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Research Papers: Piper and Riser Technology

Closed Analytical Expressions for Stress Distributions in Two-Layer Cylinders and Their Application to Offshore Lined and Clad Pipes

[+] Author and Article Information
Knut Vedeld, Håvar A. Sollund, Jostein Hellesland

Mechanics Division,
Department of Mathematics,
University of Oslo,
Oslo 0316, Norway

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received July 8, 2013; final manuscript received December 5, 2014; published online February 20, 2015. Assoc. Editor: John Halkyard.

J. Offshore Mech. Arct. Eng 137(2), 021702 (Apr 01, 2015) (9 pages) Paper No: OMAE-13-1068; doi: 10.1115/1.4029357 History: Received July 08, 2013; Revised December 05, 2014; Online February 20, 2015

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.

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References

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.
Timoshenko, S. P., 1958, Strength of Materials, Part II, 3rd ed., D. Van Nostrand Company, Princeton, NJ.
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. [CrossRef]
Xiang, H., Shi, Z., and Zhang, T., 2006, “Elastic Analyses of Heterogeneous Hollow Cylinders,” Mech. Res. Commun., 33(5), pp. 681–691. [CrossRef]
Shi, Z., Zhang, T., and Xiang, H., 2006, “Exact Solutions of Heterogeneous Elastic Hollow Cylinders,” Compos. Struct., 79(1), pp. 140–147. [CrossRef]
Smith, L. M., 2012, Engineering With Clad Steel, 2nd ed., Technical Series No. 10064, The Nickel Institute, Brussels, Belgium.
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. [CrossRef]
Olsson, J., and Grützner, H., 1989, “Experiences With a High-Alloyed Stainless Steel Under Highly Corrosive Conditions,” Mater. Corros., 40(5), pp. 279–284. [CrossRef]
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. [CrossRef]
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.
NORSOK Standard M-001, 2004, “Materials Selection,” Rev. 4, Standards Norway, Lysaker, Norway.
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. [CrossRef]
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. [CrossRef]
DNV-OS-F101, 2012, Submarine Pipeline Systems, Offshore Standard, Det Norske Veritas, Høvik, Norway.
ASME B31.8, 2003, Gas Transmission and Distribution Piping Systems, American Society of Mechanical Engineers, New York.
API RP 1111, 2009, Design, Construction, Operation and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design), American Petroleum Institute, API Publishing Services, Washington, DC.
Akcay, I. H., and Kaynak, I., 2005, “Analysis of Multilayered Composite Cylinders Under Thermal Loading,” J. Reinf. Plast. Compos., 24(11), pp. 1169–1179. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Perry, J., and Aboudi, J., 2003, “Elasto-Plastic Stresses in Thick Walled Cylinders,” ASME J. Pressure Vessel Technol., 125(3), pp. 248–252. [CrossRef]
Ootao, Y., and Tanigawa, Y., 2006, “Transient Thermoelastic Analysis for a Functionally Graded Hollow Cylinder,” J. Therm. Stresses, 29(11), pp. 1031–1046. [CrossRef]
Hsueh, C. H., 2002, “Thermal Stresses in Elastic Multilayer Systems,” Thin Solid Films, 418(2), pp. 182–188. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Guedes, R. M., 2010, “Non-Linear Viscoelastic Analysis of Thick-Walled Cylindrical Composite Pipes,” Int. J. Mech. Sci., 52(8), pp.1064–1073. [CrossRef]
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.
Timoshenko, S. P., and Goodier, J. N., 1951, Theory of Elasticity, McGraw-Hill, New York.
Vedeld, K., and Sollund, H., 2013, “Explicit Analytical Solutions for Heated, Pressurized Two-Layer Cylinders,” University of Oslo, Oslo, Norway, Report No. 13-2.
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. [CrossRef]
ABAQUS, v. 6.12, 2012, Dassault Systèmes Simulia Corporation., Providence, RI.
Manson, S. S., 1966, Thermal Stress and Low Cycle Fatigue, McGraw-Hill/The University of Michigan, New York/Ann Arbor, MI.
Khan, A. S., and Huang, S., 1995, Continuum Theory of Plasticity, Wiley, New York.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]

Figures

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Fig. 1

Cylindrical coordinate system and stress nomenclature

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Fig. 2

Cross section of a two-layer cylinder with internal and external pressure

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Fig. 3

Boundary conditions for: (a) the axially fixed condition and (b) the axially free condition. Arrow heads indicate translational and double arrow heads rotational constraints.

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Fig. 4

(a) Piping system configuration. (b) Submarine pipeline resting on the seabed. (c) Model of a pipe segment applicable to both scenario (a) and (b).

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Fig. 5

Radial stresses in liner (0.6915 m  <  r  <  0.7215 m) and backing steel (0.7215 m  <  r  <  0.8415 m) for analytical (“An”) solutions and FE solutions, for fixed (“Fix”) and free (“Free”) axial boundary conditions

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Fig. 6

Hoop stresses in liner (0.6915 m  <  r  <  0.7215 m) and backing steel (0.7215 m  <  r  <  0.8415 m) for analytical (An) solutions and FE solutions, for fixed (Fix) and free (Free) axial boundary conditions

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