考虑微尺度效应的球-平面接触问题分析

马维维; 王宇星; 沈火明; 刘娟

doi:10.21656/1000-0887.450260

考虑微尺度效应的球-平面接触问题分析

doi: 10.21656/1000-0887.450260

马维维^1,,
王宇星^{1, 2, ,},
沈火明^{1, 3},
刘娟¹

1.
西南交通大学力学与航空航天学院，成都 611756
2.
西南交通大学机械工程学院，成都 610031
3.
成都信息工程大学，成都 610225

基金项目:

国家自然科学基金(青年科学基金项目) 12402113

四川省自然科学基金(青年基金项目) 2023NSFC1300

四川省自然科学基金(重点项目) 2024NSFC0037

详细信息

作者简介:
马维维(1997—)，男，硕士生(E-mail: wei2121921@163.com)

通讯作者:
王宇星(1991—)，男，讲师，博士(通讯作者. E-mail: wangyuxing1991@163.com)

中图分类号: O343.3
计量
- 文章访问数: 129
- HTML全文浏览量: 26
- PDF下载量: 25
- 被引次数: 0
出版历程
- 收稿日期: 2024-09-25
- 修回日期: 2024-12-06
- 刊出日期: 2025-12-01

Investigation of the Sphere-Plane Contact Problem Under Micro-Scale Effects

MA Weiwei^1
,,
WANG Yuxing^{1, 2
, ,},
SHEN Huoming^{1, 3},
LIU Juan¹

1.
School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 611756, P.R.China
2.
School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China
3.
Chengdu University of Information Technology, Chengdu 610225, P.R.China

摘要

摘要: 基于表面弹性理论和偶应力理论，研究了微纳米尺度下刚性球形压头与弹性半空间体的三维接触问题. 材料的尺度效应通过表面特征长度和材料特征长度进行表征. 结合表面弹性理论和偶应力理论，推导出了弹性半空间体受法向载荷时的频响函数，并借助共轭梯度法和快速Fourier变换法，建立了三维半解析接触模型. 利用该模型分析了表面残余应力、表面材料常数和材料特征长度对接触表面的接触压力、表面应力和表面位移的影响. 结果表明，与经典接触解相比，尺度效应使表面的接触压力在接触边缘急剧下降，表面法向应力在接触边缘连续且无突变，同时切向应力非零，表面的法向位移减小. 此外，随着材料特征长度的增大，表面切向应力的方向发生反转.
- 接触问题 /
- 表面弹性理论 /
- 偶应力理论 /
- 尺度效应 /
- 共轭梯度法
Abstract: Based on the surface elasticity and couple stress theories, a 3D contact problem between a rigid spherical indenter and an elastic half-space at the micro and nano scale was studied. The size effects of materials were described with the characteristic material lengths of the surface and the material. Through combination of the surface elasticity theory and the couple stress theory, the frequency response function in the elastic half-space under normal loading was derived. Then, with the conjugate gradient method and the fast Fourier transform, a 3D semi-analytical contact model was established. The proposed model was then used to analyze the effects of surface residual stress, surface material constants, and the characteristic material lengths on the contact pressure, stress, and displacement on the contact surface. The results show that, compared with the classical contact solution, the contact pressure at the contact edge of the surface decrease sharply under the size effects. Additionally, the normal stress on the surface remains continuous and without abrupt changes at the contact edge, while the tangential stress is non-zero, and the normal displacement of the surface decreases. Furthermore, as the characteristic material length of the material increases, the direction of the tangential stress on the surface will reverse.
- contact problem /
- surface-elasticity theory /
- couple stress theory /
- size effect /
- conjugate gradient method

HTML全文

图 1 刚性球形压头-半空间法向接触示意图

Figure 1. Schematic of the contact model between an elastic half-space and the rigid sphere

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图 2 接触几何关系

Figure 2. The geometrical relationships of contact

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图 3 退化结果与Hertz解的对比

Figure 3. Comparison between our reduced results and the Hertzian solution

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图 4 退化结果与Lawongkerd等^[20]的结果对比

Figure 4. Comparison between our reduced results and the solution given by Lawongkerd et al^[20]

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图 5 表面残余应力对接触压力、应力场和位移场在接触表面分布的影响

Figure 5. The effects of the residual surface stresses on the contact pressure, the stress and the displacement at the contact surface

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图 6 表面材料常数对接触压力、应力场和位移场在接触表面分布的影响

Figure 6. The effects of the surface material constants on the contact pressure, the stress and the displacement at the contact surface

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图 7 材料特征长度对接触压力、应力场和位移场在接触表面分布的影响

Figure 7. The effects of the characteristic material lengths of the material on the contact pressure, the stress and the displacement at the contact surface

下载: 全尺寸图片幻灯片

参考文献(21)

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