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Deformation banding and recrystallization of α fibre components in heavily rolled IF steel
Acta Materialia 52 (2004) 4011–4021 www.actamat-journals.com
Deformation banding and recrystallization of a fibre components in heavily rolled IF steel M.Z. Quadir *, B.J. Duggan
*
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong Received 30 March 2004; received in revised form 9 May 2004; accepted 12 May 2004 Available online 17 June 2004
Abstract Detailed SEM work has shown that about a quarter of crystals belonging to the a fibre formed by cold rolling up to reductions of 85%, are of uniform microstructure with relatively small misorientation. The remainder are indistinguishable from the polycrystalline mass, which is mostly of c orientations. At rolling reductions above 85%, a grains begin to split their orientations by deformation banding, thus producing lattice curvature which allows recrystallization of a at the expense of other a components in the same original grain. This a recrystallization deteriorates the deep drawability of IF steel and since the process requires deformation banding a natural explanation of the optimum rolling reduction for good drawability is provided. The best cold rolling reduction is that which optimizes c recrystallization by producing deformation banding in c components without producing deformation banding in a components. Uniform microstructures and small lattice curvature allows a to be consumed by other orientations, and this condition is obtained in the 80–85% cold rolling range. Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Rolling; a and c fibres; Deformation banding; Recrystallisation; Textures
1. Introduction Deep drawability is measured by the Limiting Drawing Ratio, a test in which a cup is drawn from a circular blank and this correlates with the Lankford parameter, r, which is defined as the width to thickness strains in the tensile test [1]. Intensive early work done between the 1950s and 1970s showed the Lankford parameter to be determined by the texture of the material (e.g. [2]). For the Al-killed steels of the time, and using the X-ray technology available, this translated into a simple requirement that the ratio of the intensities of the {1 1 1} and {1 0 0} reflections be as high as possible [3]. In 1962 Whitely and Wise [4] showed that there was an optimum rolling reduction of about 75% prior to final
*
Corresponding authors. Tel.: +852-285-786-15; fax: +852-285-854-
15. E-mail addresses: [email protected] (M.Z. Quadir), [email protected] (B.J. Duggan).
annealing, beyond which the Lankford parameter declined. The reason was associated with the persistence of that part of the rolling texture close to {1 0 0}h0 1 1i. Now it must be stressed that desirable {1 1 1} recrystallization texture components for drawability increase with rolling reduction, but the intensity ratio declines because {1 0 0} components increase faster than {1 1 1} above a certain rolling degree. The situation has not changed with the introduction of interstitial free (IF) steels, there is still a maximum cold rolling reduction, but in the 80–85% range and the reasons for the high Lankford parameter are identical to those put forward for the older deep drawable AL-killed steels. Much of the early work concerning drawable sheet steels, in which many took part, was to do with the problem of this so called retained rolling texture [5–7], especially components near {1 0 0} because of their deleterious effects on the Lankford parameter. In this regard and following extensive work Duggan [8] and Duggan and Roberts [9] showed that recovery anneals of low carbon steel after cold rolling to 90% for
1359-6454/$30.00 Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.05.017
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as long as 10,000 min followed by a high temperature recrystallization treatment at 750 °C produced a relatively strong {4 1 1}h1 4 8i component in a low carbon steel. Transmission electron microscopy (TEM) was used to ensure that only recovery had occurred at 500 °C and they thought that the {4 1 1}h1 4 8i had arisen from an in situ nucleation process involving subgrains adjacent to grain boundaries. The {4 1 1} component was considered to be part of the orientation spread of a single {1 0 0} grain, was located close to grain boundaries, and, following Takechi et al. [10] had a higher stored energy than that found in the grain interior. Differential recovery was assumed to occur, happening faster in the higher energy grain boundary regions, to produce low energy blocks of sufficient misorientation to migrate into the {1 0 0}hhkli interior. Later this issue was reviewed by Hutchinson [11] and in the discussion of the optimum rolling reduction for drawable steel, the origins of {4 1 1}huvwi component was mentioned as not being satisfactorily explained because of lack of direct evidence. With the advent of the ODF by Bunge [12] and Roe [13], it became clear that among the several different ways of describing the rolling texture of BCC iron, the idea of the a and c fibres are best. The a fibre comprises orientations with RD//h1 1 0i and the c fibre the h1 1 1i orientations parallel to the sheet normal direction ND. A /2 ¼ 45° ODF section in Fig. 1(a) shows the positions of the orientation components of both fibres. A further technical development which has thrown much light on the deformation state is orientation imaging microscopy (OIM) based in the modern scanning electron microscope (SEM). It is now possible to easily couple an orientation of 1°–3° accuracy with a specific location of 1 lm in diameter. Recrystallization theory still relies on two old theories, oriented nucleation (ON) and oriented growth (OG). Even with the greatly expanded technical capabilities available today, both of these theories are still used to explain the same data sets, in other words, neither one nor the other is held to be universally true in all circumstances. Dillamore et al. [14] in fine work related to ON, proposed a model for the ‘‘in situ’’ process based upon subgrain growth, particularly in transition bands. In the further development of this model, Dillamore et al. [15] tested these ideas by compressing polycrystalline iron. This deformation mode was thought from Taylor theory [16] to rotate the crystals towards two stable orientations h0 0 1i and h1 1 1i parallel to the compression direction (CD). They then supposed that a small fraction of material would stay on a rotation path towards a metastable orientation, h4 1 1i//CD. They identified the end orientations h0 0 1i and h1 1 1i//CD as convergent planes into which material rotates away from a metastable crystallographic pathway which they called the divergent planes. These divergent planes they
Fig. 1. u2 ¼ 45° ODF sections showing the rolling and annealing textures of 85%CR and 75%WR samples. Intensity levels: 1, 2, 4, 6, 8, 11, 14 and 17.
assumed would be sites of recrystallization nuclei, and, remarkably the recrystallization texture had a h4 1 1i// CD component which apparently confirmed the ON theory for this case. However in more recent work Verbeken et al. [17–19] have used the BCC version of OG to explain the presence of near a fibre recrystallization components in heavily cold rolled relatively pure iron by using the 26° h1 1 0i orientation relationship between {1 1 3}h4 7 1i and {1 1 2}h1 1 0i components ({1 1 3}h4 7 1i is close to {4 1 1}h1 4 8i). They associated the reduction of X-ray intensities in {1 1 2}h1 1 0i components with the rise of {1 1 3}h4 7 1i because of the 26° h1 1 0i orientation relationship between them. The texture was determined by OIM, but the principle they followed was almost identical to that used by Ibe and L€ ucke [20] using X-ray global texture measurements to support OG. It is the purpose of this paper to present both the orientation and microstructural details of an intensive investigation into the origins of the a fibre recrystalli-
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zation components by means of modern OIM using heavily rolled and partially recrystallized material. This work started as part of an investigation into the warm rolling and annealing of IF steel. However because of other results from another investigation [21] it became necessary to understand the effects of additional cold rolling and annealing of the material following warm rolling. The results required the simpler case of heavy cold rolling to be investigated, and the results for both experiments are reported here.
2. Experimental procedure
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the hardnesses were also almost identical. Annealing at 710 °C in a preheated air furnace destroyed most of the a fibre leaving a single c fibre annealing texture in both the CR 85% and WR 75% samples, Fig. 1(d)–(e). The additional cold rolling to 95% total deformation, produced the texture shown in Fig. 2(a), which is very similar to the texture formed following warm rolling 75% and subsequent cold rolling by 80% to give 95% reduction in thickness, Fig. 2(b). The annealing textures of both the 95% rolled materials has weakened {1 1 1}h1 1 0i components and strengthened c components near {1 1 1}h3 2 1i which spread towards {554}h2 2 5i, giving peak type textures (Fig. 2(c)–(d)).
IF steel hot band of 70 lm average grain size of the composition shown in Table 1 was processed along two routes. Route one involved cold rolling with paraffin lubricant to 85% by 10% reduction per pass, since this ensures homogeneous deformation and gives excellent drawability after annealing. Part of this strip was further rolled to 95%. In route two the material was rolled to only 75% at 700 °C in a single pass because of the limited maximum load capacity of the mill. This was further cold rolled by 80% to give a total reduction of 95% from the original thickness. The friction in warm rolling was kept to a minimum level by using animal tallow as the lubricant. The rolling and annealing global textures were characterized by X-ray diffraction using Co Ka radiation. {1 1 0}, {2 0 0} and {2 1 1} pole figures were measured from which ODFs were calculated using the BATE software. The SEM and OIM investigations were done on the rolling plane (RP) at the mid thickness of the sheet. A pre-heated air circulation furnace held at 710 °C was used for annealing for various periods to simulate industrial heating rates which are typically in the hundreds of degrees per minute.
3. Results The rolling and annealing textures of 85%CR and 75%WR samples are shown in the /2 ¼ 45° ODF sections in Fig. 1. The cold rolled texture in Fig. 1(b) is very similar to the warm rolling texture in Fig. 1(c), with a small difference in the peak intensity which arises from the degree of deformation. It is clear that the a and c fibres are well developed. SEM examination showed the warm rolled metal to have almost identical microstructure to a cold rolled sample after the same reduction and
Fig. 2. u2 ¼ 45° ODF sections and {200} pole figures showing the rolling and annealing textures of 95%CR and 75%WR + 80%CR samples. ODF intensity levels: 1, 2, 4, 6, 8, 11, 14 and 17. Pole fig. Intensity levels: 0.5, 1, 2, 3, 4, 5, 6 and 7.
Table 1 Composition of the hot band (wt%) C
Si
Mn
P
S
Al
Ti
O
N
Cu
0.0043
<0.01
0.1
0.006
0.0065
0.035
0.057
0.0031
0.002
0.04
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The {2 0 0} pole figures shown in Fig. 2(e) and (f) clearly reveal the presence of the recrystallized a component including {4 1 1}h1 4 8i. Since the Hong Kong group has considerable evidence that the c recrystallization texture arises from the deformation banded (DB) structure in the c deformed grains [22], a detailed microstructural investigation was made of the a oriented material. As has been pointed out elsewhere [23], the longitudinal section is not helpful in observing orientation gradients where these arise by DB, because the additional surface created by orientation splitting is often parallel to the rolling plane (RP). Clearly only one segment would normally be visible in the LS if the boundary between different orientations created by DB was relatively straight, which is often the case after relatively heavy rolling. The RP, however allows more information to be readily gained when orientation splitting occurs in this manner. Figs. 3 and 4 show the SEM channelling contrast (CC) image of the RP sections of a grains in 85%CR and 75%WR samples. These are typical a grains and show a contrast pattern
Fig. 4. SEM CC image and the orientation mapping with corresponding {200} pole figure of the line scan shown in the microstructure of rolling plane section of 75%WR IF steel. Thin lines P 5° and thick lines P 15° misorientation.
Fig. 3. SEM CC image and the orientation mapping with corresponding {200} pole figure of the line scan shown in the microstructure of rolling plane section of 85%CR IF steel. Thin lines P 5° and thick lines P 15° misorientation.
which is characteristic of volumes of material having relatively small misorientations. In the corresponding OIM this is confirmed because only a few low angle boundaries, shown by the black lines, occur inside the grains. The {200} pole figures related to the line scans across the grain widths show the changes of orientation to be within 5° centered at {1 1 5}h1 1 0i. This small misorientation was found repeatedly in such a grains formed after both 85% cold rolling and 75% warm rolling. Significant microstructural changes were found in these a grains in the material further rolled to 95% reduction. Instead of showing the characteristic features demonstrated in Figs. 3 and 4 the a microstructure has become sub-divided into several segments, Figs. 5(a) and 6(a). The area inside the dotted-box of the CC image in Fig. 5(a) was selected for point-by-point orientation measurement at a 1 lm step size and the result is in the form of an OIM in Fig. 5(b). The neighboring grains, X and Y, show frequent low angle boundaries and the overall orientation of both lie within the c circle of the
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Fig. 5. CC image with the selected area OIM and corresponding {200} pole figures of RP section of 95%CR sample.
Fig. 6. CC image with the selected area OIM and corresponding {200} pole figures of RP section of 75%WR + 80%CR sample.
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{200} pole figure of the whole area shown in Fig. 5(c). The orientation along the length of each segment parallel to RD is uniform. Thus the orientation across the line along the grain width represents mostly the data from within the a volume. This showed the orientations of the four segments labeled A–D to have a spread of 45° along the a fibre, Fig. 5(d). There are also gentle orientation curvatures within individual segments, found from B1 to B2 and D1 to D2. The same procedure was adopted for the 75%WR + 80%CR sample, and identical results were found and are shown in Fig. 6. The {200} pole figure of the whole OIM area shows the orientation of the neighboring X and Y grains to be in the c circle. The line scan across the segments (1, 2, 3 and 5) shows the orientation to be a single variant version of the a fibre from {1 0 0}h0 1 1i to {2 1 1}h0 1 1i which is a 40° orientation spread, Fig. 6(d). Segment 4 is a complementary version of the a fibre close to {1 0 0}h0 1 1i. Fig. 7(a) and (b) shows a CC and OIM of partially annealed material following warm and cold rolling, and the texture of the whole area shown in Fig. 7(c), quite clearly belongs to the a fibre spread. The OIM in Fig. 7(b) reveals the microstructure to be divided into three regions A, B and C having orientation spreads within the a range, Fig. 7(c). Section B is divided into sections B1 to B3 along the line and the individual orientations A to C are plotted in Fig. 7(d). It is therefore
clear that the recovery and recrystallization that is occurring is happening within the a components. The enlarged sub-grain, 1, belonging to area A, is growing into area B, Fig. 7(d) and (e). Locations 2, 3, 4 and 5 have the orientation of area B, but it is not clear whether they are growing into C or growing in their parent volume, Fig. 7(d) and (f). Very similar results have been found for the material which has been cold rolled 95%. In contrast to these heavily deformed IF steels, the material rolled to 85% behaved as it has been reported elsewhere [12–23], a deformed material did not recrystallize at all up to a late stage, when it was consumed by invading grains mostly belonging to the c recrystallization components. Fig. 8 shows an OIM after complete recrystallization of 95% rolled material and shows a distribution of recrystallized a oriented grains. The OIM is plotted with 15° orientation spread from the exact a orientation. The relatively dark grains are a colony of {4 1 1}huvwi orientation surrounded by mostly c recrystallized grains, Fig. 8(b).
4. Discussion Grains belonging to the a fibre must have two kinds of microstructure at both 85% and 95% cold rolling. The first is that shown in Figs. 3 and 4 after 85% cold rolling
Fig. 7. Channelling contrast image and OIM with corresponding {200} pole figures of rolling plane section of partially recrystallized 75%WR + 80%CR IF steel.
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{1 0 0}h0 1 1i to a circle of radius {4 1 1} on the 200 pole figures. It is rare to find a0 material centered on {1 1 2}h1 1 0i. Now Figs. 1(b) and (c) and 2(a) and (b) shows a to have the highest intensity near {1 1 2}h1 1 0i, and it follows that {1 1 2} material has the highest volume fraction. Therefore it is most likely that the a1 material is centered on {1 1 2}h1 1 0i. 4.1. Concerning high rolling reductions (i.e. 95%)
Fig. 8. OIM with corresponding {200} pole figure showing the distribution of recrystallized grains in RP section in completely annealed material.
and after 95% reduction by that shown in Figs. 5 and 6. Both of these lower and higher rolling strain versions of a are similar in that contrast variations indicating small misorientations occurs over considerable length scales except where DB intervenes. This characteristic contrast is always associated with orientations belonging to the a fibre, and for the purpose of the discussion which follows is called a0 material. The second kind of a must be indistinguishable from c in that it has an identical finely divided microstructure characteristic of c. This is so because the X-ray measurements of Schl€ afer and Bunge [24] and more lately by Tse [25], among several reports, show that the volume fraction of a material over a strain range of 85–95% is high, between 30% and 40%. However inspection of very large CC montages covering many thousands of square microns shows a0 material to be at the 10% level, hence the remainder cannot be distinguished on grounds of microstructure alone. For the purpose of this discussion this is called a1 material. A second point can be made about a1 material. A few tens of OIMs from the four material states investigated here shows material with a0 contrast to extend from
Comparing Figs. 3 and 4 with Figs. 5 and 6 shows that the additional deformation from 85% to 95% in both cases has changed the microstructural features of a0 grains when observed in CC. At the lower reduction the a0 grains show the characteristic slowly varying contrast and the misorientation between contiguous volumes is small. On the other hand, the more heavily rolled material illustrated in Figs. 5 and 6 show the a0 grains to have developed a more complex microstructure. These montages are parts of extremely large scans and no case was found in which the orientation of characteristic a0 grains was uniform, all showed orientation splitting. The first possible explanation of what is seen in Figs. 5 and 6 is that more than one a0 grain is visible. Three facts mitigate against this view. The first and most powerful is that a0 grains of the kind shown in Figs. 3 and 4 have never been found at the higher reductions, all a0 grains are sub-divided. Secondly, assuming that the microstructure in Figs. 5 and 6 are groups of grains, no groups of a0 grains have been found in 85% rolled material with anything like the frequency that groups are found in the 95% material. Thirdly, the initial hot band grain size is 70 lm and the a0 volumes are of this order or smaller. It is therefore much more likely that single a0 grains have split their orientations along lines approximately parallel to RD, the rotation axes being h1 1 0i//RD. The misorientation from one end of the spread to the other in Fig. 5 is 50° and in Fig. 6 is 35°. The additional rolling deformation has obviously made a0 grains of the kind shown in Figs. 3 and 4 unstable, and orientation splitting, called for many decades, deformation banding, has occurred. In an intensive investigation of deformation banding (DB) Liu and Duggan [23] produced a model in which the e32 shear component was allowed to be relaxed. The displacement gradient tensor is shown in Fig. 9 together with the conditions governing the various other Taylor models. The FC Taylor requires five independent slip systems, the RC pancake, which is widely considered as a good deformation model for rolled BCC metals, requires between 2 and 4, and allows shears e31 and e21 because of the flattened grain shapes which are produced in heavy rolling. The DB model allows e32 to be relaxed, with the condition that shears in different elements are mutually cancelled, as in Fig. 9(c). They also needed in their model to ‘‘harden’’ some slip systems,
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rotation paths over the complete deformation range and at a computer rolling strain of 87% ðe ¼ 2 about 87% of the initial orientations have split into two parts and about half of these feed into the c fibre. This result has lead to a self-consistent theory of recrystallization in which c deformed material gives rise to recrystallized material [22]. The remaining DB set contributes to a and to the background of the computed pole figures and ODFs. One check of the model is that orientations known to be stable experimentally, should remain so in the model. This is the case, any orientation lying on the a fibre moves towards {1 1 2}h1 1 0i and {1 0 0}h0 1 1i depending on the precise starting location. Anything beyond {1 1 2}h1 1 0i can rotate to the common point on the c and a fibres, i.e. {1 1 1}h1 1 0i. Two more complex examples taken from Duggan et al. [26] are shown in Fig. 11. In Fig. 11(a) the original orientation is 0 and this splits early in the strain history to give the final orientations of 1 and 2, which are both close to the a fibre and separated by about 50°. Fig. 11(b) shows an orientation which rotates towards the a fibre and then splits to give two a components separated by 12°. These examples show how by using relatively simple physics it is possible to predict how orientation splitting occurs to give neighboring volumes with significant misorientaFig. 9. Rolling geometry and displacement gradient tensor with the conditions [23]: FC: e21 ¼ e31 ¼ e32 ¼ 0; RClath ¼ e31 6¼ 0, e21 ¼ e31 ¼ 0; RCpancake ¼ e31 and e21 6¼ 0, e32 ¼ 0; DB ¼ e31 , e21 and e32 6¼ 0.
which they achieved by a latent hardening parameter as well as including an estimate of the extra energy needed to create the additional surface at the band interfaces. The occurrence of deformation banding was therefore determined by an energy criterion. Another feature of the model is that the frequency of DB increases with ‘‘computer rolling’’ reduction. Fig. 10 shows the number of grains from a random distribution of 1000 orientations which are subject to DB. Furthermore by interrogating the model it is possible to follow individual
Fig. 10. Number of grains subject to DB at different strains [22].
Fig. 11. {200} pole figures showing the rotations from specific initial orientations ‘‘0’’ to a single ‘‘1’’ or to a pair of orientations ‘‘1’’ and ‘‘2’’ calculated by deformation banding theory with e32 shear relaxation [26].
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tions between them. This is what is visible in Figs. 5 and 6. DB in the model is also showing an element of strain dependence which is essential if the results shown in Figs. 3–6 are to be explained. Turning now to a1 material, which must be largely centered on the orientation {1 1 2}h1 1 0i and have the finely divided microstructure typical of c grains, it is only possible in the absence of direct evidence to put forward a speculative argument. {1 1 2}h1 1 0i is widely considered as the most stable end orientation in plane strain deformation and in fact one of the tests of the DB theory is that it remains stable in the model. Computation shows that there exists a wide range of starting orientations which rotate to {1 1 2}h1 1 0i without DB. However there is a set of starting orientations which form DB to give orientations close to {1 1 2}h1 1 0i in addition to another h1 1 0i component. Fig. 11(a) and (b) show two such orientation and it is to be noted that the angle between the final end orientation in Fig. 11(b) i.e. {4 1 1}h1 1 0i and {2 1 1}h1 1 0i is only 12°. Thus it seems likely that a1 material, because of its inherent stability, is not subject to significant DB over the deformation range of 75–95% reduction. The general problem with all models of the Taylor type is that end orientations are reached more quickly in terms of strain than is observed in real materials. Thus the texture predictions are always sharper than those developed in real materials at a given strain [27]. Hence the results shown in Figs. 10 and 11 are characteristic of larger rolling reductions, but the trends are encouragingly close to reality. The annealing of a0 structures such as are shown in Figs. 5 and 6 leads to well developed subgrain structures shown in Fig. 7 which clearly are potential recrystallization nuclei. Indeed subgrain 1 in Fig. 7 seems to have passed this stage and is in the process of invading region B which is 30–40° misoriented with the parent volume A. For a subgrain to be considered a nucleus it must have a mobile interface, which translates into a misorientation of greater than 15–20°, and a driving force. Clearly the evidence in these microstructures derived from SEM do not give any indication of stored energy, if this is in the form of randomly stored dislocations. However the OIM in Fig. 7(b) indicates low angle boundaries (5°) by the lines in the structure, and thus shows considerable energy in this form, especially compared with interior of subgrain 1. Thus both requirements are met for subgrain 1. Equally clearly, subgrains 2–5 are all possible nuclei, but the driving forces are not quite so evident. Concerning driving forces, many years ago Takechi et al. [10] showed that after cold rolling the stored energy sequence is E2 1 1 ffi E4 1 1 > E100 , and so, if it is indeed true that high stored energy components recover more rapidly than low energy ones, a result also found by Rajmohan et al. [28] then, after recovery E2re1 1cov ffi E4re1 1cov < E1re0 0cov .
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Therefore a driving force would exist in this case which would ensure viability of nuclei of {4 1 1}h1 1 0–4 1 8i orientations by DB boundary bulging into a by the Bailey and Hirsch [29] mechanism. Alternatively nucleation can be produced within the a grain by the subgrain growth mechanism of Dillamore et al. [14] if a transition band has formed between the DB components. The pole figures shown in Fig. 2 show small intensities near {1 1 2}h1 1 0i and {4 1 1}hhkli. The spread about {1 1 2} is difficult to differentiate from the overlapping spread from {1 1 1}hhkli. The completely recrystallized sample in Fig. 8 shows grains having the orientations within {4 1 1}huvwi are to be found together. This implies that in all probability they have formed from the same deformed grain. Furthermore their linear arrangement in a line along RD can be correlated with orientation splitting in the rolling plane to give boundaries roughly parallel to RD. It does not seem to be necessary for a particular misorientation to be involved, as in the OG theory, but it remains possible that some form of micro-growth selection is involved [30] because many a components are related by a rotation around a common h1 1 0i which is parallel to RD. It must be stressed however, that the results presented here do not need this theory, because all of the requirements for successful nucleation are met by the deformation banding and recovery processes. The instability of the a components above a certain critical deformation degree demonstrated by comparing Figs. 3 and 4 with Figs. 5 and 6 mean that they will form recrystallized grains of near a0 orientations. a1 material where this is close to {1 1 2}h1 1 0i after 95% rolling, although it has the same microstructure of c material, significantly lacks lattice curvature, and therefore is prone to consumption by invading neighbors, since it can only recover. Its stored energy, because of its microstructure, is likely to be higher than that found in recovered a0 grains. 4.2. Concerning lower rolling reductions (i.e. 75–85%) Turning now to the lower strain situation it is clear from the literature that a does not contribute to the final recrystallization textures, and this is a requirement for successful production of formable steel. Now the behavior of a (i.e. a0 þ a1 ) on annealing IF steel at this strain has been indirectly observed by Hutchinson et al. [31], who by using a combination of X-ray and SEM EBSP measurements was able to show that c recrystallized very readily, while the a components remained substantially unchanged until relatively late in the process. Their results are shown in Fig. 12. The problem of why a0 remains so late in the annealing process has been addressed recently by Tse [25] and Duggan and Tse [32]. In their work several c nuclei contained in original hot band grain envelopes, grew
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Fig. 12. ODFs sections ð/2 ¼ 45°Þ for steel at different stages of recrystallization, (a)–(d) global textures from X-ray measurements, (e)–(g) recrystallized fraction only from EBSP measurements, (h)–(j) textures of deformed matrix [31].
until they impinged to form recrystallized grains separated by low angle boundaries approximately perpendicular to the rolling plane. They formed, in effect, long crystals with sub-boundaries approximately perpendicular to the RD, which could enlarge by the original hot band high angle grain boundary bulging into the neighboring recovering material. In this process the new grains start as equiaxed, appear as elongated grains at an intermediate degree of recrystallization and then become equiaxed at the completion of recrystallization. Following Bailey and Hirsch [29] a high angle boundary will bulge into the neighboring deformed material if it has a critical length, 2c LP ; ð1Þ DE where c is the surface energy of the interface and DE is the difference in dislocation storage across the boundary. Assuming that such a deformed hot band c grain is going through this process of impingement of nuclei to give a growing grain with high aspect ratio and is neighbored by an a0 grain, then for successful invasion, L will have to be long since DE must be small. Duggan and Tse [32] showed that, on average the aspect ratio of new grains was 1 at 10% recrystallization, 2 at 50% and 1 when recrystallization was complete and this supports the idea that the process of c consuming a0 will occur later in the annealing cycle because several nucleation events are involved in forming one c grain, and
there is little driving force for consumption of a0 material by chance encounters with migrating high angle boundary segments of equiaxed grains. In no case was observed an a0 nucleation event in the extensive microstructural work reported here for both warm (to 75%) and cold rolling (to 85%). By inference, a1 nucleation must also be rather unsuccessful, given its probable lack of lattice curvature and the drastic reduction in intensity of the overall a fibre shown in Fig. 2. 5. Conclusions 1. There are two kinds of a deformed microstructures, one indistinguishable from c microstructure, and the other having a quite distinct appearance. One microstructure centered on {1 0 0}h1 1 0i is named a0 because it has no sharp features but a characteristic contrast, and the other a1 centered on {1 1 2}h1 1 0i, has the same microstructural appearance as deformed c. 2. a0 is of uniform orientation after 85% cold rolling, but orientation splitting into deformation bands occurs at higher strains. 3. At higher rolling strains recrystallization occurs in a0 because a0 has sharp curvatures between a components, and differential recovery is known to occur in a components. This differential recovery provides a driving force for recrystallization of a components at the expense of other a0 components in the same
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grain envelope. Because of the stability of a1 material, DB is unlikely to provide necessary lattice curvature for recrystallization and hence a1 grains are likely to be consumed. 4. Since a0 is of uniform orientation at 85% rolling reduction, it does not recrystallize because it lacks lattice curvature. a material formed at this reduction is consumed relatively late in the annealing cycle, probably by invading c grains. 5. The observations that at reductions up to 85%, a0 grains remain of homogeneous structure and without lattice curvature, while at higher reductions orientation splitting in the form of DB occurs, can be used to explain the optimum cold rolling reduction for good deep drawability performance. At 85% cold rolling a does not recrystallize, but at higher reductions it does, and this deteriorates the textures as far as drawability concerned. 6. There is no need to involve OG theory in its classical form to explain the texture results. It is possible that, if the 26° h1 1 0i has any significance, it could provide favorable micro-growth selection conditions in a deformed grains subject to DB for recrystallization. This is because the a fibre is defined as components belonging to the h1 1 0i//RD set of orientations, and DB produces contiguous volumes of a material.
Acknowledgements It is a pleasure to acknowledge the supports of this work by the grants numbered CERG/HKU 7067/97E, 7323/98E and 7316/99E given by the Hong Kong Special Administration Region of China. References [1] Lankford WT, 1950;42:1197.
Snyder
SC,
Bauscher
JA.
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[2] Wilson DV. J Inst Met 1966;94:84. [3] Held JF. Proceedings of the Conference on Mechanical working and steel processing IV. New York: The Metallurgical Society of AIME; 1965. [4] Whiteley RL, Wise DE. Flat rolled Products III. Inter-Science: New York; 1962. p. 63. [5] Dillamore IL, Smith CJE, Watson TW. Met Sci 1967;1:49. [6] Kubotera H, Nakaoka K. Proceedings of the Conference on Mechanical working and steel processing VII. New York: The Metallurgical Society of AIME; 1969. [7] Matsui M, Hayami S, Nagashima S. In: Proceedings of the ICSTIS, Suppl. Transactions, Iron Steel Institute Japan, vol. 209, 1971. p. 562. [8] Duggan BJ. Ph. D. Thesis. The University of Birmingham, UK, 1972. [9] Duggan BJ, Roberts WT. Met Sci 1975;9:449. [10] Takechi H, Katoh H, Nagishima S. Trans AIME 1968;242:56. [11] Hutchinson WB. Int Met Rev 1984;29(1):25. [12] Bunge HJ. Mathematische Methoden der Texturanalyse. Berlin: Akademie-Verlag; 1969. [13] Roe RJ. J Appl Phys 1965;6:2024. [14] Dillamore IL, Morris PL, Smith CJE, Hutchinson WB. Proc R Soc London 1972;329:405. [15] Dillamore IL, Katoh H, Haslam K. Texture 1974;1:151. [16] Taylor GIJ. Inst Met 1938;62:307. [17] Verbakim K, Kestens L, Jonas JJ. Scr Mater 2003;48:1457. [18] Verbakim K, Nave MD, Kestens L, Barnett MR. Mater Sci Forum 2003;426–432:3757. [19] Verbakim K, Kestens L. Acta Mater 2003;51:1679. [20] Ibe G, L€ ucke K. Archiv f€ ur das Eisenh€ uttenwesen 1968;39:693. [21] Quadir MZ, Lam KT, Duggan BJ. J Mech Eng Sci C, in press. [22] Tse YY, Liu GL, Duggan BJ. Scr Mater 2000;42(1):25. [23] Liu GL, Duggan BJ. Met Mater Trans A 2001;32:125. [24] Schl€afer D, Bunge HJ. Texture 1974;1:157. [25] Tse YY. Ph. D. Thesis, The University of Hong Kong, 2001. [26] Duggan BJ, Liu GL, Tse YY. In: Sakai T, Suzuki HG, editors. The Fourth International Conference On Recrystallization and Related Phenomenon. Japan Institute of Metals; 1999. p. 367. [27] Van Houtte P, Delannay L, Samajdar I. Texture Microstruct 1999;31:109. [28] Rajmohan N, Hayakawa Y, Szpunar JA, Root JH. Acta Mater 1997;45:2485. [29] Bailey JE, Hirsch PB. Proc Roy Soc London A 1962;267:11. [30] Duggan BJ, L€ ucke K, K€ ohlhoff GD, Lee CS. Acta Met Mater 1993;41:1921. [31] Hutchinson WB. Mater Sci Forum 1994;157–162:1917. [32] Duggan BJ, Tse YY. Acta Mater 2004;52:387.
Deformation banding and recrystallization of a fibre components in heavily rolled IF steel M.Z. Quadir *, B.J. Duggan
*
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong Received 30 March 2004; received in revised form 9 May 2004; accepted 12 May 2004 Available online 17 June 2004
Abstract Detailed SEM work has shown that about a quarter of crystals belonging to the a fibre formed by cold rolling up to reductions of 85%, are of uniform microstructure with relatively small misorientation. The remainder are indistinguishable from the polycrystalline mass, which is mostly of c orientations. At rolling reductions above 85%, a grains begin to split their orientations by deformation banding, thus producing lattice curvature which allows recrystallization of a at the expense of other a components in the same original grain. This a recrystallization deteriorates the deep drawability of IF steel and since the process requires deformation banding a natural explanation of the optimum rolling reduction for good drawability is provided. The best cold rolling reduction is that which optimizes c recrystallization by producing deformation banding in c components without producing deformation banding in a components. Uniform microstructures and small lattice curvature allows a to be consumed by other orientations, and this condition is obtained in the 80–85% cold rolling range. Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Rolling; a and c fibres; Deformation banding; Recrystallisation; Textures
1. Introduction Deep drawability is measured by the Limiting Drawing Ratio, a test in which a cup is drawn from a circular blank and this correlates with the Lankford parameter, r, which is defined as the width to thickness strains in the tensile test [1]. Intensive early work done between the 1950s and 1970s showed the Lankford parameter to be determined by the texture of the material (e.g. [2]). For the Al-killed steels of the time, and using the X-ray technology available, this translated into a simple requirement that the ratio of the intensities of the {1 1 1} and {1 0 0} reflections be as high as possible [3]. In 1962 Whitely and Wise [4] showed that there was an optimum rolling reduction of about 75% prior to final
*
Corresponding authors. Tel.: +852-285-786-15; fax: +852-285-854-
15. E-mail addresses: [email protected] (M.Z. Quadir), [email protected] (B.J. Duggan).
annealing, beyond which the Lankford parameter declined. The reason was associated with the persistence of that part of the rolling texture close to {1 0 0}h0 1 1i. Now it must be stressed that desirable {1 1 1} recrystallization texture components for drawability increase with rolling reduction, but the intensity ratio declines because {1 0 0} components increase faster than {1 1 1} above a certain rolling degree. The situation has not changed with the introduction of interstitial free (IF) steels, there is still a maximum cold rolling reduction, but in the 80–85% range and the reasons for the high Lankford parameter are identical to those put forward for the older deep drawable AL-killed steels. Much of the early work concerning drawable sheet steels, in which many took part, was to do with the problem of this so called retained rolling texture [5–7], especially components near {1 0 0} because of their deleterious effects on the Lankford parameter. In this regard and following extensive work Duggan [8] and Duggan and Roberts [9] showed that recovery anneals of low carbon steel after cold rolling to 90% for
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as long as 10,000 min followed by a high temperature recrystallization treatment at 750 °C produced a relatively strong {4 1 1}h1 4 8i component in a low carbon steel. Transmission electron microscopy (TEM) was used to ensure that only recovery had occurred at 500 °C and they thought that the {4 1 1}h1 4 8i had arisen from an in situ nucleation process involving subgrains adjacent to grain boundaries. The {4 1 1} component was considered to be part of the orientation spread of a single {1 0 0} grain, was located close to grain boundaries, and, following Takechi et al. [10] had a higher stored energy than that found in the grain interior. Differential recovery was assumed to occur, happening faster in the higher energy grain boundary regions, to produce low energy blocks of sufficient misorientation to migrate into the {1 0 0}hhkli interior. Later this issue was reviewed by Hutchinson [11] and in the discussion of the optimum rolling reduction for drawable steel, the origins of {4 1 1}huvwi component was mentioned as not being satisfactorily explained because of lack of direct evidence. With the advent of the ODF by Bunge [12] and Roe [13], it became clear that among the several different ways of describing the rolling texture of BCC iron, the idea of the a and c fibres are best. The a fibre comprises orientations with RD//h1 1 0i and the c fibre the h1 1 1i orientations parallel to the sheet normal direction ND. A /2 ¼ 45° ODF section in Fig. 1(a) shows the positions of the orientation components of both fibres. A further technical development which has thrown much light on the deformation state is orientation imaging microscopy (OIM) based in the modern scanning electron microscope (SEM). It is now possible to easily couple an orientation of 1°–3° accuracy with a specific location of 1 lm in diameter. Recrystallization theory still relies on two old theories, oriented nucleation (ON) and oriented growth (OG). Even with the greatly expanded technical capabilities available today, both of these theories are still used to explain the same data sets, in other words, neither one nor the other is held to be universally true in all circumstances. Dillamore et al. [14] in fine work related to ON, proposed a model for the ‘‘in situ’’ process based upon subgrain growth, particularly in transition bands. In the further development of this model, Dillamore et al. [15] tested these ideas by compressing polycrystalline iron. This deformation mode was thought from Taylor theory [16] to rotate the crystals towards two stable orientations h0 0 1i and h1 1 1i parallel to the compression direction (CD). They then supposed that a small fraction of material would stay on a rotation path towards a metastable orientation, h4 1 1i//CD. They identified the end orientations h0 0 1i and h1 1 1i//CD as convergent planes into which material rotates away from a metastable crystallographic pathway which they called the divergent planes. These divergent planes they
Fig. 1. u2 ¼ 45° ODF sections showing the rolling and annealing textures of 85%CR and 75%WR samples. Intensity levels: 1, 2, 4, 6, 8, 11, 14 and 17.
assumed would be sites of recrystallization nuclei, and, remarkably the recrystallization texture had a h4 1 1i// CD component which apparently confirmed the ON theory for this case. However in more recent work Verbeken et al. [17–19] have used the BCC version of OG to explain the presence of near a fibre recrystallization components in heavily cold rolled relatively pure iron by using the 26° h1 1 0i orientation relationship between {1 1 3}h4 7 1i and {1 1 2}h1 1 0i components ({1 1 3}h4 7 1i is close to {4 1 1}h1 4 8i). They associated the reduction of X-ray intensities in {1 1 2}h1 1 0i components with the rise of {1 1 3}h4 7 1i because of the 26° h1 1 0i orientation relationship between them. The texture was determined by OIM, but the principle they followed was almost identical to that used by Ibe and L€ ucke [20] using X-ray global texture measurements to support OG. It is the purpose of this paper to present both the orientation and microstructural details of an intensive investigation into the origins of the a fibre recrystalli-
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zation components by means of modern OIM using heavily rolled and partially recrystallized material. This work started as part of an investigation into the warm rolling and annealing of IF steel. However because of other results from another investigation [21] it became necessary to understand the effects of additional cold rolling and annealing of the material following warm rolling. The results required the simpler case of heavy cold rolling to be investigated, and the results for both experiments are reported here.
2. Experimental procedure
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the hardnesses were also almost identical. Annealing at 710 °C in a preheated air furnace destroyed most of the a fibre leaving a single c fibre annealing texture in both the CR 85% and WR 75% samples, Fig. 1(d)–(e). The additional cold rolling to 95% total deformation, produced the texture shown in Fig. 2(a), which is very similar to the texture formed following warm rolling 75% and subsequent cold rolling by 80% to give 95% reduction in thickness, Fig. 2(b). The annealing textures of both the 95% rolled materials has weakened {1 1 1}h1 1 0i components and strengthened c components near {1 1 1}h3 2 1i which spread towards {554}h2 2 5i, giving peak type textures (Fig. 2(c)–(d)).
IF steel hot band of 70 lm average grain size of the composition shown in Table 1 was processed along two routes. Route one involved cold rolling with paraffin lubricant to 85% by 10% reduction per pass, since this ensures homogeneous deformation and gives excellent drawability after annealing. Part of this strip was further rolled to 95%. In route two the material was rolled to only 75% at 700 °C in a single pass because of the limited maximum load capacity of the mill. This was further cold rolled by 80% to give a total reduction of 95% from the original thickness. The friction in warm rolling was kept to a minimum level by using animal tallow as the lubricant. The rolling and annealing global textures were characterized by X-ray diffraction using Co Ka radiation. {1 1 0}, {2 0 0} and {2 1 1} pole figures were measured from which ODFs were calculated using the BATE software. The SEM and OIM investigations were done on the rolling plane (RP) at the mid thickness of the sheet. A pre-heated air circulation furnace held at 710 °C was used for annealing for various periods to simulate industrial heating rates which are typically in the hundreds of degrees per minute.
3. Results The rolling and annealing textures of 85%CR and 75%WR samples are shown in the /2 ¼ 45° ODF sections in Fig. 1. The cold rolled texture in Fig. 1(b) is very similar to the warm rolling texture in Fig. 1(c), with a small difference in the peak intensity which arises from the degree of deformation. It is clear that the a and c fibres are well developed. SEM examination showed the warm rolled metal to have almost identical microstructure to a cold rolled sample after the same reduction and
Fig. 2. u2 ¼ 45° ODF sections and {200} pole figures showing the rolling and annealing textures of 95%CR and 75%WR + 80%CR samples. ODF intensity levels: 1, 2, 4, 6, 8, 11, 14 and 17. Pole fig. Intensity levels: 0.5, 1, 2, 3, 4, 5, 6 and 7.
Table 1 Composition of the hot band (wt%) C
Si
Mn
P
S
Al
Ti
O
N
Cu
0.0043
<0.01
0.1
0.006
0.0065
0.035
0.057
0.0031
0.002
0.04
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The {2 0 0} pole figures shown in Fig. 2(e) and (f) clearly reveal the presence of the recrystallized a component including {4 1 1}h1 4 8i. Since the Hong Kong group has considerable evidence that the c recrystallization texture arises from the deformation banded (DB) structure in the c deformed grains [22], a detailed microstructural investigation was made of the a oriented material. As has been pointed out elsewhere [23], the longitudinal section is not helpful in observing orientation gradients where these arise by DB, because the additional surface created by orientation splitting is often parallel to the rolling plane (RP). Clearly only one segment would normally be visible in the LS if the boundary between different orientations created by DB was relatively straight, which is often the case after relatively heavy rolling. The RP, however allows more information to be readily gained when orientation splitting occurs in this manner. Figs. 3 and 4 show the SEM channelling contrast (CC) image of the RP sections of a grains in 85%CR and 75%WR samples. These are typical a grains and show a contrast pattern
Fig. 4. SEM CC image and the orientation mapping with corresponding {200} pole figure of the line scan shown in the microstructure of rolling plane section of 75%WR IF steel. Thin lines P 5° and thick lines P 15° misorientation.
Fig. 3. SEM CC image and the orientation mapping with corresponding {200} pole figure of the line scan shown in the microstructure of rolling plane section of 85%CR IF steel. Thin lines P 5° and thick lines P 15° misorientation.
which is characteristic of volumes of material having relatively small misorientations. In the corresponding OIM this is confirmed because only a few low angle boundaries, shown by the black lines, occur inside the grains. The {200} pole figures related to the line scans across the grain widths show the changes of orientation to be within 5° centered at {1 1 5}h1 1 0i. This small misorientation was found repeatedly in such a grains formed after both 85% cold rolling and 75% warm rolling. Significant microstructural changes were found in these a grains in the material further rolled to 95% reduction. Instead of showing the characteristic features demonstrated in Figs. 3 and 4 the a microstructure has become sub-divided into several segments, Figs. 5(a) and 6(a). The area inside the dotted-box of the CC image in Fig. 5(a) was selected for point-by-point orientation measurement at a 1 lm step size and the result is in the form of an OIM in Fig. 5(b). The neighboring grains, X and Y, show frequent low angle boundaries and the overall orientation of both lie within the c circle of the
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Fig. 5. CC image with the selected area OIM and corresponding {200} pole figures of RP section of 95%CR sample.
Fig. 6. CC image with the selected area OIM and corresponding {200} pole figures of RP section of 75%WR + 80%CR sample.
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{200} pole figure of the whole area shown in Fig. 5(c). The orientation along the length of each segment parallel to RD is uniform. Thus the orientation across the line along the grain width represents mostly the data from within the a volume. This showed the orientations of the four segments labeled A–D to have a spread of 45° along the a fibre, Fig. 5(d). There are also gentle orientation curvatures within individual segments, found from B1 to B2 and D1 to D2. The same procedure was adopted for the 75%WR + 80%CR sample, and identical results were found and are shown in Fig. 6. The {200} pole figure of the whole OIM area shows the orientation of the neighboring X and Y grains to be in the c circle. The line scan across the segments (1, 2, 3 and 5) shows the orientation to be a single variant version of the a fibre from {1 0 0}h0 1 1i to {2 1 1}h0 1 1i which is a 40° orientation spread, Fig. 6(d). Segment 4 is a complementary version of the a fibre close to {1 0 0}h0 1 1i. Fig. 7(a) and (b) shows a CC and OIM of partially annealed material following warm and cold rolling, and the texture of the whole area shown in Fig. 7(c), quite clearly belongs to the a fibre spread. The OIM in Fig. 7(b) reveals the microstructure to be divided into three regions A, B and C having orientation spreads within the a range, Fig. 7(c). Section B is divided into sections B1 to B3 along the line and the individual orientations A to C are plotted in Fig. 7(d). It is therefore
clear that the recovery and recrystallization that is occurring is happening within the a components. The enlarged sub-grain, 1, belonging to area A, is growing into area B, Fig. 7(d) and (e). Locations 2, 3, 4 and 5 have the orientation of area B, but it is not clear whether they are growing into C or growing in their parent volume, Fig. 7(d) and (f). Very similar results have been found for the material which has been cold rolled 95%. In contrast to these heavily deformed IF steels, the material rolled to 85% behaved as it has been reported elsewhere [12–23], a deformed material did not recrystallize at all up to a late stage, when it was consumed by invading grains mostly belonging to the c recrystallization components. Fig. 8 shows an OIM after complete recrystallization of 95% rolled material and shows a distribution of recrystallized a oriented grains. The OIM is plotted with 15° orientation spread from the exact a orientation. The relatively dark grains are a colony of {4 1 1}huvwi orientation surrounded by mostly c recrystallized grains, Fig. 8(b).
4. Discussion Grains belonging to the a fibre must have two kinds of microstructure at both 85% and 95% cold rolling. The first is that shown in Figs. 3 and 4 after 85% cold rolling
Fig. 7. Channelling contrast image and OIM with corresponding {200} pole figures of rolling plane section of partially recrystallized 75%WR + 80%CR IF steel.
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{1 0 0}h0 1 1i to a circle of radius {4 1 1} on the 200 pole figures. It is rare to find a0 material centered on {1 1 2}h1 1 0i. Now Figs. 1(b) and (c) and 2(a) and (b) shows a to have the highest intensity near {1 1 2}h1 1 0i, and it follows that {1 1 2} material has the highest volume fraction. Therefore it is most likely that the a1 material is centered on {1 1 2}h1 1 0i. 4.1. Concerning high rolling reductions (i.e. 95%)
Fig. 8. OIM with corresponding {200} pole figure showing the distribution of recrystallized grains in RP section in completely annealed material.
and after 95% reduction by that shown in Figs. 5 and 6. Both of these lower and higher rolling strain versions of a are similar in that contrast variations indicating small misorientations occurs over considerable length scales except where DB intervenes. This characteristic contrast is always associated with orientations belonging to the a fibre, and for the purpose of the discussion which follows is called a0 material. The second kind of a must be indistinguishable from c in that it has an identical finely divided microstructure characteristic of c. This is so because the X-ray measurements of Schl€ afer and Bunge [24] and more lately by Tse [25], among several reports, show that the volume fraction of a material over a strain range of 85–95% is high, between 30% and 40%. However inspection of very large CC montages covering many thousands of square microns shows a0 material to be at the 10% level, hence the remainder cannot be distinguished on grounds of microstructure alone. For the purpose of this discussion this is called a1 material. A second point can be made about a1 material. A few tens of OIMs from the four material states investigated here shows material with a0 contrast to extend from
Comparing Figs. 3 and 4 with Figs. 5 and 6 shows that the additional deformation from 85% to 95% in both cases has changed the microstructural features of a0 grains when observed in CC. At the lower reduction the a0 grains show the characteristic slowly varying contrast and the misorientation between contiguous volumes is small. On the other hand, the more heavily rolled material illustrated in Figs. 5 and 6 show the a0 grains to have developed a more complex microstructure. These montages are parts of extremely large scans and no case was found in which the orientation of characteristic a0 grains was uniform, all showed orientation splitting. The first possible explanation of what is seen in Figs. 5 and 6 is that more than one a0 grain is visible. Three facts mitigate against this view. The first and most powerful is that a0 grains of the kind shown in Figs. 3 and 4 have never been found at the higher reductions, all a0 grains are sub-divided. Secondly, assuming that the microstructure in Figs. 5 and 6 are groups of grains, no groups of a0 grains have been found in 85% rolled material with anything like the frequency that groups are found in the 95% material. Thirdly, the initial hot band grain size is 70 lm and the a0 volumes are of this order or smaller. It is therefore much more likely that single a0 grains have split their orientations along lines approximately parallel to RD, the rotation axes being h1 1 0i//RD. The misorientation from one end of the spread to the other in Fig. 5 is 50° and in Fig. 6 is 35°. The additional rolling deformation has obviously made a0 grains of the kind shown in Figs. 3 and 4 unstable, and orientation splitting, called for many decades, deformation banding, has occurred. In an intensive investigation of deformation banding (DB) Liu and Duggan [23] produced a model in which the e32 shear component was allowed to be relaxed. The displacement gradient tensor is shown in Fig. 9 together with the conditions governing the various other Taylor models. The FC Taylor requires five independent slip systems, the RC pancake, which is widely considered as a good deformation model for rolled BCC metals, requires between 2 and 4, and allows shears e31 and e21 because of the flattened grain shapes which are produced in heavy rolling. The DB model allows e32 to be relaxed, with the condition that shears in different elements are mutually cancelled, as in Fig. 9(c). They also needed in their model to ‘‘harden’’ some slip systems,
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rotation paths over the complete deformation range and at a computer rolling strain of 87% ðe ¼ 2 about 87% of the initial orientations have split into two parts and about half of these feed into the c fibre. This result has lead to a self-consistent theory of recrystallization in which c deformed material gives rise to recrystallized material [22]. The remaining DB set contributes to a and to the background of the computed pole figures and ODFs. One check of the model is that orientations known to be stable experimentally, should remain so in the model. This is the case, any orientation lying on the a fibre moves towards {1 1 2}h1 1 0i and {1 0 0}h0 1 1i depending on the precise starting location. Anything beyond {1 1 2}h1 1 0i can rotate to the common point on the c and a fibres, i.e. {1 1 1}h1 1 0i. Two more complex examples taken from Duggan et al. [26] are shown in Fig. 11. In Fig. 11(a) the original orientation is 0 and this splits early in the strain history to give the final orientations of 1 and 2, which are both close to the a fibre and separated by about 50°. Fig. 11(b) shows an orientation which rotates towards the a fibre and then splits to give two a components separated by 12°. These examples show how by using relatively simple physics it is possible to predict how orientation splitting occurs to give neighboring volumes with significant misorientaFig. 9. Rolling geometry and displacement gradient tensor with the conditions [23]: FC: e21 ¼ e31 ¼ e32 ¼ 0; RClath ¼ e31 6¼ 0, e21 ¼ e31 ¼ 0; RCpancake ¼ e31 and e21 6¼ 0, e32 ¼ 0; DB ¼ e31 , e21 and e32 6¼ 0.
which they achieved by a latent hardening parameter as well as including an estimate of the extra energy needed to create the additional surface at the band interfaces. The occurrence of deformation banding was therefore determined by an energy criterion. Another feature of the model is that the frequency of DB increases with ‘‘computer rolling’’ reduction. Fig. 10 shows the number of grains from a random distribution of 1000 orientations which are subject to DB. Furthermore by interrogating the model it is possible to follow individual
Fig. 10. Number of grains subject to DB at different strains [22].
Fig. 11. {200} pole figures showing the rotations from specific initial orientations ‘‘0’’ to a single ‘‘1’’ or to a pair of orientations ‘‘1’’ and ‘‘2’’ calculated by deformation banding theory with e32 shear relaxation [26].
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tions between them. This is what is visible in Figs. 5 and 6. DB in the model is also showing an element of strain dependence which is essential if the results shown in Figs. 3–6 are to be explained. Turning now to a1 material, which must be largely centered on the orientation {1 1 2}h1 1 0i and have the finely divided microstructure typical of c grains, it is only possible in the absence of direct evidence to put forward a speculative argument. {1 1 2}h1 1 0i is widely considered as the most stable end orientation in plane strain deformation and in fact one of the tests of the DB theory is that it remains stable in the model. Computation shows that there exists a wide range of starting orientations which rotate to {1 1 2}h1 1 0i without DB. However there is a set of starting orientations which form DB to give orientations close to {1 1 2}h1 1 0i in addition to another h1 1 0i component. Fig. 11(a) and (b) show two such orientation and it is to be noted that the angle between the final end orientation in Fig. 11(b) i.e. {4 1 1}h1 1 0i and {2 1 1}h1 1 0i is only 12°. Thus it seems likely that a1 material, because of its inherent stability, is not subject to significant DB over the deformation range of 75–95% reduction. The general problem with all models of the Taylor type is that end orientations are reached more quickly in terms of strain than is observed in real materials. Thus the texture predictions are always sharper than those developed in real materials at a given strain [27]. Hence the results shown in Figs. 10 and 11 are characteristic of larger rolling reductions, but the trends are encouragingly close to reality. The annealing of a0 structures such as are shown in Figs. 5 and 6 leads to well developed subgrain structures shown in Fig. 7 which clearly are potential recrystallization nuclei. Indeed subgrain 1 in Fig. 7 seems to have passed this stage and is in the process of invading region B which is 30–40° misoriented with the parent volume A. For a subgrain to be considered a nucleus it must have a mobile interface, which translates into a misorientation of greater than 15–20°, and a driving force. Clearly the evidence in these microstructures derived from SEM do not give any indication of stored energy, if this is in the form of randomly stored dislocations. However the OIM in Fig. 7(b) indicates low angle boundaries (5°) by the lines in the structure, and thus shows considerable energy in this form, especially compared with interior of subgrain 1. Thus both requirements are met for subgrain 1. Equally clearly, subgrains 2–5 are all possible nuclei, but the driving forces are not quite so evident. Concerning driving forces, many years ago Takechi et al. [10] showed that after cold rolling the stored energy sequence is E2 1 1 ffi E4 1 1 > E100 , and so, if it is indeed true that high stored energy components recover more rapidly than low energy ones, a result also found by Rajmohan et al. [28] then, after recovery E2re1 1cov ffi E4re1 1cov < E1re0 0cov .
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Therefore a driving force would exist in this case which would ensure viability of nuclei of {4 1 1}h1 1 0–4 1 8i orientations by DB boundary bulging into a by the Bailey and Hirsch [29] mechanism. Alternatively nucleation can be produced within the a grain by the subgrain growth mechanism of Dillamore et al. [14] if a transition band has formed between the DB components. The pole figures shown in Fig. 2 show small intensities near {1 1 2}h1 1 0i and {4 1 1}hhkli. The spread about {1 1 2} is difficult to differentiate from the overlapping spread from {1 1 1}hhkli. The completely recrystallized sample in Fig. 8 shows grains having the orientations within {4 1 1}huvwi are to be found together. This implies that in all probability they have formed from the same deformed grain. Furthermore their linear arrangement in a line along RD can be correlated with orientation splitting in the rolling plane to give boundaries roughly parallel to RD. It does not seem to be necessary for a particular misorientation to be involved, as in the OG theory, but it remains possible that some form of micro-growth selection is involved [30] because many a components are related by a rotation around a common h1 1 0i which is parallel to RD. It must be stressed however, that the results presented here do not need this theory, because all of the requirements for successful nucleation are met by the deformation banding and recovery processes. The instability of the a components above a certain critical deformation degree demonstrated by comparing Figs. 3 and 4 with Figs. 5 and 6 mean that they will form recrystallized grains of near a0 orientations. a1 material where this is close to {1 1 2}h1 1 0i after 95% rolling, although it has the same microstructure of c material, significantly lacks lattice curvature, and therefore is prone to consumption by invading neighbors, since it can only recover. Its stored energy, because of its microstructure, is likely to be higher than that found in recovered a0 grains. 4.2. Concerning lower rolling reductions (i.e. 75–85%) Turning now to the lower strain situation it is clear from the literature that a does not contribute to the final recrystallization textures, and this is a requirement for successful production of formable steel. Now the behavior of a (i.e. a0 þ a1 ) on annealing IF steel at this strain has been indirectly observed by Hutchinson et al. [31], who by using a combination of X-ray and SEM EBSP measurements was able to show that c recrystallized very readily, while the a components remained substantially unchanged until relatively late in the process. Their results are shown in Fig. 12. The problem of why a0 remains so late in the annealing process has been addressed recently by Tse [25] and Duggan and Tse [32]. In their work several c nuclei contained in original hot band grain envelopes, grew
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Fig. 12. ODFs sections ð/2 ¼ 45°Þ for steel at different stages of recrystallization, (a)–(d) global textures from X-ray measurements, (e)–(g) recrystallized fraction only from EBSP measurements, (h)–(j) textures of deformed matrix [31].
until they impinged to form recrystallized grains separated by low angle boundaries approximately perpendicular to the rolling plane. They formed, in effect, long crystals with sub-boundaries approximately perpendicular to the RD, which could enlarge by the original hot band high angle grain boundary bulging into the neighboring recovering material. In this process the new grains start as equiaxed, appear as elongated grains at an intermediate degree of recrystallization and then become equiaxed at the completion of recrystallization. Following Bailey and Hirsch [29] a high angle boundary will bulge into the neighboring deformed material if it has a critical length, 2c LP ; ð1Þ DE where c is the surface energy of the interface and DE is the difference in dislocation storage across the boundary. Assuming that such a deformed hot band c grain is going through this process of impingement of nuclei to give a growing grain with high aspect ratio and is neighbored by an a0 grain, then for successful invasion, L will have to be long since DE must be small. Duggan and Tse [32] showed that, on average the aspect ratio of new grains was 1 at 10% recrystallization, 2 at 50% and 1 when recrystallization was complete and this supports the idea that the process of c consuming a0 will occur later in the annealing cycle because several nucleation events are involved in forming one c grain, and
there is little driving force for consumption of a0 material by chance encounters with migrating high angle boundary segments of equiaxed grains. In no case was observed an a0 nucleation event in the extensive microstructural work reported here for both warm (to 75%) and cold rolling (to 85%). By inference, a1 nucleation must also be rather unsuccessful, given its probable lack of lattice curvature and the drastic reduction in intensity of the overall a fibre shown in Fig. 2. 5. Conclusions 1. There are two kinds of a deformed microstructures, one indistinguishable from c microstructure, and the other having a quite distinct appearance. One microstructure centered on {1 0 0}h1 1 0i is named a0 because it has no sharp features but a characteristic contrast, and the other a1 centered on {1 1 2}h1 1 0i, has the same microstructural appearance as deformed c. 2. a0 is of uniform orientation after 85% cold rolling, but orientation splitting into deformation bands occurs at higher strains. 3. At higher rolling strains recrystallization occurs in a0 because a0 has sharp curvatures between a components, and differential recovery is known to occur in a components. This differential recovery provides a driving force for recrystallization of a components at the expense of other a0 components in the same
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grain envelope. Because of the stability of a1 material, DB is unlikely to provide necessary lattice curvature for recrystallization and hence a1 grains are likely to be consumed. 4. Since a0 is of uniform orientation at 85% rolling reduction, it does not recrystallize because it lacks lattice curvature. a material formed at this reduction is consumed relatively late in the annealing cycle, probably by invading c grains. 5. The observations that at reductions up to 85%, a0 grains remain of homogeneous structure and without lattice curvature, while at higher reductions orientation splitting in the form of DB occurs, can be used to explain the optimum cold rolling reduction for good deep drawability performance. At 85% cold rolling a does not recrystallize, but at higher reductions it does, and this deteriorates the textures as far as drawability concerned. 6. There is no need to involve OG theory in its classical form to explain the texture results. It is possible that, if the 26° h1 1 0i has any significance, it could provide favorable micro-growth selection conditions in a deformed grains subject to DB for recrystallization. This is because the a fibre is defined as components belonging to the h1 1 0i//RD set of orientations, and DB produces contiguous volumes of a material.
Acknowledgements It is a pleasure to acknowledge the supports of this work by the grants numbered CERG/HKU 7067/97E, 7323/98E and 7316/99E given by the Hong Kong Special Administration Region of China. References [1] Lankford WT, 1950;42:1197.
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