In this work, the influence of different crack arrangements in the stress distribution of hard chromium (HC) coatings was determined. Three parameters for position and length of the cracks for two different types of coatings were probabilistically modeled based on measured scanning electron microscopy (SEM) images. Probability density functions (PDF) for those parameters were obtained to characterize each kind of coating. A two-dimensional finite element (FE) model of the coating in contact with a rigid disk was developed, modeling cracks with elliptical shapes. A Monte Carlo method was used to simulate different crack distributions for each kind of coating, and values of stress and strains in the domain were obtained. Both the J-integral and the stress intensity factors (SIFs) were taken as comparative parameters of the results. Coatings which statistically present larger quantities of shorter cracks have lower values of J-integral and SIFs, and, therefore, distribute stresses better than those with low density of longer cracks.

References

References
1.
Tyler
,
J. M.
,
1995
, “
Automotive Applications for Chromium
,”
Met. Finish.
,
93
(
10
), pp.
11
14
.
2.
Lausmann
,
G. A.
,
1996
, “
Electrolytically Deposited Hardchrome
,”
Surf. Coat. Technol.
,
86–87
(Pt. 2), pp.
814
820
.
3.
Simão
,
J.
, and
Aspinwall
,
D. K.
,
1999
, “
Hard Chromium Plating of EDT Mill Work Rolls
,”
J. Mater. Process. Technol.
,
92–93
, pp.
281
287
.
4.
De Mello
,
J. D. B.
,
Gonçalves
,
J. L.
Jr., and
Costa
,
H. L.
,
2013
, “
Influence of Surface Texturing and Hard Chromium Coating on the Wear of Steels Used in Cold Rolling Mill Rolls
,”
Wear
,
302
(
1–2
), pp.
1295
1309
.
5.
Jones
,
A. R.
,
1989
, “
Microcrack in Hard Chromium Electrodeposits
,”
Plat. Surf. Finish.
,
76
(
4
), pp.
62
66
.
6.
Pina
,
J.
,
Dias
,
A.
,
Francois
,
M.
, and
Lebrun
,
J. L.
,
1997
, “
Residual Stresses and Crystallographic Texture in Hard-Chromium Electroplated Coatings
,”
Surf. Coat. Technol.
,
96
, pp.
148
162
.
7.
Jones
,
A. R.
,
1992
, “
Hard Chromium: Microcrack Formation and Sliding Wear
,”
Trans. Inst. Met. Finish.
,
70
(
1
), pp.
8
13
.
8.
Pereira
,
M.
,
Jacobus
,
H.
, and
Voorwald
,
C.
,
2008
, “
The Significance and Determination by Image Analysis of Microcrack Density in Hard Chromium Plating
,”
Plat. Surf. Finish.
,
95
(4), pp.
36
42
.
9.
Gines
,
M.
,
Tuckart
,
W.
, and
Abraham
,
S.
,
2010
, “
Dry Sliding Wear Behavior of Hard Chromium and Nickel-Based Coatings in Ball on Ring Test
,”
First International Brazilian Conference on Tribology
(
TriboBR
), Rio de Janeiro, Brazil, Nov. 24–26, pp.
287
298
.
10.
Martyak
,
N. M.
, and
McCaskie
,
J. E.
,
1995
, “
Surface Structures of Electrodeposited Chromium
,”
J. Mater. Sci. Lett.
,
14
(
19
), pp.
1329
1331
.
11.
Wakuda
,
M.
,
Yamauchi
,
Y.
,
Kanzaki
,
S.
, and
Yasuda
,
Y.
,
2003
, “
Effect of Surface Texturing on Friction Reduction Between Ceramic and Steel Materials Under Lubricated Sliding Contact
,”
Wear
,
254
(
3–4
), pp.
356
363
.
12.
Bennani
,
H. H.
, and
Takadoum
,
J.
,
1999
, “
Finite Element Model of Elastic Stresses in Thin Coatings Submitted to Applied Forces
,”
Surf. Coat. Technol.
,
111
(
1
), pp.
80
85
.
13.
Holmberg
,
K.
,
Laukkanen
,
A.
,
Ronkainen
,
H.
,
Wallin
,
K.
,
Varjus
,
S.
, and
Koskinen
,
J.
,
2006
, “
Tribological Contact Analysis of a Rigid Ball Sliding on a Hard Coated Surface—Part I: Modelling Stresses and Strains
,”
Surf. Coat. Technol.
,
200
(
12–13
), pp.
3824
3844
.
14.
Holmberg
,
K.
,
Ronkainen
,
H.
,
Laukkanen
,
A.
, and
Wallin
,
K.
,
2007
, “
Friction and Wear of Coated Surfaces—Scales, Modelling and Simulation of Tribomechanisms
,”
Surf. Coat. Technol.
,
202
(
4–7
), pp.
1034
1049
.
15.
Holmberg
,
K.
,
Ronkainen
,
H.
,
Laukkanen
,
A.
,
Wallin
,
K.
,
Erdemir
,
A.
, and
Eryilmaz
,
O.
,
2008
, “
Tribological Analysis of TiN and DLC Coated Contacts by 3D FEM Modelling and Stress Simulation
,”
Wear
,
264
(
9–10
), pp.
877
884
.
16.
Laukkanen
,
A.
,
Holmberg
,
K.
,
Koskinen
,
J.
,
Ronkainen
,
H.
,
Wallin
,
K.
, and
Varjus
,
S.
,
2006
, “
Tribological Contact Analysis of a Rigid Ball Sliding on a Hard Coated Surface—Part III: Fracture Toughness Calculation and Influence of Residual Stresses
,”
Surf. Coat. Technol.
,
200
(
12–13
), pp.
3824
3844
.
17.
Laukkanen
,
A.
,
Holmberg
,
K.
,
Ronkainen
,
H.
, and
Wallin
,
K.
,
2011
, “
Cohesive Zone Modeling of Initiation and Propagation of Multiple Cracks in Hard Thin Surface Coatings
,”
J. ASTM Int.
,
8
(
1
), pp.
1
21
.
18.
Holmberg
,
K.
,
Laukkanen
,
A.
,
Ghabchi
,
A.
,
Rombouts
,
M.
,
Turunen
,
E.
,
Waudby
,
R.
,
Suhonen
,
T.
,
Valtonen
,
K.
, and
Sarlin
,
E.
,
2014
, “
Computational Modelling Based Wear Resistance Analysis of Thick Composite Coatings
,”
Tribol. Int.
,
72
, pp.
13
30
.
19.
Tobi
,
A. L. M.
,
Shipway
,
P. H.
, and
Leen
,
S. B.
,
2013
, “
Finite Element Modelling of Brittle Fracture of Thick Coatings Under Normal and Tangential Loading
,”
Tribol. Int.
,
58
, pp.
29
39
.
20.
Zhou
,
K.
, and
Wei
,
R.
,
2014
, “
Modeling Cracks and Inclusions Near Surfaces Under Contact Loading
,”
Int. J. Mech. Sci.
,
83
, pp.
163
171
.
21.
Wei
,
R.
,
Zhou
,
K.
,
Keer
,
L. M.
, and
Fan
,
Q.
,
2016
, “
Modeling Surface Pressure, Interfacial Stresses and Stress Intensity Factors for Layered Materials Containing Multiple Cracks and Inhomogeneous Inclusions Under Contact Loading
,”
Mech. Mater.
,
92
, pp.
8
17
.
22.
Sargent
,
G. J.
,
1920
, “
Electrolytic Chromium
,”
Trans. Am. Electrochem. Soc.
,
37
, pp.
479
497
.
23.
Schneider
,
C. A.
,
Rasband
,
W. S.
, and
Eliceiri
,
K. W.
,
2012
, “
NIH Image to ImageJ: 25 Years of Image Analysis
,”
Nat. Methods
,
9
(
7
), pp.
671
675
.
24.
MATLAB
,
2010
, “
MATLAB and Statistics Toolbox Release 2010a
,”
The MathWorks Inc.
, Natick, MA.
25.
Rubinstein
,
R. Y.
, and
Kroese
,
D. P.
,
2008
,
Simulation and the Monte Carlo Method
,
2nd ed.
,
Wiley
, New York.
26.
COMSOL
,
2013
, “
Comsol Multiphysics v 4.4
,”
Comsol Inc.
, Burlington, MA.
27.
Wriggers
,
P.
,
2006
,
Computational Contact Mechanics
,
2nd ed.
,
Springer-Verlag
,
Berlin
.
28.
ASM International Handbook Committee
, ed.,
1990
,
ASM Handbook (Properties and Selection: Irons, Steels, and High-Performance Alloys)
,
10th ed.
, Vol.
1
,
ASM International
,
Materials Park, OH
.
29.
ASM International Handbook Committee
, ed.,
1990
,
ASM Handbook (Properties and Selection: Nonferrous Alloys and Special-Purpose Materials)
,
10th ed.
, Vol.
2
,
ASM International
,
Materials Park, OH
.
30.
Gear
,
C. W.
,
1971
, “
Simultaneous Numerical Solution of Differential-Algebraic Equations
,”
IEEE Trans. Circuit Theory
,
18
(
1
), pp.
89
95
.
31.
COMSOL
,
2013
, “
Comsol Reference Manual
,” Comsol Inc., Burlington, MA.
32.
Milne
,
I.
,
Ritchie
,
R. O.
, and
Karihaloo
,
B.
,
2003
,
Comprehensive Structural Integrity: Numerical and Computational Methods
, Vol.
3
,
Elsevier
, London.
33.
Rice
,
J. R.
,
1968
, “
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
,”
ASME J. Appl. Mech.
,
35
(
2
), pp.
379
386
.
34.
Ishikawa
,
H.
,
Kitagawa
,
H.
, and
Okamura
,
H.
,
1979
, “
J Integral of a Mixed Mode Crack and Its Application
,”
Mech. Behav. Mater.
,
3
, pp.
447
455
.
35.
Bui
,
H. D.
,
1983
, “
Associated Path Independent J-Integrals for Separating Mixed Modes
,”
J. Mech. Phys. Solids
,
31
(
6
), pp.
439
448
.
36.
Scrucca
,
L.
,
2001
, “
Nonparametric Kernel Smoothing Methods. The sm Library in Xlisp-Stat
,”
J. Stat. Software
,
6
(
7
), pp.
1
49
.
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