Materials with customized spatial gradients in mechanical properties are increasingly used in high performance applications requiring enhanced resistance to contact loads, wear, and fatigue. In many engineering materials, multiple property and microstructural gradients may occur simultaneously with depth. In this manuscript, two case carburized steels are analyzed for their gradient in hardness with depth, emphasizing the resulting variation in surface hardness under increasing indentation loads. A parametric study using finite element analysis is then conducted in order to characterize the influence of individual property gradients on the surface indentation response of graded materials. It is shown that the measured surface hardness value decreases rapidly under increasing surface indentation loads in materials with sharp negative hardness gradients. It is also shown that this trend is independent of the magnitude of the strain hardening exponent of the material, as well as the gradient in strain hardening exponent. Gradients in elastic properties were also shown to have negligible influence on surface hardness trends for a fixed gradient in hardness. Finally, it is revealed that the depth of subsurface plastic deformation increases with sharper gradients in hardness, while being insensitive to changes in strain hardening exponent. For elastically graded materials, a decreasing gradient in elastic modulus limits the depth of plastic deformation.

References

References
1.
Miyamoto
,
Y.
,
Kaysser
,
W. A.
, and
Rabin
,
B. H.
,
1999
,
Functionally Graded Materials: Design, Processing, and Applications
,
Springer
,
New York
.
2.
Suresh
,
S.
, and
Mortensen
,
A.
,
1998
,
Fundamentals of Functionally Graded Materials
,
IOM Communications
,
London
.
3.
Choi
,
I.
,
Dao
,
M.
, and
Suresh
,
S.
,
2008
, “
Mechanics of Indentation of Plastically Graded Materials—I: Analysis
,”
J. Mech. Phys. Solids
,
56
(
1
), pp.
157
171
.10.1016/j.jmps.2007.07.007
4.
Choi
,
I.
,
Detor
,
A.
,
Schwaiger
,
R.
,
Dao
,
M.
,
Schuh
,
C.
, and
Suresh
,
S.
,
2008
, “
Mechanics of Indentation of Plastically Graded Materials—II: Experiments on Nanocrystalline Alloys With Grain Size Gradients
,”
J. Mech. Phys. Solids
,
56
(
1
), pp.
172
183
.10.1016/j.jmps.2007.07.006
5.
Pender
,
D. C.
,
Padture
,
N. P.
,
Giannakopoulos
,
A. E.
, and
Suresh
,
S.
,
2001
, “
Gradients in Elastic Modulus for Improved Contact-Damage Resistance. Part I: The Silicon Nitride-Oxynitride Glass System
,”
Acta Mater.
,
49
(
16
), pp.
3255
3262
.10.1016/S1359-6454(01)00200-2
6.
Pender
,
D. C.
,
Thompson
,
S. C.
,
Padture
,
N. P.
,
Giannakopoulos
,
A. E.
, and
Suresh
,
S.
,
2001
, “
Gradients in Elastic Modulus for Improved Contact-Damage Resistance. Part II: The Silicon Nitride-Silicon Carbide System
,”
Acta Mater.
,
49
(
16
), pp.
3263
3268
.10.1016/S1359-6454(01)00201-4
7.
Stephens
,
L. S.
,
Liu
,
Y.
, and
Meletis
,
E. I.
,
2000
, “
Finite Element Analysis of the Initial Yielding Behavior of a Hard Coating/Substrate System With Functionally Graded Interface Under Indentation and Friction
,”
ASME J. Tribol.
,
122
(
2
), pp.
381
387
.10.1115/1.555373
8.
Suresh
,
S.
,
2001
, “
Graded Materials for Resistance to Contact Deformation and Damage
,”
Science
,
292
(
5526
), pp.
2447
2451
.10.1126/science.1059716
9.
Branch
,
N. A.
,
Arakere
,
N. K.
,
Subhash
,
G.
, and
Klecka
,
M. A.
,
2010
, “
Determination of Constitutive Response of Plastically Graded Materials
,”
Int. J. Plast.
,
27
(
5
), pp.
728
738
.10.1016/j.ijplas.2010.09.001
10.
Cao
,
Y. P.
, and
Lu
,
J.
,
2004
, “
A New Scheme for Computational Modeling of Conical Indentation in Plastically Graded Materials
,”
J. Mater. Res.
,
19
(
6
), pp.
1703
1716
.10.1557/JMR.2004.0239
11.
Fischer-Cripps
,
A. C.
,
2003
, “
Analysis of Instrumented Indentation Test Data for Functionally Graded Materials
,”
Surf. Coat. Technol.
,
168
(
2–3
), pp.
136
141
.10.1016/S0257-8972(03)00015-X
12.
Gu
,
Y.
,
Nakamura
,
T.
,
Prchlik
,
L.
,
Sampath
,
S.
, and
Wallace
,
J.
,
2003
, “
Micro-Indentation and Inverse Analysis to Characterize Elastic-Plastic Graded Materials
,”
Mater. Sci. Eng. A
,
345
(
1–2
), pp.
223
233
.10.1016/S0921-5093(02)00462-8
13.
Nakamura
,
T.
,
Wang
,
T.
, and
Sampath
,
S.
,
2000
, “
Determination of Properties of Graded Materials by Inverse Analysis and Instrumented Indentation
,”
Acta Mater.
,
48
(
17
), pp.
4293
4306
.10.1016/S1359-6454(00)00217-2
14.
Yan
,
J.
,
Karlsson
,
A.
, and
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.2006.10.017
15.
Giannakopoulos
,
A. E.
,
2002
, “
Indentation of Plastically Graded Substrates by Sharp Indentors
,”
Int. J. Solids Struct.
,
39
(
9
), pp.
2495
2515
.10.1016/S0020-7683(02)00110-5
16.
Nayebi
,
A.
,
Bartier
,
O.
,
Mauvoisin
,
G.
, and
Abdi
,
R. E.
,
2001
, “
New Method to Determine the Mechanical Properties of Heat Treated Steels
,”
Int. J. Mech. Sci.
,
43
(
11
), pp.
2679
2697
.10.1016/S0020-7403(01)00048-0
17.
Boyer
,
H.
,
1987
,
Case Hardening of Steel
,
ASM International
,
Metals Park, OH
.
18.
Parrish
,
G.
,
1999
,
Carburizing: Microstructures and Properties
,
ASM International
,
Materials Park, OH
.
19.
Klecka
,
M. A.
,
Subhash
,
G.
, and
Arakere
,
N. K.
,
2011
, “
Determination of Subsurface Hardness Gradients in Plastically Graded Materials Via Surface Indentation
,”
ASME J. Tribol.
,
133
(
3
), p.
031403
.10.1115/1.4003859
20.
Klecka
,
M. A.
,
Subhash
,
G.
, and
Arakere
,
N. K.
,
2012
, “
Microstructure-Property Relationships in M50-NiL and P675 Case Hardened Bearing Steels
,”
Tribol. Trans.
(in press).
21.
Kadkhodapour
,
J.
,
Butz
,
A.
,
Ziaei-Rad
,
S.
, and
Schmauder
,
S.
,
2011
, “
A Micro Mechanical Study on Failure Initiation of Dual Phase Steels Under Tension Using Single Crystal Plasticity Model
,”
Int. J. Plast.
,
27
(
7
), pp.
1103
1125
.10.1016/j.ijplas.2010.12.001
22.
Shen
,
Y. L.
,
Williams
,
J. J.
,
Piotrowski
,
G.
,
Chawla
,
N.
, and
Guo
,
Y. L.
,
2001
, “
Correlation Between Tensile and Indentation Behavior of Particle-Reinforced Metal Matrix Composites: An Experimental and Numerical Study
,”
Acta Mater.
,
49
(
16
), pp.
3219
3229
.10.1016/S1359-6454(01)00226-9
23.
Vena
,
P.
,
Gastaldi
,
D.
, and
Contro
,
R.
,
2008
, “
Determination of the Effective Elastic Plastic Response of Metal Ceramic Composites
,”
Int. J. Plast.
,
24
(
3
), pp.
483
508
.10.1016/j.ijplas.2007.07.001
24.
Young
,
M.
,
Almer
,
J.
,
Daymond
,
M.
,
Haeffner
,
D.
, and
Dunand
,
D.
,
2007
, “
Load Partitioning Between Ferrite and Cementite During Elasto-Plastic Deformation of an Ultrahigh-Carbon Steel
,”
Acta Mater.
,
55
(
6
), pp.
1999
2011
.10.1016/j.actamat.2006.11.004
25.
Hetzner
,
D. W.
, and
Geertruyden
,
W. V.
,
2008
, “
Crystallography and Metallography of Carbides in High Alloy Steels
,”
Mater. Charact.
,
59
(
7
), pp.
825
841
.10.1016/j.matchar.2007.07.005
26.
Giannakopoulos
,
A.
,
Larsson
,
P.
, and
Vestergaard
,
R.
,
1994
, “
Analysis of Vickers Indentation
,”
Int. J. Solids Struct.
,
31
(
19
), pp.
2679
2708
.10.1016/0020-7683(94)90225-9
27.
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.
156
1583
.10.1557/JMR.1992.1564
28.
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
29.
Larsson
,
P. L.
,
2006
, “
Modelling of Sharp Indentation Experiments: Some Fundamental Issues
,”
Philos. Mag.
,
86
(
33
), pp.
5155
5177
.10.1080/14786430600589089
30.
Qin
,
J.
,
Huang
,
Y.
,
Hwang
,
K.
,
Song
,
J.
, and
Pharr
,
G.
,
2007
, “
The Effect of Indenter Angle on the Microindentation Hardness
,”
Acta Mater.
,
55
(
18
), pp.
6127
6132
.10.1016/j.actamat.2007.07.016
31.
Gao
,
X.-L.
,
Jing
,
X.
, and
Subhash
,
G.
,
2006
, “
Two New Expanding Cavity Models for Indentation Deformations of Elastic Strain-Hardening Materials
,”
Int. J. Solids Struct.
,
43
(
7–8
), pp.
2193
2208
.10.1016/j.ijsolstr.2005.03.062
32.
Park
,
Y.
, and
Pharr
,
G.
,
2004
, “
Nanoindentation With Spherical Indenters: Finite Element Studies of Deformation in the Elastic Plastic Transition Regime
,”
Thin Solid Films
,
447–448
, pp.
246
250
.10.1016/S0040-6090(03)01102-7
33.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
,
2001
, “
A Reformulation of Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
49
(
10
), pp.
2245
2271
.10.1016/S0022-5096(01)00049-7
34.
Huang
,
Y.
,
Qu
,
S.
,
Hwang
,
K. C.
,
Li
,
M.
, and
Gao
,
H.
,
2004
, “
A Conventional Theory of Mechanism-Based Strain Gradient Plasticity
,”
Int. J. Plast.
,
20
(
4–5
), pp.
753
782
.10.1016/j.ijplas.2003.08.002
35.
Nix
,
W. D.
, and
Gao
,
H. J.
,
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
You do not currently have access to this content.