Damage characterization in a ferritic steel sheet: Experimental tests, parameter identification and numerical modeling

Digital image correlation; Ductile fracture; Finite element method; Gurson model; Strain localization; Curve fitting; Damage detection; Ferrite; Ferritic steel; Hardening; Image analysis; Inverse problems; Nucleation; Sensitivity analysis; Steel sheet; Steel testing; Strain measurement; Damage characterization; Digital image correlations; Experimental evidence; Force-displacement curves; Gurson modeling; Isotropic-kinematic hardening; Strain distributions; Strain localizations; Parameter estimation

Abstract :

[en] The Gurson–Tvergaard–Needleman (GTN) model includes several parameters of different nature. Some of them have micromechanical roots while others are strictly phenomenological. Hence, a methodology should be developed in order to obtain a robust set of parameters with both numerical and physical meaning. The material parameters of the GTN model are found using an identification methodology based on experimental-numerical results. The method is applied on a DC01 ferritic steel sheet. An extended version of the Gurson model, incorporating plastic anisotropy, mixed isotropic-kinematic hardening, void nucleation, growth, coalescence and shear is used. Material parameters are obtained based on an inverse optimization and a sensitivity analysis on specimens with different geometries. The onset of coalescence, reflected as the loss of load carrying capacity in the force-displacement curve, is correctly predicted by the extended GTN model. The strain distribution, obtained by digital image correlation, is also correctly simulated. Nevertheless, the model does not to predict the increase of strain observed experimentally, because of the decoupling between hardening and the damage variable. In this respect, the article provides experimental evidence of the limitations of a GTN model based on a strain-controlled nucleation law with heuristic extensions of hardening. © 2018 Elsevier Ltd

Disciplines :

Materials science & engineering

Author, co-author :

Felipe Guzmán, C.; Departamento de Ingeniería en Obras Civiles, Universidad de Santiago de Chile, Av. Ecuador 3659, Estación Central, Santiago, Chile

Saavedra Flores, E. I.; Departamento de Ingeniería en Obras Civiles, Universidad de Santiago de Chile, Av. Ecuador 3659, Estación Central, Santiago, Chile

Habraken, Anne ; Université de Liège - ULiège > Département ArGEnCo > Département ArGEnCo

Language :

English

Title :

Damage characterization in a ferritic steel sheet: Experimental tests, parameter identification and numerical modeling

Publication date :

2018

Journal title :

International Journal of Solids and Structures

ISSN :

0020-7683

eISSN :

1879-2146

Publisher :

Elsevier Ltd

Volume :

155

Pages :

109-122

Peer reviewed :

Peer Reviewed verified by ORBi

Name of the research project :

2.5020.11; REGULAR No.; 1160691; USA1799_SE162814

Funders :

CONICYT - Comisión Nacional de Investigación Científica y Tecnológica

Available on ORBi :

since 04 February 2019

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Bibliography

Armstrong, P., Frederick, C.O., A Mathematical Representation of the Multiaxial Bauschinger Effect. CEGB Report RD/B/N731, 1966.
Ben Bettaieb, M., Lemoine, X., Duchêne, L., Habraken, A.-M., On the numerical integration of an advanced Gurson model. Int. J. Numer. Methods Eng. 85:8 (2011), 1049–1072, 10.1002/nme.3010.
Benzerga, A.A., Besson, J., Plastic potentials for anisotropic porous solids. Eur. J. Mech. - A/Solids 20:3 (2001), 397–434, 10.1016/S0997-7538(01)01147-0.
Benzerga, A.A., Leblond, J.-B., Ductile fracture by void growth to coalescence. Adv. Appl. Mech. 44 (2010), 169–305, 10.1016/S0065-2156(10)44003-X.
Benzerga, A.A., Leblond, J.-b., Needleman, A., Tvergaard, V., Ductile failure modeling. Int. J. Fract. 201:1 (2016), 29–80, 10.1007/s10704-016-0142-6.
Besson, J., Model identification. Besson, J., (eds.) Local Approach to Fract, 2004, Presses de l'Ecole des Mines, Paris, France, 373–394 Chapter XII.
Buljac, A., Shakoor, M., Neggers, J., Bernacki, M., Bouchard, P.-O., Helfen, L., Morgeneyer, T.F., Hild, F., Experimental-numerical validation framework for micromechanical simulations. Sorić, J., Wriggers, P., Allix, O., (eds.) Multiscale Model. Heterog. Struct, 2018, Springer International Publishing, 147–161, 10.1007/978-3-319-65463-8_8.
Cescotto, S., Grober, H., Calibration and application of an elastic viscoplastic constitutive equation for steels in hot-rolling conditions. Eng. Comput. 2:2 (1985), 101–106, 10.1108/eb023607.
Chaboche, J.-L., Viscoplastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. L'Academie Pol. des Sci. Série Sci. Tech. 1977 25:1977 (1975), 33–41.
Chalal, H., Abed-Meraim, F., Hardening effects on strain localization predictions in porous ductile materials using the bifurcation approach. Mech. Mater. 91 (2015), 152–166, 10.1016/j.mechmat.2015.07.012.
Chu, C.C., Needleman, A., Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol., 102(3), 1980, 249, 10.1115/1.3224807.
Duchêne, L., El Houdaigui, F., Habraken, A.-M., Elhoudaigui, F., Length changes and texture prediction during free end torsion test of copper bars with FEM and remeshing techniques. Int. J. Plast. 23:8 (2007), 1417–1438, 10.1016/j.ijplas.2007.01.008.
Dunand, M., Mohr, D., Hybrid experimental-numerical analysis of basic ductile fracture experiments for sheet metals. Int. J. Solids Struct. 47:9 (2010), 1130–1143, 10.1016/j.ijsolstr.2009.12.011.
Dunand, M., Mohr, D., On the predictive capabilities of the shear modified Gurson and the modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and Lode angles. J. Mech. Phys. Solids 59:7 (2011), 1374–1394, 10.1016/j.jmps.2011.04.006.
Dunand, M., Mohr, D., Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading. Eng. Fract. Mech. 78:17 (2011), 2919–2934, 10.1016/j.engfracmech.2011.08.008.
Eyckens, P., van Bael, A., van Houtte, P., An extended Marciniak-Kuczynski model for anisotropic sheet subjected to monotonic strain paths with through-thickness shear. Int. J. Plast. 27:10 (2011), 1577–1597, 10.1016/j.ijplas.2011.03.008.
Faleskog, J., Gao, X., Shih, C.F., Cell model for nonlinear fracture analysis - I. Micromechanics calibration. Int. J. Fract. 89:4 (1998), 355–373, 10.1023/A:1007421420901.
Flores, P., Duchêne, L., Bouffioux, C., Lelotte, T., Henrard, C., Pernin, N., van Bael, A., He, S., Duflou, J.R., Habraken, A.-M., Model identification and FE simulations: effect of different yield loci and hardening laws in sheet forming. Int. J. Plast. 23:3 (2007), 420–449, 10.1016/j.ijplas.2006.05.006.
Frederick, C.O., Armstrong, P., A mathematical representation of the multiaxial Bauschinger effect. Mater. High Temp. 24:1 (2007), 1–26, 10.3184/096034007X207589.
Geuzaine, C., Remacle, J.-F., Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79:11 (2009), 1309–1331, 10.1002/nme.2579.
Gilles, G., Hammami, W., Libertiaux, V., Cazacu, O., Yoon, J.W., Kuwabara, T., Habraken, A.-M., Duchêne, L., Experimental characterization and elasto-plastic modeling of the quasi-static mechanical response of TA-6V at room temperature. Int. J. Solids Struct. 48:9 (2011), 1277–1289, 10.1016/j.ijsolstr.2011.01.011.
Gurson, A.L., 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(1), 1977, 2, 10.1115/1.3443401.
Guzmán, C.F., Experimental and numerical characterization of damage and application to incremental forming, 2016, Université de Liège Ph.D. thesis.
Hancock, J., Brown, D., On the role of strain and stress state in ductile failure. J. Mech. Phys. Solids 31:1 (1983), 1–24, 10.1016/0022-5096(83)90017-0.
Hasegawa, T., Yakou, T., Karashima, S., Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium. Mater. Sci. Eng. 20 (1975), 267–276, 10.1016/0025-5416(75)90159-7.
Hill, R., A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. A Math. Phys. Eng. Sci. 193:1033 (1948), 281–297, 10.1098/rspa.1948.0045.
Kim, J., Gao, X., Srivatsan, T.S., Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Eng. Fract. Mech. 71:3 (2004), 379–400, 10.1016/S0013-7944(03)00114-0.
Landron, C., Maire, É., Bouaziz, O., Adrien, J., Lecarme, L., Bareggi, A., Validation of void growth models using X-ray microtomography characterization of damage in dual phase steels. Acta Mater. 59:20 (2011), 7564–7573, 10.1016/j.actamat.2011.08.046.
Lassance, D., Fabregue, D., Delannay, F., Pardoen, T., Micromechanics of room and high temperature fracture in 6xxx Al alloys. Prog. Mater. Sci. 52:1 (2007), 62–129, 10.1016/j.pmatsci.2006.06.001.
Leblond, J.-b., Perrin, G., Introduction à la mécanique de la rupture ductile des métaux. 1996, Cours de l’École Polytechnique, Palaiseau, France.
Leblond, J.-B., Perrin, G., Devaux, J., An improved Gurson-type model for hardenable ductile metals. Eur. J. Mech. A. Solids 14:4 (1995), 499–527.
Lievers, W., Pilkey, A., Lloyd, D., Using incremental forming to calibrate a void nucleation model for automotive aluminum sheet alloys. Acta Mater. 52:10 (2004), 3001–3007, 10.1016/j.actamat.2004.03.002.
Maire, É., Quantitative measurement of damage. Besson, J., (eds.) Local Approach to Fract, 2004, Presses de l'Ecole des Mines, Paris, France, 79–108 Chapter III.
Mansouri, L.Z., Chalal, H., Abed-Meraim, F., Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis. Mech. Mater. 76 (2014), 64–92, 10.1016/j.mechmat.2014.06.005.
Mathonet, V., Manuel D'Utilisation Du Programme D'Identification Paramétrique Optim. Technical Report, 2003, Université de Liège, Liège.
Mertens, A., Guzmán, C.F., Habraken, A.-M., Behera, A.K., Lecomte-Beckers, J., 2012. Experimental Characterisation of Damage Occuring during Single Point Incremental Forming of a Ferritic Steel.
de Montleau, P., Isotropic and Kinematic Hardening - law HILL3D_KI. Technical Report, 2003, Université de Liège, Liège, Belgium.
Nahshon, K., Hutchinson, J.W., Modification of the Gurson Model for shear failure. Eur. J. Mech. - A/Solids 27:1 (2008), 1–17, 10.1016/j.euromechsol.2007.08.002.
Nielsen, K.L., Tvergaard, V., Ductile shear failure or plug failure of spot welds modelled by modified Gurson model. Eng. Fract. Mech. 77:7 (2010), 1031–1047, 10.1016/j.engfracmech.2010.02.031.
Pardoen, T., Delannay, F., Assessment of void growth models from porosity measurements in cold-drawn copper bars. Metall. Mater. Trans. A 29:7 (1998), 1895–1909, 10.1007/s11661-998-0014-4.
Peirs, J., Verleysen, P., Van Paepegem, W., Degrieck, J., Determining the stress-strain behaviour at large strains from high strain rate tensile and shear experiments. Int. J. Impact Eng. 38:5 (2011), 406–415, 10.1016/j.ijimpeng.2011.01.004.
Pineau, A., Physical mechanisms of damage. Besson, J., (eds.) Local approach to Fract, 2004, Presses de l'Ecole des Mines, Paris, France, 33–78 Chapter II.
Soyarslan, C., Malekipour Gharbi, M., Tekkaya, A., A combined experimental-numerical investigation of ductile fracture in bending of a class of ferritic-martensitic steel. Int. J. Solids Struct. 49:13 (2012), 1608–1626, 10.1016/j.ijsolstr.2012.03.009.
Tekolu, C., Hutchinson, J.W., Pardoen, T., On localization and void coalescence as a precursor to ductile fracture. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., 373(2038), 2015, 10.1098/rsta.2014.0121 20140121–20140121.
Teodosiu, C., Hu, Z., Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. Dawson, S.-F.S.P.R., (eds.) NUMIFORM ’95 Simul. Mater. Process. theory, methods Appl, 1995, A.A. Balkema, Rotterdam, Ithaca, New York, USA, 173–182.
Tvergaard, V., Influence of voids on shear band instabilities under plane strain conditions. Int. J. Fract. 17:4 (1981), 389–407, 10.1007/BF00036191.
Tvergaard, V., Needleman, A., Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32:1 (1984), 157–169, 10.1016/0001-6160(84)90213-X.
Tvergaard, V., Nielsen, K.L., Relations between a micro-mechanical model and a damage model for ductile failure in shear. J. Mech. Phys. Solids 58:9 (2010), 1243–1252, 10.1016/j.jmps.2010.06.006.
Xue, Z., Pontin, M., Zok, F., Hutchinson, J.W., Calibration procedures for a computational model of ductile fracture. Eng. Fract. Mech. 77:3 (2010), 492–509, 10.1016/j.engfracmech.2009.10.007.
Yoshida, F., Uemori, T., A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int. J. Plast. 18:5–6 (2002), 661–686, 10.1016/S0749-6419(01)00050-X.