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Analysis and design of dual-phase steel microstructure for enhanced ductile fracture resistance

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Abstract

The goal of this paper is to predict how the properties of the constituent phases and microstructure of dual phase steels (consisting of ferrite and martensite) influence their fracture resistance. We focus on two commercial low-carbon dual-phase (DP) steels with different ferrite/martensite phase volume fractions and properties. These steels exhibit similar flow behavior and tensile strength but different ductility. Our experimental observations show that the mechanism of ductile fracture in these two DP steels involves nucleation, growth and coalescence of micron scale voids. We thus employ microstructure-based finite element simulations to analyze the ductile fracture of these dual-phase steels. In the microstructure-based simulations, the individual phases of the DP steels are discretely modeled using elastic-viscoplastic constitutive relations for progressively cavitating solids. The flow behavior of the individual phases in both the steels are determined by homogenizing the microscale calibrated crystal plasticity constitutive relations from a previous study (Chen et al. in Acta Mater 65:133–149, 2014) while the damage parameters are determined by void cell model calculations. We then determine microstructural effects on ductile fracture of these steels by analyzing a series of representative volume elements with varying volume fractions, flow and damage behaviors of the constituent phases. Our simulations predict qualitative features of the ductile fracture process in good agreement with experimental observations for both DP steels. A ‘virtual’ DP microstructure, constructed by varying the microstructural parameters in the commercial steels, is predicted to have strength and ductile fracture resistance that is superior to the two commercial DP steels. Our simulations provide guidelines for improving the ductile fracture resistance of DP steels.

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References

  • Andrade F, Feucht M, Haufe A, Neukamm F (2016) An incremental stress state dependent damage model for ductile failure prediction. Int J Fract 200:127–150

    Article  Google Scholar 

  • Avramovic-Cingara G, Ososkov Y, Jain M, Wilkinson D (2009a) Effect of martensite distribution on damage behaviour in DP600 dual phase steels. Mater Sci Eng A 516:7–16

    Article  Google Scholar 

  • Avramovic-Cingara G, Saleh CA, Jain M, Wilkinson D (2009b) Void nucleation and growth in dual-phase steel 600 during uniaxial tensile testing. Metall Mater Trans A 40:3117–3127

    Article  Google Scholar 

  • Ayatollahi M, Darabi AC, Chamani H, Kadkhodapour J (2016) 3D micromechanical modeling of failure and damage evolution in dual phase steel based on a real 2D microstructure. Acta Mech Solida Sin 29:95–110

    Article  Google Scholar 

  • Bai Y, Wierzbicki T (2010) Application of extended Mohr–Coulomb criterion to ductile fracture. Int J Fract 161:1–20

    Article  Google Scholar 

  • Bao YB, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98. doi:10.1016/j.ijmecsci.2004.02.006

    Article  Google Scholar 

  • Bareggi A, Maire E, Bouaziz O, Di Michiel M (2012) Damage in dual phase steels and its constituents studied by X-ray tomography. Int J Fract 174:217–227

    Article  Google Scholar 

  • Benzerga A, Leblond J-B, Needleman A, Tvergaard V (2016) Ductile failure modeling. Int J Fract 201:29–80

    Article  Google Scholar 

  • Bhattacharya D (2011) Metallurgical perspectives on advanced sheet steels for automotive applications. In: Weng Y, Dong H, Gan Y (eds) Advanced steels. Springer, Berlin, pp 163–175. doi:10.1007/978-3-642-17665-4_18

    Chapter  Google Scholar 

  • Björklund O, Nilsson L (2014) Failure characteristics of a dual-phase steel sheet. J Mater Process Technol 214:1190–1204

    Article  Google Scholar 

  • Chen P, Ghassemi-Armaki H, Kumar S, Bower A, Bhat S, Sadagopan S (2014) Microscale-calibrated modeling of the deformation response of dual-phase steels. Acta Mater 65:133–149

    Article  Google Scholar 

  • Choi KS, Liu WN, Sun X, Khaleel MA (2009) Influence of martensite mechanical properties on failure mode and ductility of dual-phase steels. Metall Mater Trans A 40:796–809

    Article  Google Scholar 

  • Chu C, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol 102:249

    Article  Google Scholar 

  • Dassault Systemes Simulia Corp. (2010) Abaqus user’s manual version 6.10. Providence, RI, USA

  • Davis JR (1996) Carbon and alloy steels. ASM speciality handbook. ASM International, Materials Park

    Google Scholar 

  • De Moor E, Gibbs P, Speer J, Matlock D, Schroth J (2010) Strategies for third-generation advanced high-strength steel development. AIST Trans 7:133–144

    Google Scholar 

  • Drucker DC (1957) A definition of stable inelastic material. DTIC document. Brown University, Providence

    Book  Google Scholar 

  • Faleskog J, Gao X, Shih CF (1998) Cell model for nonlinear fracture analysis—I. Micromechanics calibration. Int J Fract 89:355–373

    Article  Google Scholar 

  • Gerbig D, Bower A, Savic V, Hector LG (2016) Coupling digital image correlation and finite element analysis to determine constitutive parameters in necking tensile specimens. Int J Solids Struct 97:496–509

    Article  Google Scholar 

  • 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. doi:10.1115/1.3443401

    Article  Google Scholar 

  • Hancock J, Mackenzie A (1976) On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J Mech Phys Solids 24:147–160

    Article  Google Scholar 

  • Horvath C, Fekete J (2004) Opportunities and challenges for increased usage of advanced high strength steels in automotive applications. In: Proceedings of international conference on advanced high strength sheet steels for automotive applications, AIST Golden CO, USA

  • Huang S, He C, Zhao Y (2016) Microstructure-based RVE approach for stretch-bending of dual-phase steels. J Mater Eng Perform 25:966–976

    Article  Google Scholar 

  • Joly P, Cozar R, Pineau A (1990) Effect of crystallographic orientation of austenite on the formation of cleavage cracks in ferrite in an aged duplex stainless steel. Scr Metall Mater 24:2235–2240

    Article  Google Scholar 

  • Krauss G (1990) Steels: heat treatment and processing principles, vol 24. ASM International, Materials Park

    Google Scholar 

  • Lai Q et al (2015) Damage and fracture of dual-phase steels: Influence of martensite volume fraction. Mater Sci Eng A 646:322–331

    Article  Google Scholar 

  • Landron C, Bouaziz O, Maire E, Adrien J (2010) Characterization and modeling of void nucleation by interface decohesion in dual phase steels. Scr Mater 63:973–976

    Article  Google Scholar 

  • Landron C, Maire E, Bouaziz O, Adrien J, Lecarme L, Bareggi A (2011) Validation of void growth models using X-ray microtomography characterization of damage in dual phase steels. Acta Mater 59:7564–7573

    Article  Google Scholar 

  • Lecarme L, Maire E, Kc AK, De Vleeschouwer C, Jacques L, Simar A, Pardoen T (2014) Heterogenous void growth revealed by in situ 3-D X-ray microtomography using automatic cavity tracking. Acta Mater 63:130–139

    Article  Google Scholar 

  • Luo M, Wierzbicki T (2010) Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model. Int J Solids Struct 47:3084–3102

    Article  Google Scholar 

  • Maire E, Bouaziz O, Di Michiel M, Verdu C (2008) Initiation and growth of damage in a dual-phase steel observed by X-ray microtomography. Acta Mater 56:4954–4964

    Article  Google Scholar 

  • Marcadet SJ, Mohr D (2015) Effect of compression-tension loading reversal on the strain to fracture of dual phase steel sheets. Int J Plast 72:21–43

    Article  Google Scholar 

  • Marya M, Wang K, Hector LG, Gayden X (2006) Tensile-shear forces and fracture modes in single and multiple weld specimens in dual-phase steels. J Manuf Sci Eng 128:287–298

    Article  Google Scholar 

  • Matsuno T, Teodosiu C, Maeda D, Uenishi A (2015) Mesoscale simulation of the early evolution of ductile fracture in dual-phase steels. Int J Plast 74:17–34

    Article  Google Scholar 

  • Mirza M, Barton D, Church P (1996) The effect of stress triaxiality and strain-rate on the fracture characteristics of ductile metals. J Mater Sci 31:453–461

    Article  Google Scholar 

  • Osovski S, Srivastava A, Williams J, Needleman A (2015) Grain boundary crack growth in metastable titanium \(\beta \) alloys. Acta Mater 82:167–178

    Article  Google Scholar 

  • Paul SK (2012) Micromechanics based modeling of dual phase steels: prediction of ductility and failure modes. Comput Mater Sci 56:34–42

    Article  Google Scholar 

  • Perzyński K, Madej Ł, Wang J, Kuziak R, Hodgson PD (2014) Numerical investigation of influence of the martensite volume fraction on DP steels fracture behavior on the basis of digital material representation model. Metall Mater Trans A 45:5852–5865

    Article  Google Scholar 

  • Rashid M (1981) Dual phase steels. Annu Rev Mater Sci 11:245–266

    Article  Google Scholar 

  • Roberts S, Noronha S, Wilkinson A, Hirsch P (2002) Modelling the initiation of cleavage fracture of ferritic steels. Acta Mater 50:1229–1244

    Article  Google Scholar 

  • Roth CC, Mohr D (2014) Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: experiments and modeling. Int J Plast 56:19–44

    Article  Google Scholar 

  • Sachdev AK (1983) Effect of retained austenite on the yielding and deformation behavior of a dual phase steel. Acta Metall 31:2037–2042

    Article  Google Scholar 

  • Savic V, Hector L Jr, Fekete J (2010) Digital image correlation study of plastic deformation and fracture in fully martensitic steels. Exp Mech 50:99–110

    Article  Google Scholar 

  • Savic V, Hector LG (2007) Tensile deformation and fracture of press hardened boron steel using digital image correlation. SAE Technical Paper

  • Srivastava A, Bower AF, Hector LG Jr, Carsley JE, Zhang L, Abu-Farha F (2016) A multiscale approach to modeling formability of dual-phase steels. Modell Simul Mater Sci Eng 24:025011

    Article  Google Scholar 

  • Srivastava A, Ghassemi-Armaki H, Sung H, Chen P, Kumar S, Bower AF (2015) Micromechanics of plastic deformation and phase transformation in a three-phase TRIP-assisted advanced high strength steel: experiments and modeling. J Mech Phys Solids 78:46–69

    Article  Google Scholar 

  • Srivastava A, Ponson L, Osovski S, Bouchaud E, Tvergaard V, Needleman A (2014) Effect of inclusion density on ductile fracture toughness and roughness. J Mech Phys Solids 63:62–79

    Article  Google Scholar 

  • Steinbrunner DL, Matlock D, Krauss G (1988) Void formation during tensile testing of dual phase steels. Metall Trans A 19:579–589

    Article  Google Scholar 

  • Sun D-Z, Andrieux F, Feucht M (2009a) Damage modelling of a TRIP steel for integrated simulation from deep drawing to crash. In: Proceedings of 7th European LS-DYNA user conference

  • Sun X, Choi KS, Liu WN, Khaleel MA (2009b) Predicting failure modes and ductility of dual phase steels using plastic strain localization. Int J Plast 25:1888–1909

    Article  Google Scholar 

  • Sun X, Choi KS, Soulami A, Liu WN, Khaleel MA (2009c) On key factors influencing ductile fractures of dual phase (DP) steels. Mater Sci Eng A 526:140–149

    Article  Google Scholar 

  • Tekoğlu C, Hutchinson J, Pardoen T (2015) On localization and void coalescence as a precursor to ductile fracture. Phil Trans R Soc A 373:20140121

    Article  Google Scholar 

  • Tong W, Tao H, Zhang N, Jiang X, Marya MP, Hector LG Jr, Gayden XQ (2005) Deformation and fracture of miniature tensile bars with resistance-spot-weld microstructures. Metall Mater Trans A 36:2651–2669

    Article  Google Scholar 

  • Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17:389–407

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32:157–169

    Article  Google Scholar 

  • Uthaisangsuk V, Prahl U, Bleck W (2008a) Micromechanical modelling of damage behaviour of multiphase steels. Comput Mater Sci 43:27–35

    Article  Google Scholar 

  • Uthaisangsuk V, Prahl U, Bleck W (2009a) Characterisation of formability behaviour of multiphase steels by micromechanical modelling. Int J Fract 157:55–69. doi:10.1007/s10704-009-9329-4

    Article  Google Scholar 

  • Uthaisangsuk V, Prahl U, Bleck W (2009b) Failure modeling of multiphase steels using representative volume elements based on real microstructures. Proc Eng 1:171–176

    Article  Google Scholar 

  • Uthaisangsuk V, Prahl U, Bleck W (2011) Modelling of damage and failure in multiphase high strength DP and TRIP steels. Eng Fract Mech 78:469–486

    Article  Google Scholar 

  • Uthaisangsuk V, Prahl U, Munstermann S, Bleck W (2008b) Experimental and numerical failure criterion for formability prediction in sheet metal forming. Comput Mater Sci 43:43–50. doi:10.1016/j.commatsci.2007.07.036

    Article  Google Scholar 

  • Vajragupta N, Uthaisangsuk V, Schmaling B, Münstermann S, Hartmaier A, Bleck W (2012) A micromechanical damage simulation of dual phase steels using XFEM. Comput Mater Sci 54:271–279

    Article  Google Scholar 

  • Wang L, Li M, Almer J (2014) Investigation of deformation and microstructural evolution in Grade 91 ferritic-martensitic steel by in situ high-energy X-rays. Acta Mater 62:239–249. doi:10.1016/j.actamat.2013.10.003

    Article  Google Scholar 

  • Wierzbicki T, Bao Y, Lee Y-W, Bai Y (2005) Calibration and evaluation of seven fracture models. Int J Mech Sci 47:719–743

    Article  Google Scholar 

  • Yerra S, Martin G, Veron M, Brechet Y, Mithieux J, Delannay L, Pardoen T (2013) Ductile fracture initiated by interface nucleation in two-phase elastoplastic systems. Eng Fract Mech 102:77–100

    Article  Google Scholar 

  • Zavattieri P, Savic V, Hector L, Fekete J, Tong W, Xuan Y (2009) Spatio-temporal characteristics of the Portevin–Le Châtelier effect in austenitic steel with twinning induced plasticity. Int J Plast 25:2298–2330

    Article  Google Scholar 

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Acknowledgements

The work reported in this report was supported by General Motors though the GM/Brown Collaborative Research Laboratory on Computational Materials Research. The computational resources and services of the Center for Computation and Visualization, Brown University are gratefully acknowledged. The DP980 and DF140T sheet steels were kindly provided by Dr. S. Bhat of ArcelorMittal. The authors are very grateful for the many fruitful discussions with Drs. S. Bhat and S. Sadagopan of ArcelorMittal and Dr. A.K. Sachdev of General Motors.

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Correspondence to Ankit Srivastava.

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Gerbig, D., Srivastava, A., Osovski, S. et al. Analysis and design of dual-phase steel microstructure for enhanced ductile fracture resistance. Int J Fract 209, 3–26 (2018). https://doi.org/10.1007/s10704-017-0235-x

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  • DOI: https://doi.org/10.1007/s10704-017-0235-x

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