Abstract
A non-associated/associated flow rule coupled with an anisotropic/isotropic quadratic yield function is presented to describe the mechanical responses of two distinct X65 pipeline steels. The first as a product of the cold-rolling forming (UOE) process also known as seam weld pipes and the second as a result of high temperature piercing process called seamless tube manufacturing. The experimental settings consist of a wide range of sample types, whose geometric characteristics represent different state of stresses and loading modes. For low to intermediate stress triaxiality levels, flat specimens are extracted at different material orientations along with notched round bar samples for high stress triaxialities. The results indicate that despite the existing differences in plasticity between materials due to anisotropy induced processes, material failure can be characterized by an isotropic weighting function based on the modified Mohr–Coulomb (MMC) criterion. The non-associated flow rule allows for inclusion of strain directional dependence in the definition of equivalent plastic strain by means of scalar anisotropy (Lankford) coefficients and thus keeping the original capabilities of the MMC model.
Similar content being viewed by others
References
Abi Akl R, Mohr D (2017) Paint-bake effect on the plasticity and fracture of pre-strained aluminum 6451 sheets. Int J Mech Sci, 124–125, 68–82. http://ac.els-cdn.com/S0020740317300218/1-s2.0-S0020740317300218-main.pdf?_tid=4a761a1a-10a3-11e7-b6a1-00000aacb362&acdnat=1490368097_fa4fbcdc076fe817d776341dfdacfbd4
Arakawa T et al (2013) Development of high performance UOE pipe for linepipe. JFE Technical Report (18(Mar)), pp 23–35. http://221.0.90.141
Bai Y, Wierzbicki T (2008) A new model of metal plasticity and fracture with pressure and Lode dependence. Int J Plast 24(6):1071–1096. https://doi.org/10.1016/j.ijplas.2007.09.004
Bai Y, Wierzbicki T (2010) Application of extended Mohr–Coulomb criterion to ductile fracture. Int J Fract 161(1):1–20. https://doi.org/10.1007/s10704-009-9422-8
Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7(7):693–712. https://doi.org/10.1016/0749-6419(91)90052-Z
Basu S, Benzerga AA (2015) On the path-dependence of the fracture locus in ductile materials: experiments. Int J Solids Struct. https://doi.org/10.1016/j.ijsolstr.2015.06.003
Benzerga AA, Besson J (2001) Plastic potentials for anisotropic porous solids. Eur J Mech A/Solids 20(3):397–434. https://doi.org/10.1016/S0997-7538(01)01147-0
Benzerga AA, Leblond JB (2010) Ductile fracture by void growth to coalescence. Adv Appl Mech. https://doi.org/10.1016/S0065-2156(10)44003-X
Benzerga A, Besson J, Pineau A (2004a) Anisotropic ductile fracture. Acta Mater 52(15):4623–4638. https://doi.org/10.1016/j.actamat.2004.06.020
Benzerga AA, Besson J, Pineau A (2004b) Anisotropic ductile fracture: part I: experiments. Acta Mater 52(15):4623–4638. https://doi.org/10.1016/j.actamat.2004.06.020
Benzerga AA, Besson J, Pineau A (2004c) Anisotropic ductile fracture: part II: theory. Acta Mater 52(15):4639–4650. https://doi.org/10.1016/j.actamat.2004.06.019
Benzerga AA, Surovik D, Keralavarma SM (2012) On the path dependence of the fracture locus in ductile materials—analysis. Int J Plast 37:157–170. https://doi.org/10.1016/j.ijplas.2012.05.003
Broek D (1973) The role of inclusions in ductile fracture and fracture toughness. Eng Fract Mech. https://doi.org/10.1016/0013-7944(73)90007-6
Bron F, Besson J (2004) A yield function for anisotropic materials application to aluminum alloys. Int J Plast 20(4–5):937–963. https://doi.org/10.1016/j.ijplas.2003.06.001
CIA (2014) The World Factbook 2013–14. https://www.cia.gov/library/publications/the-world-factbook/index.html
Dunand M, Mohr D (2011) Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading. Eng Fract Mech 78(17):2919–2934. https://doi.org/10.1016/j.engfracmech.2011.08.008
Garrison WM, Moody NR (1987) Ductile fracture. J Phys Chem Solids 48(11):1035–1074. https://doi.org/10.1016/0022-3697(87)90118-1
Gu G, Mohr D (2015) Anisotropic Hosford–Coulomb fracture initiation model: theory and application. Eng Fract Mech 147:480–497. https://doi.org/10.1016/j.engfracmech.2015.08.004
Guo B et al (2014) Offshore pipelines. https://doi.org/10.1016/B978-0-12-397949-0.00017-0
Hara T et al (2009) Metallurgical design and development of high deformable high strength line pipe suitable for strain-based design. Isope 1:73–79
Hara T et al (2011) Development and mass production of X60 high deformable line pipe suitable for strain-based design. Isope 8:575–580
Herynk MD et al (2007) Effects of the UOE/UOC pipe manufacturing processes on pipe collapse pressure. Int J Mech Sci 49(5):533–553. https://doi.org/10.1016/j.ijmecsci.2006.10.001
Hill R (1949) The theory of plane plastic strain for anisotropic metals. Proc R Soc Lond Ser A Math Phys Sci 198(1054):428–437. https://doi.org/10.1098/rspa.1949.0110
Iizuka E, Hashimoto K, Kuwabara T (2014) Effects of anisotropic yield functions on the accuracy of forming simulations of hole expansion. In: Procedia engineering, pp 2433–2438. https://doi.org/10.1016/j.proeng.2014.10.346
Institute AP (2007) API 5L specification for line pipe. Api Spec 5L(44):1–40. https://doi.org/10.1520/G0154-12A
Iob F, Campanelli F, Coppola T (2015) Modelling of anisotropic hardening behavior for the fracture prediction in high strength steel line pipes. Eng Fract Mech 148:363–382. https://doi.org/10.1016/j.engfracmech.2015.04.030
Jia Y, Bai Y (2016) Ductile fracture prediction for metal sheets using all-strain-based anisotropic eMMC model. Int J Mech Sci 115–116:516–531. https://doi.org/10.1016/j.ijmecsci.2016.07.022
Karafillis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41(12):1859–1886. https://doi.org/10.1016/0022-5096(93)90073-O
Ling Y (2004) Uniaxial true stress–strain after necking. AMP J Technol 5(1):37–48
Luo M, Dunand M, Mohr D (2012) Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading—part II: ductile fracture. Int J Plast, 32–33, 36–58. http://ac.els-cdn.com/S0749641911001896/1-s2.0-S0749641911001896-main.pdf?_tid=741afae0-14a2-11e7-b9c9-00000aacb360&acdnat=1490807542_9f4d9919bb5c35a050c1fcefd3c5069b
Mohr D, Dunand M, Kim KH (2010) Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading. Int J Plast 26(7):939–956. https://doi.org/10.1016/j.ijplas.2009.11.006
Morgeneyer TF et al (2009) Experimental and numerical analysis of toughness anisotropy in AA2139 Al-alloy sheet. Acta Mater 57(13):3902–3915. https://doi.org/10.1016/j.actamat.2009.04.046
Paredes M et al (2017) Ductile tearing analysis of TC128 tank car steel under mode I loading condition. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2017.10.006
Paredes M, Wierzbicki T, Zelenak P (2016) Prediction of crack initiation and propagation in X70 pipeline steels. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2016.10.006
Qian L , Fang G, Zeng P (2017) Modeling of the ductile fracture during the sheet forming of aluminum alloy considering non-associated constitutive characteristic. Int J Mech Sci 126:55–66. http://ac.els-cdn.com/S0020740316304313/1-s2.0-S0020740316304313-main.pdf?_tid=e7feb1b2-1499-11e7-bc1f-00000aab0f02&acdnat=1490803871_223b1cfa3ca17890a073a6f8b2eaa25a
Qian L et al (2016) Experimental and numerical study on shear-punch test of 6060 T6 extruded aluminum profile. Int J Mech Sci 118:205–218. https://doi.org/10.1016/j.ijmecsci.2016.09.008
Rivalin F et al (2000) Ductile tearing of pipeline-steel wide plates. II. Modeling of in-plane crack propagation. Eng Fract Mech 68(3):347–364. https://doi.org/10.1016/S0013-7944(00)00108-9
Ronalds BF (2005) Applicability ranges for offshore oil and gas production facilities. Mar Struct 18(3):251–263. https://doi.org/10.1016/j.marstruc.2005.06.001
Roth CC, Mohr D (2016) Ductile fracture experiments with locally proportional loading histories. Int J Plast 79:328–354. https://doi.org/10.1016/j.ijplas.2015.08.004
Shinohara Y, Madi Y, Besson J (2016) Anisotropic ductile failure of a high-strength line pipe steel. Int J Fract 197(2):127–145. https://doi.org/10.1007/s10704-015-0054-x
Stoughton TB (2002) A non-associated flow rule for sheet metal forming. Int J Plast. https://doi.org/10.1016/S0749-6419(01)00053-5
Suh YS, Saunders FI, Wagoner RH (1996) Anisotropic yield functions with plastic-strain-induced anisotropy. Int J Plast 12(3):417–438. https://doi.org/10.1016/S0749-6419(96)00014-9
Tanguy B et al (2008) Plastic and damage behaviour of a high strength X100 pipeline steel: experiments and modelling. Int J Press Vessels Pip 85(5):322–335. https://doi.org/10.1016/j.ijpvp.2007.11.001
Thomas N, Basu S, Benzerga AA (2016) On fracture loci of ductile materials under non-proportional loading. Int J Mech Sci. https://doi.org/10.1016/j.ijmecsci.2016.08.007
Tsuru E et al (2008) Numerical simulation of buckling resistance for UOE line pipes with orthogonal anisotropic hardening behavior. Proceedings of the Eighteenth International Offshore and Polar Engineering Conference 8:104–110
Tubb M (2001) International pipeline construction outlook: oil & gas infrastructure. Pipeline Gas J 228(8):16. http://search.proquest.com/docview/197489021?accountid=47173%5Cn, http://uf2mu7dg8q.search.serialssolutions.com/?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&rfr_id=info:sid/ProQ%3Asciencejournals&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article
Van Stone RH et al (1985) Microstructural aspects of fracture by dimpled rupture. Int Metals Rev 30(4):157–180. https://doi.org/10.1179/imtr.1985.30.1.157
Wierzbicki T, Xue L (2005) On the effect of the third invariant of the stress deviator on ductile fracture. Technical report, Impact and Crashworthiness Laboratory, Massachusetts Institute of Technology, Cambridge, MA
Acknowledgements
The work reported herein was supported by MIT Industrial Fracture Consortium—Phase III with collaboration of RWTH Aachen University and Tenaris Co. The authors are in debt with Professor Yuanli Bai and Dr. Yueqian Jia from University of Central Florida for the fruitful discussions and comments done along the execution of this work. Mr. Michal Bardadyn is also acknowledged for his support in performing tests and post-processing of measured data.
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.
Appendices
Appendix A: Numerical procedure and FE models
A detailed 3D finite element models were developed for numerical analysis for all specimen geometries selected. Exploiting symmetry conditions of them only 1/8 of tensile specimens and 1/2 of special butterfly specimen were modeled. Orthogonal symmetric planes of FE models were constrained with zero normal displacement. A typical FE model is shown in Fig. 12 of a NRB specimen with two different radii. The model is meshed with trilinear eight cubic elements (C3D8R from Abaqus library) with reduced integration and hourglass control, being the more refined those allocate in the critical region near the center specimen with a characteristic length of \(200~\upmu \hbox {m}\). Monotonic quasi-static loading conditions are applied on each FE model similar to those conditions imposed on tests. The principal axes of anisotropy are assumed to be aligned with the material coordinates, in this case the pipe, such as: longitudinal (\(\hbox {e}_{1} - 0^{\circ }\)), hoop (\(\hbox {e}_{2} - 90^{\circ }\)) and through thickness (\(\hbox {e}_{3}\)) direction.
The constitutive model of plasticity and fracture was implemented into a VUMAT user-defined subroutine. Explicit time integration scheme with finite strain setting is employed for taking account nonlinear geometric changes and mass scaling factor to reduce computation time.
Appendix B: The state of stress characterization
The stress triaxiality (\(\eta \)) and the Lode angle (\(\bar{\theta }\)) parameters are defined in terms of the invariants of the Cauchy stress tensor \({\varvec{\sigma }}\) in the form
where, \(\sigma _m =-1/3\hbox {tr}{\varvec{\sigma }}\) is the mean stress and \(\bar{\sigma } =\sqrt{1/2{{\varvec{S}}}:{{\varvec{S}}}}\) is the von Mises equivalent stress. S stands for the deviatoric stress tensor, which is defined as
1 is the fourth order identity tensor. Likewise, the normalized Lode angle (simply called Lode angle) is represented as the normalized third invariant of the Cauchy stress deviator
where \(\theta \) is the actual Lode angle, which is defined as
The corresponding strain to fracture in plane stress condition is calculated by setting \(\sigma _3 =0\) and substituting into Eq. B.2 and Eq. B.4 to obtain a functional relation between the stress triaxiality and Lode angle parameter in the form
Rights and permissions
About this article
Cite this article
Paredes, M., Lian, J., Wierzbicki, T. et al. Modeling of plasticity and fracture behavior of X65 steels: seam weld and seamless pipes. Int J Fract 213, 17–36 (2018). https://doi.org/10.1007/s10704-018-0303-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-018-0303-x