The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the “experimental” data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations (“noise”) superposed on the “experimental” data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress–strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress–strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress–strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement.

References

1.
Cheng
,
Y. T.
, and
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
.
2.
Alkorta
,
J.
,
Martinez-Esnaola
,
J. M.
, and
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
.
3.
Chen
,
X.
,
Ogasawara
,
N.
,
Zhao
,
M.
, and
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
.
4.
Dao
,
M.
,
Chollacoop
,
N. V.
,
Van Vliet
,
K. J.
,
Venkatesh
,
T. A.
, and
Suresh
,
S.
,
2001
, “
Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation
,”
Acta Mater.
,
49
(
19
), pp.
3899
3918
.
5.
Ogasawara
,
N.
,
Chiba
,
N.
, and
Chen
,
X.
,
2005
, “
Representative Strain of Indentation Analysis
,”
J. Mater. Res.
,
20
(
8
), pp.
2225
2234
.
6.
Cheng
,
Y. T.
, and
Cheng
,
C. M.
,
1998
, “
Scaling Approach to Conical Indentation in Elastic-Plastic Solids With Work Hardening
,”
J. Appl. Phys.
,
84
(
3
), pp.
1284
1291
.
7.
Huber
,
N.
, and
Tsakmakis
,
C.
,
1999
, “
Determination of Constitutive Properties From Spherical Indentation Data Using Neural Networks—Part I: The Case of Pure Kinematic Hardening in Plasticity Laws
,”
J. Mech. Phys. Solids
,
47
, pp.
1569
1588
.
8.
Huber
,
N.
, and
Tsakmakis
,
C.
,
1999
, “
Determination of Constitutive Properties From Spherical Indentation Data Using Neural Networks—Part II: Plasticity With Nonlinear Isotropic and Kinematic Hardening
,”
J. Mech. Phys. Solids
,
47
, pp.
1589
1607
.
9.
Huber
,
N.
, and
Tyulyukovskiy
,
E.
,
2004
, “
A New Loading History for Identification of Viscoplastic Properties by Spherical Indentation
,”
J. Mater. Res.
,
19
(
1
), pp.
101
113
.
10.
Tyulyukovskiy
,
E.
, and
Huber
,
N.
,
2006
, “
Identification of Viscoplastic Material Parameters From Spherical Indentation Data—Part I: Neural Networks
,”
J. Mater. Res.
,
21
(
3
), pp.
664
676
.
11.
Klötzer
,
D.
,
Ullner
,
C.
,
Tyulyukovskiy
,
E.
, and
Huber
,
N.
,
2006
, “
Identification of Viscoplastic Material Parameters From Spherical Indentation Data—Part II: Experimental Validation of the Method
,”
J. Mater. Res.
,
21
(
3
), pp.
677
684
.
12.
Wang
,
M.
,
Wu
,
J.
,
Zhan
,
X.
,
Guo
,
R.
,
Hui
,
Y.
, and
Fan
,
H.
,
2016
, “
On the Determination of the Anisotropic Plasticity of Metal Materials by Using Instrumented Indentation
,”
Mater. Des.
,
111
, pp.
98
107
.
13.
Wang
,
M.
,
Wu
,
J.
,
Hui
,
Y.
,
Zhang
,
Z.
,
Zhan
,
X.
, and
Guo
,
R.
,
2017
, “
Identification of Elastic-Plastic Properties of Metal Materials by Using the Residual Imprint of Spherical Indentation
,”
Mater. Sci. Eng.: A
,
679
, pp.
143
154
.
14.
Mostafavi
,
M.
,
Collins
,
D. M.
,
Cai
,
B.
,
Bradley
,
R.
,
Atwood
,
R. C.
,
Reinhard
,
C.
,
Jiang
,
X.
,
Galano
,
M.
,
Lee
,
P. D.
, and
Marrow
,
T. J.
,
2015
, “
Yield Behavior beneath Hardness Indentations in Ductile Metals, Measured by Three-Dimensional Computed X-Ray Tomography and Digital Volume Correlation
,”
Acta Mater.
,
82
, pp.
468
482
.
15.
Mostafavi
,
M.
,
Bradley
,
R.
,
Armstrong
,
D. E. J.
, and
Marrow
,
T. J.
,
2016
, “
Quantifying Yield Behaviour in Metals by X-Ray Nanotomography
,”
Sci. Reports
,
6
, p.
34346
.
16.
Babuska
,
I.
,
Sawlan
,
Z.
,
Scavino
,
M.
,
Szabó
,
B.
, and
Tempone
,
R.
,
2016
, “
Bayesian Inference and Model Comparison for Metallic Fatigue Data
,”
Comput. Methods Appl. Mech. Eng.
,
304
, pp.
171
196
.
17.
Rovinelli
,
A.
,
Sangid
,
M. D.
,
Proudhon
,
H.
,
Guilhem
,
Y.
,
Lebensohn
,
R. A.
, and
Ludwig
,
W.
,
2018
, “
Predicting the 3D Fatigue Crack Growth Rate of Small Cracks Using Multimodal Data Via Bayesian Networks: In-Situ Experiments and Crystal Plasticity Simulations
,”
J. Mech. Phys. Solids
,
115
, pp.
208
229
.
18.
Madireddy
,
S.
,
Sista
,
B.
, and
Vemaganti
,
K.
,
2015
, “
A Bayesian Approach to Selecting Hyperelastic Constitutive Models of Soft Tissue
,”
Comput. Methods Appl. Mech. Eng.
,
291
, pp.
102
122
.
19.
Asaadi
,
E.
, and
Heyns
,
P. S.
,
2017
, “
A Computational Framework for Bayesian Inference in Plasticity Models Characterisation
,”
Comput. Methods Appl. Mech. Eng.
,
321
, pp.
455
481
.
20.
Rappel
,
H.
,
Beex
,
L. A.
, and
Bordas
,
S. P.
,
2018
, “
Bayesian Inference to Identify Parameters in Viscoelasticity
,”
Mech. Time-Depend. Mater.
,
22
(
2
), pp.
221
258
.
21.
Worthen
,
J.
,
Stadler
,
G.
,
Petra
,
N.
,
Gurnis
,
M.
, and
Ghattas
,
O.
,
2014
, “
Towards Adjoint-Based Inversion for Rheological Parameters in Nonlinear Viscous Mantle Flow
,”
Phys. Earth Planet. Inter.
,
234
, pp.
23
34
.
22.
Prudencio
,
E. E.
,
Bauman
,
P. T.
,
Williams
,
S. V.
,
Faghihi
,
D.
,
Ravi-Chandar
,
K.
, and
Oden
,
J. T.
,
2013
, “
A Dynamic Data Driven Application System for Real-Time Monitoring of Stochastic Damage
,”
Procedia Comp. Sci.
,
18
, pp.
2056
2065
.
23.
Prudencio
,
E. E.
,
Bauman
,
P. T.
,
Faghihi
,
D.
,
Ravi-Chandar
,
K.
, and
Oden
,
J. T.
,
2015
, “
A Computational Framework for Dynamic Data-Driven Material Damage Control, Based on Bayesian Inference and Model Selection
,”
Int. J. Numer. Methods Eng.
,
102
(
3–4
), pp.
379
403
.
24.
Vigliotti
,
A.
,
Csányi
,
G.
, and
Deshpande
,
V. S.
,
2018
, “
Bayesian Inference of the Spatial Distributions of Material Properties
,”
J. Mech. Phys. Solids
,
118
, pp.
74
97
.
25.
Fernandez-Zelaia
,
P.
,
Joseph
,
V. R.
,
Kalidindi
,
S. R.
, and
Melkote
,
S. N.
,
2018
, “
Estimating Mechanical Properties From Spherical Indentation Using Bayesian Approaches
,”
Mater. Des.
,
147
, pp.
92
105
.
26.
Needleman
,
A.
,
Tvergaard
,
V.
, and
Van der Giessen
,
E.
,
2015
, “
Indentation of Elastically Soft and Plastically Compressible Solids
,”
Acta Mech. Sin.
,
31
(
4
), pp.
473
480
.
27.
Hoff
,
P. D.
,
2009
,
A First Course in Bayesian Statistical Methods
,
Springer Science & Business Media
,
New York
, pp.
67
87
.
28.
Matlab,
2016
,
MATLAB Release 2016a, Function Normrnd
,
The MathWorks
, Natick, MA.
You do not currently have access to this content.