Numerical modelling of plastic forming of aluminium single crystals
Source abstract
Abstract
The current study focused on modelling of micro-deep drawing of aluminium single crystals using a physically-based crystal plasticity model. The approach consisted in modelling the gauge area located at the centre of the crystals with boundary conditions extracted from displacement fields measured experimentally by digital image correlation. Thanks to three different geometries of samples, three loading paths were considered: uniaxial tension, plane strain tension and equi-biaxial tension. Comparisons between simulations and experimental observations were performed in terms of displacement fields, strain fields and slip traces. Data obtained from the simulations also allowed analysis of the results in terms of crystal rotation, dislocation density evolution and accumulated slip. Reasonable agreement between experimental observations and simulations was generally obtained, except for the prediction of strain localisation which was only correct in the case of uniaxial and plane strain tension. Discrepancies and validity of the modelling approach are then discussed in terms of experimental inaccuracies and numerical approximations.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Metal Forming Simulation Techniques · Metallurgy and Material Forming · Advanced Surface Polishing Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (31)
Show source-provided references
1. McDowell DL (2000) Modeling and experiments in plasticity. Int J Solids Structures 37:293–30910.1016/S0020-7683(99)00094-3 ↗
2. Voce E (1948) The relationship between stress and strain for homogeneous deformation. J Inst Met 74:537–562
3. Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transformation-based anisotropic yield functions. Int J Plasticity 21:1009–103910.1016/j.ijplas.2004.06.004 ↗
4. Peirce D, Asaro RJ, Needleman A (1982) An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall 30:1087–111910.1016/0001-6160(82)90005-0 ↗
5. Cuitiño A, Ortiz M (1992) Computational modelling of single crystals. Modell Simul Mater Sci Eng 1:225–26310.1088/0965-0393/1/3/001 ↗
6. Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of fcc metals. J Mech Phys Solids 40:537–56910.1016/0022-5096(92)80003-9 ↗
7. Meissonnier FT, Busso EP, O’Dowd NP (2001) Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains. Int J Plasticity 17:601–64010.1016/S0749-6419(00)00064-4 ↗
8. Grujicic M, Batchu S (2002) Crystal plasticity analysis of earing in deep-drawn OFHC copper cups. J Mater Sci 37:753–76410.1023/A:1013839914584 ↗
9. Cheong KS, Busso EP (2004) Discrete dislocation density modelling of single phase FCC polycrystal aggregates. Acta Mater 52:5665–567510.1016/j.actamat.2004.08.044 ↗
10. Zhao Z, Kuchnicki S, Radovitzky R, Cuitiño A (2007) Influence of in-grain mesh resolution on the prediction of deformation textures in fcc polycrystals by crystal plasticity FEM. Acta Mater 55:2361–237310.1016/j.actamat.2006.11.035 ↗
11. Nakamachi E, Tam NN, Morimoto H (2007) Multi-scale finite element analyses of sheet metals by using SEM-EBSD measured crystallographic RVE models. Int J Plasticity 23:450–48910.1016/j.ijplas.2006.06.002 ↗
12. Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater 58:1152–121110.1016/j.actamat.2009.10.058 ↗
13. Tabourot L, Dumoulin S, Balland P (2001) An attempt for a unified description from dislocation dynamics to metallic plastic behaviour. J Phys IV 11:111–118
14. Kubin L, Devincre B, Hoc T (2008) Toward a physical model for strain hardening in fcc crystals. Mater Sci Eng A 483–484:19–2410.1016/j.msea.2007.01.167 ↗
15. Alankar A, Mastorakos IN, Field DP (2009) A dislocation-density-based 3D crystal plasticity model for pure aluminum. Acta Mater 57:5936–594910.1016/j.actamat.2009.08.028 ↗
16. Fivel M, Tabourot L, Rauch E, Canova G (1998) Identification through mesoscopic simulations of macroscopic parameters of physically based constitutive equations for the plastic behaviour of fcc single crystals. J Phys IV 8:151–158
17. Groh S, Marin EB, Horstemeyer MF, Zbib HM (2009) Multiscale modeling of the plasticity in an aluminum single crystal. Int J Plasticity 25:1456–147310.1016/j.ijplas.2008.11.003 ↗
18. Dumoulin S, Tabourot L, Gradel T, Fivel M, Moreau JM (2000) Identification of constitutive laws for Al 99.5. EUROMAT’2000, Tours, France, 6 pp
19. Gradel T, Tabourot L, Dumoulin S, Castelnau O (2000) Plastic behaviour of an Al 99.5 coarse grain multicrystal during a tensile test. EUROMAT’2000, Tours, France, 6 pp
20. Erieau P, Rey C (2004) Modeling of deformation and rotation bands and of deformation induced grain boundaries in IF steel aggregate during large plane strain compression. Int J Plasticity 20:1763–178810.1016/j.ijplas.2003.11.014 ↗
21. Saai A, Louche H, Tabourot L, Chang HJ (2010) Experimental and numerical study of the thermo-mechanical behaviour of Al bi-crystal in tension using full field measurements and micromechanical modeling. Mech Mater 42:275–29210.1016/j.mechmat.2009.11.011 ↗
22. Sène NA, Balland P, Arrieux R, Moreau JM (2011) Micro-deep drawing on aluminium crystals in order to validate multiscale modelling. Exp Mech. doi: 10.1007/s11340-010-9398-310.1007/s11340-010-9398-3 ↗
23. Gronostajski J, Dolny A (1980) Determination of the forming limit curves by means of Marciniak’s punch. Mem Etud Sci Rev Met 4:570–578
24. Lee EH, Liu DT (1967) Finite-strain elastic-plastic theory with application to plane-wave analysis. J Appl Phys 38:19–2710.1063/1.1708953 ↗
25. Mandel J (1973) Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. Int J Solids Structures 9:725–74010.1016/0020-7683(73)90120-0 ↗
26. Rice JR (1971) Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity. J Mech Phys Solids 19:433–45510.1016/0022-5096(71)90010-X ↗
27. Franciosi P, Berveiller M, Zaoui A (1980) Latent hardening in copper and aluminium single crystals. Acta Metall 28:273–29310.1016/0001-6160(80)90162-5 ↗
28. Franciosi P, Zaoui A (1982) Multislip in F.C.C. crystals a theoretical approach compared with experimental data. Acta Metall 30:1627–163710.1016/0001-6160(82)90184-5 ↗
29. Dumoulin S, Hopperstad OS, Berstad T (2009) Investigation of integration algorithms for rate-dependent crystal plasticity using explicit finite element codes. Comput Mater Sci 46:785–79910.1016/j.commatsci.2009.04.015 ↗
30. Hallquist JO (2007) LS-DYNA keyword user’s manual, Version 971. Livermore Software Technology Corporation, California
31. Vacher P, Dumoulin S, Morestin F, Mguil-Touchal S (1999) Bidimensional strain measurement using digital images. J Mech Eng Sci 213:811–81710.1243/0954406991522428 ↗