DEVELOPMENT OF CROSS-ROLLING TEXTURES IN AIMnl

True cross-rolling and pseudo cross-rolling (with only one change of the rolling direction after half of 
the total deformation degree) was investigated in an alloy AlMn1 up to 93% deformation. The texture 
formation was studied in terms of ODF. After true cross-rolling (multi-stage rolling) a strong 
two-component ideal orientation near (011)[322] was found with maximum densities up to 60 times 
random. Pseudo cross-rolling (two-stage rolling) resulted in weaker, but still strong deformation 
textures with maximum densities up to twenty times random which were intermediate between 
unidirectional and true cross-rolling textures. In both cases, the originally present cube texture 
decreased continuously with increasing deformation degree.


INTRODUCTION
Texture formation by cross-rolling has been studied in several fcc metals and alloys.Wassermann (1939) studied cross-rolling textures of Fe-Ni alloys.Merlini and Beck (1953) investigated cross-rolled copper.A survey of the earlier work on cross-rolling textures was given by Wassermann and Grewen 1962.As a main component of cross-rolling textures in fcc-metals the ideal orientation (011) [322] was reported.Besides this, the occurrence of cube texture was sometimes found together with other components.Rixen et al. (1975) studying rolling and recrystallization textures of AIMn-alloys also presented a pole figure of a 95% cross-rolled sample of this alloy which confirmed the above ideal orientation.
More recently Oztiirk (1988) investigated the textures of cross-rolled copper and c-brass using the ODF representation.Young and Duggan (1966) studied structure development during cross-rolling and performed computer simulation confirming the stability of the orientation (011)[322] under cross-rolling conditions.
The true cross-rolling process consists of small rolling passes at right angles to each other.Each individual pass may be idealized as being plane strain deformation, the symmetry of this process being orthorhombic.If the deforma- tion per pass is small enough, every two consecutive passes together may be considered as a combined deformation step having tetragonal symmetry.Hence, the resulting deformation texture must also exhibit tetragonal sample symmetry.This does not hold, however, for larger deformation steps.The consecutive execution of two finite crystal rotations is not commutative.Hence, a pseudo cross-rolling process consisting of two finite deformation steps in two mutally perpendicular directions gives different results from true cross-rolling.
In a preceding paper, the present authors studied true and pseudo cross- rolling textures developing in ARMCO iron.In the present paper the textures developing in an AIMn alloy after these two modes of deformation will be studied.

EXPERIMENTAL PROCEDURE
The material studied was an AIMnl alloy which was received in the form of ingots, solution treated for 24 h at 600C.From these ingots slabs of different thickness were machined as is shown in Figure 1.They were heat treated for 168 h at 550C such that about 50% of the manganese was precipitated in the form of AI6Mn particles of about 2/m diameter.
In order to obtain a fine grained recrystallized state before the final cross- rolling, the slabs were cold rolled approximately 70% to the thicknesses also given in Figure 1.After that they were recrystallized at 550C.Since the deformation degrees were not exactly the same, this required different re- crystallization times as is also given in Figure 1.
After this treatment, the grain shape was nearly (although not exactly) equiaxed with grain sizes in the order of 60/m.The textures of the initial states are shown in Figure 2 which gives the (111) pole figures and two ODF-sections, each.As is seen in Figure 2, the starting textures are quite different.This must be attributed to differences in the primary recrystallization textures as well as to modifications of these textures by subsequent continuous grain growth.The influence of the initial texture has to be taken into consideration in the evaluation of the final cross-rolling textures.On the other hand, it will be seen that the final textures after high cross-rolling degrees are not very strongly influenced by the variations in the initial textures.The variation of the initial textures can thus be used to illustrate various "texture paths" in the intermediate states leading to similar final textures.
Cross-rolling was carried out using a two-roll laboratory mill with 180 mm roll diameter.Slabs of 60 mm,60 mm were cut from the pre-treated sheets.They were cross-rolled in two different ways: (a) Reversed rolling in the original rolling direction to about half of the final reduction in thickness followed by reverse rolling to the final thickness in the original transverse direction (two-stage rolling).The two partial rolling degrees r/1 and r/2 in the original rolling and transverse direction are shown in Figure 3.
(b) Starting with the original rolling direction the slabs were turned by 90 after each pass and rolled this way till to the final reduction (multi-stage rolling).Table 1 shows the nominal and actual deformation degrees, the number of passes, the thickness before (do) and after (d) cross-rolling, the mean reduction per pass and the initial states for the various final rolling degrees.
For texture measurements slabs of 33.9 mm in diameter were taken from the rolled sheets.They were ground with SiC-paper to approximately the middle of the sheet thickness, followed by etching with an etchant consisting of 75 ml HCI, 25 ml HNO3 and 5 ml HF.Four incomplete pole figures, i.e. (111)(200)(220) (311)   were then measured in the back-reflection mode using CuKte-radiation.The pole l, l.Slab Recryst.'for ] ,s5": j figures were measured in steps of Am 5 , Aft 3.6 up to (t'max ---70 using the automatic texture goniometer ATEMA-C.From these pole figures, ODF were calculated using the series expansion method up to g 22 for the even part and up to g 21 for the odd part using the zero range method.Inaccuracies of sample adjustment parallel to the rolling direction were corrected according to the orthorhombic symmetry of the pole figures.

RESULTS
The starting textures before cross-rolling were already shown in Figure 2.
The texture development by cross-rolling is shown in Figure 4 which gives the (111) pole figures for the different degrees of deformation.
The ODF of some of the deformation degrees calculated from pole figures are given in Figure 5.In order to estimate the convergence of the series, the mean absolute values of the coefficients C are given in Figure 6 along with the corresponding error coefficients.This figure shows that no series truncation error occurred.Multi-stage rolling corresponds to tetragonal sample symmetry which expresses itself in vanishing texture coefficients C v for v 4n.Hence, in Figure 7 the mean absolute values of the coefficients C are given separately for v 4n (4-fold) and v 4n + 2 (2-fold).The main features of the textures reached at high deformation degrees e.g.93% are different for the two types of cross-rolling.The two-stage rolling texture consists of an orientation tube extended between the orientation A and B shown in Figure 8.The multi-stage texture is nearly an ideal orientation C as is also shown in Figure 8.
The orientation tube A-B of the two-stage texture is shown in Figure 9  [010] ^-B [oo] Filre 9 The orientation tube of the texture of 93% two-stage rolled AIMnl. in Table 2 which also contains the Euler angles of orientation C of the multi-stage texture.The orientations A, B, C are near to some ideal orientations which are also given in Table 2.The main features of the two types of textures can thus be judged by the two sections t#2 0 and 2 45 which are shown in Figure 10 for all investigated rolling degrees.
The orientations A and B of the two-stage texture are slightly different for the different degrees of deformation as is shown in Figure 11.Orientation C of the multi-stage texture is virtually independent of the rolling degree.
The orientation density along the skeleton line A-B is given in Figure 12.It is seen that for lower deformation degrees the intensity at point B decreases to zero.Hence, in these cases also the two-stage texture is nearly an ideal orientation i.e. the orientation A.
The orientation densities in the three main points A, B, C as a function of the deformation degree are given in Figure 13.Hence, this figure summarizes the main features of texture development by cross-rolling in the two different modes.Finally it can be seen in Figure 5 and Figure 10 that the spread of orientations is  greater in -direction than in the other directions in Euler space.Hence, Figure 14 gives some sections of the ODF in -direction through the points A and C as is also indicated in Figure 8.

CONCLUSIONS
In the present investigation cross-rolling was carried out in two different ways i.e.
two-stage cross-rolling and multi-stage cross-rolling.The latter one can be considered to be a truely tetragonal deformation process whereas two-stage rolling is not because of two reasons.First, the two partial deformation degrees in the original rolling and transverse direction are different as is seen in Figure 3.And even if they were equal they are not commutative since two consecutive rotations are not commutative.Hence, two-stage rolling gives rise to textures with orthorhombic sample symmetry.In the case of two-stage rolling with higher deformation degrees, the second deformation step in the original transverse direction is the dominating one.Hence, these textures are very similar to the normal rolling textures of fcc metals showing the copper type if only one refers these textures to the original transverse direction as being the actual rolling direction of the second step.
Multi-stage rolling leads to a different type of texture.It can be described by an ideal orientation (consisting of two symmetry variants) which has a (110) plane parallel to the rolling plane and a [100] direction at +45 between rolling and transverse direction.This orientation does not have a low index direction in rolling direction nor in transverse direction.However, it is near to the orientation (011)[322] which has been used to describe it.
The two-stage rolling textures after smaller deformation degrees are more similar to the multi-stage texture.The orientation tube is not really developed.The peak intensity is at the orientation A which is, in this case, nearer to the orientation C of the multi-stage texture.The exact positions of the orientations A and C were taken from ODF sections as given in Figure 14.This figure shows rather broad spread ranges in the tp-direction and also the peak position varies from sample to sample, this giving rise to a rather large scatter of the points in Figure 11.This uncertainty must be attributed to variations in the actual rolling directions from pass to pass.It must be assumed that the actual rolling direction may deviate in the order of +5 from the ideal value 0 or 90.Hence, broadening and peak shift in l-direction of this order of magnitude may have occurred as is to be seen in Fig 10 .The deviation of the orientations A, B, C in Table 2 from the ideal orientations, also given in this table, must thus be seen under these premises.Nevertheless, Figure 11 indicates a certain systematic deviation which is in good agreement with the observed deviation of the orientation tube in the normal rolling texture of the copper type.
The influence of the various starting textures on the final textures can be judged by comparing Figure 2 and Figure 10.All the starting textures contain the cube texture (001) [100] and some of them contain spread orientations obtained by rotating the cube orientation through up to 45 about RD, TD, ND as is shown schematically in Figure 15.At lower to medium deformation degrees, considerable amounts of cube texture survived after both deformation modes.
The picture is, however, not very clear since the textures obtained from a pure (Okl)  cube starting texture did not show the cube texture at all.The ND-spread orientations of the cube texture did not survive even after lower degrees of deformation whereas RD and TD spread orientations seemed to have a higher stability.A clearly visible feature of the textures of medium deformation degrees are spread ranges extended between the final rolling component and the cube texture.
The formation of the true cross-rolling texture i.e. the orientation C of the multi-stage case is illustrated in Figure 16.The texture for unidirectional rolling is characterized by the orientation tube extended between the orientations A and B which are approximately (011) [111] and (112) [110] as is shown in the upper part of Figure 16.Orientation A has a second (1ll]-direction at approximately 18 to the transverse direction.In multi-stage rolling this direction becomes the second rolling direction.Hence, orientation A is also nearly stable with respect to this second rolling direction.Orientation C which is 9 apart from orientation A is the compromise orientation for alternate rolling in RD1 and RD2.Orientation B has a [110] direction in RD and there is no equivalent direction near TD.Hence, with respect to multi-stage rolling this orientation is unstable.Figure 16 gives, of course, only a qualitative illustration of the situation for unidirectional and multi-stage cross-rolling.A more quantitative explanation can be obtained by applying mathematical models of texture formation, e.g. the Taylor theory which can be easily applied in the form of flow-fields.Calculations of this type have been carried out as will be shown elsewhere.
Figure1Pretreatment of the material before cross-rolling.

Figure 3
Figure3Total deformation degree and partial deformation degrees for two-stage rolling.
Figure (i M__ean absolute values I1 of the coefficients C as well as the corresponding error quantities IACI. Figure 6 (Continued)

TwoFigure 10 Figure 11
Figure 10 Two sections of the ODF of cross-rolled AIMnl after various rolling degrees.

Figure 12 Figure 13 Figure 14
Figure12Orientation density along the skeleton line of the textures of higher rolling degrees after two-stage rolling.

Figure 15 Figure 16
Figure15The cube orientation and the main spread range between cube crystals.

Table 1
Treatment of the material before cross-rolling

Table 2
Euler angles of actual orientations