Christian Klinkenberg 1,a, Helmut Klein 2,b, Jörg Gerlach 3,c

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1 Materials Science Forum Online: ISSN: -975, Vols , pp 93-9 doi:./ 5 Trans Tech Publications, Switzerland Texture Development during mechanical r-value Determination Christian Klinkenberg 1,a, Helmut Klein,b, Jörg Gerlach 3,c 1 Niobium Products Company GmbH, Steinstrasse, 3 Düsseldorf, Germany GZG Abt. Kristallografie der Uni. Göttingen, Goldschmidtstr.1, 3777 Göttingen, Germany 3 ThyssenKrupp Stahl AG, Kaiser-Wilhelm-Strasse, 7 Duisburg, Germany a ck@niobium.de, b hklein@gwdg.de, c joerg.gerlach@tks.thyssenkrupp.com Keywords: Steel, Sheet Forming, Yield Locus, r-value, Texture, Tensile Test Abstract. This investigation aimed at the understanding of texture development during determination by uniaxial tensile testing. Special emphasis was given to examine the texture evolution in the deformation zone of the tensile test specimen during mechanical determination. The textures of different sheet steel grades were investigated in different deformation stages by the orientation distribution function (ODF) and mechanical testing. Introduction The plastic material behaviour of steel sheet materials is characterised by the yield locus and work hardening. Computer simulations can predict the plastic behaviour of steel sheet material during forming processes. The yield condition according to Hill is most frequently implemented in the simulation programs. The classical way to determine the parameters of this yield locus is their calculation from the s (Lankford parameters). In industrial practice, s are measured by uniaxial tensile tests. This method provides data for discrete measuring directions. The calculation of the yield locus and the s from the crystallographic structure or texture would give information for each sample direction from one single measurement. In this method texture is characterised by the orientation distribution function (ODF) [1, ]. Another advantage of this method is the possibility of on-line measurement [3]. Fig. 1 shows distributions in the sheet plane that have been calculated from synthetically ODFs built up from ideal orientations of a typical steel sheet texture. However, s measured by mechanical tensile testing do not always agree with those calculated from texture. In general, s calculated from the texture data are significantly higher than those, which have been mechanically determined. Fig. shows a statistical evaluation covering different steel grades. It can be seen that the difference between the s measured mechanically and those calculated from texture data increase with the absolute value of the. This investigation aimed to analyze such differences in order to improve agreement between results obtained from these measuring techniques. Experimental Methods Mechanically achieved s have been determined by uniaxial tensile testing in the uniform deformation range. X-ray reflection measurements were carried out on a conventional texture goniometer using Co K α -radiation. The complete ODFs were calculated from the three pole figures (1), () and (11) [1,]. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-13/5/,3:3:1)

2 9 Textures of Materials - ICOTOM 3, {111}-Fibre 1. {111}<1> 1..5 {111}<1> Figure 1: s calculated from ideal orientations on the g-fibre r mechanical,5, 1,5 1,,5,,,5 1, 1,5,,5 3, r from ODF Figure : Comparison of mechanically determined and from texture calculated s In this paper, the ODFs are represented by fibre components []. The cold rolling and recrystallisation textures of low carbon steel sheet are composed of two fibre-components. The so-called α-fibre contains orientations with a common <1> axis parallel to the rolling direction, especially {1}<1>, {1}<1> and {111}<1>, whereas the γ-fibre comprises orientations with a <111> axis parallel to the sheet normal, as {111}<1> and {111}<1>. As both fibres meet in the {111}<1> position, this orientation appears on both fibres at g = {ϕ 1, φ, ϕ } = {, 55, 5}. Using a conventional X-ray texture equipment only reflection measurements of relatively thick sheets can be done because of the large absorption in the material. Those texture measurements are typically made in one plane of the texture specimen, thus being representative for local textures only. However, sheet material may have in-thickness texture inhomogeneities. The mechanical properties depend on the mean value from the texture of the whole specimen, which here called the global texture [,7]. In order to clarify the influence of local and global textures on the calculation of physical properties, texture studies were carried out by X-ray reflection measurements parallel to the rolling plane at different depths beneath the surface of the sheet material and on sandwich samples cut perpendicular to one of the sheet axes. ND TD RD Figure 3: technique for global texture determination The sandwich technique has been applied for the investigation of the texture development during uniaxial tensile testing and for calculation. This method, shown in Fig. 3, enables the measurement of the global sheet texture by integration across the sheet thickness [1,,5]. The s where calculated from the texture C- coefficients by means of the Taylor theory under the assumption of pencil glide modus [,7].

3 Materials Science Forum Vols Experimental Materials The chemical compositions of the examined steel grades are given in Table 1. S1-Nb is a niobium microalloyed high strength steel. S-P is phosphorus alloyed high strength steel and is a low carbon deep drawing steel grade. Material C Si Mn P S Al N Nb S1-Nb,5,3,9,15,,,9,7 S-P,5,,,7,,,7 -,,,13,7,,, - Table 1 Chemical compositions [mass %] All materials have been received as annealed cold rolled sheet in the temper rolled state with a thickness of 1. mm (S-P) and 1. mm (S1-Nb, ). S1-Nb steel had a mean grain size of. µm, S-P of.5 µm and of about µm. The s of the as received materials are given in Table. This table contains the mechanically achieved s and also the s calculated from the midsection and sandwich textures. s Material Method Sample longitudinal (L) diagonal (D) transverse (T) rm r S1-Nb mechanical tensile test " from texture midsection " " S-P mechanical tensile test " from texture midsection " " mechanical tensile test " from texture midsection " " Table s of the as-received sheet materials The and the S-P grade have favourable mechanical s greater than unity (>1). Variation of these s with respect to the measuring direction leads to s of about.. The S1-Nb grade has quite low mechanical s around 1 and a close to zero, indicating the quasi-isotropic mechanical behaviour of this material. Differences between mechanically determined s and s calculated from texture are discussed in this paper. Experimental Results Textures and r-values in the as received condition. Fig. and Fig. 5 show the textures of the and of the S-P grades in the as received condition. They exhibit a strong γ-fibre and a α-fibre with elevated orientation densities around 5 < φ <. The maximum finds at {111}<1>. The steel has a homogenous texture over all the sheet thickness. In comparison, the S-P grade shows some variations with regard to the different measured planes. The half-midsection texture is the strongest and the surface texture is the weakest texture. The intermediate sandwich texture is therefore supposed to give the best representation of the global texture.

4 9 Textures of Materials - ICOTOM {1} <1> {113} <1> {1} <1> {1} <1> ϕ 1 = ϕ = 5 Half- {111} <1> As Received <1> II LD {1} <1> {111} <1> ϕ = 5 {111} <1> {111} <31> 7 9 Figure : Local and global textures of steel grade {1} <1> {113} <1> {1} <1> {1} <1> ϕ 1 = ϕ = 5 Half- S-P As Received {111} <1> {1} <1> <1> II LD {111} <1> ϕ = 5 {111} <1> {111} <31> 7 9 Figure 5: Local and global textures of S-P steel grade {1} <1> {113} <1> {1} <1> {1} <1> S1-Nb As Received <1> II LD {111} <1> Half- {1} <1> ϕ1 = ϕ = {111} <1> {111} <1> {111} <31> ϕ = 5 A somewhat different texture gives Fig. for the S1-Nb steel with it s weaker, but more uniform γ-fibre and an α-fibre exhibiting elevated orientation densities from < φ < 5. The superposition of these texture components is at the origin of the quasi-isotropic properties []. The maximum position of the ODF depends sensitively on the measuring plane, shifting from φ (sandwich) to φ for the surface and midsection until φ = 55 in the case of half-midsection. As for the two other steel grades, sandwich technique gives the best representation of the global texture. Fig. 7 gives the variation of the in the sheet plane of the and of the S-P steel grades in the as received condition. Although there is good agreement between the general shape of the mechanically achieved curve and those calculated from the ODF data, there are significant differences with regard to the absolute values. The s calculated from the texture data are considerably higher than those, which have been determined by mechanical tensile testing. Even though the S-P steel shows considerable texture inhomo- geneities, there are only small differences between the s calculated from these local textures. Even with its better global texture recording, the sandwich technique does not give significantly better results. Figure : Local and global textures of S1-Nb steel grade

5 Materials Science Forum Vols S-P Half Half Mechanically achieved Mechanically achieved... Figure 7: Mechanically determined and from texture calculated s Fig. shows the typical curve of a microalloyed HSLA steel grade. These steel grades have typically s around unity and a close to zero, indicating the quasi-isotropic mechanical behaviour of this material. As for the two other steel grades, there is good agreement between the general distribution of the s determined mechanically and calculated from texture but discrepancy between the absolute values even when the sandwich technique is applied S1-Nb Mechanically achieved Half-. Figure : Mechanically determined and from texture calculated s of S1-Nb steel Texture and r-value Development during uniaxial Tension Test. Texture and mechanical properties have been determined after different amount of strain in the uniaxial tensile test. For these examinations, tensile test samples where cut at angles of, 5 and 9 to the rolling direction and strained in the uniform elongation range. The texture development of a tensile test sample is represented in Fig. 9. This figure gives the global texture development during uniaxial tension test at the example of steel grade. During straining, there is an increase of the maximum f(g) value on the α-fibre while the {111}<1> orientation on the γ-fibre is constantly decreasing. The same development was observed for all three steel grades and testing directions. {1} <1> {113} <1> {1} <1> {1} <1> <1> II RD = LD Deformation: % 3% % % % {111} <1> -Sample {1} <1> ϕ 1 = ϕ = {111} <1> Figure 9: Texture development during uniaxial tensile test parallel to RD {111} <1> {111} <31> ϕ = s r5-values r9-values white symbols: grey symbols: S-P black symbols: S1-Nb.. Strain ε total [%] Figure : Mechanically determined s as a function of strain Fig. gives the development of the mechanically achieved s as function of strain. Since the must be determined in the area of a homogeneous deformation, the attainable pre-straining is naturally always smaller than uniform elongation and differs with the steel grade.

6 9 Textures of Materials - ICOTOM It is remarkable that despite the above explained relevant texture changes during tensile deformation the mechanical achieved s are nearly constant, independent of the amount of applied strain. Discussion and Conclusion This investigation aimed to analyse the differences between s determined mechanically and calculated from texture in order to improve the agreement between these measuring techniques. As a first attempt the texture measuring technique has been modified. According to our results, the global sheet texture is generally better described by the sandwich technique, which takes into account texture inhomogeneities. In special cases, like the steel grade with its perfectly homogeneous texture, conventional midsection measurements can be applied. Orientierungsdichte {1} <1> {113} <1> {1} <1> {1} <1> ϕ 1 = ϕ = 5 Simulated Deformation: % (-sample) 3% % % % Taylor fc pencil glide {111} <1> {1} <1> <1> II RD = LD {111} <1> {111} <1> {111} <31> ϕ = Figure 11: Modeled texture development during uniaxial tensile test parallel to RD Despite the use of the global texture, there was no considerable improve in agreement between the s determined mechanically and calculated from texture. Therefore, the texture development during uniaxial tension test has been examined. The experimental results revealed the characteristic behavior described above. The s are calculated from the texture C- coefficients by means of the Taylor theory under the assumption of pencil glide modus [,7]. Fig. 11 gives the texture development of steel grade, as predicted by this model. The model gives good results for the evolution of the α-fibre orientations but does not predict the typical decrease of the {111}<1> orientation on the γ-fibre that is observed in mechanical tensile testing. This difference is supposed to be one of the reasons for the discrepancies between the s determined mechanically and calculated from texture. In order to clarify whether an optimised simulation model would give better agreement between s determined mechanically and calculated from texture, the model assumptions have to be revised. This concerns mainly the choice of active glide systems activated to simulate the uniaxial tensile test. References [1] H.J. Bunge, Texture Analysis in Material Science,. Auflage, Cuvillier-Verlag, Göttingen [] Dahlem-Klein, H. Klein, N.J. Park, ODF-Analysis for cubic cystal and orthorhombic sample symmetry, Cuvillier-Verlag, Göttingen [3] C. Klinkenberg, H.-P. Schmitz, H. Tamler, in Proc. ICOTOM (Ed. Jerzy A. Szpunar), NRC Research Press Ottawa, Canada 1999, pp [] C. Klinkenberg, D. Raabe, K. Lücke, Steel research 1993,, No. 5, pp. -. [5] H. Klein, C. Heubeck, H.J. Bunge, Mat. Sci. Forum 199, 157 -, 3. [] H.J. Bunge, in Directional properties of materials (Ed. H. J. Bunge), DGM Informationsgesellschaft, Oberursel 19, 1. [7] N.J. Park, H. Klein, E. Dahlem-Klein, Physical properties of textured materials, Cuvillier-Verlag, Göttingen 199. [] W. Zimnik, K. Freier, S. Hussy, H.J. Bunge, Steel research 1993,, No. /9,.

7 Textures of Materials - ICOTOM./ Texture Development during Mechanical r-value Determination./ DOI References [] H.J. Bunge, in Directional properties of materials (Ed. H. J. Bunge), DGM Informationsgesellschaft, Oberursel 19, /TSM.-9.1 [7] N.J. Park, H. Klein, E. Dahlem-Klein, Physical properties of textured materials, Cuvillier-Verlag, Gttingen 199../