Correlation of Texture and Plastic Anisotropy in the Al-Mg Alloy AA 5005

Transcription

1 Sold State Phenomena Vol. 15 (25) pp onlne at (25) Trans Tech Publcatons, Swtzerland Correlaton of Texture and Plastc Ansotropy n the Al-Mg Alloy AA 55 Olaf Engler 1,a, Yuguo An 2,b 1 Hydro Alumnum Deutschland GmbH, R&D Center Bonn, PO Box 2468, D-5314 Bonn, Germany 2 CORUS Research Development & Technology Centre, 197 CA IJmuden, The Netherlands a olaf.engler@hydro.com, b yuguo.an@corusgroup.com Keywords: rollng texture, ansotropy, yeld locus, alumnum alloys, AA 55. Abstract. The control of the plastc ansotropy durng formng of a metallc sheet requres detaled knowledge on ts mcrostructure and, especally, crystallographc texture. In the present paper the correlaton of texture and plastc ansotropy n the Al-Mg Alloy AA 55 s studed. Two dfferent materal states wth dfferent textures are compared, namely 1.7 mm thck soft-annealed materal (O-temper) and 1. mm cold rolled strp (state H14). Tensle tests were carred out at, 45 and 9 wth respect to the sheet rollng drecton and the resultng n-plane ansotropy n yeld strength, work hardenng and stran rate ratos (r-values) was determned. On a more general approach, texture-derved yeld loc are compared wth both phenomenologcal yeld functons and expermental data. Introducton Sheets from the medum strength Al-1%Mg alloy AA 55 are manly used for applcatons requrng a combnaton of hgher strength than acheved wth commercal purty Al wth good formablty and good corroson resstance. Snce many AA 55 products are deep drawn, formablty and especally ansotropy s a crtcal requrement. For nstance, when a sheet s probed n dfferent drectons, the yeld strength and the subsequent work hardenng as well as the stran ratos (r-values) wll vary as a functon of the n-plane angle α (see Fg. 1). It was the purpose of the present study to correlate the ansotropc propertes of AA 55 sheets wth ther crystallographc texture. AA 55 s typcally suppled ether n the fully soft annealed condton (O-temper) or n varous work hardened states (tempers H1x). Therefore, two dfferent states as charactersed by dfferent textures were analysed, vz. 1.7 mm thck soft materal (O-temper) and 1. mm cold rolled strp (temper H14). Texture-nduced ansotropy can be studed wth the help of polycrystal plastcty codes lke the famlar Taylor model [1,2]. In such approaches the respectve stran state s mposed on the sheet texture and the crystal response s computed n terms of the resultng stresses and strans. In the present work the vsco-plastc self-consstent (VPSC) formulaton [3] was employed. The VPSC model s a very versatle polycrystal approach whch accounts for ansotropc propertes of both the ndvdual crystals and the aggregate as a whole. Accordngly, ths approach has already been successfully appled to predct Fg. 1. Scheme of tensle tests under dfferent n-plane angles α and geometry defntons used n ths paper. 277 All rghts reserved. No part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of the publsher: Trans Tech Publcatons Ltd, Swtzerland, (ID: /1/6,8:37:1)

2 278 Texture and Ansotropy of Polycrystals II ansotropc propertes wth mnmum effort [4-6], especally because of the possblty of prescrbng mxed stran and stress boundary condtons. Expermental procedure Samples for the correlaton of sheet texture and ensung ansotropy were taken from sheets of the Al-Mg alloy AA 55 (Al.15%S.28%Fe.84%Mg), whch were produced by standard commercal routes at the Corus rollng mll n Duffel. Hot strp wth a thckness of 5 mm was cold rolled to 1.7 mm ntermedate gauge and then soft annealed for 22 h wth a peak metal temperature of 34 C. Fnally, sheets were cold rolled to fnal H14 temper at 1 mm gauge. Tensle tests were carred out n three drectons of the sheets, vz. parallel, under 45 and perpendcular to the rollng drecton, RD (Fg. 1). For texture analyss standard X-ray pole fgure measurements were employed; for detals see Ref. [7]. In order to be able to use texture data to predct materal propertes, average textures.e. textures ntegratng over all thckness layers had to be determned. For the ansotropy smulatons, the two sheet textures were then dscretsed nto sets of about 1 ndvdual orentatons wth equal weghts, such that the polycrystal s represented by a set of dstnct orentatons or grans that reproduce the ntal texture of the materal. Fg. 2 shows the texture of AA 55 n tempers O (1.7 mm) and H14 (1. mm), plotted wth so-ntensty lnes n ϕ 2 sectons through the three-dmensonal orentaton dstrbuton functons (ODFs). The soft AA 55-O exhbted a typcal cube recrystallsaton texture wth strong scatter along the rollng drecton. The mcrostructure of ths sheet was comprsed of farly fne graned equaxed recrystallsed grans wth an average sze of ~25 µm. In contrast, the cold rolled AA 55-H14 sheet revealed a rollng texture wth some retaned cube texture (Fg. 2b). Accordngly, the sheet showed a deformed mcrostructure wth elongated grans (Fg. 3). Texture and plastc ansotropy In order to assess plastc ansotropy wth the help of polycrystal plastcty models, the texture of the sheet s subjected to the correspondng external stresses and strans. Then, the polycrystal plastcty model here, the VPSC scheme [3] s employed to derve the materals response n terms of the actve slp systems and resultng strans, stresses, reorentaton, work hardenng, etc., whch can be utlsed to predct the evoluton of hardenng and texture assocated wth plastc formng. For a tensle test the stran rate D conssts of an elongaton along drecton X 1 plus the resultng shape changes n transverse drecton, X 2, and through-thckness drecton, X 3. For a textured materal, RD (a) AA 55-O (1.7 mm) (b) AA 55-H14 (1. mm) Fg. 2. Texture of AA 55 n two dfferent tempers. 278 Fg. 3. Mcrostructure of AA 55 n temper H14.

3 Sold State Phenomena Vol the exact values of the n-plane stran rate D 2 and the through-thckness stran rate D 3 are not known a pror, however. Therefore, the boundary condtons of unaxal tenson are better descrbed by assumng zero stresses σ 2 and σ 3 n drectons X 2 and X 3, respectvely. The rato of the resultng n-plane to through-thckness stran rates D 2 /D 3 then defnes the r-value. Thus, the boundary condtons mposed consst of a mxture of stress and stran rate components: 1 * * * D = * ε& σ = * (1) ( ε& step wdth; the asterx * ndcates that the correspondng value s not prescrbed.) It s commonly assumed that the strength of a materal relates to ts texture through the Taylor factor. The Taylor factor M of a dstnct gran s defned as the sum of slp contrbutons Σγ j on the j actve slp systems necessary to fulfl deformaton under the external shape change D, dvded by the appled stran ε [1,2]. For the Taylor factor smulatons the full constrants approach was employed to model one deformaton step wth a small ncrement of ε& =.1. The average Taylor factor can then readly be computed by ntegraton over the Taylor factors of the ndvdual orentatons that make up the sheet texture. In order to determne the n-plane varaton n Taylor factor, the external load case or alternatvely the texture has to be rotated n steps of typcally α=5 about the normal drecton, X 3. The evoluton of the Taylor factor M as a functon of α, scaled to the yeld strength for say α=, then gves the texture-based contrbuton to the yeld strength ansotropy. Fg. 4a shows the results obtaned for the AA 55 sheets n tempers O and H14. Despte the farly pronounced cube texture n the O-temper, there s only a mnor n-plane ansotropy n Taylor factor and, consequently, n yeld strength. In the stran-hardened H14 temper the predcted ansotropy s somewhat hgher, whch agrees well wth the mechancal data. The r-values smulated for the two sheets are summarsed n Fg. 4b together wth the respectve expermental data. In both cases, the texture-derved r-values ft the expermental results qute well. R p.2 RD 45 TD AA 55-H14 AA 55-O α (a) yeld strength ansotropy r RD 45 TD AA 55-H14 AA 55-O α (b) r-values Fg. 4. Correlaton of texture and ansotropy. The AA 55-H14 sheet wth the characterstc rollng texture (Fg. 2b) has low r-values n the RD and under 45, before r strongly ncreases to values n excess of 1 n the TD. Note that for the soft AA 279

4 28 Texture and Ansotropy of Polycrystals II 55-O sheet whch comprses a strong cube recrystallsaton texture a rather smlar n-plane ansotropy n r s obtaned, whch most notably mples a consderable asymmetry between the values at and 9. Ths s attrbuted to the remanders of the deformaton texture observed n ths state (Fg. 2a). Texture and work hardenng Texture does not only affect the yeld strength at the onset of plastc flow (.e. R p.2 ), but also the evoluton of strength upon further deformaton. Ths behavour can be smulated wth polycrystal plastcty models by ncorporatng a texture-dependent mcroscopc yeld law whch descrbes the ncrease n crtcal resolved stress, τ, as a functon of crystallographc slp, Γ. In ths study we adopt the generalsed Voce law ntroduced by Tomé et al. [8]: * * ( ) = τ + ( τ + θ Γ) [ 1 exp( Γθ τ )] τ Γ (2a) 1 1 / * * The mcroscopc Voce parameters τ, τ 1, θ and θ 1 are lnked to the parameters descrbng the macroscopc flow curves σ(ε) through the average Taylor factor M: σ = Mτ θ = θ (2b) 2 *, M For both tempers O and H14 the macroscopc Voce parameters were determned by fttng one of the expermental tensle true stress vs. true stran curves wth the correspondng Taylor factor M. In order to smulate the tensle test, the ntal texture was subjected to the stran rate D (Eq. 1) and the ensung texture evoluton was computed. Stress/stran curves were then obtaned by nputtng the resultant Taylor factors n Eq. (2). Fg. 5b llustrates the mpact of the texture-nduced n-plane varatons n M on the work hardenng behavour of AA 55-H14. In ths case only elongatons below 3% were obtaned. Therefore, texture changes need not to be consdered, whch means that the ntal Taylor factor can be used wthout further texture update. Apparently, the n-plane varatons n M account well for the dfferences n evoluton of yeld strength upon work hardenng AA 55-O 45 RD TD AA 55-H14 TD 45 σ σ 15 RD expermental Voce law ε expermental 1 Voce law ε (a) AA 55-O (1.7 mm) (b) AA 55-H14 (1. mm) Fg. 5. Impact of texture on the ansotropc work hardenng behavour. 28

5 Sold State Phenomena Vol In AA 55-O larger strans are obtaned (Fg. 5a); hence, here texture update durng tensle testng needs to be accounted for. Agan, t can be seen that the varatons n M account qute well for the (relatvely small) dfferences n evoluton of yeld strength upon work hardenng. Texture and yeld locus The conventonal way to smulate sheet formng operatons lke deep drawng s to employ the fnte element method (FEM). In order to account for crystallographc texture, the materal nput to the FEM the so-called consttutve equatons must ncorporate the ansotropc propertes of the sheet. For ths purpose, the plastc behavour s usually descrbed by a suted phenomenologcal yeld functon [9-11]. Fg. 6 shows results for the yeld locus of AA 55 n O-temper. Here, the conventonal plane spanned by the two n-plane stresses σ 1 and σ 2 s used, assumng that the through-thckness stress σ 3 s zero. Ths relates to the queston of whch baxal stress state defned by the two stresses σ 1 and σ 2 wll cause plastc flow of a sheet. The expermental yeld locus was 5 AA 55-O 5 AA 55-O σ 2-25 exp. CORUS exp. IFU Vegter Barlat '91 PCYS σ 2-25 exp. Corus Vegter PCYS -5-5 (a) /9 secton σ 1 (b) 45 /135 secton σ 1 Fg. 6. Correlaton of texture and yeld locus n AA 55-O. constructed from a number of dfferent mechancal tests performed at Corus R&D. These tests nclude unaxal and plane-stran tensle tests, a shear test as well as a through-thckness compresson test so as to obtan the baxal pont (σ 1 = σ 2 ) [12]. The yeld loc were determned n two dfferent sectons, namely the standard RD/TD plane ( /9 ) and n a 45 -ND rotated frame (45 /135 ). Followng the suggeston of Vegter et al. [1], the expermental data ponts were then ftted wth Bézer-functons so as to yeld a contnuous yeld functon sutable for an FEM model. Addtonal data ponts were obtaned at IFU Stuttgart wth crucform specmens on a CNC stretch-drawng devce [11]. By varyng the longtudnal and transversal load actng on the specmen dfferent ponts n the frst quadrant of the yeld locus can be measured (both stresses postve). These data were ftted wth the well-known yeld crteron of Barlat et al. [9]. Apparently, both yeld functons descrbe the expermental data ponts qute well, wth only mnor dfferences among them. Although such phenomenologcal yeld crtera can readly be mplemented nto FEM codes, the accuracy acheved wth ths method s often not satsfactory. Furthermore, the expermental determnaton of the parameters requred to ft the yeld functons s tedous. Therefore, t has been proposed to derve the ansotropc yeld locus drectly from the sheet texture (e.g. [13,14]). For that purpose, the texture s probed wth equ-spaced stran rates contaned n a gven plane here, the 281

6 282 Texture and Ansotropy of Polycrystals II σ 1 / σ 2 plane through the fve-dmensonal stress space. Fnally, the polycrystal yeld surface (PCYS) s normalsed wth the crtcal resolved shear stress, τ. A qualtatve comparson shows that the texture-derved yeld surface (full lne) fts the expermental data equally well as the two phenomenologcal yeld functons (Fg. 6). For a more quanttatve assessment of the texture-derved yeld locus, the r-values at α=, 45 and 9 were read out and compared wth the results obtaned n the correspondng unaxal tensle tests for AA55-O. The r-values correspond to the tangent to the yeld surface n the respectve pont of the yeld functon shown n Fg. 6. Comparson wth the expermental data (Table 1) shows the accuracy that can be acheved wth the texture-derved PCYS. Summary and conclusons The ansotropc propertes of the alloy Al-1%Mg (AA 55) n two tempers (O and H14) were smulated from the respectve sheet textures wth the help of the vsco-plastc self-consstent (VPSC) model. For ansotropy n yeld strength, work hardenng and r-values generally a good agreement between smulaton and experment s obtaned, whch valdates the use of polycrystal plastcty approaches n tacklng ansotropy. The VPSC approach can also be utlsed to compute texture-derved yeld functons (PCYS). Comparson of the polycrystal yeld surface wth two phenomenologcal yeld functons (Barlat 91 and Vegter) reveals that the former yelds no less than comparable match wth expermental results, but obtanable wth much lower expermental effort. In prncple, only one standard tensle test s requred so as to normalse the texture-derved PCYS to the actual yeld strength. Acknowledgements Table 1. Comparson of the r-values taken from the PCYS wth expermental results exp PCYS Ths work was supported by the EU through the Ffth Framework project VIR[FORM] (contract N G5RD-CT ). The VPSC software was provded by Dr. C.N. Tomé. The authors lke to thank Prof. D. Banabc for provdng the IFU yeld locus data. References [1] P. Van Houtte: Mater. Sc. Forum Vol (1998), p. 67. [2] U.F. Kocks, C.N. Tomé and H.R. Wenk: Texture and Ansotropy: Preferred Orentatons and ther Effect on Materals Propertes, Cambrdge Unv. Press, Cambrdge, UK, [3] R.A. Lebensohn and C.N. Tomé: Acta Metall. Mater. Vol. 41 (1993), p [4] S.-H. Cho, J.C. Brem, F. Barlat and K.H. Oh: Acta Mater. Vol. 48 (2), p [5] C.N. Tomé, R.A. Lebensohn and C.T. Necker: Metall. Mater. Trans. Vol. 33A (22), p [6] O. Engler: Alumnum Vol. 8 (24), p [7] V. Randle and O. Engler: Introducton to Texture Analyss: Macrotexture, Mcrotexture and Orentaton Mappng, Gordon and Breach Scence Publ., Amsterdam, 2. [8] C. Tomé, G.R. Canova, U.F. Kocks, N. Chrstodoulou and J.J. Jonas: Acta Metall. Vol. 32 (1984), p [9] F. Barlat, D.J. Lege and J.C. Brem: Int. J. Plast. Vol. 7 (1991), p

7 Sold State Phenomena Vol [1] H. Vegter, P. Drent and J. Huétnk: n Smulaton of Materals Processng: Theory, Methods and Applcaton, Proceedngs 5 th Numform 1995 (ed. by S. F. Shen and P.R. Dawson), A.A. Balkema, Rotterdam, 1995, p [11] D. Banabc and S. Wagner: Alumnum Vol. 78 (22), p [12] Y.G. An, H. Vegter, L. Ellott and J. Bottema: Alumnum Vol. 8 (24), p [13] B. Bacrox and P. Glormn: Model. Smul. Mater. Sc. Eng. Vol. 3 (1995), p. 1. [14] S. L, E. Hoferln, A. Van Bael and P. Van Houtte: Adv. Eng. Mater. Vol. 3 (21), p