In this paper, we predict the effect of texture on the plastic anisotropy and consequently the drawing performance of polycrystalline metallic sheets. The constituent grain behavior is modeled using the new single-crystal yield criterion developed by [1]. For ideal texture components, the yield stress and plastic strain ratios can be obtained analytically. For the case of strongly textured sheets containing a spread about the ideal texture components, the polycrystalline response is obtained numerically on the basis of the same single-crystal criterion. It is shown that for textures obtained with rotationally symmetric misorientations of scatter width of up to 35° from the ideal orientation, the numerical predictions have the same trend as those obtained analytically for an ideal texture, but the anisotropy is less pronounced. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Illustrative examples for sheets with textures containing a combination of few ideal texture components are also presented. The simulations of the predicted polycrystalline behavior based on the new description of the plastic behavior of the constituent grains capture the influence of individual texture components on the overall degree of anisotropy. The polycrystalline simulation results are also compared to analytical estimates obtained using the closed-form formulas for the ideal components present in the texture in conjunction with a simple law of mixtures. The analytical estimates show the same trends as the simulation results. Therefore, the trends in plastic anisotropy of the macroscopic properties can be adequately estimated analytically.
Accepted:
Published online:
Nitin Chandola 1; Oana Cazacu 1; Benoît Revil-Baudard 1
@article{CRMECA_2018__346_8_756_0,
author = {Nitin Chandola and Oana Cazacu and Beno{\^\i}t Revil-Baudard},
title = {Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model},
journal = {Comptes Rendus. M\'ecanique},
pages = {756--769},
publisher = {Elsevier},
volume = {346},
number = {8},
year = {2018},
doi = {10.1016/j.crme.2018.05.004},
language = {en},
}
TY - JOUR AU - Nitin Chandola AU - Oana Cazacu AU - Benoît Revil-Baudard TI - Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model JO - Comptes Rendus. Mécanique PY - 2018 SP - 756 EP - 769 VL - 346 IS - 8 PB - Elsevier DO - 10.1016/j.crme.2018.05.004 LA - en ID - CRMECA_2018__346_8_756_0 ER -
%0 Journal Article %A Nitin Chandola %A Oana Cazacu %A Benoît Revil-Baudard %T Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model %J Comptes Rendus. Mécanique %D 2018 %P 756-769 %V 346 %N 8 %I Elsevier %R 10.1016/j.crme.2018.05.004 %G en %F CRMECA_2018__346_8_756_0
Nitin Chandola; Oana Cazacu; Benoît Revil-Baudard. Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model. Comptes Rendus. Mécanique, Volume 346 (2018) no. 8, pp. 756-769. doi : 10.1016/j.crme.2018.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.05.004/
[1] A yield criterion for cubic single crystals, Int. J. Solids Struct. (2017) | DOI
[2] A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci., Volume 193 (1948), pp. 281-297
[3] Generalization of Drucker's yield criterion to orthotropy, Math. Mech. Solids, Volume 6 (2001), pp. 613-630
[4] Application of the theory of representation to describe yielding of anisotropic aluminum alloys, Int. J. Eng. Sci. (2003), pp. 1367-1385
[5] A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals, Int. J. Plast., Volume 20 (2004), pp. 2027-2045
[6] Linear transformation-based anisotropic yield functions, Int. J. Plast., Volume 21 (2005), pp. 1009-1039
[7] Anisotropic response of high-purity α-titanium: experimental characterization and constitutive modeling, Int. J. Plast., Volume 26 (2010), pp. 516-532
[8] Analysis of plastic strain in a cubic crystal, Stephen Timoshenko 60th Anniversary Volume, 1938, pp. 218-224
[9] A theoretical derivation of the plastic properties of a polycrystalline face-centered metal, London, Edinburgh, Dublin Philos. Mag. J. Sci., Volume 42 (1951) no. 334, pp. 1298-1307
[10] A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, London, Edinburgh, Dublin Philos. Mag. J. Sci., Volume 42 (1951) no. 334, p. 414
[11] Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties, Cambridge University Press, 2000
[12] Taylor-type homogenization methods for texture and anisotropy (D. Raabe; L.Q. Chen; F. Barlat; F. Roters, eds.), Continuum Scale Simulation of Engineering Materials, Fundamentals – Microstructures – Process Applications, Wiley, Berlin, 2004, pp. 459-471
[13] Self-consistent homogenization methods for texture and anisotropy (D. Raabe; L.Q. Chen; F. Barlat; F. Roters, eds.), Continuum Scale Simulation of Engineering Materials, Fundamentals – Microstructures – Process Applications, Wiley, Berlin, 2004, pp. 473-499
[14] Int. J. Plast., 73 (2015), pp. 119-141
[15] A regular form of the Schmid law. Application to the ambiguity problem, Textures Microstruct., Volume 14 (1991), pp. 1121-1128
[16] The production of single crystals of aluminum and their tensile properties, Proc. R. Soc. Lond., Ser. A, Volume 704 (1921), pp. 329-353
[17] Texture and earing in deep drawing of aluminium, Acta Metall., Volume 9 (1961), pp. 275-286
[18] Yield surfaces for textured polycrystals – I. Crystallographic approach, Acta Metall., Volume 35 (1987), pp. 439-451
[19] Yield surfaces for textured polycrystals – II. Analytical approach, Acta Metall., Volume 35 (1987) no. 5, pp. 1159-1174
[20] Yield surface plasticity and anisotropy in sheet metals (D. Raabe; L.Q. Chen; F. Barlat; F. Roters, eds.), Continuum Scale Simulation of Engineering Materials, Fundamentals – Microstructures – Process Applications, Wiley, Berlin, 2004, pp. 145-167
[21] Plane stress yield function for aluminum alloy sheets – part II: FE formulation and its implementation, Int. J. Plast., Volume 20 (2004) no. 3, pp. 495-522
[22] Anisotropy and formability, Advances in Material Forming, Springer, Paris, 2007, pp. 143-173
[23] Zur Ableitung einer Fliessbedingung, Z. Ver. Dent. Ing., Volume 72 (1928), pp. 734-736
[24] Some observations on the anisotropy of yield strength in cold rolled and annealed metals, Inst. Met. J., Volume 94 (1966), pp. 284-291
[25] A six-component yield function for anisotropic materials, Int. J. Plast., Volume 7 (1991), pp. 693-712
[26] Rolling textures in fcc and bcc metals, Acta Metall., Volume 12 (1964), pp. 281-293
[27] Textures and anisotropy in industrial applications of aluminum alloys, Arch. Metall. Mater., Volume 50 (2005), pp. 21-34
[28] Prediction of tricomponent plane stress yield surfaces and associated flow and failure behavior of strongly textured F.C.C. polycrystalline sheets, Mater. Sci. Eng., Volume 95 (1987), pp. 15-29
[29] U.F. Kocks, G.R. Canova, C.N. Tomé, A.D. Rollett, S.I. Wright, Computer Cod LA-CC-88-6, Los Alamos National Laboratory, 1988.
[30] Characterization and modeling of the mechanical behavior and formability of a 2008-T4 sheet sample, Int. J. Mech. Sci., Volume 31 (1989), pp. 549-563
[31] A general anisotropic yield criterion using bounds and a transformation weighting tensor, J. Mech. Phys. Solids, Volume 41 (1993), pp. 1859-1886
Cited by Sources:
Comments - Policy