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Advances in Direct Methods for Materials and Structures pp 199–217Cite as

High Temperature Limit Analysis of Pressure Vessels and Piping with Local Wall-Thinning

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Abstract

In order to evaluate the safety and integrity of pressure vessels containing volume defects and piping with local wall-thinning at elevated temperature, a numerical method for plastic limit load of modified 9Cr-1Mo steel pressure vessel and piping is proposed in the present paper. The limit load of pressure vessel and piping at high temperature is defined as the load-carrying capacity after the structure has served for a certain time period. The power law creep behavior with Liu-Murakami damage model is implemented into the commercial software ABAQUS via CREEP for simulation, and the Ramberg-Osgood model is modified to consider the material deterioration effect of modified 9Cr-1Mo steel by introducing the creep damage factor into the elasto-plastic constitutive equation. For covering the wide ranges of defect ratios and service time periods, various 3-D numerical examples for the pressure vessels with different sizes of volume defects, the piping with local wall-thinning defects, and creep time are calculated and analyzed. The limit loads of the defected structures under high temperature are obtained through classic zero curvature criterion with the modified Ramberg-Osgood model, and the typical failure modes of these pressure vessels and piping are also discussed. The results show that the plastic limit load of pressure vessel and piping containing defect at elevated temperature depends not only on the size of defect, but also on the creep time, which is different from the traditional plastic limit analysis at room temperature without material deterioration.

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References

  1. Perrin IJ, Hayhurst DR (1996) Creep constitutive equations for a 0.5Cr-0.5Mo-0.25V ferritic steel in the temperature range 600–675 °C. J Strain Anal Eng Des 31:299–314

    Article  Google Scholar 

  2. Drucker DC (1951) A more fundamental approach to plastic stress-strain relations. J Appl Mech-T ASME 18(3):487–491

    Google Scholar 

  3. Hill R (1950) The mathematical theory of plasticity. The Oxford engineering science series. Clarendon Press, Oxford

    Google Scholar 

  4. Hodge PG (1963) Limit analysis of rotationally symmetric plates and shells. Prentice-Hall series in solid and structural mechanics, vol 147. Prentice-Hall, Englewood Cliffs, N. J.

    Google Scholar 

  5. Hodge PG Jr (1970) Limit analysis with multiple load parameters. Int J Solids Struct 6(5):661–675

    Article  MATH  Google Scholar 

  6. Belytschko T, Hodge PG (1970) Plane stress limit analysis by finite elements. J Eng Mech Div 96(6):931–944

    Google Scholar 

  7. Maier G, Munro J (1982) Mathematical programming applications to engineering plastic analysis. Appl Mech Rev 35(12):1631–1643

    Google Scholar 

  8. Chen HF (1998) Numerical methods for limit analysis and reference stress determination of structures under multi-loading systems and their engineering applications. Tsinghua University, Beijing (in Chinese)

    Google Scholar 

  9. Han LH, He SY, Wang YP, Liu CD (1999) Limit moment of local wall thinning in pipe under bending. Int J Press Vessels Pip 76(8):539–542

    Article  Google Scholar 

  10. Kim JW, Na MG, Park CY (2008) Effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load. Nucl Eng Des 238(6):1275–1285

    Article  Google Scholar 

  11. Kim YJ, Kim J, Ahn J, Hong SP, Park CY (2008) Effects of local wall thinning on plastic limit loads of elbows using geometrically linear FE limit analyses. Eng Fract Mech 75(8):2225–2245

    Article  Google Scholar 

  12. Mackenzie D, Shi J, Boyle JT (1994) Finite-element modeling for limit analysis by the elastic compensation method. Comput Struct 51(4):403–410. doi:10.1016/0045-7949(94)90325-5

    Article  MATH  Google Scholar 

  13. Liu YH, Cen ZZ, Xu BY (1995) Numerical limit analysis of cylindrical-shells with part-through slots. Int J Press Vessels Pip 64(1):73–82

    Article  Google Scholar 

  14. Liu YH, Cen ZZ, Xu BY (1995) Numerical investigation of limit loads for the pressure vessels with part-through slots. Acta Mech Solida Sin 8(3):263–276

    Google Scholar 

  15. Liu YH, Cen ZZ, Xu BY (1995) A numerical-method for plastic limit analysis of 3-D structures. Int J Solids Struct 32(12):1645–1658

    Article  MATH  Google Scholar 

  16. Liu YH, Zhang XF, Cen ZZ (2004) Numerical determination of limit loads for three-dimensional structures using boundary element method. Eur J Mech A-Solid 23(1):127–138

    Article  MATH  Google Scholar 

  17. Liu YH, Zhang XF, Cen ZZ (2005) Lower bound shakedown analysis by the symmetric Galerkin boundary element method. Int J Plast 21(1):21–42

    Article  MATH  Google Scholar 

  18. Du XH, Liu DH, Liu YH (2015) Numerical limit load analysis of 3D pressure vessel with volume defect considering creep damage behavior. Math Probl Eng 1–13

    Google Scholar 

  19. Arzt E, Wilkinson DS (1986) Threshold stresses for dislocation climb over hard particles—the effect of an attractive interaction. Acta Metall Mater 34(10):1893–1898

    Article  Google Scholar 

  20. Fournier B, Sauzay M, Pineau A (2011) Micromechanical model of the high temperature cyclic behavior of 9–12%Cr martensitic steels. Int J Plast 27(11):1803–1816

    Article  MATH  Google Scholar 

  21. Böck N, Kager F (2005) Finite element simulation of the creep behaviour of 9% chromium steels based on micromechanical considerations. Paper presented at the materials science and technology 2005 conference and exhibition, Pittsburgh, PA, USA, 25–28 Sept 2005

    Google Scholar 

  22. Sklenička V, Kuchařová K, Dlouh SA, Krejci J (1994) Creep behaviour and microstructure of a 9%Cr steel. Paper presented at the proceedings of the conference on materials for advanced power engineering, Dordrecht, Netherlands

    Google Scholar 

  23. Graham A, Walles KFA (1955) Relations between long and short time properties of commercial alloys. J Iron Steel Inst 193:105

    Google Scholar 

  24. McVetty G (1933) Factors affecting the choice of working stresses for high temperature service. Trans ASME 55:99

    Google Scholar 

  25. Conway JB, Mullikin MJ (1962) An evaluation of various first stage creep equations. Paper presented at the proceedings of AIME conference, Detroit, Michigan

    Google Scholar 

  26. Norton FN (1929) The creep of steel at high temperature. McGraw-Hill, New York

    Google Scholar 

  27. Kachanov LM (1958) On destruction in creeping of materials. Izvestia Akademii Nauk SSSR, Otdelenie Tekhnicheskich Nauk 8:26–31

    Google Scholar 

  28. Rabotnov YN (1969) Creep problems in structural members. North-Holland series in applied mathematics and mechanics, vol 7. North-Holland Publishing Company, Amsterdam, London

    Google Scholar 

  29. Liu DH, Li HS, Liu YH (2015) Numerical simulation of creep damage and life prediction of superalloy turbine blade. Math Probl Eng 1–10

    Google Scholar 

  30. Saanouni K, Chaboche JL, Bathias C (1986) On the creep crack growth prediction by a local approach. Eng Fract Mech 25(5–6):677–691

    Article  Google Scholar 

  31. Benallal A, Billardon R, Lemaitre J (1991) Continuum damage mechanics and local approach to fracture: numerical procedures. Comput Methods Appl Mech Eng 92(2):141–155

    Article  MATH  Google Scholar 

  32. Hall FR, Hayhurst DR, Brown PR (1996) Prediction of plane-strain creep-crack growth using continuum damage mechanics. Int J Damage Mech 5(4):353–383

    Article  Google Scholar 

  33. Hayhurst DR (2005) CDM mechanisms-based modelling of tertiary creep: ability to predict the life of engineering components. Arch Mech 57(2–3):103–132

    MATH  Google Scholar 

  34. Liu Y, Murakami S (1998) Damage localization of conventional creep damage models and proposition of a new model for creep damage analysis. JSME Int J Ser A: Solid Mech Mater Eng 41(1):57–65

    Article  Google Scholar 

  35. Murakami S, Liu Y, Mizuno M (2000) Computational methods for creep fracture analysis by damage mechanics. Comput Methods Appl Mech Eng 183(1–2):15–33

    Article  MATH  Google Scholar 

  36. McLean M, Dyson BF (2000) Modeling the effects of damage and microstructural evolution on the creep behavior of engineering alloys. J Eng Mater Technol Trans ASME 122(3):273–278

    Article  Google Scholar 

  37. Hyde TH, Becker AA, Sun W, Williams JA (2006) Finite-element creep damage analyses of P91 pipes. Int J Press Vessels Pip 83(11–12):853–863

    Article  Google Scholar 

  38. Cocks ACF, Ashby MF (1980) Intergranular fracture during power-law creep under multiaxial stresses. Metal Sci 14(8–9):395–402

    Article  Google Scholar 

  39. Basirat M, Shrestha T, Potirniche GP, Charit I, Rink K (2012) A study of the creep behavior of modified 9Cr-1Mo steel using continuum-damage modeling. Int J Plast 37(0):95–107

    Google Scholar 

  40. Xue JL, Zhou C, Wang B, Peng J (2013) Stress-strain constitutive relation of P91 steel based on creep damage. J Nanjing Univ Technol (Natural Science Edition) 35(4):33–37 (in Chinese)

    Google Scholar 

  41. Wang N, Liu H-Q, Tu S-T (2014) Elasto-plastic constitutive model of 2.25Cr1Mo steel considering initial creep damage. Press Vessel Technol 31(1):1–14 (in Chinese)

    Google Scholar 

  42. Goyal S, Laha K, Das CR, Panneerselvi S, Mathew MD (2013) Finite element analysis of effect of triaxial state of stress on creep cavitation and rupture behaviour of 2.25Cr–1Mo steel. Int J Mech Sci 75:233–243

    Article  Google Scholar 

  43. Rouse JP, Sun W, Hyde TH, Morris A (2013) Comparative assessment of several creep damage models for use in life prediction. Int J Press Vessels Pip 108–109(0):81–87

    Google Scholar 

  44. ASME (2010) Boiler & Pressure Vessel Code Division 1. Subsection NH III. ASME, USA

    Google Scholar 

  45. Masuyama F (2006) Creep degradation in welds of Mod. 9Cr-1Mo steel. Int J Press Vessels Pip 83(11–12):819–825

    Article  Google Scholar 

  46. Ramberg W, Osgood WR (1943) Description of stress-strain curves by three parameters. Technical Note No. 902. National Advisory Committee For Aeronautics, Washington DC

    Google Scholar 

  47. ASME (2010) Fitness-For-Service. API 579-1. ASME, USA

    Google Scholar 

  48. Takahashi Y (2008) Study on creep-fatigue evaluation procedures for high-chromium steels—part I: test results and life prediction based on measured stress relaxation. Int J Press Vessels Pip 85(6):406–422. doi:10.1016/j.ijpvp.2007.11.008

    Article  Google Scholar 

  49. Du XH, Zhang J, Peng H, Liu YH (2017) Plastic limit analysis of modified 9Cr-1Mo steel pressure vessel containing volume defect with creep damage law. Int J Appl Mech 9(2):1750025(1–29)

    Google Scholar 

  50. Du XH, Zhang J, Liu YH (2017) Plastic failure analysis of defective pipes with creep damage under multi-loading systems. Int J Mech Sci 128–129:428–444

    Google Scholar 

  51. Chen G, Liu YH (2006) Numerical theories and engineering methods for structural limit and shakedown analyses. Science Press, Beijing (in Chinese)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation for Distinguished Young Scholars of China (Project No. 11325211) and National Natural Science Foundation of China (Project No. 11302023).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    X. Du & Y. Liu

  2. Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai, China

    J. Zhang

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  1. X. Du
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  2. Y. Liu
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  3. J. Zhang
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Correspondence to Y. Liu .

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Editors and Affiliations

  1. Department of Engineering Science, University of Oxford, Oxford, Oxfordshire, United Kingdom

    Olga Barrera

  2. Department of Engineering Science, University of Oxford, Oxford, Oxfordshire, United Kingdom

    Alan Cocks

  3. Department of Engineering, University of Leicester, Leicester, Leicestershire, United Kingdom

    Alan Ponter

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Du, X., Liu, Y., Zhang, J. (2018). High Temperature Limit Analysis of Pressure Vessels and Piping with Local Wall-Thinning. In: Barrera, O., Cocks, A., Ponter, A. (eds) Advances in Direct Methods for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-59810-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-59810-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59808-6

  • Online ISBN: 978-3-319-59810-9

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