Advertisement

International Journal of Fracture

, Volume 214, Issue 2, pp 185–200 | Cite as

Numerical study on the effect of the Lüders plateau on the ductile crack growth resistance of SENT specimens

  • Shengwen Tu
  • Xiaobo Ren
  • Jianying He
  • Zhiliang ZhangEmail author
Original Paper
  • 128 Downloads

Abstract

The increasing demand of energy prompts the petroleum industry exploitation activities to the Arctic region where the low temperature is a strong challenge, both for structural design and material selection. For structural materials exhibiting the Lüders plateau, it has been reported that lowering the temperature will increase the Lüders plateau length. In order to obtain a deep understanding of the Lüders plateau effect on ductile crack growth resistance, we performed numerical analyses with SENT specimens and the Gurson damage model. The Lüders plateau was simplified by keeping the flow stress constant and varying the plateau length. The results show that the existence of the Lüders plateau does not influence the initiation toughness, however, will alter the material’s fracture resistance significantly. It is found that the Lüders plateau effect is in general controlled by the stress triaxiality level in front of the crack tip. Both the strain hardening and the crack depth effects on resistance curves are alleviated due to the Lüders plateau. For materials with very small initial void volume fraction, the Lüders plateau effect is more pronounced. Since the Lüders plateau intensifies the crack driving force and may lower down crack resistance curve, special attention should be paid to the application of materials with the Lüders plateau in the Arctic.

Keywords

Lüders plateau Ductile crack growth Resistance curve Constraint Stress triaxiality 

Notes

Funding

Chinese Scholarship Council; Research Council of Norway, Grant/Award No.: 228513/E30.

References

  1. Bai Y, Teng X, Wierzbicki T (2009) On the application of stress triaxiality formula for plane strain fracture testing. J Eng Mater Technol 131(2):021002CrossRefGoogle Scholar
  2. Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98CrossRefGoogle Scholar
  3. Beardsmore DW, da Fonseca JQ, Romero J, English CA, Ortner SR, Sharples J, Sherry AH, Wilkes MA (2013) Study of Lüders phenomena in reactor pressure vessel steels. Mater Sci Eng A 588:151–166CrossRefGoogle Scholar
  4. Cravero S, Ruggieri C (2005) Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens–part I: plane-strain analyses. Eng Fract Mech 72:1344–1360CrossRefGoogle Scholar
  5. Dahl BA, Ren XB, Akselsen OM, Nyhus B, Zhang ZL (2018) Effect of low temperature tensile properties on crack driving force for Arctic applications. Theor Appl Fract Mech 93:88–96CrossRefGoogle Scholar
  6. Eikrem PA, Zhang ZL, Østby E, Nyhus B (2008) Numerical study on the effect of prestrain history on ductile fracture resistance by using the complete Gurson model. Eng Fract Mech 75:4568–4582CrossRefGoogle Scholar
  7. Ermida G (2014) Strategic decisions of international oil companies: Arctic versus other regions. Energy Strat Rev 2:265–272CrossRefGoogle Scholar
  8. Gautier DL, Bird KJ, Charpentier RR, Grantz A (2009) Assessment of undiscovered oil and gas in the Arctic. Science 324:1175–1179CrossRefGoogle Scholar
  9. Grange M, Besson J, Andrieu E (2000) An anisotropic gurson type model to represent the ductile rupture of hydrided zircaloy-4 sheets. Int J Fract 105:273–293CrossRefGoogle Scholar
  10. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth Part I—yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99:2–15CrossRefGoogle Scholar
  11. Hallai JF, Kyriakides S (2011a) On the effect of Lüders bands on the bending of steel tubes. Part I: experiments. Int J Solids Struct 48:3275–3284CrossRefGoogle Scholar
  12. Hallai JF, Kyriakides S (2011b) On the effect of Lüders bands on the bending of steel tubes. Part II: analysis. Int J Solids Struct 48:3285–3298CrossRefGoogle Scholar
  13. Hallai JF, Kyriakides S (2013) Underlying material response for Lüders-like instabilities. Int J Plast 47:1–12CrossRefGoogle Scholar
  14. Han J, Lu C, Wu B, Li J, Li H, Lu Y, Gao Q (2017) Innovative analysis of Luders band behaviour in X80 pipeline steel. Mater Sci Eng A 683:123–128CrossRefGoogle Scholar
  15. Han KJ, Shuai J, Deng X, Kong L, Zhao X, Sutton M (2014) The effect of constraint on CTOD fracture toughness of API X65 steel. Eng Fract Mech 124–125:167–181CrossRefGoogle Scholar
  16. Harsem Ø, Eide A, Heen K (2011) Factors influencing future oil and gas prospects in the Arctic. Energy Policy 39:8037–8045CrossRefGoogle Scholar
  17. Henry BS, Luxmoore AR (1997) The stress triaxiality constraint and the Q-value as a ductile fracture parameter. Eng Fract Mech 57:375–390CrossRefGoogle Scholar
  18. Liu Y, Kyriakides S, Hallai JF (2015) Reeling of pipe with Lüders bands. Int J Solids Struct 72:11–25CrossRefGoogle Scholar
  19. Mazière M, Luis C, Marais A, Forest S, Gaspérini M (2017) Experimental and numerical analysis of the Lüders phenomenon in simple shear. Int J Solids Struct 106–107:305–314CrossRefGoogle Scholar
  20. Nahshon K, Hutchinson JW (2008) Modification of the Gurson Model for shear failure. Eur J Mech A/Solids 27:1–17CrossRefGoogle Scholar
  21. Nourpanah N, Taheri F (2011) Ductile crack growth and constraint in pipelines subject to combined loadings. Eng Fract Mech 78:2010–2028CrossRefGoogle Scholar
  22. O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter–I. Structure of fields. J Mech Phys Solids 39:981–1015Google Scholar
  23. O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter—II. Fracture applications. J Mech Phys Solids 40:939–963CrossRefGoogle Scholar
  24. Ostby E, Thaulow C, Zhang ZL (2007a) Numerical simulations of specimen size and mismatch effects in ductile crack growth—Part I: tearing resistance and crack growth paths. Eng Fract Mech 74:1770–1792CrossRefGoogle Scholar
  25. Ostby E, Thaulow C, Zhang ZL (2007b) Numerical simulations of specimen size and mismatch effects in ductile crack growth—Part II: near-tip stress fields. Eng Fract Mech 74:1793–1809CrossRefGoogle Scholar
  26. Ren X, Nordhagen HO, Zhang Z, (2015). Tensile properties of 420MPa steel at low temperature. In: Twenty-fifth international ocean and polar engineering conference, HawaiiGoogle Scholar
  27. Tsuchida N, Tomota Y, Nagai K, Fukaura K (2006) A simple relationship between Lüders elongation and work-hardening rate at lower yield stress. Scripta Materialia 54:57–60CrossRefGoogle Scholar
  28. Tu S, Ren X, He J, Zhang Z (2018) Study of low temperature effect on the fracture locus of a 420 MPa structural steel with the edge tracing method. Fatig Fract Eng Mater Struct 41:1649–1661CrossRefGoogle Scholar
  29. Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17:389–407CrossRefGoogle Scholar
  30. Tvergaard V (1982) On localization in ductile materials containing spherical voids. Int J Fract 18:237–252Google Scholar
  31. Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta metall 32:157–169CrossRefGoogle Scholar
  32. Xia L, Shih CF (1995) Ductile crack growth—I. A numerical study using computational cells with microstructurally-based length scales. J Mech Phys Solids 43:233–259CrossRefGoogle Scholar
  33. Xia L, Shih CF, Hutchinson JW (1995) A computational approach to ductile crack growth under large scale yielding conditions. J Mech Phys Solids 43:389–413CrossRefGoogle Scholar
  34. Xu J, Zhang ZL, Østby E, Nyhus B, Sun DB (2009) Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels. Int J Press Vess Pip 86:787–797CrossRefGoogle Scholar
  35. Xu J, Zhang ZL, Østby E, Nyhus B, Sun DB (2010) Constraint effect on the ductile crack growth resistance of circumferentially cracked pipes. Eng Fract Mech 77:671–684CrossRefGoogle Scholar
  36. Zhang Z, Thaulow C, Ødegård J (2000) A complete Gurson model approach for ductile fracture. Eng Fract Mech 67:155–168CrossRefGoogle Scholar
  37. Zhang ZL (1996) A sensitivity analysis of material parameters for for the Gurson constitutive model. Fatig Fract Eng Mater Struct 19:561–570CrossRefGoogle Scholar
  38. Zhang ZL, Thaulow C, Hauge M (1997) Effects of crack size and weld metal mismatch on the has cleavage toughness of wide plates. Eng Fract Mech 57:653–664CrossRefGoogle Scholar
  39. Zhang ZL, Hauge M, Thaulow C (1996) Two parameter characterization of the near-tip stress field for a bi-material elastic-plastic interface crack. Int J Fract 79:65–83CrossRefGoogle Scholar
  40. Zhao L, Jing H, Xiu J, Han Y, Xu L (2014) Experimental investigation of specimen size effect on creep crack growth behavior in P92 steel welded joint. Mater Des 57:736–743CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Structural EngineeringNorwegian University of Science and Technology (NTNU)TrondheimNorway
  2. 2.SINTEF IndustryTrondheimNorway

Personalised recommendations