Abstract

Residual stress can strongly affect the mechanical behaviors of engineering components. In this work, the authors revisit the role of equi-biaxial residual stress in the spherical indentation of elastoplastic solids by the finite element method. When specified residual stress remains in the body, the material hardness and the corresponding indentation depth at the inception of fully plastic deformation are examined for the first time. It is found that the hardness is remarkably dependent on the value of residual stress, especially for materials with a relatively small ratio of modulus to yield strength. Based on the dimensional analysis as well as numerical calculations, explicit expressions of the hardness and the critical indentation depth are generalized with respect to residual stress, indentation modulus, and yield strength. These results can be employed in the analysis and determination of residual stress by spherical indentation tests.

References

References
1.
Kokubo
,
S.
,
1932
, “
On the Change in Hardness of a Plate Caused by Bending
,”
Sci. Rep. Tohoku Imp. Univ.
,
21
, pp.
256
267
.
2.
Sines
,
G.
, and
Carlson
,
R.
,
1952
, “
Hardness Measurements for the Determination of Residual Stresses
,”
ASTM Bull.
,
180
, pp.
35
57
.
3.
Oliver
,
W. C.
, and
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.1992.1564
4.
Oliver
,
W. C.
, and
Pharr
,
G. M.
,
2004
, “
Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refinements to Methodology
,”
J. Mater. Res.
,
19
(
1
), pp.
3
20
. 10.1557/jmr.2004.19.1.3
5.
Tsui
,
T. Y.
,
Oliver
,
W. C.
, and
Pharr
,
G. M.
,
1996
, “
Influences of Stress on the Measurement of Mechanical Properties Using Nanoindentation: Part I. Experimental Studies in an Aluminum Alloy
,”
J. Mater. Res.
,
11
(
3
), pp.
752
759
. 10.1557/JMR.1996.0091
6.
Bolshakov
,
A.
,
Oliver
,
W. C.
, and
Pharr
,
G. M.
,
1996
, “
Influences of Stress on the Measurement of Mechanical Properties Using Nanoindentation: Part II. Finite Element Simulations
,”
J. Mater. Res.
,
11
(
3
), pp.
760
768
. 10.1557/JMR.1996.0092
7.
Chen
,
X.
,
Yan
,
J.
, and
Karlsson
,
A. M.
,
2006
, “
On the Determination of Residual Stress and Mechanical Properties by Indentation
,”
Mater. Sci. Eng. A
,
416
(
1–2
), pp.
139
149
. 10.1016/j.msea.2005.10.034
8.
Suresh
,
S.
, and
Giannakopoulos
,
A. E.
,
1998
, “
A New Method for Estimating Residual Stresses by Instrumented Sharp Indentation
,”
Acta Mater.
,
46
(
16
), pp.
5755
5767
. 10.1016/S1359-6454(98)00226-2
9.
Swadener
,
J. G.
,
Taljat
,
B.
, and
Pharr
,
G. M.
,
2001
, “
Measurement of Residual Stress by Load and Depth Sensing Indentation With Spherical Indenters
,”
J. Mater. Res.
,
16
(
7
), pp.
2091
2102
. 10.1557/JMR.2001.0286
10.
Lu
,
Z.
,
Feng
,
Y.
,
Peng
,
G.
,
Yang
,
R.
,
Huan
,
Y.
, and
Zhang
,
T.
,
2014
, “
Estimation of Surface Equi-Biaxial Residual Stress by Using Instrumented Sharp Indentation
,”
Mater. Sci. Eng. A
,
614
, pp.
264
272
. 10.1016/j.msea.2014.07.041
11.
Lee
,
Y. H.
,
Takashima
,
K.
,
Higo
,
Y.
, and
Kwon
,
D.
,
2004
, “
Prediction of Stress Directionality From Pile-Up Morphology Around Remnant Indentation
,”
Scr. Mater.
,
51
(
9
), pp.
887
891
. 10.1016/j.scriptamat.2004.06.034
12.
Shen
,
L.
,
He
,
Y.
,
Liu
,
D.
,
Gong
,
Q.
,
Zhang
,
B.
, and
Lei
,
J.
,
2015
, “
A Novel Method for Determining Surface Residual Stress Components and Their Directions in Spherical Indentation
,”
J. Mater. Res.
,
30
(
8
), pp.
1078
1089
. 10.1557/jmr.2015.87
13.
Lee
,
Y. H.
, and
Kwon
,
D.
,
2003
, “
Measurement of Residual-Stress Effect by Nanoindentation on Elastically Strained (100) W
,”
Scr. Mater.
,
49
(
5
), pp.
459
469
. 10.1016/S1359-6462(03)00290-2
14.
Ahn
,
S. M.
,
Park
,
S. Y.
,
Kim
,
Y. C.
,
Lee
,
K. S.
, and
Kim
,
Y.
,
2015
, “
Surface Residual Stress in Soda-Lime Glass Evaluated Using Instrumented Spherical Indentation Testing
,”
J. Mater. Sci.
,
50
(
23
), pp.
7752
7759
. 10.1007/s10853-015-9345-x
15.
Peng
,
G.
,
Lu
,
Z.
,
Ma
,
Y.
,
Feng
,
Y.
,
Huan
,
Y.
, and
Zhang
,
T.
,
2018
, “
Spherical Indentation Method for Estimating Equibiaxial Residual Stress and Elastic-Plastic Properties of Metals Simultaneously
,”
J. Mater. Res.
,
33
(
8
), pp.
884
897
. 10.1557/jmr.2018.57
16.
Taljat
,
B.
, and
Pharr
,
G. M.
,
1999
, “
Measurement of Residual Stresses by Load and Depth Sensing Spherical Indentation
,”
Mater. Res. Soc. Symp. Proc.
,
594
, pp.
519
524
. 10.1557/PROC-594-519
17.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
18.
Kogut
,
L.
, and
Komvopoulos
,
K.
,
2004
, “
Analysis of the Spherical Indentation Cycle for Elastic-Perfectly Plastic Solids
,”
J. Mater. Res.
,
19
(
12
), pp.
3641
3653
. 10.1557/JMR.2004.0468
19.
Song
,
Z.
, and
Komvopoulos
,
K.
,
2013
, “
Elastic-Plastic Spherical Indentation: Deformation Regimes, Evolution of Plasticity, and Hardening Effect
,”
Mech. Mater.
,
61
, pp.
91
100
. 10.1016/j.mechmat.2013.01.003
20.
Mesarovic
,
S. D.
, and
Fleck
,
N. A.
,
1999
, “
Spherical Indentation of Elastic-Plastic Solids
,”
Proc. R. Soc. A
,
455
(
1987
), pp.
2707
2728
. 10.1098/rspa.1999.0423
21.
Tabor
,
D.
,
1951
,
The Hardness of Metals
,
Clarendon Press
,
Oxford, UK
.
22.
Nix
,
W. D.
, and
Gao
,
H.
,
1998
, “
Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
46
(
3
), pp.
411
425
. 10.1016/S0022-5096(97)00086-0
23.
Huang
,
Y.
,
Zhang
,
F.
,
Hwang
,
K. C.
,
Nix
,
W. D.
,
Pharr
,
G. M.
, and
Feng
,
G.
,
2006
, “
A Model of Size Effects in Nano-Indentation
,”
J. Mech. Phys. Solids
,
54
(
8
), pp.
1668
1686
. 10.1016/j.jmps.2006.02.002
24.
Gerberich
,
W. W.
,
Tymiak
,
N. I.
,
Grunlan
,
J. C.
,
Horstemeyer
,
M. F.
, and
Baskes
,
M. I.
,
2002
, “
Interpretations of Indentation Size Effects
,”
ASME J. Appl. Mech.
,
69
(
4
), pp.
433
442
. 10.1115/1.1469004
25.
Long
,
J.
,
Ding
,
Y.
,
Yuan
,
W.
,
Chen
,
W.
, and
Wang
,
G.
,
2017
, “
General Relations of Indentations on Solids With Surface Tension
,”
ASME J. Appl. Mech.
,
84
(
5
), p.
051007
. 10.1115/1.4036214
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