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.
Similar content being viewed by others
References
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):021002
Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98
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 588:151–166
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 72:1344–1360
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 93:88–96
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 75:4568–4582
Ermida G (2014) Strategic decisions of international oil companies: Arctic versus other regions. Energy Strat Rev 2:265–272
Gautier DL, Bird KJ, Charpentier RR, Grantz A (2009) Assessment of undiscovered oil and gas in the Arctic. Science 324:1175–1179
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 105:273–293
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 99:2–15
Hallai JF, Kyriakides S (2011a) On the effect of Lüders bands on the bending of steel tubes. Part I: experiments. Int J Solids Struct 48:3275–3284
Hallai JF, Kyriakides S (2011b) On the effect of Lüders bands on the bending of steel tubes. Part II: analysis. Int J Solids Struct 48:3285–3298
Hallai JF, Kyriakides S (2013) Underlying material response for Lüders-like instabilities. Int J Plast 47:1–12
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 683:123–128
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 124–125:167–181
Harsem Ø, Eide A, Heen K (2011) Factors influencing future oil and gas prospects in the Arctic. Energy Policy 39:8037–8045
Henry BS, Luxmoore AR (1997) The stress triaxiality constraint and the Q-value as a ductile fracture parameter. Eng Fract Mech 57:375–390
Liu Y, Kyriakides S, Hallai JF (2015) Reeling of pipe with Lüders bands. Int J Solids Struct 72:11–25
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 106–107:305–314
Nahshon K, Hutchinson JW (2008) Modification of the Gurson Model for shear failure. Eur J Mech A/Solids 27:1–17
Nourpanah N, Taheri F (2011) Ductile crack growth and constraint in pipelines subject to combined loadings. Eng Fract Mech 78:2010–2028
O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter–I. Structure of fields. J Mech Phys Solids 39:981–1015
O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter—II. Fracture applications. J Mech Phys Solids 40:939–963
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 74:1770–1792
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 74:1793–1809
Ren X, Nordhagen HO, Zhang Z, (2015). Tensile properties of 420MPa steel at low temperature. In: Twenty-fifth international ocean and polar engineering conference, Hawaii
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 54:57–60
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 41:1649–1661
Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17:389–407
Tvergaard V (1982) On localization in ductile materials containing spherical voids. Int J Fract 18:237–252
Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta metall 32:157–169
Xia L, Shih CF (1995) Ductile crack growth—I. A numerical study using computational cells with microstructurally-based length scales. J Mech Phys Solids 43:233–259
Xia L, Shih CF, Hutchinson JW (1995) A computational approach to ductile crack growth under large scale yielding conditions. J Mech Phys Solids 43:389–413
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 86:787–797
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 77:671–684
Zhang Z, Thaulow C, Ødegård J (2000) A complete Gurson model approach for ductile fracture. Eng Fract Mech 67:155–168
Zhang ZL (1996) A sensitivity analysis of material parameters for for the Gurson constitutive model. Fatig Fract Eng Mater Struct 19:561–570
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 57:653–664
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 79:65–83
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 57:736–743
Funding
Chinese Scholarship Council; Research Council of Norway, Grant/Award No.: 228513/E30.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tu, S., Ren, X., He, J. et al. Numerical study on the effect of the Lüders plateau on the ductile crack growth resistance of SENT specimens. Int J Fract 214, 185–200 (2018). https://doi.org/10.1007/s10704-018-0327-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-018-0327-2