A dynamic, partially permeable crack model for orthotropic materials is established with the crack full of thermal medium. Besides external thermal and elastic loadings, the heat flux generated by the crack interior full of a medium also contributes to the crack boundary conditions, which is dependent on the crack opening displacement. Thus, the heat conduction is dependent on elastic field. First, the heat conduction equation is solved exactly in terms of unknown heat flux of the crack interior. Then, the elastic field is presented for real or complex eigenvalue cases on the basis of the operator theory. Finally, the thermal and elastic fields are presented analytically, and the heat flux of the crack interior is determined explicitly. Numerical results are offered to show the influences of the thermal conductivity coefficient, normal and shear loadings and crack velocity on the distributions of the heat flux, temperature difference across the crack surfaces, and thermal stress intensity factor. Figures illustrate that increasing the crack velocity leads to a more thermally impermeable crack and produces a bigger temperature difference across the crack surfaces.

References

References
1.
Chang
,
C. Y.
, and
Ma
,
C. C.
,
2001
, “
Transient Thermal Conduction of a Rectangular Plate With Multiple Insulated Cracks by the Alternating Method
,”
Int. J. Heat Mass Transfer
,
44
(
13
), pp.
2423
2437
.
2.
Tsai
,
Y. M.
,
2000
, “
Thermoelastic Problem of Uniform Heat Flow Disturbed by a Flat Toroidal Crack in a Transversely Isotropic Medium
,”
J. Therm. Stresses
,
23
(
3
), pp.
217
231
.
3.
Chen
,
Y. Z.
, and
Hasebe
,
N.
,
2003
, “
Solution for a Curvilinear Crack in a Thermoelastic Medium
,”
J. Therm. Stresses
,
26
(
3
), pp.
245
259
.
4.
Tsang
,
D. K. L.
,
Oyadiji
,
S. O.
, and
Leung
,
A. Y. T.
,
2007
, “
Two-Dimensional Fractal-Like Finite Element Method for Thermoelastic Crack Analysis
,”
Int. J. Solids Struct.
,
44
(
24
), pp.
7862
7876
.
5.
Lee
,
G. H.
, and
Beom
,
H. G.
,
2014
, “
Interfacial Edge Crack Between Dissimilar Orthotropic Thermoelastic Materials Under Uniform Heat Flow
,”
J. Mech. Sci. Technol.
,
28
(
8
), pp.
3041
3050
.
6.
Itou
,
S.
,
2014
, “
Thermal Stresses Around Two Upper Cracks Placed Symmetrically About a Lower Crack in an Infinite Orthotropic Plane Under Uniform Heat Flux
,”
J. Theor. Appl. Mech.
,
52
(3), pp.
617
628
.http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-d8d7f9fe-2ce4-4133-9f32-26d232177953
7.
Erdogan
,
F.
,
1998
, “
Crack Problems in Nonhomogeneous Materials
,”
Fracture: A Topical Encyclopedia of Current Knowledge
,
G. P.
Cherepanov
, ed.,
Krieger
,
Malabar, FL
, pp.
72
98
.
8.
Chen
,
J.
,
2005
, “
Determination of Thermal Stress Intensity Factors for an Interface Crack in a Graded Orthotropic Coating-Substrate Structure
,”
Int. J. Fract.
,
133
(
4
), pp.
303
328
.
9.
Dag
,
S.
,
2006
, “
Thermal Fracture Analysis of Orthotropic Functionally Graded Materials Using an Equivalent Domain Integral Approach
,”
Eng. Fract. Mech.
,
73
(
18
), pp.
2802
2828
.
10.
Dag
,
S.
,
Yildirim
,
B.
, and
Sarikaya
,
D.
,
2007
, “
Mixed-Mode Fracture Analysis of Orthotropic Functionally Graded Materials Under Mechanical and Thermal Loads
,”
Int. J. Solids Struct.
,
44
(
24
), pp.
7816
7840
.
11.
El-Borgi
,
S.
,
Erdogan
,
F.
, and
Hidri
,
L.
,
2004
, “
A Partially Insulated Embedded Crack in an Infinite Functionally Graded Medium Under Thermo-Mechanical Loading
,”
Int. J. Eng. Sci.
,
42
(3–4), pp.
371
393
.
12.
Rekik
,
M.
,
Neifar
,
M.
, and
El-Borgi
,
S.
,
2011
, “
An Axisymmetric Problem of a Partially Insulated Crack Embedded in a Graded Layer Bonded to a Homogeneous Half-Space Under Thermal Loading
,”
J. Therm. Stresses
,
34
(
3
), pp.
201
227
.
13.
Chiu
,
T. C.
,
Tsai
,
S. W.
, and
Chue
,
C. H.
,
2013
, “
Heat Conduction in a Functionally Graded Medium With an Arbitrarily Oriented Crack
,”
Int. J. Heat Mass Transfer
,
67
, pp.
514
522
.
14.
Barber
,
J. R.
,
1980
, “
Steady-State Thermal Stresses Caused by an Imperfectly Conducting Penny-Shaped Crack in an Elastic Solid
,”
J. Therm. Stresses
,
3
(
1
), pp.
77
83
.
15.
Choi
,
H. J.
,
2011
, “
Thermoelastic Problem of Steady-State Heat Flows Disturbed by a Crack at an Arbitrary Angle to the Graded Interfacial Zone in Bonded Materials
,”
Int. J. Solids Struct.
,
48
(6), pp.
893
909
.
16.
Zhong
,
X. C.
, and
Lee
,
K. Y.
,
2012
, “
A Thermal-Medium Crack Model
,”
Mech. Mater.
,
51
, pp.
110
117
.
17.
Zhong
,
X. C.
, and
Wu
,
B.
,
2012
, “
Thermoelastic Analysis for an Opening Crack in an Orthotropic Material
,”
Int. J. Fract.
,
173
(
1
), pp.
49
55
.
18.
Zhong
,
X. C.
, and
Zhang
,
K. S.
,
2013
, “
An Opening Crack Model for Thermopiezoelectric Solids
,”
Eur. J. Mech., A
,
41
, pp.
101
110
.
19.
Li
,
X. F.
, and
Lee
,
K. Y.
,
2004
, “
Fracture Analysis of Cracked Piezoelectric Materials
,”
Int. J. Solids Struct.
,
41
(
15
), pp.
4137
4161
.
20.
Itou
,
S.
,
2005
, “
Stress Intensity Factors for a Moving Cylindrical Crack in a Nonhomogeneous Cylindrical Layer in Composite Materials
,”
Arch. Appl. Mech.
,
75
(
1
), pp.
18
30
.
21.
Bagheri
,
R.
, and
Ayatollahi
,
M.
,
2012
, “
Multiple Moving Cracks in a Functionally Graded Strip
,”
Appl. Math. Modell.
,
36
(
10
), pp.
4677
4686
.
22.
Wu
,
J.
, and
Ru
,
C. Q.
,
2014
, “
A Speed-Dependent Cohesive Zone Model for Moving Cracks With Non-Uniform Traction Force
,”
Eng. Fract. Mech.
,
117
, pp.
12
27
.
23.
Tzou
,
D. Y.
,
1990
, “
Thermal Shock Waves Induced by a Moving Crack
,”
ASME J. Heat Transfer
,
112
(
1
), pp.
21
27
.
24.
Tzou
,
D. Y.
,
1990
, “
Thermal Shock Waves Induced by a Moving Crack—A Heat Flux Formulation
,”
Int. J. Heat. Mass Transfer
,
33
(5), pp.
817
885
.
25.
Boley
,
B. A.
, and
Weiner
,
J. H.
,
1997
,
Theory of Thermal Stresses
,
Dover Publications
,
Mineola, NY
.
26.
Gurtin
,
M. E.
,
2000
,
Configurational Forces as a Basic Concept of Continuum Physics
,
Springer-Verlag
,
Berlin
.
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