contours of the higher-order stress $\tau _{122}^{\text{E}}$ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$ under different periods

    图 10周期正弦边界条件

    Figure 10.Periodic sinusoidal boundary condition

    图 11不同边界条件下归一化的切应力−位移关系

    Figure 11.Normalized shear stress-displacement relation under different boundary conditions

    图 12${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$时的塑性切应变$ {\gamma _{\text{P}}} $分布云图

    Figure 12.Contours of the plastic shear strain $ {\gamma _{\text{P}}} $ at ${{{u_1}} \mathord{\left/ {\vphantom {{{u_1}} H}} \right. } H} = 0.02$

    图 13SGP理论预测结果与受限剪切实验结果[11]的比较

    Figure 13.Comparison between SGP predictions and experimental results of confined shear[11]

    表 1材料参数[41]

    Table 1.Meterial parameters[41]

    Attribute ${{{\sigma _Y}} \mathord{\left/ {\vphantom {{{\sigma _Y}} E}} \right. } E}$ $N$ $ \nu $ ${\dot \varepsilon _0}$ ${\ell / H}$ ${L / H}$
    Value 0.003 0 0.3 0.0001 $ \in \left[ {0,1} \right]$ $ \in \left[ {0,1} \right]$
    下载: 导出CSV
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出版历程
  • 收稿日期:2023-07-20
  • 录用日期:2023-10-08
  • 网络出版日期:2023-10-09

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