[en] The main objective of this paper is to study the bendability of metallic sheets by using the finite element method. In this aim, two variants of an advanced Gurson-Tvergaard-Needleman model [1, 2] are implemented in the home made FE code LAGAMINE [3, 4] and coupled with the Thomason model to predict the coalescence of voids. This advanced model is an extension of the original one to take into account of the plastic anisotropy and the mixed (isotropic + kinematic) hardening of the matrix. The difference between the two variants is related to the modeling of the damage evolution. As the advanced model is used to study the bending process, its yield function is slightly modified in order to take into account the loadings with negative triaxiality ratios. These present implementations are used to simulate the pure bending process and to predict the bendability of dual phase (DP) steel. The combined effect of an initial geometrical imperfection and damage evolution on the bendability is also studied.
Disciplines :
Materials science & engineering
Author, co-author :
Ben Bettaieb, Mohamed ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Département Argenco : Secteur MS2F
Lemoine, Xavier
Bouaziz, O.
Habraken, Anne ; Université de Liège - ULiège > Département ArGEnCo > Département ArGEnCo
Duchene, Laurent ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Analyse multi-échelles des matériaux et struct. du gén. civ.
Language :
English
Title :
A finite element analysis of the bending and the bendability of metallic sheets
Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth, 1. Yield criteria and flow rules for porous ductile media. J Eng Mater-T ASME 99: 2-15.
Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fracture 17: 389-407.
Zhu YY, Cescotto S, Habraken AM (1992) A fully coupled elastoplastic damage modeling and fracture criteria in metal forming processes. J Eng Mater-T ASME 32: 197-204.
Zhu YY, Cescotto S (1995) A fully coupled elasto-visco-plastic damage theory for anisotropic materials. Int J Solids Struct 32: 1607-1641.
Borah U, Venugopal S, Nagarajan R, Sivaprasad PV, Venugopal S, Raj B (2008) Estimation of springback in double-curvature forming of plates: experimental evaluation and process modeling. Int J Mech Sci 50: 704-718.
Hama T, Nagata T, Teodosiu C, Makinouchi A, Takuda H (2008) Finite-element simulation of springback in sheet metal forming using local interpolation for tool surfaces. Int J Mech Sci 50: 175-192.
Jeunechamps PP, Ho KC, Lin J, Ponthot JP, Dean TA (2006) A closed form technique to predict springback in creep age-forming. Int J Mech Sci 48: 621-629.
Gan W, Wagoner RH (2004) Die design method for sheet springback. Int J Mech Sci 46: 1097-1113.
Yoshida F, Uemori T (2003) A model of large-strain cyclic plasticity and its application to springback simulation. Int J Mech Sci 45: 1687-1702.
Jain M, Allin J, Bull MJ (1998) Deep drawing characteristics of automotive aluminum alloys. Mat Sci Eng A-Struct 256: 69-82.
Sarkar J, Kutty TRG, Conlon KT, Wilkinson DS, Embury JD, Lloyd DJ (2001) Tensile and bending properties of AA5754 aluminium alloys. Mat Sci Eng A-Struct 316: 52-59.
Lievers WB, Pilkey AK, Lloyd DJ (2003) The influence of iron content on the bendability of AA6111 sheet. Mat Sci Eng A-Struct 361: 312-320.
Sarkar J, Kutty TRG, Wilkinson DS, Embury JD, Lloyd DJ (2004) Tensile properties and bendability of T4 treated AA6111 aluminum alloys. Mat Sci Eng A-Struct 369: 258-266.
Rossi B, Habraken AM, Pascon F (2007) On the evaluation of the through thickness residual stresses distribution of cold formed profiles. Proceedings of the 10th ESAFORM Conference on Material Forming, Zaragoza, pp 570-577.
Lievers WB, Pilkey AK, Worswick M (2003) The cooperative role of voids and shear bands in strain localization during bending. Mech Mater 35: 661-674.
Chien WY, Pan J, Tang SC (2004) A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions. Int J Plasticity 20: 1953-1981.
Kuroda M, Tvergaard V (2004) Shear band development in anisotropic bent specimens. Eur J Mech A-Solid 23: 811-821.
Kuroda M, Tvergaard V (2007) Effects of texture on shear band formation in plane strain tension/compression and bending. Int J Plasticity 23: 244-272.
Wang X (1993) Modélisation numérique des problèmes avec localisation de la déformation en bandes de cisaillement. Ph. D. thesis, University of Liège (Belgium).
Hambli R, Mkadem A, Potiron A (2004) Finite element damage modeling in bending processes. J Mater Process Tech 147: 302-310.
Ben Bettaieb M, Lemoine X, Bouaziz O, Habraken AM. Numerical simulation of damage in DP steels validated by X-ray tomography measurements, submitted to publication in Mech Mat.
Bouaziz O, Maire E, Giton M, Lamarre J, Salingue Y, Dimichiele M (2008) A model for initiation and growth of damage in dualphase steels identified by X-ray micro-tomography. Rev Metall 2: 102-107.
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.
Aravas N (1987) On the numerical integration of a class of pressure-dependent plasticity models. Int J Numer Meth Eng 24: 1395-1416.
Ben Bettaieb M, Lemoine X, Duchêne L, Habraken AM (2010) On the numerical integration of an advanced Gurson model, accepted for publication in Int J Numer Meth Eng.
Miehe C (1996) Numerical computation of algorithmic (consistent) tangent moduli in large strain computational inelasticity. Comput Method Appl M 134: 223-240.
Triantafyllidis N, Needleman A, Tvergaard V (1982) On the development of shear bands in pure bending. Int J Solids Struct 18: 121-138.
Kuroda M, Ikawa S (2004) Texture optimization of rolled aluminum alloy sheets using a genetic algorithm. Mat Sci Eng A-Struct 385: 235-244.
Besson J (2009) Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms. Int J Plasticity 11: 2204-2221.
Arndt S, Svendsen B, Klingbeil D (1997) Modellierung der Eigenspannungen and der Rißspitze mit einem Schägigungsmodell. Tech Mech 17: 323-332.
Mühlich U, Brocks W (2003) On the numerical integration of a class of pressure-dependant plasticity models including kinematic hardening. Comput Mech 31: 479-488.
Helbert AL, Feaugas X, Clavel M (1996) The Influence of the Back Stress (X) and the Hardening Rate (dX/xεpeg) on void Nucleation in α/β Titanium Alloys. J Phys-PARIS 6: 101-111.
Helbert AL, Feaugas X, Clavel M (1999) The influence of internal stresses on the fracture toughness of α/β titanium alloys. Metall Mater Trans A 30: 2853-2863.
Huez J, Helbert A, Feaugas X, Guillot I, Clavel M (1998) Damage process in commercially pure α-titanium alloy without (Ti40) and with (Ti40-H) hydrides. Metall Mater Trans A 29: 1615-1628.
Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17: 201-217.
Thomason PF (1990) Ductile fracture of metals. Pergamon, Oxford.
Zhang ZL, Thaulow C, Ødegård J (2000) A complete Gurson model approach for ductile fracture. Eng Fract Mech 67: 155-168.
Betegón C, del Coz JJ (2006) Peñuelas I. Comput Method Appl M 195: 6146-6157.
Simo JC, Hughes TJR (1986) On the variational foundations of assumed strain methods. J Appl Mech, ASME 53: 51-54.
Li KP, Cescotto S (1997) An 8-node brick element with mixed formulation for large deformation analyses. Comput Methods Appl Mech Engrg 141: 157-204.
Duchêne L, de Montleau P, El Houdaigui F, Bouvier S, Habraken AM (2005) Analysis of texture evolution and hardening behavior during deep drawing with an improved mixed type FEM element. In: Smith LM, Pourboghrat F, Yoon J-W, Stoughton TB (Eds) Proceedings of int. Conf. NUMISHEET 2005, Melville (New York), 1, p 409-414.
Choi Y, Han C-S, Lee JK, Wagoner RH (2006) Modeling multi-axial deformation of planar anisotropic elasto-plastic materials, part I: Theory. Int J Plasticity 22(9): 1745-1764.
Cescotto S (1984) Finite deformation of solids. In: Hartley P, Pillinger I, Sturgess C (Eds) Numerical modelling of material deformation processes. Spinger-Verlag, pp 20-67.
Munhoven S, Habraken AM (1995) Application of an anisotropic yield locus based on texture to a deep drawing simulation. In: Shen SE, Dawson PR (Eds) Proceedings of the International Conference NUMIFORM 95 (Simulation of Materials Processing: Theory, Methods and Applications), Balkema, Rotterdam.
de Montleau P, Habraken AM, Duchêne L (2008) A new finite element integration scheme. Application to a simple shear test of anisotropic material. Int J Numer Meth Eng 73: 1395-1412.
Jagota A, Hui CY, Dawson PR (1987) The determination of fracture toughness for a porous elastic-plastic solid. Int J Fracture 33: 111-124.
Tvergaard V, Vadillo G (2007) Influence of porosity on cavitation instability predictions for elastic-plastic solids. Int J Mech Sci 49: 210-216.
Ragab AR, Saleh ChA (2005) Evaluation of bendability of sheet metals using void coalescence models. Mat Sci Eng A-Struct 395: 102-109.
Chakrabarty J, Lee WB, Chan KC (2004) An analysis of the plane-strain bending of an orthotropic sheet in the elastic/plastic range. J Mater Process Tech 104: 48-52.
Chakrabarty J, Lee WB, Chan KC (2001) An exact solution for the elastic/plastic bending of anisotropic sheet metal under conditions of plane strain. Int J Mech Sci 43: 1871-1880.
Ben Bettaieb M, Lemoine X, Duchêne L, Habraken AM (2008) Study of bendability of steel sheets. Steel Res Int 79: 225-232.
Zhang ZT, Hu SJ (1998) Stress and residual stress distributions in plane strain bending. Int J Mech Sci 40: 533-543.
Zhang ZT, Lee D (1995) Development of a new model for plane strain bending and spring-back analysis. J Mater Eng Perform 4: 291-300.
Tvergaard V (1987) Effect of yield surface curvature and void nucleation on plastic flow localization. J Mech Phys Solids 35: 43-60.