Sensitivity to experimental errors determines the reliability and usefulness of any experimental investigation. Thus, it is important to understand how various test techniques are affected by expected experimental errors. Here, a semi-analytical method based on the concept of condition number is explored for systematic investigation of the sensitivity of spherical indentation to experimental errors. The method is employed to investigate the reliability of various possible spherical indentation protocols, providing a ranking of the selected data reduction protocols from least to most sensitive to experimental errors. Explicit Monte Carlo sensitivity analysis is employed to provide further insight of selected protocol, supporting the ranking. The results suggest that the proposed method for estimating the sensitivity to experimental errors is a useful tool. Moreover, in the case of spherical indentation, the experimental errors must be very small to give reliable material properties.
Issue Section:
Research Papers
References
References
1.
Van Vliet
, K. J.
Prchlik
, L.
Smith
, J. F.
2004
, “Direct Measurement of Indentation Frame Compliance
,” J. Mater. Res.
, 19
(1
), pp. 325
–331
.10.1557/jmr.2004.19.1.3252.
Field
, J. S.
Swain
, M. V.
1995
, “Determining the Mechanical Properties of Small Volumes of Material From Submicrometer Spherical Indentations
,” J. Mater. Res.
, 10
(1
), pp. 101
–112
.10.1557/JMR.1995.01013.
Kim
, J.-Y.
Kang
, S.-K.
Lee
, J.-J.
Jang
, J.-I.
Lee
, Y.-H.
Kwon
, D.
2007
, “Influence of Surface-Roughness on Indentation Size Effect
,” Acta Mater.
, 55
(10
), pp. 3555
–3562
.10.1016/j.actamat.2007.02.0064.
Huang
, Y.
Zhang
, F.
Hwang
, K. C.
Nix
, W. D.
Pharr
, G. M.
Feng
, G.
2006
, “A Model of Size Effects in Nano-Indentation
,” J. Mech. Phys. Solids
, 54
(8
), pp. 1668
–1686
.10.1016/j.jmps.2006.02.0025.
Higuchi
, R.
Mochizuki
, M.
Toyoda
, M.
2010
, “A Method for Evaluating the Stress–Strain Relationship of Materials in the Microstructural Region Using a Triangular Pyramidal Indenter
,” Weld. Int.
, 24
(8
), pp. 611
–619
.10.1080/09507116.2010.4862426.
Feng
, G.
Ngan
, A. H. W.
2002
, “Effects of Creep and Thermal Drift on Modulus Measurement Using Depth-Sensing Indentation
,” J. Mater. Res.
, 17
(3
), pp. 660
–668
.10.1557/JMR.2002.00947.
Ahn
, J.-H.
Kwon
, D.
2001
, “Derivation of Plastic Stress–Strain Relationship From Ball Indentations: Examination of Strain Definition and Pileup Effect
,” J. Mater. Res.
, 16
(11
), pp. 3170
–3178
.10.1557/JMR.2001.04378.
Jiang
, P.
Zhang
, T.
Feng
, Y.
Yang
, R.
Liang
, N.
2009
, “Determination of Plastic Properties by Instrumented Spherical Indentation: Expanding Cavity Model and Similarity Solution Approach
,” J. Mater. Res.
, 24
(3
), pp. 1045
–1053
.10.1557/jmr.2009.01089.
Lan
, H.
Venkatesh
, T. A.
2007
, “Determination of the Elastic and Plastic Properties of Materials Through Instrumented Indentation With Reduced Sensitivity
,” Acta Mater.
, 55
(6
), pp. 2025
–2041
.10.1016/j.actamat.2006.11.01210.
Lan
, H.
Venkatesh
, T. A.
2007
, “On the Sensitivity Characteristics in the Determination of the Elastic and Plastic Properties of Materials Through Multiple Indentation
,” J. Mater. Res.
, 22
(4
), pp. 1043
–1063
.10.1557/jmr.2007.012311.
Lan
, H.
Venkatesh
, T. A.
2007
, “On the Uniqueness and Sensitivity Issues in Determining the Elastic and Plastic Properties of Power-Law Hardening Materials Through Sharp and Spherical Indentation
,” Philos. Mag.
, 87
(30
), pp. 4671
–4729
.10.1080/1478643070158934312.
Phadikar
, J. K.
Bogetti
, T. A.
Karlsson
, A. M.
2013
, “On the Uniqueness and Sensitivity of Indentation Testing of Isotropic Materials
,” Int. J. Solids Struct.
, 50
(20–21
), pp. 3242
–3253
.10.1016/j.ijsolstr.2013.05.02813.
Oliver
, W. C.
Pharr
, G. M.
1992
, “An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,” J. Mater. Res.
, 7
(6
), pp. 1564
–1583
.10.1557/JMR.1992.156414.
Phadikar
, J. K.
Bogetti
, T. A.
Kaliakin
, V. N.
Karlsson
, A. M.
2013
, “Conical Indentation of a Viscoelastic Sphere
,” ASME J. Eng. Mater. Technol.
, 135
(4
), p. 041001
.10.1115/1.402439515.
Cheng
, Y.-T.
Cheng
, C.-M.
2004
, “Scaling, Dimensional Analysis, and Indentation Measurements
,” Mater. Sci. Eng.: R: Reports
, 44
(4–5
), pp. 91
–149
.10.1016/j.mser.2004.05.00116.
Phadikar
, J. K.
Bogetti
, T. A.
Karlsson
, A. M.
2012
, “On Establishing Elastic-Plastic Properties of a Sphere by Indentation Testing
,” Int. J. Solids Struct.
, 49
(14
), pp. 1961
–1972
.10.1016/j.ijsolstr.2012.04.00117.
Dieter
, G. E.
Bacon
, D.
1986
, Mechanical Metallurgy
, McGraw-Hill
, New York
.18.
Lubliner
, J.
1990
, Plasticity Theory
, Macmillan
, New York
.19.
Cao
, Y. P.
Qian
, X. Q.
Lu
, J.
Yao
, Z. H.
2005
, “An Energy-Based Method to Extract Plastic Properties of Metal Materials From Conical Indentation Tests
,” J. Mater. Res.
, 20
(5
), pp. 1194
–1206
.10.1557/JMR.2005.014720.
Dao
, M.
Lim
, C.
Suresh
, S.
2003
, “Mechanics of the Human Red Blood Cell Deformed by Optical Tweezers
,” J. Mech. Phys. Solids
, 51
(11–12
), pp. 2259
–2280
.10.1016/j.jmps.2003.09.01921.
Ogasawara
, N.
Chiba
, N.
Chen
, X.
2009
, “A Simple Framework of Spherical Indentation for Measuring Elastoplastic Properties
,” Mech. Mater.
, 41
(9
), pp. 1025
–1033
.10.1016/j.mechmat.2009.04.01022.
Yan
, J.
Chen
, X.
Karlsson
, A.
2007
, “Determining Equi-Biaxial Residual Stress and Mechanical Properties From the Force-Displacement Curves of Conical Microindentation
,” ASME J. Eng. Mater. Technol.
, 129
(2
), pp. 200
–206
.10.1115/1.240028023.
Yan
, J.
Karlsson
, A.
Chen
, X.
2007
, “Determining Plastic Properties of a Material With Residual Stress by Using Conical Indentation
,” Int. J. Solids Struct.
, 44
(11–12
), pp. 3720
–3737
.10.1016/j.ijsolstr.2006.10.01724.
Buckingham
, E.
1914
, “On Physically Similar Systems; Illustrations of the Use of Dimensional Equations
,” Phys. Rev.
, 4
(4
), pp. 345
–376
.10.1103/PhysRev.4.34525.
Alkorta
, J.
Martínez-Esnaola
, J. M.
Sevillano
, J. G.
2005
, “Absence of One-to-One Correspondence Between Elastoplastic Properties and Sharp-Indentation Load–Penetration Data
,” J. Mater. Res.
, 20
(2
), pp. 432
–437
.10.1557/JMR.2005.005326.
Capehart
, T. W.
Cheng
, Y.-T.
2003
, “Determining Constitutive Models From Conical Indentation: Sensitivity Analysis
,” J. Mater. Res.
, 18
(4
), pp. 827
–832
.10.1557/JMR.2003.011327.
Cheng
, Y.-T.
Cheng
, C.-M.
1999
, “Can Stress–Strain Relationships be Obtained From Indentation Curves Using Conical and Pyramidal Indenters?
,” J. Mater. Res.
, 14
(9
), pp. 3493
–3496
.10.1557/JMR.1999.047228.
Liu
, L.
Ogasawara
, N.
Chiba
, N.
Chen
, X.
2009
, “Can Indentation Technique Measure Unique Elastoplastic Properties?
,” J. Mater. Res
, 24
(3
), pp. 784
–800
.10.1557/jmr.2009.010029.
Tho
, K. K.
Swaddiwudhipong
, S.
Liu
, Z. S.
Zeng
, K.
Hua
, J.
2004
, “Uniqueness of Reverse Analysis From Conical Indentation Tests
,” J. Mater. Res.
, 19
(8
), pp. 2498
–2502
.10.1557/JMR.2004.030630.
Cao
, Y.
Qian
, X.
Huber
, N.
2007
, “Spherical Indentation Into Elastoplastic Materials: Indentation-Response Based Definitions of the Representative Strain
,” Mater. Sci. Eng.: A
, 454–455
, pp. 1
–13
.10.1016/j.msea.2007.01.00231.
Zhao
, M.
Ogasawara
, N.
Chiba
, N.
Chen
, X.
2006
, “A New Approach to Measure the Elastic-Plastic Properties of Bulk Materials Using Spherical Indentation
,” Acta Mater.
, 54
(1
), pp. 23
–32
.10.1016/j.actamat.2005.08.02032.
Cao
, Y. P.
Lu
, J.
2004
, “A New Method to Extract the Plastic Properties of Metal Materials From an Instrumented Spherical Indentation Loading Curve
,” Acta Mater.
, 52
(13
), pp. 4023
–4032
.10.1016/j.actamat.2004.05.01833.
Xu
, B.
Chen
, X.
2010
, “Determining Engineering Stress-Strain Curve Directly From the Load-Depth Curve of Spherical Indentation Test
,” J. Mater. Res.
, 25
(12
), pp. 2297
–2307
.10.1557/jmr.2010.031034.
Kang
, B. S. J.
Yao
, Z.
Barbero
, E. J.
2006
, “Post-Yielding Stress-Strain Determination Using Spherical Indentation
,” Mech. Adv. Mater. Struct.
, 13
(2
), pp. 129
–138
.10.1080/1537649050044860735.
Haušild
, P.
Materna
, A.
Nohava
, J.
2012
, “On the Identification of Stress–Strain Relation by Instrumented Indentation With Spherical Indenter
,” Mater. Des.
, 37
, pp. 373
–378
.10.1016/j.matdes.2012.01.02536.
Kang
, S.-K.
Kim
, Y.-C.
Kim
, K.-H.
Kim
, J.-Y.
Kwon
, D.
2013
, “Extended Expanding Cavity Model for Measurement of Flow Properties Using Instrumented Spherical Indentation
,” Int. J. Plasticity
, 49
, pp. 1
–15
.10.1016/j.ijplas.2013.02.01437.
Chen
, X.
Ogasawara
, N.
Zhao
, M.
Chiba
, N.
2007
, “On the Uniqueness of Measuring Elastoplastic Properties From Indentation: The Indistinguishable Mystical Materials
,” J. Mech. Phys. Solids
, 55
(8
), pp. 1618
–1660
.10.1016/j.jmps.2007.01.01038.
Cao
, Y. P.
Lu
, J.
2004
, “Depth-Sensing Instrumented Indentation With Dual Sharp Indenters: Stability Analysis and Corresponding Regularization Schemes
,” Acta Mater.
, 52
(5
), pp. 1143
–1153
.10.1016/j.actamat.2003.11.00139.
Chollacoop
, N.
Dao
, M.
Suresh
, S.
2003
, “Depth-Sensing Instrumented Indentation With Dual Sharp Indenters
,” Acta Mater.
, 51
(13
), pp. 3713
–3729
.10.1016/S1359-6454(03)00186-140.
Hyun
, H. C.
Kim
, M.
Lee
, J. H.
Lee
, H.
2011
, “A Dual Conical Indentation Technique Based on FEA Solutions for Property Evaluation
,” Mech. Mater.
, 43
(6
), pp. 313
–331
.10.1016/j.mechmat.2011.03.00341.
Le
, M.-Q.
2008
, “A Computational Study on the Instrumented Sharp Indentations With Dual Indenters
,” Int. J. Solids Struct.
, 45
(10
), pp. 2818
–2835
.10.1016/j.ijsolstr.2007.12.02242.
Swaddiwudhipong
, S.
Tho
, K. K.
Liu
, Z. S.
Zeng
, K.
2005
, “Material Characterization Based on Dual Indenters
,” Int. J. Solids Struct.
, 42
(1
), pp. 69
–83
.10.1016/j.ijsolstr.2004.07.02743.
3DS,
2009
, abaqus, Version 6.9-2
, Dassault Systèmes, Waltham, MA.44.
Bowden
, F. P.
Tabor
, D.
2001
, “Appendix: Some Typical Values of Friction
,” The Friction and Lubrication of Solids
, Oxford University Press
, New York
.45.
Datta
, B. N.
2010
, Numerical Linear Algebra and Applications
, Society for Industrial and Applied Mathematics
, Philadelphia, PA
, Chap. 4.46.
Wang
, L.
Ganor
, M.
Rokhlin
, S. I.
2005
, “Inverse Scaling Functions in Nanoindentation With Sharp Indenters: Determination of Material Properties
,” J. Mater. Res.
, 20
(4
), pp. 987–1001
.10.1557/JMR.2005.0147.
Xu
, Z.-H.
Li
, X.
2006
, “Sample Size Effect on Nanoindentation of Micro-/Nanostructures
,” Acta Mater.
, 54
(6
), pp. 1699
–1703
.10.1016/j.actamat.2005.11.04348.
Moussa
, C.
Hernot
, X.
Bartier
, O.
Delattre
, G.
Mauvoisin
, G.
2014
, “Evaluation of the Tensile Properties of a Material Through Spherical Indentation: Definition of an Average Representative Strain and a Confidence Domain
,” J. Mater. Sci.
, 49
(2
), pp. 592
–603
.10.1007/s10853-013-7739-149.
Phadikar
, J. K.
Bogetti
, T. A.
Karlsson
, A. M.
On the Construction of Confidence Interval for Indentation Testing
” (in press).50.
Higham
, N. J.
1996
, Accuracy and Stability of Numerical Algorithms
, Society for Industrial and Applied Mathematics
, Philadelphia, PA
, Chap. 7.51.
Rheinboldt
, W. C.
1976
, “On Measures of Ill-Conditioning for Nonlinear Equations
,” Math. Comput.
, 30
(133
), pp. 104
–111
.10.1090/S0025-5718-1976-0400702-1Copyright © 2014 by ASME
You do not currently have access to this content.
