Damage prediction in single point incremental forming using an extended Gurson model

[en] Single point incremental forming (SPIF) has several advantages over traditional forming, such as the high formability attainable by the material. Different hypotheses have been proposed to explain this behavior, but there is still no straightforward relation between the particular stress and strain state induced by SPIF and the material degradation leading to localization and fracture. A systematic review of the state of the art about formability and damage in SPIF is presented and an extended Gurson–Tvergaard–Needleman (GTN) model was applied to predict damage in SPIF through finite element (FE) simulations. The line test was used to validate the simulations by comparing force and shape predictions with experimental results. To analyze the failure prediction, several simulations of SPIF cones at different wall angles were performed. It is concluded that the GTN model underestimates the failure angle on SPIF due to wrong coalescence modeling. A physically-based Thomason coalescence criterion was then used leading to an improvement on the results by delaying the onset of coalescence.

Disciplines :

Materials science & engineering
Mechanical engineering

Author, co-author :

Guzman, Carlos Felipe

Yuan, Sibo ; Université de Liège > Département ArGEnCo > Département Argenco : Secteur MS2F

Duchene, Laurent ; Université de Liège > Département ArGEnCo > Analyse multi-échelles des matériaux et struct. du gén. civ.

Flores, Erick I. Saavedra

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

Language :

English

Title :

Damage prediction in single point incremental forming using an extended Gurson model

Publication date :

2018

Journal title :

International Journal of Solids and Structures

ISSN :

0020-7683

eISSN :

1879-2146

Publisher :

Pergamon Press (part of Elsevier Science), Oxford, United Kingdom

Volume :

151

Pages :

45-56

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 29 June 2017

Statistics

Number of views

153 (57 by ULiège)

Number of downloads

1121 (35 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Aerens, R., Eyckens, P., van Bael, A., Duflou, J.R., Force prediction for single point incremental forming deduced from experimental and FEM observations. Int. J. Adv. Manuf. Technol. 46:9–12 (2009), 969–982 http://www.springerlink.com/index/10.1007/s00170-009-2160-2.
Allwood, J.M., Shouler, D.R., Tekkaya, A., The increased forming limits of incremental sheet forming processes. Geiger, M., Duflou, J., Shirvani, B., Clarke, R., Di Lorenzo, R., Fratini, L., (eds.) Key Engineering Materials, 344, 2007, Trans Tech Publications, Palermo, Italy, 621–628 http://www.scientific.net/KEM.344.621.
Alves de Sousa, R.J., Cardoso, R.P., Fontes Valente, R.A., Yoon, J.W., Grácio, J.J., Natal Jorge, R.M., A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness – Part I: geometrically linear applications. Int. J. Numer. Methods Eng. 62:7 (2005), 952–977 http://doi.wiley.com/10.1002/nme.1226.
Alves de Sousa, R.J., Cardoso, R.P., Fontes Valente, R.A., Yoon, J.W., Grácio, J.J., Natal Jorge, R.M., A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness – Part II: nonlinear applications. Int. J. Numer. Methods Eng. 67:2 (2006), 160–188 http://doi.wiley.com/10.1002/nme.1609.
Armstrong, P., Frederick, C.O., A Mathematical Representation of the Multiaxial Bauschinger Effect. 1966, Central Electricity Generating Board Technical report.
Bai, Y., Wierzbicki, T., A new model of metal plasticity and fracture with pressure and lode dependence. Int. J. Plast. 24:6 (2008), 1071–1096 http://linkinghub.elsevier.com/retrieve/pii/S0749641907001246.
Barsoum, I., Faleskog, J., Rupture mechanisms in combined tension and shear-micromechanics. Int. J. Solids Struct. 44:6 (2007), 5481–5498 http://linkinghub.elsevier.com/retrieve/pii/S0020768306003921.
Behera, A.K., Shape Feature Taxonomy Development for Toolpath Optimisation in Incremental Sheet Forming (Ontwikkeling van een taxonomie van vormkenmerken voor optimalisatie van gereedschapsbanen voor incrementeel omvormen)Shape feature taxonomy development for toolpath optimisation in incremental sheet forming (ontwikkeling van een taxonomie van vormkenmerken voor optimalisatie van gereedschapsbanen voor incrementeel omvormen), 2013, Katholieke Universiteit Leuven Ph.D. Thesis https://lirias.kuleuven.be/handle/123456789/422489.
Ben Bettaieb, A., Sena, J.I.V., Alves de Sousa, R.J., Valente, R., Habraken, A.M., Duchêne, L., On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications. Finite Elem. Anal. Des. 107 (2015), 44–59 http://linkinghub.elsevier.com/retrieve/pii/S0168874X15001286.
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 http://doi.wiley.com/10.1002/nme.3010.
Ben Hmida, R., Identification de Lois de Comportement de Tôles en Faibles épaisseurs par Développement et Utilisation du Procédé de Microformage Incrémental, 2014, Franche-Comté électronique Mécanique Thermique et Optique – Sciences et Technologies Ph.D. thesis.
Benzerga, A.A., Besson, J., Plastic potentials for anisotropic porous solids. Eur. J. Mech. A/Solids 20:3 (2001), 397–434 http://linkinghub.elsevier.com/retrieve/pii/S0997753801011470.
Bouffioux, C., Lequesne, C., Vanhove, H., Duflou, J.R., Pouteau, P., Duchêne, L., Habraken, A.M., Experimental and numerical study of an AlMgSc sheet formed by an incremental process. J. Mater. Process. Technol. 211:11 (2011), 1684–1693 http://linkinghub.elsevier.com/retrieve/pii/S0924013611001439.
Brünig, M., An anisotropic ductile damage model based on irreversible thermodynamics. Int. J. Plast. 19:10 (2003), 1679–1713 http://linkinghub.elsevier.com/retrieve/pii/S0749641902001146.
Brünig, M., Berger, S., Obrecht, H., Numerical simulation of the localization behavior of hydrostatic-stress-sensitive metals. Int. J. Mech. Sci. 42:11 (2000), 2147–2166 http://linkinghub.elsevier.com/retrieve/pii/S0020740300000023.
Cescotto, S., Charlier, R., Frictional contact finite elements based on mixed variational principles. Int. J. Numer. Methods Eng. 36:10 (1993), 1681–1701 http://doi.wiley.com/10.1002/nme.1620361005.
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 http://www.emeraldinsight.com/10.1108/eb023607.
Chaboche, J.-L., Viscoplastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. L'Acad. Pol. des Sci. Série Sci. Tech. 25:1 (1977), 33–42.
Chow, C., Wang, J., An anisotropic theory of continuum damage mechanics for ductile fracture. Eng. Fract. Mech. 27:5 (1987), 547–558 http://linkinghub.elsevier.com/retrieve/pii/0013794487901081.
Chu, C.C., Needleman, A., Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol., 102(3), 1980, 249 http://link.aip.org/link/JEMTA8/v102/i3/p249/s1&Agg=doi.
Duchêne, L., Guzmán, C.F., Behera, A.K., Duflou, J.R., Habraken, A.M., Numerical simulation of a pyramid steel sheet formed by single point incremental forming using solid-shell finite elements. Clarke, R., Leacock, A., Duflou, J.R., Merklein, M., Micari, F., (eds.) Key Engineering Material, 549, 2013, Trans Tech Publications, Belfast, United Kingdom, 180–188.
Duflou, J.R., Verbert, J., Belkassem, B., Gu, J., Sol, H., Henrard, C., Habraken, A.M., Process window enhancement for single point incremental forming through multi-step toolpaths. CIRP Ann. Manuf. Technol. 57:1 (2008), 253–256 http://linkinghub.elsevier.com/retrieve/pii/S0007850608000310.
Elford, M., Saha, P., Seong, D., Haque, M.Z., Yoon, J.W., Benchmark 3 – incremental sheet forming. Yoon, J.W., Stoughton, T.B., Rolfe, B., Beynon, J.H., Hodgson, P., (eds.) Proceedings of the 2013 AIP Conference, 227, 2013, American Institute of Physics, Melbourne, Australia, 227–261 http://link.aip.org/link/APCPCS/v1567/i1/p227/s1&Agg=doi.
Emmens, W.C., Formability. 2011, Springer, Berlin Heidelberg, Berlin http://link.springer.com/10.1007/978-3-642-21904-7.
Emmens, W.C., van den Boogaard, A., Tensile tests with bending: a mechanism for incremental forming. Int. J. Mater. Form. 1 (2008), 1155–1158, 10.1007/s12289-010-0978-7 Springer-Verlag.
Emmens, W.C., van den Boogaard, A.H., Contact effects in bending affecting stress and formability. Int. J. Mater. Form. 3:S1 (2010), 1159–1162.
Emmens, W.C., van den Boogaard, A.H., Strain in shear, and material behaviour in incremental forming. Key Eng. Mater. 344 (2007), 519–526.
Emmens, W.C., van den Boogaard, A.H., An overview of stabilizing deformation mechanisms in incremental sheet forming. J. Mater. Process. Technol. 209:8 (2009), 3688–3695 http://dx.doi.org/10.1016/j.jmatprotec.2008.10.003 http://linkinghub.elsevier.com/retrieve/pii/S0924013608007267.
Eyckens, P., van Bael, A., van Houtte, P., Marciniak–Kuczynski type modelling of the effect of through-thickness shear on the forming limits of sheet metal. Int. J. Plast. 25:12 (2009), 2249–2268 http://linkinghub.elsevier.com/retrieve/pii/S0749641909000163.
Eyckens, P., Belkassem, B., Henrard, C., et al. Strain evolution in the single point incremental forming process: digital image correlation measurement and finite element prediction. Int. J. Mater. Form. 4 (2011), 55–71 http://www.springerlink.com/index/10.1007/s12289-010-0995-6.
Eyckens, P., He, S., van Bael, A., van Houtte, P., Duflou, J.R., Forming limit predictions for the serrated strain paths in single point incremental sheet forming. Proceedings of the 2007 AIP Conference, 908, 2007, AIP, Porto, Portugal, 141–146 http://link.aip.org/link/APCPCS/v908/i1/p141/s1&Agg=doi.
Filice, L., Fratini, L., Micari, F., Analysis of material formability in incremental forming. CIRP Ann. Manuf. Technol. 51:1 (2002), 199–202 http://linkinghub.elsevier.com/retrieve/pii/S0007850607614991.
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 http://linkinghub.elsevier.com/retrieve/pii/S0749641906001136.
Frederick, C.O., Armstrong, P., A mathematical representation of the multiaxial bauschinger effect. Mater. High Temp. 24:1 (2007), 1–26.
Gao, X., Zhang, G., Roe, C., A study on the effect of the stress state on ductile fracture. Int. J. Damage Mech. 19:1 (2009), 75–94 http://ijd.sagepub.com/cgi/doi/10.1177/1056789509101917.
Garrison, W., Moody, N., Ductile fracture. J. Phys. Chem. Solids 48:11 (1987), 1035–1074 http://linkinghub.elsevier.com/retrieve/pii/0022369787901181.
Gologanu, M., Leblond, J.-B., Perrin, G., Devaux, J., Recent extensions of Gurson's model for porous ductile materials. Proceedings of the 1996 International Seminar on Micromechanics, 1996, Udine, Italy, 61–130.
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), 2–15.
Guzmán, C.F., Experimental and Numerical Characterization of Damage and Application to Incremental Forming. 2016, Université de Liège Ph.D Thesis.
Guzmán, C.F., Ben Bettaieb, A., Sena, J.I.V., Alves de Sousa, R.J., Habraken, A.M., Duchêne, L., Evaluation of the Enhanced Assumed Strain and Assumed Natural Strain in the SSH3D and RESS3 Solid Shell Elements for Single Point Incremental Forming Simulation. Merklein, M., Hagenah, H., (eds.) Key Engineering Materials, 504–506, 2012, Erlangen, Germany, 913–918 http://www.scientific.net/KEM.504-506.913.
Guzmán, C.F., Gu, J., Duflou, J.R., Vanhove, H., Flores, P., Habraken, A.M., Study of the geometrical inaccuracy on a SPIF two-slope pyramid by finite element simulations. Int. J. Solids Struct. 49:25 (2012), 3594–3604 http://linkinghub.elsevier.com/retrieve/pii/S0020768312003010.
Guzmán, C.F., Saavedra Flores, E.I., Numerical integration of anisotropic yield criterion for porous solids. Cuad. Mecánica Comput. 14 (2016), 151–158 Arica, Chile.
Habraken, A.M., Cescotto, S., Contact between deformable solids: the fully coupled approach. Math. Comput. Model 28:4–8 (1998), 153–169 http://linkinghub.elsevier.com/retrieve/pii/S0895717798001150.
Ham, M., Jeswiet, J., Forming limit curves in single point incremental forming. CIRP Ann. Manuf. Technol. 56 (2007), 277–280.
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 http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1948.0045 http://rspa.royalsocietypublishing.org/content/193/1033/281.abstract.
Hirt, G., Ames, J., Bambach, M., Kopp, R., Forming strategies and process modelling for CNC incremental sheet forming. CIRP Ann. Manuf. Technol. 53:1 (2004), 203–206 http://www.sciencedirect.com/science/article/pii/S0007850607606799.
Jeswiet, J., Micari, F., Hirt, G., Bramley, A., Duflou, J.R., Allwood, J.M., Asymmetric single point incremental forming of sheet metal. CIRP Ann. Manuf. Technol. 54:2 (2005), 88–114 http://linkinghub.elsevier.com/retrieve/pii/S0007850607600213 http://www.sciencedirect.com/science/article/B8CXH-4SRVXM5-5/2/260e56998a9f7ed28f6f8ed20bf363cc.
Jeswiet, J., Young, D., Forming limit diagrams for single-point incremental forming of aluminium sheet. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 219:4 (2005), 359–364 http://pib.sagepub.com/lookup/doi/10.1243/095440505X32210.
Keeler, S.P., Backofen, W.A., Plastic instability and fracture in sheets stretched over rigid punches. Trans. Am. Soc. Metals 56 (1963), 25–28.
Lemaitre, J., A continuous damage mechanics model for ductile fracture. J. Eng. Mater. Technol., 107(1), 1985, 83 http://link.aip.org/link/JEMTA8/v107/i1/p83/s1&Agg=doi.
Li, K., Cescotto, S., An 8-node brick element with mixed formulation for large deformation analyses. Comput. Methods Appl. Mech. Eng. 141:1–2 (1997), 157–204 http://linkinghub.elsevier.com/retrieve/pii/S0045782596010717.
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.
Malcher, L., Andrade Pires, F.M., César de Sá J., An assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality. Int. J. Plast. 30–31 (2012), 81–115 http://linkinghub.elsevier.com/retrieve/pii/S0749641911001690.
Malcher, L., Andrade Pires, F.M., César de Sá J., An extended GTN model for ductile fracture under high and low stress triaxiality. Int. J. Plast. 54 (2014), 193–228 http://linkinghub.elsevier.com/retrieve/pii/S0749641913001708.
Malhotra, R., Xue, L., Belytschko, T., Cao, J., Mechanics of fracture in single point incremental forming. J. Mater. Process. Technol. 212:7 (2012), 1573–1590 http://linkinghub.elsevier.com/retrieve/pii/S0924013612000726.
Marciniak, Z., Kuczynski, K., Limit strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9:9 (1967), 609–620 http://linkinghub.elsevier.com/retrieve/pii/0020740367900665.
Mühlich, U., Brocks, W., On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening. Comput. Mech. 31:6 (2003), 479–488 http://link.springer.com/10.1007/s00466-003-0454-z.
Nahshon, K., Hutchinson, J.W., Modification of the Gurson model for shear failure. Eur. J. Mech. A/Solids 27:1 (2008), 1–17 http://linkinghub.elsevier.com/retrieve/pii/S0997753807000721.
Nielsen, K.L., Tvergaard, V., Effect of a shear modified Gurson model on damage development in a FSW tensile specimen. Int. J. Solids Struct. 46:3–4 (2009), 587–601 http://linkinghub.elsevier.com/retrieve/pii/S0020768308003752.
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 http://linkinghub.elsevier.com/retrieve/pii/S0013794410001128.
Reddy, N.V., Lingam, R., Cao, J., Incremental metal forming processes in manufacturing. Nee, A.Y.C., (eds.) Handbook of Manufacturing Engineering and Technology, 2015, Springer London, London, 411–452 http://link.springer.com/10.1007/978-1-4471-4670-4.
Sena, J.I.V., Guzmán, C.F., Duchêne, L., Habraken, A.M., Valente, R.A.F., de Sousa. J., A., Numerical simulation of a conical shape made by single point incremental. Yoon, J.W., Stoughton, T.B., Rolfe, B., Beynon, J.H., Hodgson, P., (eds.) Proceedings of the 2013 AIP Conference, 2013, American Institute of Physics, Melbourne, Australia, 852–855 http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4850104 http://link.aip.org/link/APCPCS/v1567/i1/p852/s1&Agg=doi.
Sena, J.I.V., Lequesne, C., Duchene, L., Habraken, A.-M., Valente, R.A., Alves de Sousa, R.J., Single point incremental forming simulation with adaptive remeshing technique using solid-shell elements. Eng. Comput. 33:5 (2016), 1388–1421 http://www.emeraldinsight.com/doi/10.1108/EC-06-2015-0172.
Seong, D., Haque, M.Z., Kim, J.B., Stoughton, T.B., Yoon, J.W., Suppression of necking in incremental sheet forming. Int. J. Solids Struct. 51:15–16 (2014), 2840–2849 http://dx.doi.org/10.1016/j.ijsolstr.2014.04.007.
Silva, M.B., Nielsen, P.S., Bay, N., Martins, P., Failure mechanisms in single-point incremental forming of metals. Int. J. Adv. Manuf. Technol. 56:9–12 (2011), 893–903 http://www.springerlink.com/index/10.1007/s00170-011-3254-1.
Silva, M.B., Skjoedt, M., Martins, P., Bay, N., Revisiting the fundamentals of single point incremental forming by means of membrane analysis. Int. J. Mach. Tools Manuf. 48:1 (2008), 73–83 http://linkinghub.elsevier.com/retrieve/pii/S0890695507001289.
Simo, J.C., Rifai, M.S., A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Eng. 29:8 (1990), 1595–1638 http://doi.wiley.com/10.1002/nme.1620290802.
Stoughton, T.B., Yoon, J.W., A new approach for failure criterion for sheet metals. Int. J. Plast. 27:3 (2011), 440–459 http://linkinghub.elsevier.com/retrieve/pii/S0749641910000951.
Thomason, P., Ductile Fracture of Metals. 1990, Pergamon Press.
Tvergaard, V., Influence of voids on shear band instabilities under plane strain conditions. Int. J. Fract. 17:4 (1981), 389–407 http://www.springerlink.com/index/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 http://linkinghub.elsevier.com/retrieve/pii/000161608490213X.
Voyiadjis, G.Z., Kattan, P.I., A plasticity-damage theory for large deformation of solids-i. theoretical formulation. Int. J. Eng. Sci. 30:9 (1992), 1089–1108 http://linkinghub.elsevier.com/retrieve/pii/002072259290059P.
Xue, L., Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading. Int. J. Solids Struct. 44:16 (2007), 5163–5181 http://linkinghub.elsevier.com/retrieve/pii/S002076830600552X.
Xue, L., Belytschko, T., Fast methods for determining instabilities of elastic-plastic damage models through closed-form expressions. Int. J. Numer. Methods Eng. 84:12 (2010), 1490–1518.
Zhang, K., Bai, J., François, D., Numerical analysis of the influence of the lode parameter on void growth. Int. J. Solids Struct. 38:32–33 (2001), 5847–5856 http://www.sciencedirect.com/science/article/pii/S0020768300003917 http://linkinghub.elsevier.com/retrieve/pii/S0020768300003917.
Zhang, Z., Thaulow, C., Ødegård, J., A complete Gurson model approach for ductile fracture. Eng. Fract. Mech. 67:2 (2000), 155–168 http://linkinghub.elsevier.com/retrieve/pii/S0013794400000552.