| Author Name | Affiliation | | Yiquan Li | School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 130022, China | | Xiaozhou Li | School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 130022, China | | Jinkai Xu | School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 130022, China | | Huadong Yu | School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 130022, China |
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| Abstract: |
| The contact problem for the elastic sphere indenting a layered half-space is considered. Analytical methods for solving this problem have been developed on the basis of the 3-D fundamental solution of a half space with a single coating layer under a normal concentrated force on the surface. The normal pressure distribution within the contact zone is assumed as Hertzian type. The solutions are constructed using superposition principle in the form of infinite series. Through comparing with the numerical results of FEM, it can be verified that the exact solutions have a rapid convergence rate and the stresses and displacements are mainly determined by the first term, which is corresponding to the solution of homogeneous half-space under Hertzian loading. The contact radius can be predicted applying the method. |
| Key words: fundamental solution image method coated half space spherical indentation contact radius |
| DOI：10.11916/j.issn.1005-9113.16067 |
| Clc Number:TH114 |
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| Descriptions in Chinese: |
| 弹性球压入单涂层半空间解析解 李一全,李晓舟,许金凯,于化东 （长春理工大学 机电工程学院，长春 130022） 中文摘要：本文针对弹性球压入表面涂层半空间的接触问题，在单涂层半空间表面作用法向集中力的基本解基础上进行了理论分析。接触区域内压力分布采用Hertz假定，利用叠加原理构造了级数解。通过与有限元结果对比分析，可知解析解具有很快的收敛速度，而且应力和位移主要取决于级数解首项，即Hertz接触压力下均质弹性半空间的理论解。利用本文的解析方法，可以预测接触半径。 研究目的： 本文的主要研究目的是给出球体与涂层材料接触的理论解答，从而为相关应力分析提供理论方法，同时可进一步利用本文的方法和结果指导涂层材料的压痕实验。 研究方法： 本文为理论分析，主要采用镜像法和叠加法，同时利用有限元法对理论解进行对比验证。 结果： 弹性球压入表面涂层半空间的接触问题的理论解可通过构造无穷级数来实现。 结论： 理论解为显式级数表达式，且具有很快的收敛速度，而且应力和位移主要取决于首项，因此在实际应用时只取级数的前几项即可得到足够精确的结果。 关键词：基本解；镜像法；涂层半空间；球形压入；接触半径 |
