Closed-form analytical expressions are derived for the displacement field and corresponding stress state in two-layer cylinders subjected to pressure and thermal loading. Solutions are developed both for cylinders that are fully restrained axially (plane strain) and for cylinders that are axially loaded and spring-mounted. In the latter case, it is assumed that the combined two-layer cross section remains plane after deformation (generalized plane strain). The analytical solutions are verified by means of detailed three-dimensional finite element (FE) analyses, and they are easily implemented in, and suitable for, engineering applications. The chosen axial boundary conditions are demonstrated to be particularly relevant for pipeline and piping applications. By applying the exact solutions derived in the present study to typical offshore lined or clad pipelines, it is demonstrated that thermal expansion of the liner or clad layer may cause higher tensile hoop stresses in the pipe steel wall than accounted for in current engineering practice. It is shown that repeated cycles of start-up and shut-down phases for lined or clad pipelines cause significant plastic stress cycles in liners or claddings, which may pose a risk to the integrity of such pipelines.

References

References
1.
Lamé
,
G.
, and
Clapeyron
,
B.
,
1831
, “
Mémoire sur l’équilibre intérieur des corps solides homogènes
,”
J. Reine Angew. Math. (Crelle's J.)
,
7
, pp.
145
169
.
2.
Timoshenko
,
S. P.
,
1958
,
Strength of Materials, Part II
,
3rd ed.
,
D. Van Nostrand Company
,
Princeton, NJ
.
3.
Eraslan
,
A. N.
, and
Akis
,
T.
,
2006
, “
Plane Strain Analytical Solutions for a Functionally Graded Elastic–Plastic Pressurized Tube
,”
Int. J. Pressure Vessels Piping
,
83
(
9
), pp.
635
644
.10.1016/j.ijpvp.2006.07.003
4.
Xiang
,
H.
,
Shi
,
Z.
, and
Zhang
,
T.
,
2006
, “
Elastic Analyses of Heterogeneous Hollow Cylinders
,”
Mech. Res. Commun.
,
33
(
5
), pp.
681
691
.10.1016/j.mechrescom.2006.01.005
5.
Shi
,
Z.
,
Zhang
,
T.
, and
Xiang
,
H.
,
2006
, “
Exact Solutions of Heterogeneous Elastic Hollow Cylinders
,”
Compos. Struct.
,
79
(
1
), pp.
140
147
.10.1016/j.compstruct.2005.11.058
6.
Smith
,
L. M.
,
2012
,
Engineering With Clad Steel
,
2nd ed.
, Technical Series No. 10064,
The Nickel Institute
,
Brussels, Belgium
.
7.
Vedeld
,
K.
,
Osnes
,
H.
, and
Fyrileiv
,
O.
,
2012
, “
Analytical Expressions for Stress Distributions in Lined Pipes: Axial Stress and Contact Pressure Interaction
,”
Mar. Struct.
,
26
(
1
), pp.
1
26
.10.1016/j.marstruc.2011.12.003
8.
Olsson
,
J.
, and
Grützner
,
H.
,
1989
, “
Experiences With a High-Alloyed Stainless Steel Under Highly Corrosive Conditions
,”
Mater. Corros.
,
40
(
5
), pp.
279
284
.10.1002/maco.19890400504
9.
Marie
,
S.
,
2004
, “
Analytical Expression of the Thermal Stresses in a Vessel or Pipe With Cladding Submitted to Any Thermal Restraint
,”
Int. J. Pressure Vessels Piping
,
81
(
4
), pp.
303
312
.10.1016/j.ijpvp.2004.03.005
10.
Kloewer
,
J.
,
Behrens
,
R.
, and
Lettner
,
J.
,
2002
, “
Clad Plates and Pipes in Oil and Gas Production: Applications—Fabrication - Welding
,”
Proc. CORROSION 2002, NACE International
,
Houston, TX
, Paper No. 02062, pp.
1
18
.
11.
NORSOK Standard M-001
,
2004
, “
Materials Selection
,” Rev. 4, Standards Norway, Lysaker, Norway.
12.
Zhang
,
Q.
,
Wang
,
Z. W.
,
Tang
,
C. Y.
,
Hu
,
D. P.
, and
Xia
,
L. Z.
,
2012
, “
Analytical Solution of the Thermo-Mechanical Stresses in a Multilayered Composite Pressure Vessel Considering the Influence of Closed Ends
,”
Int. J. Pressure Vessels Piping
,
98
, pp.
102
110
.10.1016/j.ijpvp.2012.07.009
13.
Barbezat
,
G.
,
2005
, “
Advanced Thermal Spray Technology and Coating for Lightweight Engine Blocks for the Automotive Industry
,”
Surf. Coat. Technol.
,
200
(
5–6
), pp.
1990
1993
.10.1016/j.surfcoat.2005.08.017
14.
DNV-OS-F101
,
2012
,
Submarine Pipeline Systems, Offshore Standard
,
Det Norske Veritas
,
Høvik, Norway
.
15.
ASME B31.8
,
2003
,
Gas Transmission and Distribution Piping Systems
,
American Society of Mechanical Engineers
,
New York
.
16.
API RP 1111
,
2009
,
Design, Construction, Operation and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design)
,
American Petroleum Institute, API Publishing Services
,
Washington, DC
.
17.
Akcay
,
I. H.
, and
Kaynak
,
I.
,
2005
, “
Analysis of Multilayered Composite Cylinders Under Thermal Loading
,”
J. Reinf. Plast. Compos.
,
24
(
11
), pp.
1169
1179
.10.1177/0731684405048840
18.
Jabbari
,
M.
,
Sohrabpour
,
S.
, and
Eslami
,
M. R.
,
2002
, “
Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads
,”
Int. J. Pressure Vessels Piping
,
79
(
7
), pp.
493
497
.10.1016/S0308-0161(02)00043-1
19.
Shao
,
Z. S.
,
2005
, “
Mechanical and Thermal Stresses of a Functionally Graded Circular Hollow Cylinder With Finite Length
,”
Int. J. Pressure Vessels Piping
,
82
(
3
), pp.
155
163
.10.1016/j.ijpvp.2004.09.007
20.
Kandil
,
A.
,
El-Kady
,
A.
, and
El-Kafrawy
,
A.
,
1995
, “
Transient Thermal Stress Analysis of Thick-Walled Cylinders
,”
Int. J. Mech. Sci.
,
37
(
7
), pp.
721
732
.10.1016/0020-7403(94)00105-S
21.
Jane
,
K. C.
, and
Lee
,
Z. Y.
,
1999
, “
Thermoelastic Transient Response of an Infinitely Long Annular Multilayered Cylinder
,”
Mech. Res. Commun.
,
26
(
6
), pp.
709
718
.10.1016/S0093-6413(99)00082-8
22.
Lee
,
Z. Y.
,
Chen
,
C. K.
, and
Hung
,
C.-I.
,
2001
, “
Transient Thermal Stress Analysis of Multilayered Hollow Cylinder
,”
Acta Mech.
,
151
(
1–2
), pp.
75
88
.10.1007/BF01272526
23.
Radu
,
V.
,
Taylor
,
N.
, and
Paffumi
,
E.
,
2008
, “
Development of New Analytical Solutions for Elastic Thermal Stress Components in a Hollow Cylinder Under Sinusoidal Transient Thermal Loading
,”
Int. J. Pressure Vessels Piping
,
85
(
12
), pp.
885
893
.10.1016/j.ijpvp.2008.04.010
24.
Ansari
,
R.
,
Alisafaei
,
F.
, and
Ghaedi
,
P.
,
2010
, “
Dynamic Analysis of Multi-Layered Filament-Wound Composite Pipes Subjected to Cyclic Internal Pressure and Cyclic Temperature
,”
Compos. Struct.
,
92
(
5
), pp.
1100
1109
.10.1016/j.compstruct.2009.09.058
25.
Hung
,
C.-I.
,
Chen
,
C. K.
, and
Lee
,
Z. Y.
,
2001
, “
Thermoelastic Transient Response of Multilayered Hollow Cylinder With Initial Interface Pressure
,”
J. Therm. Stresses
,
24
(
10
), pp.
987
1006
.10.1080/014957301753191086
26.
Perry
,
J.
, and
Aboudi
,
J.
,
2003
, “
Elasto-Plastic Stresses in Thick Walled Cylinders
,”
ASME J. Pressure Vessel Technol.
,
125
(
3
), pp.
248
252
.10.1115/1.1593078
27.
Ootao
,
Y.
, and
Tanigawa
,
Y.
,
2006
, “
Transient Thermoelastic Analysis for a Functionally Graded Hollow Cylinder
,”
J. Therm. Stresses
,
29
(
11
), pp.
1031
1046
.10.1080/01495730600710356
28.
Hsueh
,
C. H.
,
2002
, “
Thermal Stresses in Elastic Multilayer Systems
,”
Thin Solid Films
,
418
(
2
), pp.
182
188
.10.1016/S0040-6090(02)00699-5
29.
Xia
,
M.
,
Kemmochi
,
K.
, and
Takayanagi
,
H.
,
2001
, “
Analysis of Filament-Wound Fiber-Reinforced Sandwich Pipe Under Combined Internal Pressure and Thermomechanical Loading
,”
Compos. Struct.
,
51
(
3
), pp.
273
283
.10.1016/S0263-8223(00)00137-9
30.
Xia
,
M.
,
Kemmochi
,
K.
, and
Takayanagi
,
H.
,
2001
, “
Analysis of Multi-Layered Filament-Wound Composite Pipes Under Thermal Pressure
,”
Compos. Struct.
,
53
(
4
), pp.
483
491
.10.1016/S0263-8223(01)00061-7
31.
Bakaiyan
,
H.
,
Hosseini
,
H.
, and
Ameri
,
E.
,
2009
, “
Analysis of Multi-Layered Filament Wound Composite Pipes Under Combined Internal Pressure and Thermomechanical Loading With Thermal Variations
,”
Compos. Struct.
,
88
(
4
), pp.
532
541
.10.1016/j.compstruct.2008.05.017
32.
Guedes
,
R. M.
,
2010
, “
Non-Linear Viscoelastic Analysis of Thick-Walled Cylindrical Composite Pipes
,”
Int. J. Mech. Sci.
,
52
(
8
), pp.
1064
1073
.10.1016/j.ijmecsci.2010.04.003
33.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
2002
,
Concepts and Applications of Finite Element Analysis
,
4th ed.
,
Wiley, The University of Wisconsin
,
Madison, WI
.
34.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
,
1951
,
Theory of Elasticity
,
McGraw-Hill
,
New York
.
35.
Vedeld
,
K.
, and
Sollund
,
H.
,
2013
, “
Explicit Analytical Solutions for Heated, Pressurized Two-Layer Cylinders
,” University of Oslo, Oslo, Norway, Report No. 13-2.
36.
Carr
,
M.
,
Bruton
,
D.
, and
Leslie
,
D.
,
2008
, “
Pipeline Walking: Understanding the Field Layout Challenges and Analytical Solutions Developed for the Safebuck JIP
,”
SPE Proj. Facil. Constr.
,
3
(
3
), pp.
1
9
.10.2118/120022-PA
37.
ABAQUS, v. 6.12
,
2012
, Dassault Systèmes Simulia Corporation., Providence, RI.
38.
Manson
,
S. S.
,
1966
,
Thermal Stress and Low Cycle Fatigue
,
McGraw-Hill/The University of Michigan
,
New York/Ann Arbor, MI
.
39.
Khan
,
A. S.
, and
Huang
,
S.
,
1995
,
Continuum Theory of Plasticity
,
Wiley
,
New York
.
40.
Jiao
,
R.
, and
Kyriakides
,
S.
,
2011
, “
Ratcheting and Wrinkling of Tubes Due to Axial Cycling Under Internal Pressure: Part I Experiments
,”
Int. J. Solids Struct.
,
48
(
20
), pp.
2814
2826
.10.1016/j.ijsolstr.2011.05.027
41.
Jiao
,
R.
, and
Kyriakides
,
S.
,
2011
, “
Ratcheting and Wrinkling of Tubes Due to Axial Cycling Under Internal Pressure: Part II Analysis
,”
Int. J. Solids Struct.
,
48
(
20
), pp.
2827
2836
.10.1016/j.ijsolstr.2011.05.026
42.
Jiao
,
R.
, and
Kyriakides
,
S.
,
2009
, “
Ratcheting, Wrinkling and Collapse of Tubes Under Axial Cycling
,”
Int. J. Solids Struct.
,
46
(
14–15
), pp.
2856
2870
.10.1016/j.ijsolstr.2009.03.018
You do not currently have access to this content.