This paper investigates the frictionally excited thermoelastic instability (TEI) of a functionally graded material (FGM) half-plane sliding against a homogeneous half-plane at the out-of-plane direction with the thermal contact resistance. A uniform pressure presses these two half-planes together. The material properties of FGMs are assumed to be varied as an exponential form. Using the perturbation method, we derive the characteristic equation for the TEI problem to solve the unknown critical heat flux and critical sliding speed. The effects of the thermal contact resistance, gradient index, friction coefficient, and heat generation factor on the stability boundaries are discussed for four different material combinations. The results may provide a possible method to improve the contact stability in the sliding system by using FGMs.

References

References
1.
Dow
,
T. A.
, and
Burton
,
R. A.
,
1972
, “
Thermoelastic Instability of Sliding Contact in the Absence of Wear
,”
Wear
,
19
(
3
), pp.
315
328
.
2.
Barber
,
J. R.
,
1969
, “
Thermoelastic Instability in the Sliding of Conforming Solids
,”
Proc. R. Soc. London, Ser. A
,
312
(
1510
), pp.
381
394
.
3.
Bryant
,
M. D.
,
Wang
,
T. P.
, and
Lin
,
J. W.
,
1995
, “
Thermal Mounding in High Speed Dry Sliders-Experiment, Theory and Comparison
,”
Wear
,
181
, pp.
668
677
.
4.
Kennedy
,
F. E.
, and
Ling
,
F. F.
,
1974
, “
A Thermal, Thermoelastic and Wear Simulation of a High Energy Sliding Contact Problem
,”
ASME J. Lubr. Technol.
,
96
(3), pp.
497
507
.
5.
Panier
,
S.
,
Dufrénoy
,
P.
, and
Weichert
,
D.
,
2004
, “
An Experimental Investigation of Hot Spots in Railway Disc Brakes
,”
Wear
,
256
, pp.
764
773
.
6.
Anderson
,
A. E.
, and
Knapp
,
R. A.
,
1990
, “
Hot Spotting in Automotive Friction Systems
,”
Wear
,
135
(
2
), pp.
319
337
.
7.
Lee
,
K.
, and
Dinwiddie
,
R. B.
,
1998
, “
Conditions of Frictional Contact in Disk Brakes and Their Effects on Brake Judder
,”
SAE
Technical Paper No. 980598.
8.
Burton
,
R. A.
,
Nerlikar
,
V.
, and
Kilaparti
,
S. R.
,
1973
, “
Thermoelastic Instability in a Seal-Like Configuration
,”
Wear
,
24
(
2
), pp.
177
188
.
9.
Lee
,
K.
, and
Barber
,
J. R.
,
1993
, “
Frictionally-Excited Thermoelastic Instability in Automotive Disk Brakes
,”
ASME J. Tribol.
,
115
(
4
), pp.
607
614
.
10.
Du
,
S.
,
Zagrodzki
,
P.
,
Barber
,
J. R.
, and
Hulbert
,
G. M.
,
1997
, “
Finite Element Analysis of Frictionally-Excited Thermoelastic Instability
,”
J. Therm. Stresses
,
20
(
2
), pp.
185
201
.
11.
Yi
,
Y. B.
,
Fash
,
J. W.
,
Du
,
S.
, and
Barber
,
J. R.
,
1999
, “
Effect of Geometry on Thermoelastic Instability in Disk Brakes and Clutches
,”
ASME J. Tribol.
,
121
(
4
), pp.
661
666
.
12.
Yi
,
Y. B.
,
Barber
,
J. R.
, and
Zagrodzki
,
P.
,
2000
, “
Eigenvalue Solution of Thermoelastic Instability Problems Using Fourier Reduction
,”
Proc. R. Soc. London, Ser. A
,
456
(
2003
), pp.
2799
2821
.
13.
Zagrodzki
,
P.
,
1990
, “
Analysis of Thermomechanical Phenomena in Multidisc Clutches and Brakes
,”
Wear
,
140
(
2
), pp.
291
308
.
14.
Johansson
,
L.
,
1993
, “
Model and Numerical Algorithm for Sliding Contact Between Two Elastic Half-Planes With Frictional Heat Generation and Wear
,”
Wear
,
160
(
1
), pp.
77
93
.
15.
Zagrodzki
,
P.
,
Lam
,
K. B.
,
Al-Bahkali
,
E.
, and
Barber
,
J. R.
,
2001
, “
Nonlinear Transient Behavior of a Sliding System With Frictionally Excited Thermoelastic Instability
,”
ASME J. Tribol.
,
123
(
4
), pp.
699
708
.
16.
Lee
,
K.
,
2000
, “
Frictionally Excited Thermoelastic Instability in Automotive Drum Brakes
,”
ASME J. Tribol.
,
122
(
4
), pp.
849
855
.
17.
Decuzzi
,
P.
,
Ciaverella
,
M.
, and
Monno
,
G.
,
2001
, “
Frictionally Excited Thermoelastic Instability in Multi-Disk Clutches and Brakes
,”
ASME J. Tribol.
,
123
(
4
), pp.
865
871
.
18.
Shlykov
,
Y. P.
, and
Ganin
,
Y. A.
,
1964
, “
Thermal Resistance of Metallic Contacts
,”
Int. J. Heat Mass Transfer
,
7
(
8
), pp.
921
929
.
19.
Clausing
,
A. M.
, and
Chao
,
B. T.
,
1965
, “
Thermal Contact Resistance in a Vacuum Environment
,”
ASME J. Heat Transfer
,
87
(
2
), pp.
243
251
.
20.
Thomas
,
T. R.
, and
Probert
,
S. D.
,
1970
, “
Thermal Contact Resistance: The Directional Effect and Other Problems
,”
Int. J. Heat Mass Transfer
,
13
(
5
), pp.
789
807
.
21.
Barber
,
J. R.
,
1978
, “
Contact Problems Involving a Cooled Punch
,”
J. Elasticity
,
8
, pp.
409
423
.
22.
Barber
,
J. R.
,
1987
, “
Stability of Thermoelastic Contact
,”
Institution of Mechanical Engineering
,
International Conference on Tribology
, London, July 1–3, Paper No. C157/87, pp.
981
986
.
23.
Zhang
,
R.
, and
Barber
,
J. R.
,
1990
, “
Effect of Material Properties on the Stability of Static Thermoelastic Contact
,”
ASME J. Appl. Mech.
,
57
(
2
), pp.
365
369
.
24.
Yeo
,
T.
, and
Barber
,
J. R.
,
1991
, “
Stability of Thermoelastic Contact of a Layer and a Half-Plane
,”
J. Therm. Stresses
,
14
(
4
), pp.
371
388
.
25.
Li
,
C.
, and
Barber
,
J. R.
,
1997
, “
Stability of Thermoelastic Contact of Two Layers of Dissimilar Materials
,”
J. Therm. Stresses
,
20
(
2
), pp.
169
184
.
26.
Schade
,
D. T.
,
Oditt
,
K.
, and
Karr
,
D. G.
,
2000
, “
Thermoelastic Stability of Two Bonded Half Planes
,”
J. Eng. Mech.
,
126
(
9
), pp.
981
985
.
27.
Schade
,
D. T.
, and
Karr
,
D. G.
,
2002
, “
Thermoelastic Stability of Layer Bonded to Half Plane
,”
J. Eng. Mech.
,
128
(
12
), pp.
1285
1294
.
28.
Ciavarella
,
M.
,
Johansson
,
L.
,
Afferrante
,
L.
,
Klarbring
,
A.
, and
Barber
,
J. R.
,
2003
, “
Interaction of Thermal Contact Resistance and Frictional Heating in Thermoelastic Instability
,”
Int. J. Solids Struct.
,
40
(
21
), pp.
5583
5597
.
29.
Afferrante
,
L.
, and
Ciavarella
,
M.
,
2004
, “
Frictionally Excited Thermoelastic Instability in the Presence of Contact Resistance
,”
J. Strain Anal. Eng. Des.
,
39
(
4
), pp.
351
357
.
30.
Afferrante
,
L.
, and
Ciavarella
,
M.
,
2004
, “
Instability of Thermoelastic Contact for Two Half-Planes Sliding Out-of-Plane With Contact Resistance and Frictional Heating
,”
J. Mech. Phys. Solids
,
52
(
7
), pp.
1527
1547
.
31.
Afferrante
,
L.
, and
Ciavarella
,
M.
,
2004
, “
The Thermoelastic Aldo Contact Model With Frictional Heating
,”
J. Mech. Phys. Solids
,
52
(
3
), pp.
617
640
.
32.
Ciavarella
,
M.
, and
Barber
,
J. R.
,
2005
, “
Stability of Thermoelastic Contact for a Rectangular Elastic Block Sliding Against a Rigid Wall
,”
Eur. J. Mech.: A/Solids
,
24
(
3
), pp.
371
376
.
33.
Guler
,
M. A.
, and
Erdogan
,
F.
,
2006
, “
Contact Mechanics of Two Deformable Elastic Solids With Graded Coatings
,”
Mech. Mater.
,
38
(
7
), pp.
633
647
.
34.
El-Borgi
,
S.
,
Abdelmoula
,
R.
, and
Keer
,
L.
,
2006
, “
A Receding Contact Plane Problem Between a Functionally Graded Layer and a Homogeneous Substrate
,”
Int. J. Solids Struct.
,
43
, pp.
658
674
.
35.
Ke
,
L. L.
, and
Wang
,
Y. S.
,
2007
, “
Two-Dimensional Sliding Frictional Contact of Functionally Graded Materials
,”
Eur. J. Mech.: A/Solids
,
26
(
1
), pp.
171
188
.
36.
Choi
,
H. J.
, and
Paulino
,
G. H.
,
2008
, “
Thermoelastic Contact Mechanics for a Flat Punch Sliding Over a Graded Coating/Substrate System With Frictional Heat Generation
,”
J. Mech. Phys. Solids
,
56
(
4
), pp.
1673
1692
.
37.
Barik
,
S. P.
,
Kanoria
,
M.
, and
Chaudhuri
,
P. K.
,
2008
, “
Steady State Thermoelastic Contact Problem in a Functionally Graded Material
,”
Int. J. Eng. Sci.
,
46
(
8
), pp.
775
789
.
38.
Shahzamanian
,
M. M.
,
Sahari
,
B. B.
,
Bayat
,
M.
,
Mustapha
,
F.
, and
Ismarrubie
,
Z. N.
,
2010
, “
Finite Element Analysis of Thermoelastic Contact Problem in Functionally Graded Axisymmetric Brake Disks
,”
Compos. Struct.
,
92
(
7
), pp.
1591
1602
.
39.
Liu
,
J.
,
Ke
,
L. L.
, and
Wang
,
Y. S.
,
2011
, “
Two-Thermoelastic Contact Problem of Functionally Graded Materials Involving Frictional Heating
,”
Int. J. Solids Struct.
,
48
(
18
), pp.
2536
2548
.
40.
Aizikovich
,
S. M.
,
Vasil’ev
,
A. S.
, and
Krenev
,
L. I.
,
2011
, “
Contact Problems for Functionally Graded Materials of Complicated Structure
,”
Mech. Compos. Mater.
,
47
(
5
), pp.
539
548
.
41.
Comez
,
I.
,
2013
, “
Contact Problem of a Functionally Graded Layer Resting on a Winkler Foundation
,”
Acta Mech.
,
224
(
11
), pp.
2833
2843
.
42.
Chidlow
,
S. J.
, and
Teodorescu
,
M.
,
2014
, “
Sliding Contact Problems Involving Inhomogeneous Materials Comprising a Coating-Transition Layer-Substrate and a Rigid Punch
,”
Int. J. Solids Struct.
,
51
(
10
), pp.
1931
1945
.
43.
Chen
,
P. J.
, and
Chen
,
S. H.
,
2013
, “
Thermo-Mechanical Contact Behavior of a Finite Graded Layer Under a Sliding Punch With Heat Generation
,”
Int. J. Solids Struct.
,
50
, pp.
1108
1119
.
44.
Chen
,
P. J.
,
Chen
,
S. H.
, and
Peng
,
J.
,
2015
, “
Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitrary Gradient Direction
,”
ASME J. Appl. Mech.
,
82
(4),
p.
041008.
45.
Kulchystsky-Zhyhailo
,
R.
, and
Bajkowski
,
A. S.
,
2015
, “
Three-Dimensional Analytical Elasticity Solution for Loaded Functionally Graded Coated Half-Space
,”
Mech. Res. Commun.
,
65
, pp.
43
50
.
46.
Krenev
,
L. I.
,
Aizikovich
,
S. M.
,
Tokovyy
,
Y. V.
, and
Wang
,
Y. C.
,
2015
, “
Axisymmetric Problem on the Indentation of a Hot Circular Punch Into an Arbitrarily Nonhomogeneous Half-Space
,”
Int. J. Solids Struct.
,
59
, pp.
18
28
.
47.
Jang
,
Y. H.
, and
Ahn
,
S. H.
,
2007
, “
Frictionally-Excited Thermoelastic Instability in Functionally Graded Material
,”
Wear
,
262
, pp.
1102
1112
.
48.
Lee
,
S.
, and
Jang
,
Y. H.
,
2009
, “
Effect of Functionally Graded Material on Frictionally Excited Thermoelastic Instability
,”
Wear
,
266
, pp.
139
146
.
49.
Lee
,
S.
, and
Jang
,
Y. H.
,
2009
, “
Frictionally Excited Thermoelastic Instability in a Thin Layer of Functionally Graded Material Sliding Between Two Half-Panes
,”
Wear
,
267
, pp.
1715
1722
.
50.
Mao
,
J. J.
,
Ke
,
L. L.
, and
Wang
,
Y. S.
,
2015
, “
Thermoelastic Instability of Functionally Graded Materials in Frictionless Contact
,”
Acta Mech.
,
226
(
7
), pp.
2295
2311
.
51.
Mao
,
J. J.
,
Ke
,
L. L.
, and
Wang
,
Y. S.
,
2014
, “
Thermoelastic Contact Instability of a Functionally Graded Layer and a Homogeneous Half-Plane
,”
Int. J. Solids Struct.
,
51
, pp.
3962
3972
.
52.
Mao
,
J. J.
,
Ke
,
L. L.
, and
Wang
,
Y. S.
,
2015
, “
Thermoelastic Instability of a Functionally Graded Layer Interacting With a Homogeneous Layer
,”
Int. J. Mech. Sci.
,
99
, pp.
218
227
.
53.
Barber
,
J. R.
,
1967
, “
The Distribution of Heat Between Sliding Surfaces
,”
J. Mech. Eng. Sci.
,
9
(
5
), pp.
351
354
.
54.
Barber
,
J. R.
,
1970
, “
The Conduction of Heat From Sliding Solids
,”
Int. J. Heat Mass Transfer
,
13
(
5
), pp.
857
869
.
55.
Jin
,
Z. H.
, and
Noda
,
N.
,
1994
, “
Transient Thermal Stress Intensity Factors for a Crack in Semi-Infinite Plate of a Functionally Gradient Material
,”
Int. J. Solids Struct.
,
31
, pp.
203
218
.
56.
Shodja
,
H. M.
, and
Ghahremaninejad
,
A.
,
2006
, “
An FGM Coated Elastic Solid Under Thermomechanical Loading: A Two Dimensional Linear Elastic Approach
,”
Surf. Coat. Technol.
,
200
, pp.
4050
4064
.
57.
Dundurs
,
J.
,
1974
, “
Distortion of a Body Caused by Free Thermal Expansion
,”
Mech. Res. Commun.
,
1
(
3
), pp.
121
124
.
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