On the Taylor principles for plastic deformation of polycrystalline metals

doi:10.1007/s11706-016-0358-4

Front. Mater. Sci.

2016, Vol. 10

Issue (4) : 335-345 https://doi.org/10.1007/s11706-016-0358-4

RESEARCH ARTICLE

On the Taylor principles for plastic deformation of polycrystalline metals

Weimin MAO^1,²(

)

¹. School of Materials and Metallurgy, Inner Mongolia University of Science and Technology, Arding Street 7, Baotou 014010, China
². Department of Materials, University of Science and Technology Beijing, Xue-Yuan Road 30, Beijing 100083, China

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Abstract

Grain orientation evolutions and texture formation based on the Taylor principles offer important references to reveal crystallographic mechanisms of deformation behaviors. Strain equilibrium between grains is achieved in Taylor theory, however, stress equilibrium has not yet been reached perfectly even in many modifications of the theory though the textures predicted become very close to those of experimental observations. A reaction stress model is proposed, in which mechanical interactions between grains are considered in details and grain deformation is conducted by penetrating and non-penetrating slips. The new model offers both of the stress and strain equilibria and predicts the same textures indicated by Taylor theory. The rolling texture simulated comes very close to the experimental observations if the relaxation effect of the non-penetrating slips on the up-limits of reaction stresses is included. The reaction stress principles open theoretically a new field of vision to consider deformation behaviors of polycrystalline materials, whereas the Taylor principles become unnecessary both theoretically and practically. Detailed engineering conditions have to be included in simulations if the deformation textures of industrial products should be predicted.

Keywords Taylor principles micormechanical equilibrium plastic deformation dislocation slip texture simulation

Corresponding Author(s): Weimin MAO

Online First Date: 02 November 2016 Issue Date: 24 November 2016

Cite this article:

Weimin MAO. On the Taylor principles for plastic deformation of polycrystalline metals[J]. Front. Mater. Sci., 2016, 10(4): 335-345.

URL:

https://academic.hep.com.cn/foms/EN/10.1007/s11706-016-0358-4
https://academic.hep.com.cn/foms/EN/Y2016/V10/I4/335

Fig.1 (a) Texture of a 95% rolled Al sheet, and the rolling texture simulation based on (b) NC, (c) FC (Reproduced with permission from Ref. [10]), (d) RC, (e) PC models which are shown in φ₂ = 45° sections of ODFs (density levels: 2, 4, 8, 16, 32, 64, 99), as well as (g) the corresponding orientation density distributions along the β orientation fiber (Reproduced with permission from Ref. [9]). (f) The positions of {112}⟨111⟩, {110}⟨112⟩ and {110}⟨001⟩ texture in the φ₂ = 45° sections.

Fig.2 Experimental observation of grain structure in an Fe sample (a) before and (b) after 18% compression (Reproduced with permission from Ref. [18]), as well as corresponding grain boundary distribution (c) before and (d) after the compression. The dashed lines in (d) indicate the boundary distribution if the grains are deformed according the Taylor principles in comparison with the experimental observation.

Fig.3 Grain deformation conducted (a) by activation of a penetrating slip and (b) followed by multiple penetrating slips.

Fig.4 φ₂ = 45° ODF sections of circa elastic isotropic Al at 95% rolling reduction calculated based on RS model: (a)α = 1, max.:92 (Reproduced with permission from Ref. [10]); (b)α = 0.5, max.:82; (c)α = 0.35, max.:72. Density levels: 2, 4, 8, 16, 32, 64.

Fig.5 Penetrating slips inducing additional local slips in neighboring grains near boundary areas and (b) mutual interactions of penetrating and non-penetrating slips between neighboring grains. Fine real lines: traces of penetrating slips; dashed lines: additionally penetrating slips.

Fig.6 The effect of external shear stress during rolling and the rotation of main stress tensor induced: (a) sketch of stresses during rolling (1= RD, 2= TD, 3= ND); (b) combination of normal stresses and external shear stress; (c) rotation of main stress tensor round TD; (d)φ₂ = 45° ODF section of 95% rolled Al sheet simulated according to Eqs. (7) and (5) (density levels: 2, 4, 8, 16).

1	Sachs G.Zur Ableitung einer Fließbedingdung. Zeitschrift des Vereines deutscher Ingeniere, 1928, 72: 732–736
2	Taylor G I. Plastic strain in metals. Journal of the Institute of Metals, 1938, 62: 307–324
3	Hirsch J, Lücke K. Mechanism of deformation and development of rolling texture in polycrystalline fcc metals — II. Acta Metallurgica, 1988, 36(11): 2883–2904 https://doi.org/10.1016/0001-6160(88)90173-3
4	Bishop J F W, Hill R. A theory of the plastic distribution of a polycrystalline aggregate under combined stresses. Philosophical Magazine, 1951, 42(327): 414–427 https://doi.org/10.1080/14786445108561065
5	Kocks U F. The relation between polycrystal deformation and single-crystal deformation. Metallurgical & Materials Transactions B, 1970, 1(5): 1121–1143
6	Lin T H. Analysis of elastic and plastic strains of a face-centered cubic crystal. Journal of the Mechanics and Physics of Solids, 1957, 5(2): 143–149 https://doi.org/10.1016/0022-5096(57)90058-3
7	Chapuis A, Liu Q. Simulations of texture evolution for HCP metals: Influence of the main slip systems. Computational Materials Science, 2015, 97: 121–126 https://doi.org/10.1016/j.commatsci.2014.10.017
8	Leffers T. A modified Sachs approach to the plastic deformation of polycrystals as a realistic alternative to the Taylor mode. In: Haasen P, Gerold V, Kostorz G, eds. The Fifth International Conference on the Strength of Metals and Alloys, 1979, 769–774
9	Mao W. Modeling of rolling texture in aluminum. Materials Science and Engineering A, 1998, 257(1): 171–177 https://doi.org/10.1016/S0921-5093(98)00836-3
10	Mao W. Intergranular mechanical equilibrium during the rolling deformation of polycrystalline metals based on Taylor principles. Materials Science and Engineering A, 2016, 672: 129–134 https://doi.org/10.1016/j.msea.2016.06.085
11	Lebensohn R A, Tomé C N, Castañeda P P. Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations. Philosophical Magazine, 2007, 87(28): 4287–4322 https://doi.org/10.1080/14786430701432619
12	Engler O, Schäfer V, Brinkman H J. Crystal-plasticity simulation of the correlation of microtexture and roping in AA 6xxx Al–Mg–Si sheet alloys for automotive applications. Acta Materialia, 2012, 60(13–14): 5217–5232 https://doi.org/10.1016/j.actamat.2012.06.039
13	Van Houtte P, Li S, Seefeldt M, . Deformation texture prediction: from the Taylor model to the advanced lamel model. International Journal of Plasticity, 2005, 21(3): 589–624 https://doi.org/10.1016/j.ijplas.2004.04.011
14	Xie Q, Van Bael A, Sidor J, . A new cluster-type model for the simulation of textures of polycrystalline metals. Acta Materialia, 2014, 69(5): 175–186
15	Crumbach M, Goerdeler M, Gottstein G. Modelling of recrystallisation textures in aluminium alloys. Acta Materialia, 2006, 54(12): 3275–3289 https://doi.org/10.1016/j.actamat.2006.03.017
16	Mu S, Tang F, Gottstein G. A cluster-type grain interaction deformation texture model accounting for twinning-induced texture and strain-hardening evolution: Application to magnesium alloys. Acta Materialia, 2014, 68(15): 310–324 https://doi.org/10.1016/j.actamat.2013.12.007
17	Saleh A A, Haase C, Pereloma E V, . On the evolution and modelling of brass-type texture in cold-rolled twinning-induced plasticity steel. Acta Materialia, 2014, 70: 259–271 https://doi.org/10.1016/j.actamat.2014.02.033
18	Mao W, Yu Y. Reaction stress model and relaxation of reaction stress among the grains during tensile deformation of fcc metals. Materials Science Forum, 2005, 495–497: 995–1000 https://doi.org/10.4028/www.scientific.net/MSF.495-497.995
19	Zhao Z, Mao W, Roters F, . A texture optimization study for minimum earing in aluminum by use of a texture component crystal plasticity finite element method. Acta Materialia, 2004, 52(4): 1003–1012 https://doi.org/10.1016/j.actamat.2003.03.001
20	Roters F, Eisenlohr P, Hantcherli L, . Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Materialia, 2010, 58(4): 1152–1211 https://doi.org/10.1016/j.actamat.2009.10.058
21	Lebensohn R A, Rollet A D, Suquet P. Fast Fourier transform-based modeling for the determination of micromechanical fields in polycrystals. JOM, 2011, 63(3): 13–18 https://doi.org/10.1007/s11837-011-0037-y
22	Delannay L, Jacques P J, Kalidindi S R. Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons. International Journal of Plasticity, 2006, 22(10): 1879–1898 https://doi.org/10.1016/j.ijplas.2006.01.008
23	Zecevic M, Knezevic M, Beyerlein I J, . Texture formation in orthorhombic alpha-uranium under simple compression and rolling to high strains. Journal of Nuclear Materials, 2016, 473: 143–156 https://doi.org/10.1016/j.jnucmat.2016.02.021
24	Mao W, Yu Y. Effect of elastic reaction stress on plastic behaviors of grains in polycrystalline aggregate during tensile deformation. Materials Science and Engineering A, 2004, 367(1–2): 277–281 https://doi.org/10.1016/j.msea.2003.10.244
25	Hornbogen E, Warlimont H. Metallkunde. <Date>2nd ed</Date>. New York: Springer-Verlag, 1991, 204
26	Truszkowski W, Król J, Major B. Inhomogeneity of rolling texture in fcc metals. Metallurgical Transactions A: Physical Metallurgy and Materials Science, 1980, 11(5): 749–758 https://doi.org/10.1007/BF02661204

[1]	Weimin MAO. The currently predominant Taylor principles should be disregarded in the study of plastic deformation of metals[J]. Front. Mater. Sci., 2018, 12(3): 322-326.

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