Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

A Conical Indentation Technique Based on FEA Solutions for Property Evaluation

유한요소해에 기초한 원뿔형 압입 물성평가법

  • 현홍철 (서강대학교 대학원 기계공학과) ;
  • 김민수 (서강대학교 대학원 기계공학과) ;
  • 이진행 (서강대학교 대학원 기계공학과) ;
  • 이형일 (서강대학교 기계공학과)
  • Published : 2009.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity in theory, but different materials have the same load-depth curve in case of single indentation. In this study, we analyze the load-depth curves of conical indenter with angles of indenter via finite element method. From FE analyses of dual-conical indentation test, we investigate the relationships between indentation parameters and load-deflection curves. With numerical regressions of obtained data, we finally propose indentation formulae for material properties evaluation. The proposed approach provides stress-strain curve and the values of elastic modulus, yield strength and strain-hardening exponent with an average error of less than 2%. It is also discussed that the method is valid for any elastically deforming indenters made of tungsten carbide and diamond for instance. The proposed indentation approach provides a substantial enhancement in accuracy compared with the prior methods.

물성치와 하중-변위곡선을 일대일 대응 시킬 수 있는 함수를 생성함으로써, 미지 재료에 대한 압입시험 데이터로부터 바로 재료물성을 찾는 압입물성평가 기법을 제시했다. 원뿔형 압입 유한요소해석으로 압입자 중심각이 압입 하중-변위 곡선에 주는 영향을 살펴 보았다. 이로부터 한 압입자 중심각에 대해 같은 Kick's law 계수 C를 갖는 두 재료들이 압입자 중심각이 변하면 서로 다른 C 값들을 가짐을 확인했다. 이어 영률, 항복강도, 변형경화지수와 하중-변위곡선 사이의 상관관계들을 분석하고, 항복변형률이 변형경화 지수와 더불어 중요한 변수임을 확인했다. 이 두 특성들을 바탕으로 이중원뿔형 압입 물성평가 수식들을 작성했다. 1회 압입 후 재료의 영률을 평가하고, 두 압입자를 이용해 얻은 하중-변위 곡선들로부터 곡률계수들을 구해 항복변형률과 변형경화 지수를 구했다. 제시된 물성평가법은 압입 하중-변위곡선들로부터, 압입자 물성과 선단반경에 상관없이, 평균오차 2% 내에서 재료 물성값들을 준다.

Keywords

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. 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
  4. 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
  5. 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
  6. 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
  7. Lee, J. H., 2006, A Numerical Approach and Experimental Verification of the Indentation Techniques for Material Property and Residual Stress Evaluation, Ph. D. Dissertation, Department of Mechanical Engineering, Sogang University
  8. Shim, S., Oliver, W. C. and Pharr, G. M., 2007, 'A Comparison of 3D Finite Element Simulation for Berkovich and Conical Indentation of Fused Silica,' International Journal of Surface Science and Engineering, Vol. 1, pp. 259~273 https://doi.org/10.1504/IJSURFSE.2007.015028
  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. Xu, Z. -H. and Li, X., 2008, 'Effect of Indenter Geometry and Material Properties on the Correction Factor of Sneddon's Relationship for Nanoindentation of Elastic-plastic Materials,' Acta Materialia, Vol. 56, pp. 1399~1405 https://doi.org/10.1016/j.actamat.2007.11.030
  11. Lee, J. H., Lee, H. and Pharr, G. M., 2005, 'A Numerical Approach to Spherical Indentation Tech-niques for Material Property Evaluation,' Journal of the Mechanics and Physics Solid, Vol. 53, pp. 2037~ 2069 https://doi.org/10.1016/j.jmps.2005.04.007
  12. Lee, J. H. and Lee, H., 2007, 'Enhanced Spherical Indentation Techniques for Property Evaluation,' Transactions of KSME, Vol. 31, No. 43, pp. 461~471 https://doi.org/10.3795/KSME-A.2007.31.4.461
  13. 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
  14. Capehart, T. W., Cheng, Y. -T., 2003, 'Determination Constitutive Models from Conical Indentation: Sensitivity Analysis,' Journal of Materials Research, Vol. 18, pp. 827~832 https://doi.org/10.1557/JMR.2003.0113
  15. Tho, K. K., Swaddiwudhipong, S., Liu, Z. S., Zeng, K., Hua, J., 2004, 'Uniqueness of Reverse Analysis from Conical Indentation Test,' Journal of Materials Research, Vol. 19, pp. 2498~2502 https://doi.org/10.1557/JMR.2004.0306
  16. Chen, X., Ogasawara, N., Zhao, M. and Chiba, N., 2007, 'On the Uniqueness of Measuring Elastoplastic Properties from Indentation: The Indistinguishable Mystical Materials,' Journal of the Mechanics and Physics Solid, Vol. 55, pp. 1618 ~ 1660 https://doi.org/10.1016/j.jmps.2007.01.010
  17. Lee, J. H., Lee, H. and Kim, D. H., 2008, 'A Numerical Approach to Elastic Modulus Evaluation Using Conical Indenter with Finite Tip Radius,' Journal of Materials Research, Vol. 23, No.1, pp. 2528~2537 https://doi.org/10.1557/jmr.2008.0314
  18. Chollacoop, N., Dao, M. and Suresh, S., 2003, 'Depth-sensing Instrumented Indentation with Dual Sharp Indenters,' Acta Materialia, Vol. 51, pp. 3713~ 3729 https://doi.org/10.1016/S1359-6454(03)00186-1
  19. Bucaille, J. L., Stauss, S., Felder, E. and Michler, J., 2003, 'Determination of Plastic Properties of Metals by Instrumented Indentation Using Different Sharp Indenters,' Acta Materialia, Vol. 51, pp. 1663~1678 https://doi.org/10.1016/S1359-6454(02)00568-2
  20. ABAQUS User's Manual, 2005, Version 6.5, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, RI
  21. Sneddon, I. N., 1965, 'The Relation between Load and Penetration in the Axisymmetric Boussinesq Problem 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
  22. 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
  23. Rice, J. R. and Rosengren, G. F., 1968, 'Plane Strain Deformation Near a Crack-tip in a Power Law Hardening Material,' Journal of the Mechanics and Physics of Solids, Vol. 16, pp. 1~12 https://doi.org/10.1016/0022-5096(68)90013-6
  24. Hyun, H. C., Lee, J. H. and Lee, H., 2008, 'Mathematical Expressions for Stress-strain Curve of Metallic Material,' Transactions of KSME, Vol. 32, No. 1, pp. 21~28 https://doi.org/10.3795/KSME-A.2008.32.1.021

Cited by

  1. A Dual Triangular Pyramidal Indentation Technique Based on FEA Solutions for Material Property Evaluation vol.36, pp.1, 2012, https://doi.org/10.3795/KSME-A.2012.36.1.017