On the Development and Identification of Phenomenological Damage Models - Application to Industrial Wire Drawing and Rolling Processes

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The continuum thermodynamics-based Lemaitre damage model is nowadays widely used to deal with coupled damage analyses for various mechanical applications (e.g. forming process simulations). However, such a model, which only accounts for the stress triaxiality (the ratio between the first and the second invariants of stress tensor) has been found to give incorrect results under shear dominated loading (in terms of damage location as well as risk of crack). Several recent studies have demonstrated the importance of the third stress invariant in damage prediction; the Lode angle parameter is generally used to include it. The idea is to describe completely the stress state in damage model’s formulations, which is defined by the equivalent stress, the stress triaxiality ratio and the Lode angle parameter. This later parameter has proved to have an important influence on ductile damage under low stress triaxiality. Xue’s coupled damage model accounts for the third invariant of the deviatoric stress tensor, allowing a better balance between respective effects of shear and elongation on damage. Some extensions of more physically based damage models, such as the Gurson-Tvergaard-Needleman model, have also been presented to account for this influence of the third stress invariant. In the present work, the phenomenological damage models have been implemented in Forge® Finite Element (FE) software to investigate ductile damage occurring during industrial forming processes. This paper presents the comparative study of Xue’s model and Lemaitre’s model. A complete procedure is detailed to identify the material and damage parameters from experimental mechanical tests on high carbon steel. This identification process has been carried out both for Lemaitre’s coupled damage model and Xue’s coupled damage model. Application to wire drawing followed by flat rolling shows that in such shear-inducing processes, these models predict damage at different locations, due to their different emphasis on shear with respect to elongational strain damage.

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Key Engineering Materials (Volumes 554-557)

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213-226

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June 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] J. Lemaitre, "Local approach of fracture," Engineering Fracture Mechanics, vol. 25, no. 5-6, pp.523-537, 1986.

DOI: 10.1016/0013-7944(86)90021-4

Google Scholar

[2] J. Lemaitre and R. Desmorat, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Berlin: Springer, 2005.

Google Scholar

[3] L. Xue, "Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading," International Journal of Solids and Structures, vol. 44, no. 16, pp.5163-5181, 2007.

DOI: 10.1016/j.ijsolstr.2006.12.026

Google Scholar

[4] G. R. Johnson and W. H. Cook, "Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures," Engineering Fracture Mechanics, vol. 21, no. 1, pp.31-48, 1985.

DOI: 10.1016/0013-7944(85)90052-9

Google Scholar

[5] M. Wilkins, R. Streit, and J. Reaugh, "Cumulative-strain-damage model of ductile fracture: Simulation and prediction of engineering fracture tests," Technical Report UCRL-53058, Lawrence Livermore National Laboratory, 1980.

DOI: 10.2172/6628920

Google Scholar

[6] M. Cockcroft and D. J. Latham, Ductility and workability of metals, vol. 96. 1 Carlton House Terrace, London SW1Y 5DB, England: Inst Materials, 1968.

Google Scholar

[7] M. Oyane, T. Sato, K. Okimoto, and S. Shima, "Criteria for ductile fracture and their applications," Journal of Mechanical Working Technology, vol. 4, no. 1, pp.65-81, 1980.[8] L. Kachanov, "On creep rupture time," Proc. Acad. Sci. USSR Div. Eng. Sci., vol. 8, p.2631, 1958.

DOI: 10.1016/0378-3804(80)90006-6

Google Scholar

[9] J. Chaboche, "Anisotropic creep damage in the framework of continuum damage mechanics," Nuclear Engineering and Design, vol. 79, no. 3, pp.309-319, 1984.

DOI: 10.1016/0029-5493(84)90046-3

Google Scholar

[10] P. O. Bouchard, L. Bourgeon, S. Fayolle, and K. Mocellin, "An enhanced lemaitre model formulation for materials processing damage computation," International Journal of Material Forming, vol. 4, pp.299-315, 2011.

DOI: 10.1007/s12289-010-0996-5

Google Scholar

[11] A. L. Gurson, "Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part IYield Criteria and Flow Rules for Porous Ductile Media," Journal of Engineering Materials and Technology, vol. 99, no. 1, pp.2-15, 1977.

DOI: 10.1115/1.3443401

Google Scholar

[12] A. Needleman and V. Tvergaard, "An analysis of ductile rupture in notched bars," Journal of the Mechanics and Physics of Solids, vol. 32, no. 6, pp.461-490, 1984.

DOI: 10.1016/0022-5096(84)90031-0

Google Scholar

[13] G. Rousselier, "Ductile fracture models and their potential in local approach of fracture," Nuclear Engineering and Design, vol. 105, no. 1, pp.97-111, 1987.

DOI: 10.1016/0029-5493(87)90234-2

Google Scholar

[14] L. Xue and T. Wierzbicki, "Numerical simulation of fracture mode transition in ductile plates," International Journal of Solids and Structures, vol. 46, no. 6, pp.1423-1435, 2009.

DOI: 10.1016/j.ijsolstr.2008.11.009

Google Scholar

[15] K. Nahshon and J. Hutchinson, "Modification of the Gurson Model for shear failure," European Journal of Mechanics - A/Solids, vol. 27, no. 1, pp.1-17, 2008.

DOI: 10.1016/j.euromechsol.2007.08.002

Google Scholar

[16] Y. Bai and T. Wierzbicki, "Application of extended Mohr-Coulomb criterion to ductile fracture," International Journal of Fracture, vol. 161, no. 1, pp.1-20, 2010.

DOI: 10.1007/s10704-009-9422-8

Google Scholar

[17] Y. Bai and T. Wierzbicki, "A new model of metal plasticity and fracture with pressure and Lode dependence," International Journal of Plasticity, vol. 24, no. 6, pp.1071-1096, 2008.

DOI: 10.1016/j.ijplas.2007.09.004

Google Scholar

[18] P. W. Bridgman, Studies in large plastic flow and fracture. Cambridge, Massachusetts: Harvard University Press, 1952.

Google Scholar

[19] Y. Bao and T. Wierzbicki, "On the cut-off value of negative triaxiality for fracture," Engineering Fracture Mechanics, vol. 72, no. 7, pp.1049-1069, 2005.

DOI: 10.1016/j.engfracmech.2004.07.011

Google Scholar

[20] W. Lode, "Versuche ¨uber den einflußder mittleren hauptspannung auf die fließgrenze," Zeitschrift f¨ur angewandte mathematik und mechanik, vol. 5, pp.142-144, 1925.

DOI: 10.1002/zamm.19250050215

Google Scholar

[21] T. Coupez, H. Digonnet, and R. Ducloux, "Parallel meshing and remeshing," Applied Mathematical Modelling, vol. 25, no. 2, pp.153-175, 2000.

DOI: 10.1016/s0307-904x(00)00045-7

Google Scholar

[22] D. Arnold, F. Brezzi, and M. Fortin, "A stable finite element for the stokes equations," Calcolo, vol. 21, pp.337-344, 1984.

DOI: 10.1007/bf02576171

Google Scholar

[23] H.-P. P. Schwefel, Evolution and Optimum Seeking: The Sixth Generation. New York, NY, USA: John Wiley & Sons, Inc., 1993.

Google Scholar

[24] H. G. Beyer, The theory of evolution strategies. Springer, 2001.

Google Scholar

[25] H. Swift, "Plastic instability under plane stress," Journal of the Mechanics and Physics of Solids, vol. 1, no. 1, pp.1-18, 1952.

Google Scholar

[26] P. Ludwik, Elemente Der Technologischen Mechanik. Berlin: J. Springer, 1996.[27] E. Voce, "A practical strain-hardening function," Metallurgica, vol. 51, pp.219-226, 1955.

Google Scholar

[28] M. Jir´asek, "Nonlocal models for damage and fracture: Comparison of approaches," International Journal of Solids and Structures, vol. 35, no. 3132, pp.4133-4145, 1998.

DOI: 10.1016/s0020-7683(97)00306-5

Google Scholar

[29] S. Fayolle, Mod´elisation num´erique de la mise en forme et de la tenue m´ecanique des assemblages par d´eformation plastique : application au rivetage auto-poinc¸onneur. PhD thesis, Ecole nationale sup´erieure des Mines de Paris, 11 2008.

Google Scholar

[30] R. H. J. Peerlings, R. D. Borst, W. A. M. Brekelmans, and J. H. P. D. Vree, "Gradient enhanced damage for quasi-brittle materials," International Journal for Numerical Methods in Engineering, vol. 39, pp.3391-3403, 1996.

DOI: 10.1002/(sici)1097-0207(19961015)39:19<3391::aid-nme7>3.0.co;2-d

Google Scholar

[31] R. H. J. Peerlings, M. G. D. Geers, R. de Borst, and W. A. M. Brekelmans, "A critical comparison of nonlocal and gradient-enhanced softening continua," International Journal of Solids and Structures, vol. 38, no. 44-45, pp.7723-7746, 2001.

DOI: 10.1016/s0020-7683(01)00087-7

Google Scholar

[32] R. A. Engelen, M. G. Geers, and F. P. Baaijens, "Nonlocal implicit gradient-enhanced elastoplasticity for the modelling of softening behaviour," International Journal of Plasticity, vol. 19, no. 4, pp.403-433, 2003.

DOI: 10.1016/s0749-6419(01)00042-0

Google Scholar

[33] N. V. Reddy, P. M. Dixit, and G. K. Lal, "Central bursting and optimal die profile for axisymmetric extrusion," Journal of Manufacturing Science and Engineering, vol. 118, no. 4, pp.579-584, 1996.

DOI: 10.1115/1.2831070

Google Scholar

[34] N. V. Reddy, P. M. Dixit, and G. K. Lal, "Ductile fracture criteria and its prediction in axisymmetric drawing," International Journal of Machine Tools and Manufacture, vol. 40, no. 1, pp.95-111, 2000.

DOI: 10.1016/s0890-6955(99)00045-0

Google Scholar

[35] P. McAllen and P. Phelan, "Numerical analysis of axisymmetric wire drawing by means of a coupled damage model," Journal of Materials Processing Technology, vol. 183, no. 2-3, pp.210-218, 2007.

DOI: 10.1016/j.jmatprotec.2006.10.014

Google Scholar

[36] T. Mass´e, Study and optimization of high carbon steel flat wires. PhD thesis, Ecole nationale sup´erieure des Mines de Paris, 01 2010.

Google Scholar