THE ORIENTATION DEPENDENCE OF GROWTH RATE OF GRAIN BOUNDARIES AND THE FORMATION OF RECRYSTALLIZATION TEXTURES

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THE ORIENTATION DEPENDENCE OF GROWTH RATE OF GRAIN BOUNDARIES AND THE

FORMATION OF RECRYSTALLIZATION TEXTURES

K. Lücke

To cite this version:

K. Lücke. THE ORIENTATION DEPENDENCE OF GROWTH RATE OF GRAIN BOUNDARIES

AND THE FORMATION OF RECRYSTALLIZATION TEXTURES. Journal de Physique Colloques,

1975, 36 (C4), pp.C4-339-C4-343. �10.1051/jphyscol:1975434�. �jpa-00216340�

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JOURNAL DE PHYSIQUE Colloque C4, supple'ment au no 10, Tome 36, Octobre 1975, page C4-339

THE ORIENTATION DEPENDENCE OF GROWTH RATE OF GRAIN BOUNDARIES AND THE FORMATION OF RECRYSTALLIZATION TEXTURES

Institut fiir Allgemeine Metallkunde und Metallphysik der Technischen Hochschule Aachen, W.-Germany

RCsumC.

-

On a discutt B quelle mesure les textures de recristallisation peuvent &re interprtttes par la thtorie de croissance orient&, baste sur les relations d'orientation pour vitesse de croissance maximale trouvkes dans des monocristaux. On a aussi abordt le r61e de la nuclCation orientke.

Abstract. - It has been discussed to what extent the recrystallization textures can be interpreted by the theory of oriented growth based on the maximum growth rate orientation relationships found in single crystals. Also the possible role of oriented nucleation has been discussed.

1. Maximum growth rate orientation and textures formation.

-

The formation of recrystallization textures can only be understood if the orientation dependence of the rate of grain boundary motion is known. On the other hand, the investigation of the recrystallization textures has given strong stimuli to the development of the theory of grain boundaries.

It is the purpose of the present paper t o discuss the present state of this interrelation.

The first explanation of the formation of recrystallization textures was given by Burgers [I]. Start- ing with the observation that after plastic deformation the slip planes were bent (Laueasterism), he assumed that the most strongly disoriented parts would act as recrystallization nuclei and thus determine the recrystallization texture (Theory of oriented nucleation). But no quantitative success could be achieved by this theory. 20 years later, mainly Beck [2] recognized that, depending on their orientation, different grains have different growth rates and proposed that the texture is determined

ORlENMlON DIFFERENCE (&qrl ABOUT COMMON <Ill>

FIG. I .

-

Rate of boundary migration as . I I~~nction of t h e

oriention difference. (Rotations around common < 11 I > axis.)

by the orientation of the fastest growing grains (Theory of oriented growth).

This theory is insofar more successful as, in some cases, it could explain the orientation relationship between recrystallization texture and deformation texture on the basis of a 40"

<

11 1

>

-rotation which, at the same time, could be identified as the orientation relationship for maximum growth rate (MGR-orientation) [3]. The latter is shown e. g. in figure 1 where the growth rate of

<

11 1

>

-tilt boundaries is plotted as function of the angle of rotation [ 4 ] , and in figure 2

FIG. 2.

-

Growth selection in 20 % rolled aluminium single crystals as observed at three different stages. (a) { 111 } poles of the new crystals (deformed matrix in standard projection).

The dashed lines characterize a 42" rotation around a common < 11 1 > axis. ( b ) Frequency of the rotation angles

around the best fitting < 111 > rotation axes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975434

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where the orientation of different grains being in a growth competition is plotted for different stages of growth selection [ S , 31. In such experiments it had been also repeatedly found that the growth rate of a 40" < 111 > -tilt boundary is considerably larger 20

than that of a 40"

<

1 1 1

>

-twist boundary [3].

A

40"

<

11 1 > -relationship for maximum growth rate has also been found for other f. c. c. metals in particular for copper, although there, because of the formation of annealing twins, the occurence of this relationship is not quite as clear. In other types of metals, e. g. Al-Mn-alloys, b. c. c. and hexagonal metals, maximum growth rate relationships could

also be established [6]. They will, however, not be ^-Ig6'' discussed here.

2. Interpretation of recrystallization textures of Cu-alloys by MGR-orientations.

-

The formation of

recrystallization textures by oriented growth shall ^FIG.^4.^-^{¹¹¹⁾-pole figures of the rolling and recrystallization textures of Cu-P after 95 % rolling at 20 "C and - 196 OC.

be discussed for rolled copper based solid solu- tions. It is known that here the rolling textures exhibit a transition from the copper type to the brass type rolling texture, if a sufficient amount of foreign elements is added to the copper [7].

Figure 3 gives an example for the Cu-Ge- and figure 4 for the Cu-P-alloys [S]. Concerning the texture for primary recrystallization it has been shown very thoroughly for the Cu-Zn-alloys [S], but can be recognized also in figure 3 for the Cu-Ge-alloys [8] that the copper type rolling texture leads to the cube texture (001) [I001 and the brass type rolling texture to the brass recrystallization texture (326) [8351. The transition range where the recrystallization textures are somewhat more complicated will not be considered here.

The fact that due to the symmetry with respect to

nents, leads to an important modification of the theory of oriented growth. Whereas in a single crystal grains with exactly the MGR-orientation will assume the maximum volume, in polycrystals orientations having to all the components approxi- mately the MGR-orientation will be preferred, since they do not grow only into one rolling component, but rather fast into all components (compromise orientations). In this way Beck interpreted the cube texture which has to all 4 components of the main orientation (123) [634] (S-orientation) of the copper type rolling texture an approximate 40°

<

1 1 1

>

-relationship.

Figure 5 shows such considerations for the brass type rolling texture [8, 91 (011) [21il which rolling direction and rolling plane the rolling texture

of polycrystals consists of several (in general 4) crystallographically identical orientation compo-

a b

0 04 1 3 9XGe

c d

FIG. 5 . - 40" < 1 1 1 > rotations of both components of the (01 1) [2 1 i] orientation. ( a ) A (00 1) [2 1 i] orientation, A (326) [a351 orientation, ( b ) A (01 1) [21i] rotated D+, B-, A (326) Frc. 3 . - { 1 1 1 } -pole figures of the rolling and recrystallization 183-31, ( c ) A (01 I )

121

i ] rotated H , C'

.

4 (013)-[100], ( d ) A (01 1 ) textures of Cu-Ge after 95 % rolling at 20 OC and - 196°C. [21 11 rotated A', A (21 1 ) [Oll].

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THE ORIENTATION DEPENDENCE OF GROWTH RATE OF GRAIN BOUNDARIES C4-34 1

consists, because of its symmetry, only of 2 components. One recognizes that the observed recrystallization orientation (326) [835] can be obtained by an approximate 40" < 11 1 > -rotation with respect to the one and also to the other roll- i n g - component (Fig. 5 b ) . This observed orientation (326) [835] can thus be interpreted as a compromise orientation being able to grow fast into both rolling components. Figure 5c and 5d also show that, by 40" < 11 1

>

-rotations around different axes, two other compromise orientations can be obtained. The first one ((013) [loo]), however, is only seldom, the second one ((211) [Oli]), is never observed. This means that now the problem is reversed : it is not so much the question, why the orientation (326) [835] is found, but why the other two possible compromise orientations are not found.

Another argument against this interpretation of recrystallization textures seems to follow from recent investigations of the Cu-P-alloys [8]. There, quite different recrystallization textures have been found (Fig. 4), although the rolling textures are exactly the same as in the cases Cu-Zn and Cu-Ge.

Particularly at large P-content one observes the (011) [loo] - and (113) [332] -orientations.

These results can be included in the above scheme, however, if one assumes that for larger P-contents no longer 40" < 11 1 >

-

but 35' to 40" < 110 >

rotations form the MGR relationship. As to be seen in figure 6, for 39" rotations 4 compromise orientations can be obtained in this way from the brass rolling texture (011) [21i], and the two best ones are indeed those which are observed as recrystallization textures at high P-content, namely (113) [332] and (011) [loo] (Fig. 4).

A MGR-relationship different from 40"

<

11 1

>

should in principle not be impossible ; it has been observed also for AI-Mn-alloys and might be connected with changes of the boundary structure with increasing alloy content. That 35" to 40"

<

110

>

is really a MGR-relationship is also made probable by the fact, that this, relation is fullfilled not only with respect to one, but to both observed recrystallization orientations. However, also here other good compromise orientations are possible which have not been observed, e. g. (1 11) [oii] (Fig. 6c).

3. Possible influence of nucleation.

-

In the foregoing it has been shown that the recrystallization orientations arising from the brass type rolling texture can be explained by the assumption of the formation of compromise orientations based on the theory of growth selection. The. question is here now reversed : the difficulty is to explain why, as shown above, certain orientations which would form a good compromise are not observed. Similar problems arise for the recrystallization of single crystals. I n s t e a d of all eight 40"

<

111

>

-orientations (four

<

11 1

>

axes each with

+

and -40") mostly only a smaller number is found.

Since these difficulties have not been resolved for many years and also because of the fact that no atomic reason for the observed MGR-orientations could be given, the interest has shifted recently by a certain amount to oriented nucleation. In the following, therefore, some of the ideas and obser- vations on nucleation will be briefly discussed.

For recent recrystallization experiments on Al- single crystals [lo] figure 7 a gives the rolling

FIG. 7. - { 1 1 1 1 pole figures of the rolling and recrystallization textures of an Al-sipgle crystal with the initial orientation (2 1 10) [4 2 I]-: (a) rolling texture : A initial orientation (2 10) [4 2 11, A orientation a f t e r 80 % rolling (1 13) [353], (b) recrystallization texture : A (001) [310]

FIG. 6. - 39O < 110 > rotations of both components of rotated around ND, (c) rolling orientation rotated ? 40° < 111 >

the (01 1) [21i] orientation. (a) % (1 13) [332], (b) (1 10) [loo], around pole C. Dashed line = 0.1 contour of the deformation (c) = (111) [ ~ l i ] , ( d ) 2 (131) 14171. texture.

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texture after 80 % rolling, figure 7b the recrystallization texture, and figure 7 c the orientation rela- tionship between both. Figure 7 c shows (i) that the recrystallizations texture (empty triangles) is related t o the rolling texture (full triangles) by a 40"

<

1 1 1

>

-rotation (dashed line), and (ii) that the one of the eight 40" < 1 1 1 > rotations which is

observed is the one lying closest to the (anisotropic) scattering of the rolling texture (the latter being characterized e. g. by the 0.1 - iso

-

intensity lines). This indicates strongly that here the nuclei a r e part of the deformed matrix and that 40" < 1 1 1

>

component will grow for which a sufficient number of nuclei is available. In agreement with this interpretation one finds for the same orientation, but after only 20 % rolling, all eight the 40" < 1 1 1 > components. Since here the observed scattering of the rolling texture is much smaller, apparently none of the 40" < 1 1 1 > components is prefered with respect to nucleation. Similar results were obtained for crystals with different orientations [lo].

In these experiments the crystallographic nature of the orientation relationship (i. e. 40°

<

1 1 1 >) is obviously determined by the maximum growth rate.

This interpretation is in contrast to the oriented nucleation concept recently given by Dillamore and Katoh [ll]. These authors assume that, due to the mechanism of the deformation process, only nudei of defined orientations are formed and that these determine the recrystallization textures. According to these authors these orientations are those at which, during the change of crystal orientation in the cause of deformation, the orientations either converge or diverge. They can be calculated applying the Taylor theory of poly-slip and are found t o lie in the same cases in the vicinity of observed polycrystalline recrystallization textures.

This would mean that the agreement between the 40" < 11 1

>

-MGR relationship observed in single crystals and the orientation relationship formed during recrystallization would be acciden- tal. Furthermore it is not obvious how this theory can explain the selection between the eight different 40" < 1 1 1

>

components in the above described single crystal experiments.

Summarizing it must be stated that the extent to which oriented growth and oriented nucleation determine the recrystallization texture is not yet clear in all cases. The role of oriented growth in single crystal experiments seems to be widdy accepted. For polycrystal experiments, however, some authors assume oriented nucleation as the only mechanism, i. e. they assume that single crystal experiments are not relevant for the formation of recrystallization textures of polycrystals. In

the following, two arguments will be given in favour of the effect of oriented growth and thus in favour of the relevancy of single crystal recrystallization experiments also for polycrystals :

(i) Not in all cases are the fiuclei for the new grains part of the deformed .matrix. It has been shown that often recrystallization twins are the origin of the new grains [12, 131 (see Fig. 8) and circumstancial evidence is given that in some cases the inverse Rowland transformation might take place [13, 141. Also in these cases, however, where obviously the Dillamore-Katoh concept of oriented nucleation does not apply, again 40"

<

1 1 1

->

orientation relationships are observed.

FIG. 8. - Recrystallized grains in c o p b r , single crystals elongated at high temperatures. The new grains are in an approximate 40° < 1 1 1 > or first or higher order twin rela- tionship with respect to the matrix, to the deformation bands and

to each other.

(ii) Liicke and Rixen [IS] were able to show that also in hexagonal metals the recrystallization textures could be interpreted as compromise textures.

The compromise was based also here on the maximum growth rate orientation relationships which were found in hexagonal single crystals and which are quite different from those found in fcc metals. It is quite surprising in what great detail the differences of the recrystallization textures of different hexagonal metals can be explained in this way.

Acknowledgements. - The author would like to thank Dr. Ursula Schmidt for valuable discussions and for her help in preparing the manuscript. He also thanks Dr. Schmidt, Dr. Senna and Mr. Zabar- djadi for making available some of their experimen- tal results. He acknowledges gratefully the financial support of the Deutsche Forschungsgemeinschaft for some of the work described here.

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T H E ORIENTATION DEPENDENCE O F GROWTH RATE O F GRAIN BOUNDARIES C4-343

References

[ I ] BURGERS, W. G . and LOUWERSE, P. C., Z. Phys. 61 (1931) 605.

[2] BECK, P. A., Advances in Physics (Phil. Mag. Sup.)3 (1954) 245.

[3] e. g. LUCKE, K., Can. Metall. Q. 13 (1974) 261.

[4] LIEBMANN, B . , LUCKE, K. and MASING, G., 2. Metallkd. 47 (1956) 57.

[51 SIXT, G., Diplom Thesis, T H Aachen (1969).

[6] IBE, G. and LUCKE, K., in Recrystallization, Grain Growth and Textures (ASM, Metals Park, Ohio) 434 (1966).

[7] SMALLMANN, R. E., J . Inst. Met. 83 (1955) 10.

[8] SCHMIDT, U . , Thesis, T H Aachen (1975).

[9] LUCKE, K., RIXEN, R. and ROSENBAUM, F. W., in The Nature and Behaviour of Grain Boundaries, ed. H . Hu (Plenum Publishing Co., New York) 1972, p. 245.

[lo] LUCKE, K., RIXEN, R. and SENNA, M., Acta Metall. in press.

[ l l ] DILLAMORE, I. L . and KATOH, H., Metal Sci. 8 (1974) 73.

1121 PETERS, B. F., Met. Trans. 4 (1973) 757.

[13] SLAKHORST, J . W. H. G., Acta Metall. 23 (1975) 301.

[14] VERBRAAK, C. A., Acta Metall. 6 (1958) 580.

[15] LUCKE, K. and RIXEN, R., Met. Trans. 1 (1970) 259.

DISCUSSION

D. SMITH, R. POND : R. Pond and D. Smith have guishing factors, apart from the trigonal nature of investigated the nature of the

2

⁼7, 38.21/< 111

>

the coincidence site lattice unit cell, were found for coincidence from a geometrical structural point of the l$ = 7 boundaries. This symmetry may imply view together with the energetics of absorption of that the energy of the

2

= 7 boundary is unusually lattice dislocations. In addition these factors were insensitive to variation of the boundary plane.

studied for other low

2

boundaries. No distin-