Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch
The contact problem on indentation of an elastic coated half-space by a conical punch is considered. To obtain an explicit analytical solution suitable for applications, the bilateral asymptotic method is used in a simplified form. For that purpose, kernel transform of the integral equation is appro...
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| Format: | Article |
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MDPI AG
2020-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/6/983 |
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| author | Andrey S. Vasiliev Sergey S. Volkov Evgeniy V. Sadyrin Sergei M. Aizikovich |
| author_facet | Andrey S. Vasiliev Sergey S. Volkov Evgeniy V. Sadyrin Sergei M. Aizikovich |
| author_sort | Andrey S. Vasiliev |
| collection | DOAJ |
| description | The contact problem on indentation of an elastic coated half-space by a conical punch is considered. To obtain an explicit analytical solution suitable for applications, the bilateral asymptotic method is used in a simplified form. For that purpose, kernel transform of the integral equation is approximated by a ratio of two quadratic functions containing only one parameter. Such an approach allows us to obtain explicit analytical expressions for the distribution of contact stresses and relations between the indentation force, depth, stiffness and contact radius. The obtained solution is suitable both for homogeneous and functionally graded coatings. The dependence of the characteristics of contact interaction on a relative Young’s modulus of the coating and relative coating thickness is analyzed and illustrated by the numerical examples. Ranges of values of elastic and geometrical parameters are obtained, for which the presence of a coating sufficiently changes the contact characteristics. The accuracy of the obtained simplified expressions is studied in detail. Results of the paper sufficiently simplify engineering calculations and are suitable for inverse analysis, e.g., analysis of indentation experiments of coated materials using either a conical or a pyramidal (Berkovich) indenter. |
| first_indexed | 2024-03-10T19:08:03Z |
| format | Article |
| id | doaj.art-51536936cb66497f98422d03a71c47d6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:08:03Z |
| publishDate | 2020-06-01 |
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| spelling | doaj.art-51536936cb66497f98422d03a71c47d62023-11-20T04:00:55ZengMDPI AGMathematics2227-73902020-06-018698310.3390/math8060983Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical PunchAndrey S. Vasiliev0Sergey S. Volkov1Evgeniy V. Sadyrin2Sergei M. Aizikovich3Research and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, RussiaResearch and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, RussiaResearch and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, RussiaResearch and Education Center “Materials”, Don State Technical University, 344000 Rostov-on-Don, RussiaThe contact problem on indentation of an elastic coated half-space by a conical punch is considered. To obtain an explicit analytical solution suitable for applications, the bilateral asymptotic method is used in a simplified form. For that purpose, kernel transform of the integral equation is approximated by a ratio of two quadratic functions containing only one parameter. Such an approach allows us to obtain explicit analytical expressions for the distribution of contact stresses and relations between the indentation force, depth, stiffness and contact radius. The obtained solution is suitable both for homogeneous and functionally graded coatings. The dependence of the characteristics of contact interaction on a relative Young’s modulus of the coating and relative coating thickness is analyzed and illustrated by the numerical examples. Ranges of values of elastic and geometrical parameters are obtained, for which the presence of a coating sufficiently changes the contact characteristics. The accuracy of the obtained simplified expressions is studied in detail. Results of the paper sufficiently simplify engineering calculations and are suitable for inverse analysis, e.g., analysis of indentation experiments of coated materials using either a conical or a pyramidal (Berkovich) indenter.https://www.mdpi.com/2227-7390/8/6/983contact problemindentationcoatingsanalytical solutionssimplified solutionsconical indenter |
| spellingShingle | Andrey S. Vasiliev Sergey S. Volkov Evgeniy V. Sadyrin Sergei M. Aizikovich Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch Mathematics contact problem indentation coatings analytical solutions simplified solutions conical indenter |
| title | Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch |
| title_full | Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch |
| title_fullStr | Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch |
| title_full_unstemmed | Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch |
| title_short | Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Conical Punch |
| title_sort | simplified analytical solution of the contact problem on indentation of a coated half space by a conical punch |
| topic | contact problem indentation coatings analytical solutions simplified solutions conical indenter |
| url | https://www.mdpi.com/2227-7390/8/6/983 |
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