- Email: [email protected]
Rolling and recrystallization textures in directionally solidified aluminium
A& melall. Vol. 35, No. 2, pp. 427438, 1987 Printed in Great Britain. All rights reserved
Copyright 0
oooi-6160/87 $3.00f0.00 Journals Ltd
1987 Pergamon
ROLLING AND RECRYSTALLIZATION TEXTURES IN DIRECTIONALLY SOLIDIFIED ALUMINIUM J. HIRSCH’, E. IVES’ and K. L&IKE’ ‘Institut fur Allg. Metallkunde und Metallphysik, RWTH Aachen, F.R.G. and *Department of Physical Metallurgy, 7034 Trondheim-NTH,
Norway
(Receirred 10 April 1986)
A&&a&-From dir~tionaliy solidified aluminium with a (IOO} fibre texture specimens of different orientations were cut and the textures after rolling (95% reduction) and recrystallization were determined. The results are discussed on the basis of the current concepts on deformation and recrystallization in single and polycrystalline materials. Due to the strong influence of the different starting textures, characteristic differences in the rolling textures are obtained. For the first time, a case is reported for which an experimental rolling texture is completely explicable in terms of the Taylor theory under full constraints condition. Further, the recrystallization textures, although appearing more uniform, exhibit clear differences which yield new evidence with respect to the mechanisms of formation of the cube texture. It shows that in the present case for obtaining a pronounced cube texture, both the conditions of oriented growth (in the sense of 40” (111) rotations) and oriented nucleation (in the sense of properly oriented transition bands) must occur.
R&urn&--Nousavons d&coup6 des Bchantillons de diffitrentes orientations dans de I’aluminium obtenu par solidification directionnelle et prbsentant une texture fibreuse (IOO), et nous avons dbtermini les textures apr&s laminage (rkduction de 9.5%) et recristallisation. Nous discutons les r6sultats sur la base des concepts actuels de la d~fo~ation et de la r~ristallisation dans les mat~riaux mono- et ~lycristallins. A cause de la forte influence des diffhrentes textures de dCpart, on obtient des diffkrences caractbristiques dans les textures de laminage. Pour la premitre fois, nous signalons un cas pour lequel une texture de laminage exgrimentale est complttement d&rite B l’aide de la thkorie de Taylor. De plus, les textures de r~ristallisation, bien qu’apparaissant plus uniformes, prksentent des differences nettes qui donnent de nouvelles donndes sur les mkcanismes de formation de la texture cubique. Si l’on veut obtenir dans le cas pr6sent une texture cubique prononcie, il fait satisfaire B la fois les conditions de la croissance orientte (c’est H dire des rotations de 40” autour de (111)) et de la germination orientCe (c’est B dire deux bandes de transition convenablement orient&s). Zusanunenfasaung-Aus einem gerichtet erstarrten Aluminium GuDblock mit einer (100) Fasertextur wurden unter~hi~lich orientierte Proben geschnitten und die Walztexturen (95% Walzgrad) und die Rekristallisaionstexturen ermittelt. Die Ergebnisse werden auf der Basis aktueller Konzepte iiber die Verformung und Rekristallisation ein- und vielkristalliner Metalle diskutiert. Der starke EinfluD der verschiednen Ausgangstexturen bewirkt charakteristische Unterschiede in den Walztexturen, So wird hier zum ersten Male der Fall gezeigt, bei dem eine experimentelle Walztextur mit der Vorhersage der strikten Taylor-Theorie v6llig iibereinstimmt. Die Rekristallisationstexturen ergeben ein sehr einheitliches Bild. Dennoch treten einige charakteristische Unterschiede auf, aus denen sich neu Erkenntnisse iiber die Ausbiidung der Wiirfeltextur ergeben. So zeigt der vorliegende Fall, daB fiir die Ausbildung einer ausgepriigten Wiirfeitextur beide Bedingungen, die des orientierten Wachstums (im Sinne einer 40” (11 l)-Orientierungsbeziehung) und die der orientierten Keimbildung (im Sinne entsprechend orientierter UbergangsbInder) erfiillt sein miissen.
1. I~RODU~ION
Based on the earlier experiments of Nes (11, rolling and recrystallization textures were determined on dir~tionalIy solidified aiuminium with a (100) fibre texture. By choosing different directions of rolling with respect to the fibre axis, the rolling texture as well as the alignment of boundary structures could systematically be varied. After numerous single crystal experiments, this work represents a further step in the investigation of the deformation and recrystallization behaviour of polycrystaltine materials, and, at the same time, reveals the influence of the starting texture on the roliing and r~rystalli~tion
textures. This latter aspect has received very little attention so far. The present work is concerned mainly with two important questions: (a) The extent of application of predictions, like the Taylor theory, in understanding particularly when the influence of the starting conditions, e.g. the initial texture and the grain boundary alignment is considered [2,3]. (b) The old question about the mechanism of formation of the cube orientation in recrystallization dominates the retextures. This orientation crystalIization textures of rolled pure f.c.c. metals
427
428
HIRSCH et al.:
TEXTURES
IN DIRECTIONALLY
with a high stacking fault energy, e.g. Al, but is never observed after rolling and annealing in single crystals, even if they have typical rolling texture orientations. The only known exception giving the cube orientation as a single crystal recrystallization component is after rolling the cube orientation itself. At high rolling reductions, this orientation is unstable with respect to rolling and splits into usual rolling texture orientations separated by large angle grain boundaries [4]. This demonstrates that the appearance of the cube texture depends on the presence and structure of grain boundaries in the rolled state. A particular aim of the present work is to investigate whether (i) the formation of the cube orientation during recrystallization requires cube orientations to be present in the structure before deformation [5], or whether (ii) cube nuclei will be formed during deformation, e.g. in transition bands or “divergent bands” (e.g. [6, 7]), or whether (iii) they are formed during recrystallization by a special nucleation mechanism (e.g. PI). The textures are analysed with the help of orientation distribution functions (“ODF”) which were determined by the series expansion method [9] and corrected with respect to ghost errors according to the method of Liicke et al. [lo]. ODF’s exhibit much better resolution than the (also shown) pole figures. These texture investigations are supplemented by electron microscope studies published in a separate paper [ 1I]. 2. EXPERIMENTAL The starting material was a directionally solidified high purity (99.999%) aluminium ingot [l] with nearly parallel columnar grains of a few millimetres in diameter and a (100) fibre texture. From this ingot plates of 15 x 25 x 50 mm3 of four different orientations were cut out and rolled. They were oriented in such a way that the (100) fibre axis was parallel to (1) (2) (3) (4) angle
the normal direction (ND) the transverse direction (TD) the rolling direction (RD) the direction bisecting ND and TD under 45” (Fig. 1).
They shall be denoted as SND, STD, SRD and S45, respectively. The plates were homogeneously cold rolled (I,/d > 1) to a reduction of 95%. From the resulting sheets of 0.75 mm thickness two sets of specimens of 15 x 25 mm* were cut out, one for measuring the roiling, the other for measuring the recrystallization textures. For the determination of the as-cast texture, i.e. before rolling, an average over eight specimens was taken because of the large initial grain size of l-5 mm (dia). In order to avoid surface effects, about 0.2mm were etched off. Recrystallization was achieved by heating for 10 s at 500°C in a salt bath.
SOLIDIFIED
Al
fibre axis (100)
Fig. 1. Orientation of samples with respect to the solidification direction, i.e. the (100) fibre axis. At this temperature definititely no in situ recrystallization which is observed at lower temperatures in high purity aluminium [12] occurs. The texture measurements were carried out on a fully automatic and computer-controlled texture goniometer [13] which is able to collect the data for four incomplete pole figures (1 ll}, (200}, {220}, {113) up to a tilting angle (a,,,,, = 85”) from which the three-dimensional orientation distribution functions (ODF’s) f(g) were calculated by the series expansion method of Bunge [9]. g represents an orientation here given by the three Euler angles ‘pi, 4, ‘p2. The ODF’s are represented in the three-dimensional Euler angle space for the range 0 < ‘p, ,4, cp2< a/2 of the coordinate axes. They are plotted in this space as iso intensity contour lines given in multiples of the random orientation density in sections where (p2 is constant. By a minimization procedure, each ODF could be fitted very well by a model consisting of several Gauss-type scattering components [13, 141. The resulting data for central orientations g,, volume fractions Mi and scattering width iji of the model components i (cf. Tables 1 and 2) represent a simple and quantitative description of the rather complicated textures. According to Liicke et al. [lo], the decomposition into Gauss-type components also allows the correction of the so-called “ghost errors”. These errors which cause artificial peaks and falsifications of the intensities f(g),,,, are due to the fact that the series expansion method yields only even (expansion) coefficients from the pole figure data [15]. By using odd coefficients calculated from the model ODF, the experimental ODF can be corrected and a complete and approximately ghost-free (“true”) ODF can be obtained. In the following only complete ODF data are used.
HIRSCH et al.:
TEXTURES
IN DIRECTIONALLY
SOLIDIFIED
Tables 1 and 2. Results of the ODF analysis with the help of Gaussscattering texture components. (The components are indicated by common names, the jhkQ(ww) give the rough Miller indices, co,, rp,(pzthe Euler angles of the central position of the Gauss component, SW,the calculated fraction and $, the half width of the best fitting Gauss components. The J(g) denote orientation density maxima present in the complete (true) ODF (L,, = 22)) Table I. Rolline texture comoonents Component
{h&1} (UBW)
‘p,
@
p2
M,
SND (Fibre r&s {IOU> ~~~al~~lm normal direction PiD) 84’ 27” 45’ 30% 112 111 CU
C&40 s/cu SNII Cube,, Cub+,
Random
12f 443 412 610 02i
113 124 123 001 012 -
-
70” 72‘ 45” 81 86’
27” 28“ 31 4” 27”
-
-
(Fibre axis (l&I> p~ruIl~I to fnmswrve 67‘ 30” 112 132 123 412 41’ 36” Cube 001 100 90” 4” 100 IO” 15” 013 Cube,, 90” 24’ Cube,, 012 OZI 84” 45” 011 Rot. Goss Ofl
STL,
CU,, s. ND
45 58’
68 IY 0 --
18% 20%
S45” (Fibre axis (100) Cu
II2
s/cu Bs Bs/Goss Goss Random
236 011 011 011 -
6%
-
jhkl)
45” 40” 45’ 14” 30: -
0” 77 0 0” 0” -
13% 23% 10% 2% 5% 2%
II1 322 211 311 I00 -
85” 61” 35” 23” 8” -
27’ 28’ 45” 45” 45’ -
45” 53’ 0’ 0” 0” -
025 011 -
Q,
+
qt
M,
+,,
100 100 -
0” 0’ -
21’ 37“ -
0” 0”
-
17% 7% 5%
Random
-
Rot. Goss Random
011 -
S4Y (Fibre axis (100) Cube,, cube Goss
BsjR Rot. Goss Random
3 5
16 I4 -
17 29 3 -
IO 36 -
texture components
{WV>
direrlion TD)
SRD (Fibre axis (100) cube 001 Cub+, 02.5 Goss 011
1.2” 5.4” 6.0” 6.8“ 5.7” 0.2” -
6.6” 8.6” 6.8” 6.9” 7.1’ -
STD (Fibre axis ( 100) parallri to iransoerse 025 I00 O^ 2” cutx CU~,lZ. 025 100 0‘ 20‘ Goss 01 I 100 0” 31” Oil 86” 45” Rot. Goss 011
-
7.x”
6% 27% 9% 29% 18% 11%
SND (Fibre axis (IO@> parallel IO normal direction ND) o0 71% 001 100 2” 3” Cube
Cuber0 Goss Random
-
-
rilted 45’ berween normal-transverse direction)
Table 2. Recrystallization Component
27’ 38” 12 8’ 90” -
33
3% 15%
8%
SRD (Fibre axis < IO0> parallel lo rolling direction RD) 236 322 61” 20” 58” 36% S/CU IIT 90” 28’ 60” 8% S 213
21T 273 617 100 021 -
6.3
6.7’ 7.6” 7.5” 7.1” 12.2’
0%
011 415 011 0.13 0.12 -
.fkN
di~eeIi~~ TD) 45’ 55% 9.6” 70‘ 8% 6.4” 0 2% 7.6” 0’ 2% 6.1” 0’ 27% 10.3” 0 6% 11.3”
Random
BY BS/S Bs/Goss Cab+, Cube,, Random
*0,
-
-
-
0”
51%
0” 0” 0”
28% 8% 3%
7%
II.1 7.3’ 6.7’ 9.2” 7.7’ 6.6‘~ 6.1’
-
f(gP
-5o 65 8
-
parallel to roiling direrlion RD)
100 100 loo OT1 -
0” 0” 0” 0‘ -
20%
9.1’ 6.x”
52 -
8%
6.Y
-
9%
8.6
5” 20” 38”
0’ 0” 0”
56%
84”
45”
-
-
7%
-
IO
-
449
lilted 45” between normal-transverse direction) 100 2” 24” 0” 41% 7.5” 40 100 0” 0” 0” 20% 7.1” 100 5” 35” 0” 10% 5.8’ 271 67” 33’ 42” 8% 6.8“ 5
011 -
011 -
025 017
011
0” -
84” -
45’ -
7% 14%
7.0’ -
10 -
Al
429
HIRSCH
430
ef
al.: TEXTURES
IN DIRECTIONALLY
(b)
(4
SOLIDIFIED
Al
‘pi
gi$-If_T
7
0
2 715
25 40 50 59 tp,=O”
Fig. 2. Texture
3. EXPERIMENTAL
of the as-cast
ingot.
(a) (200) pole figure.
RESULTS
General The ODF and the recalculated {200} pole figures of the starting material, as measured on sections perpendicular to the solidification direction of the ingot, are plotted in the coordinate system of the casting mould in Fig. 2. They show a strong (100) fibre texture with a preference of the cube orientation { lOO}(loo), caused by the quadratic form of the
(b) ODF
((p2 = Oq section).
casting mould. The maximum intensity along the fibre in the true ODF is f = 59 at (001 } (100) and the minimum is f = 5.9 at (001) (110). The starting textures with respect to the rolling coordinate system are indicated for the four specimens in Fig. 3(a) in a {11 l} pole figure and in Fig. 3(b) and (c) in the cpzand cpr= 0” sections of the Euler angle space. In Fig. 3(a) the fibre positions of the (100) fibre axis in the four specimens are indicated by numbers (see also Fig. 1). The { Ill} poles of each
hkl uvw - IJ too11(100)
- 0 -
-@
bl Fig. 3. Scheme of the starting
1001t (110)
q to111 (100) q 10111 COll) (223) CliO)
Cl textures of the four samples. (a) { 11 I} pole figure. (b) ODF ((p2 = 0” section). (c) ODF (cp, = 0” section).
HIRSCH
et al.:
TEXTURES
Fig. 4. {ill}
pole figures
IN DIRECTIONALLY
of the rolling
lying on 110” circles around these axes (solid lines). In the ODF’s for specimens SND, STD and SRD, the fibres are situated in the section ‘pZ= 0” given by the line 4 = @, ‘p, = 90” and cp, = O”, respectively (Fig. 3b). For S45 it can be located in the section cpl = 0’ at 4 = 45” (Fig. 3b). By these transformations the cube orientation of the original (ascast) fibre goes over into the position cube, cube and Goss {Oll}(lOO) for the specimens STD, SRD and S45, respectively, and the original (001) (110) orientation into rotated Goss {Oll}(Oll), Goss and (223) (110). These resulting orientations which characterize the starting texture of the four specimens are indicated in Fig. 3(aHc) by appropriate symbols. Figure 4(a)-(d) show the incomplete {11I} pole figures of the rolling textures and Fig. S(aHd) those of the corresponding recrystallization textures. Some of them are rather unsymmetric, but the main texture components are clearly visible. Characteristic orientation peaks are indicated by symbols and connected by dashed lines. In specimens SND, STD and SRD for which the texture was symmetric before rolling (cf. Figs 2 and 3) the unsymmetry is only a result of the large initial grain size. For specimen S45, in contrast, the unsymmetry of the rolling and recrystallization textures mainly stem from the unsymmetry of the texture before rolling. The corresponding complete ODF’s are given in Fig. 6(aHd) for the rolling textures and Fig. 7(aHd) for the recrystallization textures. For calculating them, the intensities were averaged over the four quadrants of the pole figures, according to the symmetry of the rolling process (also for specimen S45). They were decomposed into Gauss-type scattering components and corrected for the ghost error [lo]. fibre are
textures
Al
431
(95% red.).
For demonstrating the good fit which can be achieved by only a few model components, Fig. 8 shows the difference ODF between the experimental and model ODF’s for the rolling texture of the specimen SND as an example. (For Fig. 8 incomplete ODF’s without i.e. only l-even expansion ghost correction, coefficients, are used.) Only a few curves are visible which exceed the very low level of f5% of the maximum true intensity (see Fig. 6a). For the other ODF’s presented here the adaptations are of similar quality. For each component i the approximate Miller indices and the exact Euler angles of the best fitting centre orientation g, are listed in Tables 1 and 2, together with its volume fractions Mi and scattering width rji. f; is also listed which give heights of corresponding maxima of the complete ODF (also indicated in the ODF plots in Figs 6 and 7) for I,,, = 22. The components are denoted by the common names used for description of the pure metaltype rolling texture [16] or by their combination in cases where a peak is positioned in between two typical positions (e.g. S/Cu). Indices RD, TD, ND, indicate a certain rotation of a component about the rolling, transverse or normal direction, respectively. In the rolling textures, the main components are arranged along an orientation tube (p tube [17]). Figure 9(a) shows the positions of the skeleton lines of these tubes by plotting the angles cp, and 4 of the density maxima in the sections (p2= const. as function of (p2 (for one subspace only [lS]). Figure 9(b) gives the orientation densities f(g) along these lines. For comparison, the curves of a 95% rolled polycrystalline Al sheet (with some initial cube texture) are also plotted in Fig. 9.
Fig. 5. { I1 I j pole figures of the recrystallization AM. 35,2--K
SOLIDIFIED
textures.
432
HIRSCH et a/.:
a)SND
(lOO>\lND
TEXTURES
95%red.
IN DIRECTIONALLY
Ipz=const b)STD
SOLIDIFIED
(1OO)llTO
Al
95%red
20-25-30
20-25 cl
SRD
~100~11RD
95%red
q-cons'
tpz=const diS45
(100) 4 45" NDlTD 95%red
y2=const
Fig. 6. Complete ODF’s of the rolling textures (95% red.). Specimen SND (( 100) 11 ND) Rolling texture (Figs 4a and 6a). As in the former
investigation [ 11, the { 111) pole figures show the two symmetrically equivalent variants of the Cu orientation {112)(111) (better {44 ll}(ll 11 8)). This is also visible in the ODF where the maximum at ‘p, , #, (p2= 90”, 27”, 45” reaches an intensity of J; = 34 with a strong scattering in the rp, direction corresponding to a rotation around ND. To better adapt this scattering the centre of the isotropic Giiuss model component is positioned here at the non-symmetrical orientation at ‘p, = 84” (Table 1) instead of 90”. (The superposition of the two symmetrically equivalent
variants still produces the maximum at ‘pi = 90”.) To fully adapt the large scattering of this ~mponent, the auxiliary component Cu,, at cp, = 70” as well as the “S/Cu” component situated between the S and the Cu orientation together with the auxiliary component Go had to be introduced. The latter two components describe a scattering leading towards the S position {123} (634) which is the main polycrystalline rolling texture component [16] and part of the “orientation tube”. This tube presented by its skeleton line (Fig. 9) virtually ends at ‘pz= 70”. Together with all these scattering ranges the Cu component reaches a volume fraction of Mi 1: 75%. The rest of the texture is given
HIRSCH
a) SND
(100)II ND
et al.:
TEXTURES
recr
I
0 SRD
IN DIRECTIONALLY
v2=const.
I
(1OO)ll
RD
recr Fig. 7. Complete
b 1 STD
SOLIDIFIED
(100) II TO
433
Al
recr
ip,=const
I
Ip?=const. d)SLS ODF’s
by {012}(021) (-15%) whichcorresponds toacube orientation rotated around TD (cube,,) and by the background component (6%) which is a component constant over the whole orientation space and represents the more or less random part of the texture. Recrystallization texture (Figs 5a and 7a). After recrystallization, a strong cube texture is found both in the pole figure and the ODF. The latter additionally exhibits some scattering by rotation around RD which can well be described by two texture components, cube,, and the Goss orientation. The random component has here about the same value as in the rolling texture.
(100) U45" NO/TO
of the recrystallization
recr
q=const
textures.
Specimen STD (( 100) )IRD) Rolling texture (Figs 46 and 66). The
rather unsymmetric pole figure shows two equivalent variants of the ideal orientation {112) (132), a Cu orientation rotated around ND (Cu,,). This is also the main component in the ODF (Table 1). Together with an auxiliary component (S,,) covering the scatter towards the S orientation, it possesses a volume fraction of 63%. Again the skeleton line shows only a weak intensity at (p2> 70” (Fig. 9). The only other major component is (as before) (012) (021) (cube,,). Recrystallization texture (Figs 56 and B). Here again, a pronounced cube texture with a scattering by
HIRSCH ef al.: TEXTURES IN DIRECTIONALLY SOLIDIFIED Al
434
Specimen SRD (( 100) 11 RD)
+25 0
.
0
d
,
Rolling texture (Figs 4c and 6c). The slightly unsymmetric pole figure is formed mainly by three of the four equivalent variants of the S/Cu orientation (236) (322). The ODF data clearly reveals two main texture components: the S/Cu component with 45% volume fraction (together with an auxiliary component SND), and additionally the Bs component {011}(211) also with auxiliary components for the scattering towards S and Goss. Although these components overlap at 4z = 70” and form a continuous orientation tube in the Euler space (Fig. 6c) they can clearly be separated by the skeleton line analysis (Fig. 9). Some rotated Cube components again occur as very minor components. Recrystallization texture (Figs 5c and 7~). This texture is very similar to those of SND and SRD, but the rotated Goss component is somewhat more pronounced (cf. Table 2).
I 1 1 o I
1
+19
A
0
I
I
c
1
G
t2.6
01fference
0 0
-l.Vb
L,
e+19
- L.
Intensity ? 14 (S%fm.&
Fig. 8. Difference ODF (experimental minus model ODF) for SND rolling texture (Fig. 6a). rotations around RD is found. The latter is again adapted by the components cube,, and Goss. It also exhibits a peak (in the ODF) at the rotated Goss position {01 l} (011). (123) -(634)
(1121 -(ill)
I
f(g)
El q •l 0 0 -
50I
x -
Specimen S4.5 (( 1001145” ND-TD) Roiling texture (Figs 4d and 6~). Due to the unsymmetric starting texture (Fig. 3) only half the number of texture components to be expected from the symmetry of the rolling process appear in the pole figures. Two major components, the S/Cu and Bs/Goss orientation can be recognized already in the pole figure and are clearly visible as separate components in the ODF (Fig. 9). For the component
.
(100) (100) (100) (100)
IIND IITD IIRD &Y
ISNO) (ST01 (SROI w+S)
polycrystal FC model (normalized)
40 t
I
01 al
, ’
5o”
60’
v2iP-fibre)
.
7v
“P
80” -
I
‘O”
b)
I
50”
60°
q2 (P-fibre)
80°
70” -
Fig. 9. Skeleton line analysis of the rolling textures. (a) Orientation density distributions along the fl fibres. (b) Orientations of the fi fibre.
HIRSCH ef al.:
TEXTURES
IN DIRECTIONALLY
analysis of the ODF (Table l), the Bs and Goss orientation must be added as auxiliary components to adapt the strong ND scattering of the Bs/Goss orientation (together they reach 56%) and the Cu position covers the scattering of S/Cu. In this texture a rather strong background component (11%) is observed. Recrystallization texture (Figs 5d and 7d). The pole figure and the ODF clearly show that in this case the component is texture main recrystallization {025}(100), a cube position rotated -23” around RD. The scattering of this component around RD reaches the cube and Goss orientation which serve as auxiliary components, with only small intensities. As minor components the rotated Goss and an orientation (449) (274) similar to the Bs/R component {236) (385) known from the recrystallization texture of tl brass occur. As in the rolling textures here also the background component is rather strong (14%).
4. DISCUSSION AND INTERPRETATION Rolling textures
The large variety in the textures after 95% rolling reduction demonstrates the strong influence of the starting texture. The final rolling texture components are mostly situated on the well-known stable texture fibre (a fibre), but the differences in the initial texture results in different density distributions along this fibre (Fig. 9) e.g. in specimens SND and STD virtually no Bs component is formed, which is the main component in SRD and S45. This rolling texture development can be interpreted on the basis of calculations and experiments of the rolling texture development in single crystals and strongly textured sheets. From such investigations it is known that the (001) (100) cube orientation is transformed into the S component by rolling deformation [4, 191, and the cube,, (001) (110) into the Cu component [19-211. This explains the SND rolling texture with its initial orientation fibre between cube and cube,, that form the strong Cu and S/Cu orientation (still smeared out in ND). The Goss-oriented grains are known to rotate around the sheet normal towards the Bs component {Oil} (211) [19-211, which is the main rolling texture component in low stacking fault energy f.c.c. metals. Thus for SRD a component close to Bs is formed by orientations initially situated around the Goss position. The also present S/Cu component is again due to some originally cube oriented grains. In specimen STD the density maximum in the rolling texture lies in the Cu,, position. In this texture, however, a relatively large amount of the original cube,, orientations is left with a strong concentration at 4 = 24”. Even though this is not one of the typical stable orientations it can be noted that the cube,, is present in all rolling textures as was also found in
SOLIDIFIED
Al
435
electromicroscopal investigations of the material [ 111. Except for STD, this orientation must be formed during deformation. The relative large fraction of the newly formed cubern in SND probably stems from initially cube-oriented grains, situated close to cube,, grains, since the latter preferentially rotate around TD into the Cu orientation imposing some shear strain on its neighbourhood. This interpretation is supported by the coincidence of the TD rotation angle in both components of 27” (Table 1). In all these rolling textures at least small parts of the initial cube texture fibre are still present, which shows that some of these orientations have certain stability in rolling deformation. The strong Bs/Goss intensities in specimen S45 can be explained by rotations of the Goss orientation which in the initial texture is the one with the highest intensity. The other orientations of the initial fibre near (223) (110) are close to {Ill} (1 lo), which is known to be an unstable orientation in rolling deformation and rotates towards the Cu and Cu/S orientations [23]. Due to the stability of Cu and Cu/S these components reach a volume fraction of 33%. The rather high random volume fraction must be caused by a more diffuse type of rotation of the rest of the initial orientations due to their unsymmetrical position and the influence of other adjoining orientations. The Taylor model for ideal plane strain compression predicts (full constraints “FC”) the skeleton lines indicated in Fig. 9 by heavy lines and crosses. The experimental results for polycrystalline materials as well as for the present samples STD, SRD, and S45 show a systematic deviation of the /? fibre orientation (Fig. 9a) which can be explained by a relaxation of the Taylor constraints of ideal plane strain compression (relaxed constraints “RC”) [24,25] (also given in Fig. 9a). Here it is assumed that after rolling the grains, having taken the shape of thin bands, will be able to undergo also shear parallel to the rolling plane. However, as can be seen in Fig. 9, for the specimen SND the exact FC Taylor lines for the fi fibre orientation (Fig. 9a) and the (normalized) orientation density distribution (Fig. 9b) are resumed, i.e. here indeed plane strain compression has taken place. This is the first time that this has been observed in rolling in much detail and strongly supports the above interpretation. Because the dimension of the grains in ND is very large, and each grain is in contact with the rolling mill even after heavy rolling no relaxation of the constraints occurs. Further discussion of these aspects will be given in [26]. Recrystallization textures
Concerning the recrystallization textures, the use of specimens differing only in the direction of cutting (Fig. 1) allowed the study of the influence of the starting texture in isolation keeping all other parameters constant. The present work has yielded two rather striking results:
436
HIRSCH ef al.:
TEXTURES
IN DIRECTIONALLY
The first is that for the specimens SND, STD and SRD the recrystallization textures are nearly identical, although the rolling textures are very different. These recrystallization textures are very simple and consist, except for an additional small (011) (011) component in STD and SRD, in all the three cases of a strong cube texture (001) (100) with a scattering around RD. This is in accordance with the dominance of the cube texture in polycrystalline recrystallization of Al. It underlines the importance of grain boundaries, since the cube texture is never observed in recrystallized rolled single crystals having one of the typical rolling texture orientations as initial textures. The second striking result is that the recrystallization texture contains a dominant cube component only in these cases where the cube orientation was also present in the initial texture before rolling. Thus a strong cube component is found for the specimens SND, STD and SRD, but not for S45. There the cube orientation appears only as scattering from other maxima, although the rolling textures of specimens SRD and S45 are rather similar. This result agrees with the ones on rolled single crystals where the cube recrystallization texture was only found when an initial cube oriented crystal was rolled and annealed [4]. It does not agree with the assumption of the mechanism of “inverse Rowland transformation” [8] by which cube nuclei should be formed at twin boundaries of complementary variants of the Cu or Bs components in the deformed structure, e.g. in the STD rolling texture neither exact Cu nor Bs orientations occur and the ND scattering of the Cu component is not transformed into the cube recrystallization texture. Concerning the interpretation of these results two theoretical concepts are available in literature. First we have the concept of oriented growth [27] which says that the recrystallization texture is determined by those orientations which have the fastest growth rate with respect to the orientations of the deformed matrix. Growth rate measurements [28] and growth selection experiments [29] on Al single crystals showed a strong preference of 40” (111) orientation relationship which in most cases also explains the recrystallization textures of rolled f.c.c. single
LO0 (111) transformation
SOLIDIFIED
Al
crystals, e.g. [20,30] and some polycrystalline f.c.c. materials [12,31]. Often this theory is modified by assuming that the texture is determined not by the orientations with the maximum growth rate with respect to one rolling texture component but by “compromise orientations” having a medium high growth rate with respect to several matrix orientations [32]. The other concept is that of oriented nucleation which says that the recrystallization texture is determined by the orientations of the available nuclei. They are mainly found in transition bands, i.e. close to strong orientation gradients where they are able to build up fast high-angle grain boundaries of high mobility. This was specified by Dillamore and Katoh [7] who postulated that these transition bands are formed in divergent orientation zones, i.e. in regions where one orientation splits into two orientations by slip on different, but symmetrically equivalent (slip) systems. It follows further from this theory that during rolling certain grains (with an initial orientation belonging to (001) (WV) which correspond to the line ‘p,, with $J and cpZ= 0’) rotate towards the cube orientation and from these around RD. Therby they tend to split off and form transition bands which are capable of nucleating the cube and cube,,. For one case of polycrystalline copper, the cube grains were indeed shown to originate from small band-like subgrains within this type of transition bands [6]. However, in Al also other types of transition bands were found with preferred TD rotations around the cube grains [33]. Concerning the present recrystallization textures, it has been argued that the cube orientation cannot be formed by oriented growth, since none of the observed principal rolling orientations is related to it by 40” (111). Such an argument, however, carries little weight. Such a highly symmetrical maximum can easily be formed by a superposition of the 40” (111) rotated components and their symmetrically equivalent variants. This is indeed the case here as can be seen in the calculated transformation ODF’s in which the density not only of the maxima but of each orientation is transformed by the eight possible k40” rotations around its four (111) poles. In all four cases this leads to a maximum in {001}(100) as shown in Fig. 10. The (OOl}(lOO) orientation will
OOF
scale:l-2-3-4-S (L?#W
SND ST0 a) b) SRD 545 c) d1 Fig. 10. 40” (111) transformation ODFs (q2 = 0” sections) of the experimental rolling textures.
HIRSCH et al.: TEXTURES IN DIRECTIONALLY SOLIDIFIED Al further be amplified by its compromise character, i.e. by the fact that it possesses a preferred growth orientation relationship with respect to all four equivalent variants of the rolling components [32]. In the case of SND the strong (4 4 1l} (11 11 8) component should cause a pronounced scattering of orientations around ND. Even though not very pronounced, this type of scattering is indeed strongest in the SND recrystallization texture (Fig. 7a) compared to the others. In cases were no cube orientation was present before rolling, and as a consequence no preferred nucleation can occur, a strong Cu orientation in the rolling texture forms a strong ND rotated cube with an almost ideal 40” (111) orientation relationship 1191. On the other hand, the result that for the specimens SND, STD and SRD the recrystallization textures are rather similar despite the different preceding rolling textures and are given by the cube orientation and its rotations around RD represents a confirmation of the Dillamore-Katoh theory. Particularly convincing is that this theory predicts the scattering of the cube orientation corresponding to a rotation around RD which cannot be explained by the growth theories and also does not appear in the transformation ODF’s (Fig. 10). Moreover, the theory also explains the absence of the cube maximum for specimen S45. There the starting texture is far away from (0Ol}(u~) and the chance of obtaining cubeoriented nuclei should in this case be much less than for SND, STD and SRD. In spite of this, the unsymmetric initial S45 texture may give rise to similar transition bands. It follows from the RD rotated (100) fibre texture that RD rotated cube orientations ((hkl} (100)) may form during rolling, which subsequently give rise to divergent zones which contain similarly preferred nucleation sites. A 34” (111) orientation relationship to the main rolling texture component Bs/Goss can be found but cannot explain its dominance alone. The slower growth capacity of this component may also be the reason for the high random volume fraction and the appearance of the Bs/R component which has a good 40” (111) orientation relationship to the main rolling texture component, the Bs/Goss position, but which does not have these preferred nucleation sites. This component is very close to the main recrystallization component of c( brass {236} (385) for which it could be shown that the nuclei were formed by rccrystallization twinning. But since in Al no twinning occurs, here the nuclei must already be present in the rolling texture. The ODF’s show that this recrystallization component falls into the scattering of the ND rotated Cu orientation. The fact that the observed Bs/R component is shifted towards this position confirms the assumption that it might nucleate from such edge orientations. The origin of the minor recrystallization texture components, the Goss and rotated Goss position {all} (011) is not yet clear. The latter is observed as
437
a major recrystallization component only in strip cast aluminium alloys [34]. It is interesting to note that strip cast aluminium has an as-cast texture which can be derived from the present material by orienting the (100) fibre axis in between the normal and the casting direction of the as cast sheet. The angle between the casting direction and the (100) axis is about 20”. There might also be a certain preference in the nucleation of this orientation. Since it is not visible in the rolling texture it might also nucleate out of divergent zones formed between equivalent variants of the TD rotated cube orientations which occur in the rolling texture when grain boundaries are present. work is the resuit of Acknowledgements-This Norwegian-German research cooperation. The authors thank BFMT (Germany), NTNF (Norway), Vereinigte Aluminiumwerke AC and Ardal og Sunndal Verk AS for financial support. Special thanks are due to Mr S. Johanson (SINTEF) for providing the directionally solidified aluminium.
REFERENCES 1. E. Nes, SINTEF-Report No. 83-595-3050-3 (1983). 2. H. Mecking, Proc. 6th Int. Conf on Textures, Tokyo, p. 53 (1981). 3. J. Hirsch, H. Mecking and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 83 (1984). 4. G. D. Kohlhoff, B. Krentscher and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 95 (1984). 5. J. Grewen and J. Huber. Proc. 4th Eur. Colloq. on Textures, Cambridge, p. 138 (1975). 6. A. A. Ridha and W. B. Hutchingson, Acta metall. 30, 1129 (1982). 7. I. L. Dillamore and K. Katoh, Metal Sci. 8, 73 (1974). 8. C. A. Verbraak, Proc. ICOTOM 5, Aachen, p. Ill (1978). 9. H. J. Bunge, Mathematische Methoden der Texturanalyse. Akademie Verlag, Berlin (1969). 10. K. Liicke, J. Pospiech, K. H. Virnich and J. Jura, Acta mefall. 20, 167 (1981). 1I. E. Nes, J. Hirsch and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 663 (1984). 12. J. Hirsch and K. Liicke, Acta metall. 33, 1927 (1985). 13. J. Hirsch, M. Loeck, L. Loof and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 765 (1984). 14. W. Truszkowski, J. Pospiech, J. Jura and B. Major, Proc. 3rd Eur. Colloq. on Textures. Pont-a-Mousson (1973). 15. S. Matthies, Physica status solidi 92, 135 (1979). 16. J. Pospiech and K. Lticke, Acta Me&. 24; 997’(1975). 17. J. Hirsch and K. Liicke, submitted to Acta metall. 18. J. Hansen, J. Pospiech and K. Lticke, Tables for Texture Analysis of Cubic Crystals. Springer, Berlin (1978). 19. K. Liicke and J. Hirsch, Aluminium Technology, B. The Institute of Metals, London p. 66 (1986). In press. 20. G. D. Kohlhoff, J. Hirsch and U. V. Schlippenbach, Proc. ICOTOM 6, Tokyo, p. 489 (1981). and H. P. Stiiwe, 2. Metallk. 61, 128 21. E. Aernoudt (1970). 22. W. Heye and G. Wassermann, Z. Metallk. 59, 617 (1968). 23. A. Malin, J. Huber and M. Hatherly, Z. Mefallk. 72, 310 (1981). 24. H. Mecking, Proc. ICOTOM 6, Tokyo, p. 53 (1981). 25. J. Hirsch, K. Liicke and H. Mecking, Proc. 7th Int. Conf. on Textures, Noordwijkerhout, p. 83 (1984). 26. J. Hirsch and K. Liicke, in preparation.
HIRSCH et al.:
438
TEXTURES
IN DIRECTIONALLY
27. P. A. Beck, P. R. Sperry and H. Hu, J. appl. Physi. 21, 20 (1950).
28. B. Liebmann, K. Liicke and G. Masing, Z. Metaflk. 47, 57 (1956). 29. G. Ibe, W. Die&, C. A. Z. Metallk. 61, 498 (1970).
Fraker
and K. Liicke,
30. K. Liicke, R. Rixen and M. Senna, Acra metall. 24, 103 (1976).
SOLIDIFIED
Al
31. K. Liicke, Proc. 7th Int. Conf. on Textures, Noordwijkerhout, p. 185 (1984). 32. R. Rixen, R. Musick and H. GBker, Z. Metallk. 68, 16 (1975).
33. A. L. Dons and E. Nes, Proc. 7th Inc. Conf. on Textures, Noordwijkerhout, p. 53 (1984). 34. E. Nes and B. Andersson, Central Inst. of Industrial Research, Report No. 780138 (1980).
Copyright 0
oooi-6160/87 $3.00f0.00 Journals Ltd
1987 Pergamon
ROLLING AND RECRYSTALLIZATION TEXTURES IN DIRECTIONALLY SOLIDIFIED ALUMINIUM J. HIRSCH’, E. IVES’ and K. L&IKE’ ‘Institut fur Allg. Metallkunde und Metallphysik, RWTH Aachen, F.R.G. and *Department of Physical Metallurgy, 7034 Trondheim-NTH,
Norway
(Receirred 10 April 1986)
A&&a&-From dir~tionaliy solidified aluminium with a (IOO} fibre texture specimens of different orientations were cut and the textures after rolling (95% reduction) and recrystallization were determined. The results are discussed on the basis of the current concepts on deformation and recrystallization in single and polycrystalline materials. Due to the strong influence of the different starting textures, characteristic differences in the rolling textures are obtained. For the first time, a case is reported for which an experimental rolling texture is completely explicable in terms of the Taylor theory under full constraints condition. Further, the recrystallization textures, although appearing more uniform, exhibit clear differences which yield new evidence with respect to the mechanisms of formation of the cube texture. It shows that in the present case for obtaining a pronounced cube texture, both the conditions of oriented growth (in the sense of 40” (111) rotations) and oriented nucleation (in the sense of properly oriented transition bands) must occur.
R&urn&--Nousavons d&coup6 des Bchantillons de diffitrentes orientations dans de I’aluminium obtenu par solidification directionnelle et prbsentant une texture fibreuse (IOO), et nous avons dbtermini les textures apr&s laminage (rkduction de 9.5%) et recristallisation. Nous discutons les r6sultats sur la base des concepts actuels de la d~fo~ation et de la r~ristallisation dans les mat~riaux mono- et ~lycristallins. A cause de la forte influence des diffhrentes textures de dCpart, on obtient des diffkrences caractbristiques dans les textures de laminage. Pour la premitre fois, nous signalons un cas pour lequel une texture de laminage exgrimentale est complttement d&rite B l’aide de la thkorie de Taylor. De plus, les textures de r~ristallisation, bien qu’apparaissant plus uniformes, prksentent des differences nettes qui donnent de nouvelles donndes sur les mkcanismes de formation de la texture cubique. Si l’on veut obtenir dans le cas pr6sent une texture cubique prononcie, il fait satisfaire B la fois les conditions de la croissance orientte (c’est H dire des rotations de 40” autour de (111)) et de la germination orientCe (c’est B dire deux bandes de transition convenablement orient&s). Zusanunenfasaung-Aus einem gerichtet erstarrten Aluminium GuDblock mit einer (100) Fasertextur wurden unter~hi~lich orientierte Proben geschnitten und die Walztexturen (95% Walzgrad) und die Rekristallisaionstexturen ermittelt. Die Ergebnisse werden auf der Basis aktueller Konzepte iiber die Verformung und Rekristallisation ein- und vielkristalliner Metalle diskutiert. Der starke EinfluD der verschiednen Ausgangstexturen bewirkt charakteristische Unterschiede in den Walztexturen, So wird hier zum ersten Male der Fall gezeigt, bei dem eine experimentelle Walztextur mit der Vorhersage der strikten Taylor-Theorie v6llig iibereinstimmt. Die Rekristallisationstexturen ergeben ein sehr einheitliches Bild. Dennoch treten einige charakteristische Unterschiede auf, aus denen sich neu Erkenntnisse iiber die Ausbiidung der Wiirfeltextur ergeben. So zeigt der vorliegende Fall, daB fiir die Ausbildung einer ausgepriigten Wiirfeitextur beide Bedingungen, die des orientierten Wachstums (im Sinne einer 40” (11 l)-Orientierungsbeziehung) und die der orientierten Keimbildung (im Sinne entsprechend orientierter UbergangsbInder) erfiillt sein miissen.
1. I~RODU~ION
Based on the earlier experiments of Nes (11, rolling and recrystallization textures were determined on dir~tionalIy solidified aiuminium with a (100) fibre texture. By choosing different directions of rolling with respect to the fibre axis, the rolling texture as well as the alignment of boundary structures could systematically be varied. After numerous single crystal experiments, this work represents a further step in the investigation of the deformation and recrystallization behaviour of polycrystaltine materials, and, at the same time, reveals the influence of the starting texture on the roliing and r~rystalli~tion
textures. This latter aspect has received very little attention so far. The present work is concerned mainly with two important questions: (a) The extent of application of predictions, like the Taylor theory, in understanding particularly when the influence of the starting conditions, e.g. the initial texture and the grain boundary alignment is considered [2,3]. (b) The old question about the mechanism of formation of the cube orientation in recrystallization dominates the retextures. This orientation crystalIization textures of rolled pure f.c.c. metals
427
428
HIRSCH et al.:
TEXTURES
IN DIRECTIONALLY
with a high stacking fault energy, e.g. Al, but is never observed after rolling and annealing in single crystals, even if they have typical rolling texture orientations. The only known exception giving the cube orientation as a single crystal recrystallization component is after rolling the cube orientation itself. At high rolling reductions, this orientation is unstable with respect to rolling and splits into usual rolling texture orientations separated by large angle grain boundaries [4]. This demonstrates that the appearance of the cube texture depends on the presence and structure of grain boundaries in the rolled state. A particular aim of the present work is to investigate whether (i) the formation of the cube orientation during recrystallization requires cube orientations to be present in the structure before deformation [5], or whether (ii) cube nuclei will be formed during deformation, e.g. in transition bands or “divergent bands” (e.g. [6, 7]), or whether (iii) they are formed during recrystallization by a special nucleation mechanism (e.g. PI). The textures are analysed with the help of orientation distribution functions (“ODF”) which were determined by the series expansion method [9] and corrected with respect to ghost errors according to the method of Liicke et al. [lo]. ODF’s exhibit much better resolution than the (also shown) pole figures. These texture investigations are supplemented by electron microscope studies published in a separate paper [ 1I]. 2. EXPERIMENTAL The starting material was a directionally solidified high purity (99.999%) aluminium ingot [l] with nearly parallel columnar grains of a few millimetres in diameter and a (100) fibre texture. From this ingot plates of 15 x 25 x 50 mm3 of four different orientations were cut out and rolled. They were oriented in such a way that the (100) fibre axis was parallel to (1) (2) (3) (4) angle
the normal direction (ND) the transverse direction (TD) the rolling direction (RD) the direction bisecting ND and TD under 45” (Fig. 1).
They shall be denoted as SND, STD, SRD and S45, respectively. The plates were homogeneously cold rolled (I,/d > 1) to a reduction of 95%. From the resulting sheets of 0.75 mm thickness two sets of specimens of 15 x 25 mm* were cut out, one for measuring the roiling, the other for measuring the recrystallization textures. For the determination of the as-cast texture, i.e. before rolling, an average over eight specimens was taken because of the large initial grain size of l-5 mm (dia). In order to avoid surface effects, about 0.2mm were etched off. Recrystallization was achieved by heating for 10 s at 500°C in a salt bath.
SOLIDIFIED
Al
fibre axis (100)
Fig. 1. Orientation of samples with respect to the solidification direction, i.e. the (100) fibre axis. At this temperature definititely no in situ recrystallization which is observed at lower temperatures in high purity aluminium [12] occurs. The texture measurements were carried out on a fully automatic and computer-controlled texture goniometer [13] which is able to collect the data for four incomplete pole figures (1 ll}, (200}, {220}, {113) up to a tilting angle (a,,,,, = 85”) from which the three-dimensional orientation distribution functions (ODF’s) f(g) were calculated by the series expansion method of Bunge [9]. g represents an orientation here given by the three Euler angles ‘pi, 4, ‘p2. The ODF’s are represented in the three-dimensional Euler angle space for the range 0 < ‘p, ,4, cp2< a/2 of the coordinate axes. They are plotted in this space as iso intensity contour lines given in multiples of the random orientation density in sections where (p2 is constant. By a minimization procedure, each ODF could be fitted very well by a model consisting of several Gauss-type scattering components [13, 141. The resulting data for central orientations g,, volume fractions Mi and scattering width iji of the model components i (cf. Tables 1 and 2) represent a simple and quantitative description of the rather complicated textures. According to Liicke et al. [lo], the decomposition into Gauss-type components also allows the correction of the so-called “ghost errors”. These errors which cause artificial peaks and falsifications of the intensities f(g),,,, are due to the fact that the series expansion method yields only even (expansion) coefficients from the pole figure data [15]. By using odd coefficients calculated from the model ODF, the experimental ODF can be corrected and a complete and approximately ghost-free (“true”) ODF can be obtained. In the following only complete ODF data are used.
HIRSCH et al.:
TEXTURES
IN DIRECTIONALLY
SOLIDIFIED
Tables 1 and 2. Results of the ODF analysis with the help of Gaussscattering texture components. (The components are indicated by common names, the jhkQ(ww) give the rough Miller indices, co,, rp,(pzthe Euler angles of the central position of the Gauss component, SW,the calculated fraction and $, the half width of the best fitting Gauss components. The J(g) denote orientation density maxima present in the complete (true) ODF (L,, = 22)) Table I. Rolline texture comoonents Component
{h&1} (UBW)
‘p,
@
p2
M,
SND (Fibre r&s {IOU> ~~~al~~lm normal direction PiD) 84’ 27” 45’ 30% 112 111 CU
C&40 s/cu SNII Cube,, Cub+,
Random
12f 443 412 610 02i
113 124 123 001 012 -
-
70” 72‘ 45” 81 86’
27” 28“ 31 4” 27”
-
-
(Fibre axis (l&I> p~ruIl~I to fnmswrve 67‘ 30” 112 132 123 412 41’ 36” Cube 001 100 90” 4” 100 IO” 15” 013 Cube,, 90” 24’ Cube,, 012 OZI 84” 45” 011 Rot. Goss Ofl
STL,
CU,, s. ND
45 58’
68 IY 0 --
18% 20%
S45” (Fibre axis (100) Cu
II2
s/cu Bs Bs/Goss Goss Random
236 011 011 011 -
6%
-
jhkl)
45” 40” 45’ 14” 30: -
0” 77 0 0” 0” -
13% 23% 10% 2% 5% 2%
II1 322 211 311 I00 -
85” 61” 35” 23” 8” -
27’ 28’ 45” 45” 45’ -
45” 53’ 0’ 0” 0” -
025 011 -
Q,
+
qt
M,
+,,
100 100 -
0” 0’ -
21’ 37“ -
0” 0”
-
17% 7% 5%
Random
-
Rot. Goss Random
011 -
S4Y (Fibre axis (100) Cube,, cube Goss
BsjR Rot. Goss Random
3 5
16 I4 -
17 29 3 -
IO 36 -
texture components
{WV>
direrlion TD)
SRD (Fibre axis (100) cube 001 Cub+, 02.5 Goss 011
1.2” 5.4” 6.0” 6.8“ 5.7” 0.2” -
6.6” 8.6” 6.8” 6.9” 7.1’ -
STD (Fibre axis ( 100) parallri to iransoerse 025 I00 O^ 2” cutx CU~,lZ. 025 100 0‘ 20‘ Goss 01 I 100 0” 31” Oil 86” 45” Rot. Goss 011
-
7.x”
6% 27% 9% 29% 18% 11%
SND (Fibre axis (IO@> parallel IO normal direction ND) o0 71% 001 100 2” 3” Cube
Cuber0 Goss Random
-
-
rilted 45’ berween normal-transverse direction)
Table 2. Recrystallization Component
27’ 38” 12 8’ 90” -
33
3% 15%
8%
SRD (Fibre axis < IO0> parallel lo rolling direction RD) 236 322 61” 20” 58” 36% S/CU IIT 90” 28’ 60” 8% S 213
21T 273 617 100 021 -
6.3
6.7’ 7.6” 7.5” 7.1” 12.2’
0%
011 415 011 0.13 0.12 -
.fkN
di~eeIi~~ TD) 45’ 55% 9.6” 70‘ 8% 6.4” 0 2% 7.6” 0’ 2% 6.1” 0’ 27% 10.3” 0 6% 11.3”
Random
BY BS/S Bs/Goss Cab+, Cube,, Random
*0,
-
-
-
0”
51%
0” 0” 0”
28% 8% 3%
7%
II.1 7.3’ 6.7’ 9.2” 7.7’ 6.6‘~ 6.1’
-
f(gP
-5o 65 8
-
parallel to roiling direrlion RD)
100 100 loo OT1 -
0” 0” 0” 0‘ -
20%
9.1’ 6.x”
52 -
8%
6.Y
-
9%
8.6
5” 20” 38”
0’ 0” 0”
56%
84”
45”
-
-
7%
-
IO
-
449
lilted 45” between normal-transverse direction) 100 2” 24” 0” 41% 7.5” 40 100 0” 0” 0” 20% 7.1” 100 5” 35” 0” 10% 5.8’ 271 67” 33’ 42” 8% 6.8“ 5
011 -
011 -
025 017
011
0” -
84” -
45’ -
7% 14%
7.0’ -
10 -
Al
429
HIRSCH
430
ef
al.: TEXTURES
IN DIRECTIONALLY
(b)
(4
SOLIDIFIED
Al
‘pi
gi$-If_T
7
0
2 715
25 40 50 59 tp,=O”
Fig. 2. Texture
3. EXPERIMENTAL
of the as-cast
ingot.
(a) (200) pole figure.
RESULTS
General The ODF and the recalculated {200} pole figures of the starting material, as measured on sections perpendicular to the solidification direction of the ingot, are plotted in the coordinate system of the casting mould in Fig. 2. They show a strong (100) fibre texture with a preference of the cube orientation { lOO}(loo), caused by the quadratic form of the
(b) ODF
((p2 = Oq section).
casting mould. The maximum intensity along the fibre in the true ODF is f = 59 at (001 } (100) and the minimum is f = 5.9 at (001) (110). The starting textures with respect to the rolling coordinate system are indicated for the four specimens in Fig. 3(a) in a {11 l} pole figure and in Fig. 3(b) and (c) in the cpzand cpr= 0” sections of the Euler angle space. In Fig. 3(a) the fibre positions of the (100) fibre axis in the four specimens are indicated by numbers (see also Fig. 1). The { Ill} poles of each
hkl uvw - IJ too11(100)
- 0 -
-@
bl Fig. 3. Scheme of the starting
1001t (110)
q to111 (100) q 10111 COll) (223) CliO)
Cl textures of the four samples. (a) { 11 I} pole figure. (b) ODF ((p2 = 0” section). (c) ODF (cp, = 0” section).
HIRSCH
et al.:
TEXTURES
Fig. 4. {ill}
pole figures
IN DIRECTIONALLY
of the rolling
lying on 110” circles around these axes (solid lines). In the ODF’s for specimens SND, STD and SRD, the fibres are situated in the section ‘pZ= 0” given by the line 4 = @, ‘p, = 90” and cp, = O”, respectively (Fig. 3b). For S45 it can be located in the section cpl = 0’ at 4 = 45” (Fig. 3b). By these transformations the cube orientation of the original (ascast) fibre goes over into the position cube, cube and Goss {Oll}(lOO) for the specimens STD, SRD and S45, respectively, and the original (001) (110) orientation into rotated Goss {Oll}(Oll), Goss and (223) (110). These resulting orientations which characterize the starting texture of the four specimens are indicated in Fig. 3(aHc) by appropriate symbols. Figure 4(a)-(d) show the incomplete {11I} pole figures of the rolling textures and Fig. S(aHd) those of the corresponding recrystallization textures. Some of them are rather unsymmetric, but the main texture components are clearly visible. Characteristic orientation peaks are indicated by symbols and connected by dashed lines. In specimens SND, STD and SRD for which the texture was symmetric before rolling (cf. Figs 2 and 3) the unsymmetry is only a result of the large initial grain size. For specimen S45, in contrast, the unsymmetry of the rolling and recrystallization textures mainly stem from the unsymmetry of the texture before rolling. The corresponding complete ODF’s are given in Fig. 6(aHd) for the rolling textures and Fig. 7(aHd) for the recrystallization textures. For calculating them, the intensities were averaged over the four quadrants of the pole figures, according to the symmetry of the rolling process (also for specimen S45). They were decomposed into Gauss-type scattering components and corrected for the ghost error [lo]. fibre are
textures
Al
431
(95% red.).
For demonstrating the good fit which can be achieved by only a few model components, Fig. 8 shows the difference ODF between the experimental and model ODF’s for the rolling texture of the specimen SND as an example. (For Fig. 8 incomplete ODF’s without i.e. only l-even expansion ghost correction, coefficients, are used.) Only a few curves are visible which exceed the very low level of f5% of the maximum true intensity (see Fig. 6a). For the other ODF’s presented here the adaptations are of similar quality. For each component i the approximate Miller indices and the exact Euler angles of the best fitting centre orientation g, are listed in Tables 1 and 2, together with its volume fractions Mi and scattering width rji. f; is also listed which give heights of corresponding maxima of the complete ODF (also indicated in the ODF plots in Figs 6 and 7) for I,,, = 22. The components are denoted by the common names used for description of the pure metaltype rolling texture [16] or by their combination in cases where a peak is positioned in between two typical positions (e.g. S/Cu). Indices RD, TD, ND, indicate a certain rotation of a component about the rolling, transverse or normal direction, respectively. In the rolling textures, the main components are arranged along an orientation tube (p tube [17]). Figure 9(a) shows the positions of the skeleton lines of these tubes by plotting the angles cp, and 4 of the density maxima in the sections (p2= const. as function of (p2 (for one subspace only [lS]). Figure 9(b) gives the orientation densities f(g) along these lines. For comparison, the curves of a 95% rolled polycrystalline Al sheet (with some initial cube texture) are also plotted in Fig. 9.
Fig. 5. { I1 I j pole figures of the recrystallization AM. 35,2--K
SOLIDIFIED
textures.
432
HIRSCH et a/.:
a)SND
(lOO>\lND
TEXTURES
95%red.
IN DIRECTIONALLY
Ipz=const b)STD
SOLIDIFIED
(1OO)llTO
Al
95%red
20-25-30
20-25 cl
SRD
~100~11RD
95%red
q-cons'
tpz=const diS45
(100) 4 45" NDlTD 95%red
y2=const
Fig. 6. Complete ODF’s of the rolling textures (95% red.). Specimen SND (( 100) 11 ND) Rolling texture (Figs 4a and 6a). As in the former
investigation [ 11, the { 111) pole figures show the two symmetrically equivalent variants of the Cu orientation {112)(111) (better {44 ll}(ll 11 8)). This is also visible in the ODF where the maximum at ‘p, , #, (p2= 90”, 27”, 45” reaches an intensity of J; = 34 with a strong scattering in the rp, direction corresponding to a rotation around ND. To better adapt this scattering the centre of the isotropic Giiuss model component is positioned here at the non-symmetrical orientation at ‘p, = 84” (Table 1) instead of 90”. (The superposition of the two symmetrically equivalent
variants still produces the maximum at ‘pi = 90”.) To fully adapt the large scattering of this ~mponent, the auxiliary component Cu,, at cp, = 70” as well as the “S/Cu” component situated between the S and the Cu orientation together with the auxiliary component Go had to be introduced. The latter two components describe a scattering leading towards the S position {123} (634) which is the main polycrystalline rolling texture component [16] and part of the “orientation tube”. This tube presented by its skeleton line (Fig. 9) virtually ends at ‘pz= 70”. Together with all these scattering ranges the Cu component reaches a volume fraction of Mi 1: 75%. The rest of the texture is given
HIRSCH
a) SND
(100)II ND
et al.:
TEXTURES
recr
I
0 SRD
IN DIRECTIONALLY
v2=const.
I
(1OO)ll
RD
recr Fig. 7. Complete
b 1 STD
SOLIDIFIED
(100) II TO
433
Al
recr
ip,=const
I
Ip?=const. d)SLS ODF’s
by {012}(021) (-15%) whichcorresponds toacube orientation rotated around TD (cube,,) and by the background component (6%) which is a component constant over the whole orientation space and represents the more or less random part of the texture. Recrystallization texture (Figs 5a and 7a). After recrystallization, a strong cube texture is found both in the pole figure and the ODF. The latter additionally exhibits some scattering by rotation around RD which can well be described by two texture components, cube,, and the Goss orientation. The random component has here about the same value as in the rolling texture.
(100) U45" NO/TO
of the recrystallization
recr
q=const
textures.
Specimen STD (( 100) )IRD) Rolling texture (Figs 46 and 66). The
rather unsymmetric pole figure shows two equivalent variants of the ideal orientation {112) (132), a Cu orientation rotated around ND (Cu,,). This is also the main component in the ODF (Table 1). Together with an auxiliary component (S,,) covering the scatter towards the S orientation, it possesses a volume fraction of 63%. Again the skeleton line shows only a weak intensity at (p2> 70” (Fig. 9). The only other major component is (as before) (012) (021) (cube,,). Recrystallization texture (Figs 56 and B). Here again, a pronounced cube texture with a scattering by
HIRSCH ef al.: TEXTURES IN DIRECTIONALLY SOLIDIFIED Al
434
Specimen SRD (( 100) 11 RD)
+25 0
.
0
d
,
Rolling texture (Figs 4c and 6c). The slightly unsymmetric pole figure is formed mainly by three of the four equivalent variants of the S/Cu orientation (236) (322). The ODF data clearly reveals two main texture components: the S/Cu component with 45% volume fraction (together with an auxiliary component SND), and additionally the Bs component {011}(211) also with auxiliary components for the scattering towards S and Goss. Although these components overlap at 4z = 70” and form a continuous orientation tube in the Euler space (Fig. 6c) they can clearly be separated by the skeleton line analysis (Fig. 9). Some rotated Cube components again occur as very minor components. Recrystallization texture (Figs 5c and 7~). This texture is very similar to those of SND and SRD, but the rotated Goss component is somewhat more pronounced (cf. Table 2).
I 1 1 o I
1
+19
A
0
I
I
c
1
G
t2.6
01fference
0 0
-l.Vb
L,
e+19
- L.
Intensity ? 14 (S%fm.&
Fig. 8. Difference ODF (experimental minus model ODF) for SND rolling texture (Fig. 6a). rotations around RD is found. The latter is again adapted by the components cube,, and Goss. It also exhibits a peak (in the ODF) at the rotated Goss position {01 l} (011). (123) -(634)
(1121 -(ill)
I
f(g)
El q •l 0 0 -
50I
x -
Specimen S4.5 (( 1001145” ND-TD) Roiling texture (Figs 4d and 6~). Due to the unsymmetric starting texture (Fig. 3) only half the number of texture components to be expected from the symmetry of the rolling process appear in the pole figures. Two major components, the S/Cu and Bs/Goss orientation can be recognized already in the pole figure and are clearly visible as separate components in the ODF (Fig. 9). For the component
.
(100) (100) (100) (100)
IIND IITD IIRD &Y
ISNO) (ST01 (SROI w+S)
polycrystal FC model (normalized)
40 t
I
01 al
, ’
5o”
60’
v2iP-fibre)
.
7v
“P
80” -
I
‘O”
b)
I
50”
60°
q2 (P-fibre)
80°
70” -
Fig. 9. Skeleton line analysis of the rolling textures. (a) Orientation density distributions along the fl fibres. (b) Orientations of the fi fibre.
HIRSCH ef al.:
TEXTURES
IN DIRECTIONALLY
analysis of the ODF (Table l), the Bs and Goss orientation must be added as auxiliary components to adapt the strong ND scattering of the Bs/Goss orientation (together they reach 56%) and the Cu position covers the scattering of S/Cu. In this texture a rather strong background component (11%) is observed. Recrystallization texture (Figs 5d and 7d). The pole figure and the ODF clearly show that in this case the component is texture main recrystallization {025}(100), a cube position rotated -23” around RD. The scattering of this component around RD reaches the cube and Goss orientation which serve as auxiliary components, with only small intensities. As minor components the rotated Goss and an orientation (449) (274) similar to the Bs/R component {236) (385) known from the recrystallization texture of tl brass occur. As in the rolling textures here also the background component is rather strong (14%).
4. DISCUSSION AND INTERPRETATION Rolling textures
The large variety in the textures after 95% rolling reduction demonstrates the strong influence of the starting texture. The final rolling texture components are mostly situated on the well-known stable texture fibre (a fibre), but the differences in the initial texture results in different density distributions along this fibre (Fig. 9) e.g. in specimens SND and STD virtually no Bs component is formed, which is the main component in SRD and S45. This rolling texture development can be interpreted on the basis of calculations and experiments of the rolling texture development in single crystals and strongly textured sheets. From such investigations it is known that the (001) (100) cube orientation is transformed into the S component by rolling deformation [4, 191, and the cube,, (001) (110) into the Cu component [19-211. This explains the SND rolling texture with its initial orientation fibre between cube and cube,, that form the strong Cu and S/Cu orientation (still smeared out in ND). The Goss-oriented grains are known to rotate around the sheet normal towards the Bs component {Oil} (211) [19-211, which is the main rolling texture component in low stacking fault energy f.c.c. metals. Thus for SRD a component close to Bs is formed by orientations initially situated around the Goss position. The also present S/Cu component is again due to some originally cube oriented grains. In specimen STD the density maximum in the rolling texture lies in the Cu,, position. In this texture, however, a relatively large amount of the original cube,, orientations is left with a strong concentration at 4 = 24”. Even though this is not one of the typical stable orientations it can be noted that the cube,, is present in all rolling textures as was also found in
SOLIDIFIED
Al
435
electromicroscopal investigations of the material [ 111. Except for STD, this orientation must be formed during deformation. The relative large fraction of the newly formed cubern in SND probably stems from initially cube-oriented grains, situated close to cube,, grains, since the latter preferentially rotate around TD into the Cu orientation imposing some shear strain on its neighbourhood. This interpretation is supported by the coincidence of the TD rotation angle in both components of 27” (Table 1). In all these rolling textures at least small parts of the initial cube texture fibre are still present, which shows that some of these orientations have certain stability in rolling deformation. The strong Bs/Goss intensities in specimen S45 can be explained by rotations of the Goss orientation which in the initial texture is the one with the highest intensity. The other orientations of the initial fibre near (223) (110) are close to {Ill} (1 lo), which is known to be an unstable orientation in rolling deformation and rotates towards the Cu and Cu/S orientations [23]. Due to the stability of Cu and Cu/S these components reach a volume fraction of 33%. The rather high random volume fraction must be caused by a more diffuse type of rotation of the rest of the initial orientations due to their unsymmetrical position and the influence of other adjoining orientations. The Taylor model for ideal plane strain compression predicts (full constraints “FC”) the skeleton lines indicated in Fig. 9 by heavy lines and crosses. The experimental results for polycrystalline materials as well as for the present samples STD, SRD, and S45 show a systematic deviation of the /? fibre orientation (Fig. 9a) which can be explained by a relaxation of the Taylor constraints of ideal plane strain compression (relaxed constraints “RC”) [24,25] (also given in Fig. 9a). Here it is assumed that after rolling the grains, having taken the shape of thin bands, will be able to undergo also shear parallel to the rolling plane. However, as can be seen in Fig. 9, for the specimen SND the exact FC Taylor lines for the fi fibre orientation (Fig. 9a) and the (normalized) orientation density distribution (Fig. 9b) are resumed, i.e. here indeed plane strain compression has taken place. This is the first time that this has been observed in rolling in much detail and strongly supports the above interpretation. Because the dimension of the grains in ND is very large, and each grain is in contact with the rolling mill even after heavy rolling no relaxation of the constraints occurs. Further discussion of these aspects will be given in [26]. Recrystallization textures
Concerning the recrystallization textures, the use of specimens differing only in the direction of cutting (Fig. 1) allowed the study of the influence of the starting texture in isolation keeping all other parameters constant. The present work has yielded two rather striking results:
436
HIRSCH ef al.:
TEXTURES
IN DIRECTIONALLY
The first is that for the specimens SND, STD and SRD the recrystallization textures are nearly identical, although the rolling textures are very different. These recrystallization textures are very simple and consist, except for an additional small (011) (011) component in STD and SRD, in all the three cases of a strong cube texture (001) (100) with a scattering around RD. This is in accordance with the dominance of the cube texture in polycrystalline recrystallization of Al. It underlines the importance of grain boundaries, since the cube texture is never observed in recrystallized rolled single crystals having one of the typical rolling texture orientations as initial textures. The second striking result is that the recrystallization texture contains a dominant cube component only in these cases where the cube orientation was also present in the initial texture before rolling. Thus a strong cube component is found for the specimens SND, STD and SRD, but not for S45. There the cube orientation appears only as scattering from other maxima, although the rolling textures of specimens SRD and S45 are rather similar. This result agrees with the ones on rolled single crystals where the cube recrystallization texture was only found when an initial cube oriented crystal was rolled and annealed [4]. It does not agree with the assumption of the mechanism of “inverse Rowland transformation” [8] by which cube nuclei should be formed at twin boundaries of complementary variants of the Cu or Bs components in the deformed structure, e.g. in the STD rolling texture neither exact Cu nor Bs orientations occur and the ND scattering of the Cu component is not transformed into the cube recrystallization texture. Concerning the interpretation of these results two theoretical concepts are available in literature. First we have the concept of oriented growth [27] which says that the recrystallization texture is determined by those orientations which have the fastest growth rate with respect to the orientations of the deformed matrix. Growth rate measurements [28] and growth selection experiments [29] on Al single crystals showed a strong preference of 40” (111) orientation relationship which in most cases also explains the recrystallization textures of rolled f.c.c. single
LO0 (111) transformation
SOLIDIFIED
Al
crystals, e.g. [20,30] and some polycrystalline f.c.c. materials [12,31]. Often this theory is modified by assuming that the texture is determined not by the orientations with the maximum growth rate with respect to one rolling texture component but by “compromise orientations” having a medium high growth rate with respect to several matrix orientations [32]. The other concept is that of oriented nucleation which says that the recrystallization texture is determined by the orientations of the available nuclei. They are mainly found in transition bands, i.e. close to strong orientation gradients where they are able to build up fast high-angle grain boundaries of high mobility. This was specified by Dillamore and Katoh [7] who postulated that these transition bands are formed in divergent orientation zones, i.e. in regions where one orientation splits into two orientations by slip on different, but symmetrically equivalent (slip) systems. It follows further from this theory that during rolling certain grains (with an initial orientation belonging to (001) (WV) which correspond to the line ‘p,, with $J and cpZ= 0’) rotate towards the cube orientation and from these around RD. Therby they tend to split off and form transition bands which are capable of nucleating the cube and cube,,. For one case of polycrystalline copper, the cube grains were indeed shown to originate from small band-like subgrains within this type of transition bands [6]. However, in Al also other types of transition bands were found with preferred TD rotations around the cube grains [33]. Concerning the present recrystallization textures, it has been argued that the cube orientation cannot be formed by oriented growth, since none of the observed principal rolling orientations is related to it by 40” (111). Such an argument, however, carries little weight. Such a highly symmetrical maximum can easily be formed by a superposition of the 40” (111) rotated components and their symmetrically equivalent variants. This is indeed the case here as can be seen in the calculated transformation ODF’s in which the density not only of the maxima but of each orientation is transformed by the eight possible k40” rotations around its four (111) poles. In all four cases this leads to a maximum in {001}(100) as shown in Fig. 10. The (OOl}(lOO) orientation will
OOF
scale:l-2-3-4-S (L?#W
SND ST0 a) b) SRD 545 c) d1 Fig. 10. 40” (111) transformation ODFs (q2 = 0” sections) of the experimental rolling textures.
HIRSCH et al.: TEXTURES IN DIRECTIONALLY SOLIDIFIED Al further be amplified by its compromise character, i.e. by the fact that it possesses a preferred growth orientation relationship with respect to all four equivalent variants of the rolling components [32]. In the case of SND the strong (4 4 1l} (11 11 8) component should cause a pronounced scattering of orientations around ND. Even though not very pronounced, this type of scattering is indeed strongest in the SND recrystallization texture (Fig. 7a) compared to the others. In cases were no cube orientation was present before rolling, and as a consequence no preferred nucleation can occur, a strong Cu orientation in the rolling texture forms a strong ND rotated cube with an almost ideal 40” (111) orientation relationship 1191. On the other hand, the result that for the specimens SND, STD and SRD the recrystallization textures are rather similar despite the different preceding rolling textures and are given by the cube orientation and its rotations around RD represents a confirmation of the Dillamore-Katoh theory. Particularly convincing is that this theory predicts the scattering of the cube orientation corresponding to a rotation around RD which cannot be explained by the growth theories and also does not appear in the transformation ODF’s (Fig. 10). Moreover, the theory also explains the absence of the cube maximum for specimen S45. There the starting texture is far away from (0Ol}(u~) and the chance of obtaining cubeoriented nuclei should in this case be much less than for SND, STD and SRD. In spite of this, the unsymmetric initial S45 texture may give rise to similar transition bands. It follows from the RD rotated (100) fibre texture that RD rotated cube orientations ((hkl} (100)) may form during rolling, which subsequently give rise to divergent zones which contain similarly preferred nucleation sites. A 34” (111) orientation relationship to the main rolling texture component Bs/Goss can be found but cannot explain its dominance alone. The slower growth capacity of this component may also be the reason for the high random volume fraction and the appearance of the Bs/R component which has a good 40” (111) orientation relationship to the main rolling texture component, the Bs/Goss position, but which does not have these preferred nucleation sites. This component is very close to the main recrystallization component of c( brass {236} (385) for which it could be shown that the nuclei were formed by rccrystallization twinning. But since in Al no twinning occurs, here the nuclei must already be present in the rolling texture. The ODF’s show that this recrystallization component falls into the scattering of the ND rotated Cu orientation. The fact that the observed Bs/R component is shifted towards this position confirms the assumption that it might nucleate from such edge orientations. The origin of the minor recrystallization texture components, the Goss and rotated Goss position {all} (011) is not yet clear. The latter is observed as
437
a major recrystallization component only in strip cast aluminium alloys [34]. It is interesting to note that strip cast aluminium has an as-cast texture which can be derived from the present material by orienting the (100) fibre axis in between the normal and the casting direction of the as cast sheet. The angle between the casting direction and the (100) axis is about 20”. There might also be a certain preference in the nucleation of this orientation. Since it is not visible in the rolling texture it might also nucleate out of divergent zones formed between equivalent variants of the TD rotated cube orientations which occur in the rolling texture when grain boundaries are present. work is the resuit of Acknowledgements-This Norwegian-German research cooperation. The authors thank BFMT (Germany), NTNF (Norway), Vereinigte Aluminiumwerke AC and Ardal og Sunndal Verk AS for financial support. Special thanks are due to Mr S. Johanson (SINTEF) for providing the directionally solidified aluminium.
REFERENCES 1. E. Nes, SINTEF-Report No. 83-595-3050-3 (1983). 2. H. Mecking, Proc. 6th Int. Conf on Textures, Tokyo, p. 53 (1981). 3. J. Hirsch, H. Mecking and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 83 (1984). 4. G. D. Kohlhoff, B. Krentscher and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 95 (1984). 5. J. Grewen and J. Huber. Proc. 4th Eur. Colloq. on Textures, Cambridge, p. 138 (1975). 6. A. A. Ridha and W. B. Hutchingson, Acta metall. 30, 1129 (1982). 7. I. L. Dillamore and K. Katoh, Metal Sci. 8, 73 (1974). 8. C. A. Verbraak, Proc. ICOTOM 5, Aachen, p. Ill (1978). 9. H. J. Bunge, Mathematische Methoden der Texturanalyse. Akademie Verlag, Berlin (1969). 10. K. Liicke, J. Pospiech, K. H. Virnich and J. Jura, Acta mefall. 20, 167 (1981). 1I. E. Nes, J. Hirsch and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 663 (1984). 12. J. Hirsch and K. Liicke, Acta metall. 33, 1927 (1985). 13. J. Hirsch, M. Loeck, L. Loof and K. Liicke, Proc. 7th Int. Conf on Textures, Noordwijkerhout, p. 765 (1984). 14. W. Truszkowski, J. Pospiech, J. Jura and B. Major, Proc. 3rd Eur. Colloq. on Textures. Pont-a-Mousson (1973). 15. S. Matthies, Physica status solidi 92, 135 (1979). 16. J. Pospiech and K. Lticke, Acta Me&. 24; 997’(1975). 17. J. Hirsch and K. Liicke, submitted to Acta metall. 18. J. Hansen, J. Pospiech and K. Lticke, Tables for Texture Analysis of Cubic Crystals. Springer, Berlin (1978). 19. K. Liicke and J. Hirsch, Aluminium Technology, B. The Institute of Metals, London p. 66 (1986). In press. 20. G. D. Kohlhoff, J. Hirsch and U. V. Schlippenbach, Proc. ICOTOM 6, Tokyo, p. 489 (1981). and H. P. Stiiwe, 2. Metallk. 61, 128 21. E. Aernoudt (1970). 22. W. Heye and G. Wassermann, Z. Metallk. 59, 617 (1968). 23. A. Malin, J. Huber and M. Hatherly, Z. Mefallk. 72, 310 (1981). 24. H. Mecking, Proc. ICOTOM 6, Tokyo, p. 53 (1981). 25. J. Hirsch, K. Liicke and H. Mecking, Proc. 7th Int. Conf. on Textures, Noordwijkerhout, p. 83 (1984). 26. J. Hirsch and K. Liicke, in preparation.
HIRSCH et al.:
438
TEXTURES
IN DIRECTIONALLY
27. P. A. Beck, P. R. Sperry and H. Hu, J. appl. Physi. 21, 20 (1950).
28. B. Liebmann, K. Liicke and G. Masing, Z. Metaflk. 47, 57 (1956). 29. G. Ibe, W. Die&, C. A. Z. Metallk. 61, 498 (1970).
Fraker
and K. Liicke,
30. K. Liicke, R. Rixen and M. Senna, Acra metall. 24, 103 (1976).
SOLIDIFIED
Al
31. K. Liicke, Proc. 7th Int. Conf. on Textures, Noordwijkerhout, p. 185 (1984). 32. R. Rixen, R. Musick and H. GBker, Z. Metallk. 68, 16 (1975).
33. A. L. Dons and E. Nes, Proc. 7th Inc. Conf. on Textures, Noordwijkerhout, p. 53 (1984). 34. E. Nes and B. Andersson, Central Inst. of Industrial Research, Report No. 780138 (1980).