The co-operative role of voids and shear bands in strain localization during bending

Lievers, W. B.; Pilkey, A. K.; Worswick, M. J.

Affiliations

¹Centre for Automotive Materials and Manufacturing, 945 Princess Street, Kingston, Ont., Canada K7L 5L9

²Department of Mechanical Engineering, Queen’s University, Nicol Hall, Union Street, Kingston, Ont., Canada K7L 3N6

³Department of Mechanical Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

Abstract and keywords

The use of kinematic hardening is known to promote shear band formation as a result of increased yield surface curvature. Hence, the implementation of kinematic hardening in a Gurson-type model facilitates the combined effect of shear bands and voids on strain localization behaviour. An alternative formulation of the kinematic hardening Gurson–Tvergaard–Needleman (GTN) constitutive softening equations is presented herein. The resulting equations are implemented as a user material subroutine (umat) in the commercial finite element code LS-DYNA and the implementation is verified against published results. A numerical study is used to establish the role of various GTN parameters in the development of macroscopic shear localization during bending.

Keywords: Kinematic hardening; Gurson; Shear bands; Localization; Void damage; FEM

Links

DOI: 10.1016/S0167-6636(02)00275-2

WoS: 000182006600005

Cited Works (23)

Year	Entry
1982	Triantafyllidis N, Needleman A, Tvergaard V. On the development of shear bands in pure bending. Int J Solids Struct. 1982;18(2):121-138.
1985	Mear ME, Hutchinson JW. Influence of yield surface curvature on flow localization in dilatant plasticity. Mech Mater. 1985;4(3-4):395-407.
1955	Prager W. The theory of plasticity: a survey of recent achievements. Proc Inst Mech Eng. 1955;169:41-57.
1981	Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions. Int J Fract. 1981;17(4):389-407.
1992	Becker R. An analysis of shear localization during bending of a polycrystalline sheet. J Appl Mech. 1992;59(3):491-496.
1984	Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 1984;32(1):157-169.
1987	Tvergaard V. Effect of yield surface curvature and void nucleation on plastic flow localization. J Mech Phys Solids. 1987;35(1):43-60.
1977	Gurson AL. Continuum theory of ductile rupture by void nucleation and growth, I: yield criteria and flow rules for porous ductile media. J Eng Mater Technol. 1977;99(1):2-15.
1998	Worswick MJ, Pelletier P. Numerical simulation of ductile fracture during high strain rate deformation. Euro Phys J Appl Phys. 1998;4(3):257-267.
1982	Saje M, Pan J, Needleman A. Void nucleation effects on shear localization in porous plastic solids. Int J Fract. 1982;19(3):163-182.
1981	Hutchinson JW, Tvergaard V. Shear band formation in plane strain. Int J Solids Struct. 1981;17(5):451-470.
1981	Tvergaard V, Needleman A, Lo KK. Flow localization in the plane strain tensile test. J Mech Phys Solids. 1981;29(2):115-142.
1987	Tvergaard V. Ductile shear fracture at the surface of a bent specimen. Mech Mater. 1987;6(1):53-69.
1996	Zhang ZL. A sensitivity analysis of material parameters for the Gurson constitutive model. Fatigue Fract Eng Mater Struct. 1996;19(5):561-570.
1979	Morris L, Kenny L, Ryvola M. A metallographic examination of the failure of thin sheet during bending. In: Microstructural Science. Vol 7. Proceedings of the 11th annual technical meeting of the International Metallographic Society; 1979.59-67.
2000	Hildebrand BG, Sterling SG, Price MA. An evaluation of three material models used in the finite element simulation of a sheet stretching process. J Mater Proc Technol. 2000;103(1):57-64.
1980	Chu CC, Needleman A. Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol. 1980;102(3):249-256.
1982	Steninger J, Melander A. The relation between bendability, tensile properties and particle structure of low carbon steel. Scand J Metall. 1982;11(2):55-71.
1959	Ziegler H. A modification of Prager’s hardening rule. Quart Appl Math. 1959;17:55-65.
1997	Tvergaard V, Needleman A. Nonlocal effects on localization in a void-sheet. Int J Solids Struct. 1997;34(18):2221-2238.
1986	Becker R, Needleman A. An analysis of shear localization during bending of a polycrystalline sheet. J Appl Mech. 1986;53(3):491-499.
1978	Akeret R. Failure mechanisms in the bending of aluminum sheets and limits of bendability. Aluminium. 1978;54(2):117-123.
1987	Aravas N. On the numerical integration of a class of pressure-dependent plasticity models. Int J Num Meth Eng. 1987;24(7):1395-1416.

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2008	Ben Bettaieb M, Lemoine X, Duchene L, Habraken AM. Study of bendability of steel sheets. Steel Res Int. 2008;79(sp. iss. 1):225-232.
2009	Ben Bettaieb M, Lemoine X, Duchêne L, Habraken AM. The role of void evolution on the bendability of steel sheets. In: Oñate E, Owen DRJ, eds. COMPLAS X: X International Conference on Computational Plasticity: Fundamentals and Applications. September 2-4, 2009; Barcelona, Spain.
2008	Chhibber R, Arora N, Gupta SR, Dutta BK. Estimation of Gurson material parameters in bimetallic weldments for the nuclear reactor heat transport piping system. Proc Inst Mech Eng Part C-J Eng Mech Eng Sci. 2008;222(12):2331-2349.
2004	Duan X, Metzger D, Jian M. Influence of yield criteria on the prediction of shear localization considering the inhomogeneous distribution of microstructure. In: Computer Technology and Applications. ASME/JSME 2004 Pressure Vessels and Piping Conference (PVP2004); July 25-29, 2004; San Diego, CA.59-65.
2015	Liimatainen M. The Effect of Microstructure on Bendability of Ultra-High Strength Steels [Master's thesis]. Tampere, Finland: Tampere University of Technology; March 2015.
2011	Mattei L. Pliabilité des tôles en alliages d'aluminium pour la carrosserie automobile: Analyse des mécanismes d'endommagement [PhD thesis]. École Nationale Supérieure des Mines de Saint-Étienne; February 22, 2011.
2006	Pilkey AK, Bayley CJ, Györffy M. Influence of surface defect geometry on the localization and failure of AA6111 sheet: necking versus shear. Mater Sci Forum. 2006;519-521:131-138.
2004	Worswick MJ, Chen Z, Pilkey K, Lloyd D. Damage percolation modeling in aluminum alloy sheet. In: Raabe D, Roters F, Barlat F, Chen L-Q, eds. Continuum Scale Simulation of Engineering Materials: Fundamentals - Microstructures - Process Applications. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA; 2004:805-816.
2004	Lievers WB, Pilkey AK, Lloyd DJ. Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys. Acta Mater. June 7, 2004;52(10):3001-3007.
2006	Kang J, Wilkinson DS, Jain M, Embury JD, Beaudoin AJ, Kim S, Mishira R, Sachdev AK. On the sequence of inhomogeneous deformation processes occurring during tensile deformation of strip cast AA5754. Acta Mater. January 1, 2006;54(1):209-218.
2008	Hu XH, Jain M, Wilkinson DS, Mishra RK. Microstructure-based finite element analysis of strain localization behavior in AA5754 aluminum sheet. Acta Mater. August 2008;56(13):3187-3201.
2014	Crété JP, Longère P, Cadou JM. Numerical modelling of crack propagation in ductile materials combining the GTN model and X-FEM. Comput Meth Appl Mech Eng. June 15, 2014;275:204-233.
2016	Klingbeil D, Svendsen B, Reusch F. Gurson-based modelling of ductile damage and failure during cyclic loading processes at large deformation. Eng Fract Mech. July 2016;160:95-123.
2011	Chhibber R, Biswas P, Arora N, Gupta SR, Dutta BK. Micromechanical modelling of weldments using GTN model. Int J Fract. 2011;167(1):71-82.
2007	Williams BW, Oliveira DA, Simha CHM, Worswick MJ, Mayer R. Crashworthiness of straight section hydroformed aluminium tubes. Int J Impact Eng. 2007;34(8):1451-1464.
2011	Ben Bettaieb M, Lemoine X, Bouaziz O, Habraken AM, Duchêne L. A finite element analysis of the bending and the bendability of metallic sheets. Int J Mater Form. 2011;4(3):283-297.
2022	Kumar A, Naveen KS, Arora KS, Singh H, Chhibber R. Micromechanical modelling of API X80 linepipe steel. Int J Press Vessel Pip. October 1, 2022;199:104755.
2012	Soyarslan C, Malekipour Gharbi M, Tekkay AE. A combined experimental-numerical investigation of ductile fracture in bending of a class of ferritic-martensitic steel. Int J Solids Struct. June 15, 2012;49(13):1608-1626.
2009	Reyes A, Eriksson M, Lademo O-G, Hopperstad OS, Langseth M. Assessment of yield and fracture criteria using shear and bending tests. Mater Des. 2009;30(3):596-608.
2012	Chhibber R, Singh H, Arora N, Dutta BK. Micromechanical modelling of reactor pressure vessel steel. Mater Des. April 2012;36:258-274.
2003	Lievers WB, Pilkey AK, Lloyd DJ. The influence of iron content on the bendability of AA6111 sheet. Mater Sci Eng. November 2003;A361(1-2):312-320.
2005	Bayley CJ, Pilkey AK. Influence of welding defects on the localization behaviour of an aluminum alloy tailor-welded blank. Mater Sci Eng. August 25, 2005;A403(1-2):1-10.
2006	Bayley CJ, Pilkey AK. A bifurcation criterion for predicting weld-line failures in AA5754 alloy tailor-welded blanks. Mater Sci Eng. November 5, 2006;A435-436:62-70.
2010	Ben Bettaieb M, Lemoine X, Duchêne L, Habraken AM. Simulation of the bending process of hardening metallic sheets using damage model, I: theoretical development and numerical implementation. Mater Sci Eng. 2010;A528(1):434-441.
2010	Ben Bettaieb M, Lemoine X, Duchêne L, Habraken AM. Simulation of the bending process of hardening metallic sheets using damage model, II: numerical investigations. Mater Sci Eng. 2010;A528(1):442-448.
2011	Davidkov A, Petrov RH, Smet PD, Schepers B, Kestens LAI. Microstructure controlled bending response in AA6016 Al alloys. Mater Sci Eng. August 25, 2011;A528(22-23):7068-7076.
2015	Mendoza I, Villalobos D, Alexandrov BT. Crack propagation of Ti alloy via adiabatic shear bands. Mater Sci Eng. October 1, 2015;A645:306-310.
2019	Muhammad W, Brahme AP, Ali U, Hirsch J, Engler O, Aretz H, Kang J, Mishra RK, Inal K. Bendability enhancement of an age-hardenable aluminum alloy, II: multiscale numerical modeling of shear banding and fracture. Mater Sci Eng. April 29, 2019;A754:161-177.
2004	Bayley CJ. Incorporating External and Internal Weld-Line Defects Into Ductility Predictions for AA5182 and AA5754 Tailor-Welded Blanks [PhD thesis]. Queen's University; April 2004.
2005	Donaldson AG. Modelling the Effect of Surface Roughness on the Localization and Failure Behaviour of AA6111 Sheet [Master's thesis]. Queen's University; April 2005.
2011	Sloan ADC. The Role of Non-Ferritic Phase in the Micro-Void Damage Accumulation and Failure of Dual-Phase Steels [Master's thesis]. Kingston, ON: Queen's University; September 2011.
2015	Hollenberg F. Bending Dual-Phase Steel: A Finite Element Analysis [Master's thesis]. Delft University of Technology; August 15, 2015.
2005	Baradari JG. Damage in Hydroforming of Pre-Bent Aluminum Alloy Tubes [PhD thesis]. University of Waterloo; 2005.
2005	Imbert Boyd JMS. Increased Formability and the Effects of the Tool/sheet Interaction in Electromagnetic Forming of Aluminum Alloy Sheet [Master's thesis]. Waterloo, ON: University of Waterloo; 2005.
2006	Orlov OS. A Three-Dimensional Damage Percolation Model [PhD thesis]. Waterloo, ON: University of Waterloo; 2006.
2007	Williams BW. A Study of the Axial Crush Response of Hydroformed Aluminum Alloy Tubes [PhD thesis]. Waterloo, ON: University of Waterloo; 2007.