1. About the Enhanced Formability of Single Point Incremental Forming AM Habraken, CF Guzmán

2. SPIF Description SPIF Single Point Incremental Forming process 2

3. SPIF Description 3 [Jeswiet et al. 2005]Vasilakos et al., 2011

4. Formed Parts 4 [Duflou et al. 2008] Cranial Plate Headlight reflector Solar cooker Funnel

5. SPIF applications Airbus A320 hydraulic door Honda S800 hood [Hirt et al., 2015] [Emmens et al., 2010]

6. SPIF deformation mechanisms Plane strain ? - Through Thickness Shear -Hydrostatic component Hirt et al. ICTP conf (2002) γ nt n t (neg.) γ ng n g Wall angle α Tool rotation Frict coeff γ 13 γ 23 NO 0.00-7°6° 0.05-7°9° 0.09-7°11° 0.35-5°22° YES0.09-4°7° Eycken et al. Int J Mat Forming 4 (1) 2011 Henrard et al. Comp Mech 47 (5) 2010

7. SPIF deformation mechanisms Serrated strain path Minor principal strain (  in circumferential direction) Major principal strain (  in radial direction) Cone 50° Outer element Bending Compression within sheet thickness

8. FLC Forming Limit Curves -Radial strain path -Plane strain (no normal stress, no shear stress) Assumptions 1) Necking event 2) Crak event SPIF does not respect these hypotheses

9. Formability approach [Eyckens et al., 2009] Effect of TTS (Through Thickness Shear) Extended version of Marciniak–Kuczynski method By Eyckens  FLC curve increases

10. Formability approach Effect of compression stress in thickness direction coupled with plane stress Nurcheshmeh & Green ESAFORM (2011)

11. [Reddy et al., 2015] SPIF formability reported in FLC SPIF formability closer to failure prediction and not necking one Jeswiet et al. 2005 Emmens et al. 2009 Effect of tool radius (effect of thickness and material…) If↘ triaxiality T ↘  SPIF formability ↗ ( Necking then fracture) If ↗ triaxiality T ↗  SPIF formability ↘ (Fracture without necking)

12. Damage approach: phenomenological model Malhotra et al. [2012]: Cone test simulated by Xue [2007] damage model. Phenomenological mode, based on I1-J2-J3 J3 Lode angle + Pressure term [Malhotra et al., 2012] Cone Funnel

13. Noodle Theory (Malhotra 2012 ) diffuse necking in SPIF begins earlier compare to punch forming, but localized necking occurs later. In SPIF, a material point undergoes diffused necking but the tool moves and deforms new material. The previously formed region is able to take up some of the deformation caused in next paths. Too simple scheme forget 3D strain…

14. Let us try an extended Gurson model DC01 steel Damage approach: Gurson model

15. GTN model (Guzman’s PhD thesis 1-02-2016 ULg) Yield criterion [Gurson, 1977]: Void evolution: Nucleation [Chu and Needleman, 1980] Growth Coalescence [Tvergaard and Needleman, 1984] Shear [Nahshon and Hutchinson, 2008] +Voce or Swift isotropic hardening +Armstrong Frederick Kinematic hardening + Hill Anisotropic yield locus + careful identification: tensile test, notch tensile test, shear test, line test for DC01 steel

16. SPIF Cone Simulations Material: DC01 steel (1.0mm thickness) Experimental failure angle: 67°. Simulation using the LAGAMINE FE code, RESS solid-shell element [Alves de Sousa, 2006], GTN + shear damage model.

17. SPIF Cone simulation Aerens et al. [2009] formula: F_z=1222 [N] Force overestimated (quite classical, see benchmark NUMISHEET 2014 + Sena et. al 2015) Predicted limit angle: 47° Experimental one: 67°

18. Discussion GTN + shear: failure location OK but failure moment OK Why? No strong coupling between damage evolution and hardening Localized necking not accurately predicted  Link with a localization criterion ? Thomason ? not convinced too early prediction, not too late  Modify the coalescence model // Xue [2007] damage model based on I1-J2-J3 further from physic ?? shear extension… Coalescence model not adapted to SPIF where gradient effect through the thickness happens… Needleman nucleation law : not correctly linked with hydrostatic stress (see Balan et. al 2015) What about mesh sensitivity…

19. References R. Aerens, P. Eyckens, A. van Bael, and J. Duflou, “Force prediction for single point incremental forming deduced from experimental and FEM observations,” Int. J. Adv. Manuf. Technol., vol. 46, no. 9–12, pp. 969–982, 2009. T. Balan, X. Lemoine, E. Maire, A. Habraken, (2015, September) Implementation of a damage evolution law for dualphase steels in Gurson-type models. Materials and Design, (88), 1213-1222. C. C. Chu and A. Needleman, “Void Nucleation Effects in Biaxially Stretched Sheets,” J. Eng. Mater. Technol., vol. 102, no. 3, p. 249, 1980. J. Duflou, J. Verbert, B. Belkassem, J. Gu, H. Sol, C. Henrard, and A. M. Habraken, “Process window enhancement for single point incremental forming through multi-step toolpaths,” CIRP Ann. - Manuf. Technol., vol. 57, no. 1, pp. 253–256, 2008. W. C. Emmens, G. Sebastiani, and A. H. van den Boogaard, “The technology of Incremental Sheet Forming-A brief review of the history,” J. Mater. Process. Technol., vol. 210, no. 8, pp. 981–997, Jun. 2010. P. Eyckens, A. van Bael, and P. van Houtte, “Marciniak-Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal,” Int. J. Plast., vol. 25, no. 12, pp. 2249–2268, 2009. A. L. Gurson, “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., vol. 99, no. 1, pp. 2–15, 1977. Jeswiet, J., Duflou, J., Szekeres, A., Levebre, P. “Custom Manufacture of a Solar Cooker – a case study” in Journal Advanced Materials Research, Vols. 6- 8, May 2005, pp 487-492.

20. References J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, and J. Allwood, “Asymmetric Single Point Incremental Forming of Sheet Metal,” CIRP Ann. - Manuf. Technol., vol. 54, no. 2, pp. 88–114, Jan. 2005. W. C. Emmens and a. H. van den Boogaard, “An overview of stabilizing deformation mechanisms in incremental sheet forming,” J. Mater. Process. Technol., vol. 209, no. 8, pp. 3688–3695, Apr. 2009. CF. Guzman PhD thesis 1/2/2016 (soon uploaded on institutional library ORBI ULg) G. Hirt, M. Bambach, W. Bleck, U. Prahl, and J. Stollenwerk, “The Development of Incremental Sheet Forming from Flexible Forming to Fully Integrated Production of Sheet Metal Parts,” in Advances in Production Technology, C. Brecher, Ed. Cham: Springer International Publishing, 2015, pp. 117–129. R. Malhotra, L. Xue, T. Belytschko, and J. Cao, “Mechanics of fracture in single point incremental forming,” J. Mater. Process. Technol., vol. 212, no. 7, pp. 1573–1590, 2012. K. Nahshon and J. W. Hutchinson, “Modification of the Gurson Model for shear failure,” Eur. J. Mech. - A/Solids, vol. 27, no. 1, pp. 1–17, 2008. N. V. Reddy, R. Lingam, and J. Cao, “Incremental Metal Forming Processes in Manufacturing,” in Handbook of Manufacturing Engineering and Technology, A. Y. C. Nee, Ed. London: Springer London, 2015, pp. 411–452. V. Tvergaard and A. Needleman, “Analysis of the cup-cone fracture in a round tensile bar,” Acta Metall., vol. 32, no. 1, pp. 157–169, 1984. I. Vasilakos, J. Gu, H. Vanhove, H. Sol, and J. Duflou, “Deviations between FE Simulation and Experiments in the SPIF Process,” in Key Engineering Materials, 2011, vol. 473, pp. 937–946. L. Xue, “Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading,” Int. J. Solids Struct., vol. 44, no. 16, pp. 5163–5181, 2007.