DOI QR코드

DOI QR Code

A Numerical Approach to Young's Modulus Evaluation by Conical Indenter with Finite Tip-Radius

유한선단반경을 갖는 원뿔형 압입자에 의한 영률평가 수치접근법

  • 이진행 (서강대학교 대학원 기계공학과) ;
  • 김덕훈 (서강대학교 대학원 기계공학과) ;
  • 이형일 (서강대학교 기계공학과)
  • Published : 2008.01.01

Abstract

Instrumented sharp indentation test is a well-directed method to measure hardness and elastic modulus. The sharp indenter such as Berkovich and conical indenters have a geometrical self-similarity in theory, but the self-similarity ceases to work in practice due to inevitable indenter tip-blunting. In this study we analyzed the load-depth curves of conical indenter with finite tip-radius via finite element method. Using the numerical regression data obtained from Kick's law, we first confirmed that loading curvature is significantly affected by tip radius as well as material properties. We then established a new method to evaluate Young's modulus, which successfully provides the value of elastic modulus with an average error of less than 2%, regardless of tip-radius and material properties of both indenter and specimen.

Keywords

Indentation Test;Tip Radius;Young's Modulus;Material Property;FEA

References

  1. Giannakopoulos, A. E., Larsson, P.-L. and Vestergaard, R., 1994, 'Analysis of Vickers Indentation,' International Journal of Solids and Structures, Vol. 31, pp. 2679-2708 https://doi.org/10.1016/0020-7683(94)90225-9
  2. Larsson, P.-L., Giannakopoulos, A. E., Soderlund, E., Rowcliffe, D. J. and Vestergaard, R., 1996, 'Analysis of Berkovich Indentation,' International Journal of Solids and Structures, Vol. 33, pp. 221-248 https://doi.org/10.1016/0020-7683(95)00033-7
  3. Giannakopoulos, A. E. and Suresh, S., 1999, 'Determination of Elastoplastic Properties by Instrumented Sharp Indentation,' Scripta Materialia, Vol. 40, pp. 1191-1198 https://doi.org/10.1016/S1359-6462(99)00011-1
  4. Taljat, B., Zacharia, T. and Kosel, F., 1997, 'New Analytical Procedure to Determine Stress-Strain Curve from Spherical Indentation Data,' International Journal of Solids and Structures, Vol. 35, pp. 4411-4426 https://doi.org/10.1016/S0020-7683(97)00249-7
  5. Cheng, Y. T. and Cheng, C. M., 1998, 'Scaling Approach to Conical Indentation in Elasto-plastic Solids with Work Hardening,' Journal of Applied Physics, Vol. 84, pp. 1284-1291 https://doi.org/10.1063/1.368196
  6. Dao, M., Chollacoop, N., Van Vliet, K. J., Venkatesh, T. A. and Suresh, S., 2001, 'Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation,' Acta Materialia, Vol. 49, pp. 3899-3918 https://doi.org/10.1016/S1359-6454(01)00295-6
  7. Lee, J. H. and Lee, H., 2006, 'An Indentation Method Based on FEA for Equi-biaxial Residual Stress Evaluation,' Transactions of KSME, Vol. 30, No. 1, pp. 42-51 https://doi.org/10.3795/KSME-A.2006.30.1.042
  8. Lee, J. H., 2006, A Numerical Approach and Experi-mental Verification of the Indentation Techniques for Material Property and Residual Stress Evaluation, Ph. D. Thesis, Department of Mechanical Engineering, Sogang University
  9. Lee, J. H., Yu, H. S. and Lee, H., 2007, 'A Numerical Approach to Indentation Techniques for Thin-film Property Evaluation,' Transactions of KSME, Vol. 31, No. 3, pp. 313-321 https://doi.org/10.3795/KSME-A.2007.31.3.313
  10. ABAQUS User's Manual, 2005, Version 6.5, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, RI
  11. Pharr, G. M., Oliver, W. C. and Brotzen, F. R., 1992, 'On the Generality of the Relationship among Contact Stiffness, Contact Area and Elastic Modulus during Indentation,' Journal of Material Research, Vol. 7, pp. 613-617 https://doi.org/10.1557/JMR.1992.0613
  12. Xue, Z., Huang, Y., Hwang, K. C. and Li, M., 2002, 'The Influence of Indenter Tip Radius on the Micro-Indentation Hardness,' Journal of Engineering Mate-rials and Technology, Vol. 124, pp. 371-379 https://doi.org/10.1115/1.1480409
  13. Sneddon, I. N., 1965, 'The Relation between Load and Penetration in the Axisymmetric Boussinesq Pro-blem for a Punch of Arbitrary Profile,' International Journal of Engineering Science, Vol. 3, pp. 47-57 https://doi.org/10.1016/0020-7225(65)90019-4