hansen- metalurgia física

.4&z mater. Vol. 45, No. 9, pp. 3871-3886, 1997 m,C 1997 Acta Metallureica Inc.

Published by Elsevier S%sm Ltd. All rights kserved Printed in Great Britain

Pergamon

PII: S1359-6454(97)00027-X 1359.6454197 $17.00 + 0.00

HIGH ANGLE BOUNDARIES FORMED BY GRAIN SUBDIVISION MECHANISMS

D. A. HUGHES’ and N. HANSEN2 ‘Center for Materials and Engineering Sciences, Sandia National Laboratories, Livermore, CA 94550,

U.S.A. and 2Materials Department, Risa National Laboratory, DK 4000. Roskilde, Denmark

(Received 9 August 1996: accepted 25 Nocember 1996)

Abstract-Deformation of metals from medium to high strains introduces significant changes in the microstructure and the texture. The microstructure evolves into a lamellar structure with boundaries of small to medium misorientation angles mixed with high angle boundaries. The latter category consists of deformation induced boundaries plus the original grain boundaries. The number of deformation induced high angle boundaries is significantly larger than the number of original grain boundaries. Mechanisms for the formation of the deformation induced boundaries are suggested based on grain subdivision processes which can lead to formation of different texture components within an original grain. The distribution of their misorientations is estimated based on these mechanisms. This estimate is compared to experimental findings for Al, Ni and Ta deformed to large strain by rolling or in torsion. This estimate and the findings are discussed and good support is established for the basic assumption that grain subdivision accompanied by a strong texture evolution can lead to a very significant increase in the fraction of high angle boundaries in a deformed metal. These findings provide the essential physical background for the construction of theoretical models for the distributions. C 1997Acta Metallurgica Inc.

1. INTRODUCTION

Heavily cold worked metals are subdivided by grain boundaries and dislocation boundaries which are arranged in a lamellar or subgrain structure [lb3]. The frequency and distribution of these boundaries determines the properties of the deformed metal, including the flow stress, texture, recrystallization behavior and the formability. A comprehensive review of the general microstructure and texture for the large strain state of metals was last given in 1980 in Ref. [4].

The boundaries in heavily cold worked metals originate not only from grain boundaries present in the undeformed metal, but also from dislocation boundaries which form during plastic deformation in grains that are subdivided into regions that are smaller than the original grain size. Qualitatively it has been known that these boundaries have a large angular spread and that the misorientation across many boundaries is of the magnitude characteristic of ordinary high angle boundaries [2]. A quantitative analysis of this angular spread has, however, only recently been possible by the introduction of semi-automatic and automatic microscopic techniques for the determination of local crystallographic orientations on the micrometer and submicrometer scale [e.g. 5-101.

As a result, a framework for the formation of dislocation boundaries during plastic deformation has been formulated [e.g. 111. This framework has been supported by many quantitative experimental observations of a variety of metals [e.g. 51. Both this

framework and experimental results will be discussed in this paper.

2. PREVIOUS WORK

The development of boundaries with a large spread in misorientations has been known qualitatively since the discovery of grain break-up by Barrett and Levenson [e.g. I]. Further, it has been shown that the misorientation across many of these boundaries is of a magnitude characteristic of high angle boundaries, e.g. through X-ray, optical and electron microscopic techniques [14]. High angle boundaries are defined as those with angles above 15-20” [12]. Because the size scale of these boundary spacings is frequently less than one micrometer, it is difficult to obtain quantitative microstructural and crystallographic data. Thus there are but a handful of reports that have observed and measured individual high angle deformation boundaries following medium to large strain deformation. These include the observations in wire drawn Fe-Si [2], an unstable Al single crystal following channel die deformation [ 131, friction deformed Cu [14], torsion deformed Al [15], rolled Al-Zr-Si alloy containing particles [ 161, aluminum rolled to intermediate strains [17] in heavily rolled nickel [18], and heavily rolled aluminum [19, 201. A statistical analysis of the expected grain boundaries compared to the observed high angle boundaries shows that most of these high angle boundaries are formed by the deformation process at the places where grains subdivide and are not original grain boundaries [ 181. These different observations show

3871

3872 HUGHES and HANSEN: GRAIN SUBDIVISION MECHANISMS

that high angle boundaries formed during deformation are common to a diverse set of materials and conditions from single crystals to polycrystals, pure materials, alloys and particle containing materials, f.c.c. and b.c.c. crystal structures; different deformation modes; and different deformation tempera- tures. Many of these observations have shown that the number of high angle boundaries formed across a grain depends on the crystal orientation. For example, some crystal orientations maintain their average orientation with increasing deformation and are thus called stable. Certain symmetric orientations have the possibility of rotating to more than one end orientation during deformation and are thus called unstable. Stable single crystals develop low to medium sized misorientations, while unstable single crystals develop high angles [13, 21-251. For polycrystals earlier observations have shown an effect of grain orientation on the subdivision with high angle boundaries in coarse grained samples [26, 271.

increasing strain the misorientation angle across the two types of boundary increases and that the spacing between the boundaries decreases.

At large strain this evolution leads to structures composed of dislocation boundaries having a wide range of misorientations and having spacings in the submicrometer range. With increasing strain it is also observed that there is an increasing tendency for the dislocation boundaries to reorient from a typical cell block structure into a lamellar structure (see Fig. 1 showing a schematic representation of this change). In the typical cell block structure the GNBs include microbands (MBs) and single dense dislocation walls (DDWs) that surround blocks of equiaxed cells. In a typical lamellar structure at large strain, the lamellar boundaries (LBs) sandwich thin layers of cells and subgrains oriented along the material flow direction.

3.2. Formation of high angle boundaries

3. DEFORMATION INDUCED HIGH ANGLE BOUNDARIES

3. I. D<formation microstructures andgrain subdivision

Extensive experimental observations show that key dislocation structures are common to a range of metals, alloys and deformation modes. These dislocation structures have been analyzed within a common framework for the evolution of microstructures during cold deformation. This framework is based on a subdivision of grains by deformation induced dislocation boundaries which at 10~’ and medium strains have been separated into two groups: (i) geometrically necessary boundaries (GNBs) separating crystallites that deform by different selections of slip systems and/or different strain or strain amplitudes and (ii) incidental dislocation boundaries (IDBs) formed by the trapping of glide dislocations [28-331. It has been observed that with

The continued subdivision of grains into crystallites surrounded by dislocation boundaries leads to a large orientation spread based on dislocation accumulation processes. The formation of complex dislocation boundaries indicates an operation of different slip system combinations within the individual crystallites. As a result, different parts of a grain may rotate towards different stable end orientations. If such end orientations are not too far apart, the grain subdivision will lead to a scatter in the macroscopic texture. However, the individual end orientations may also represent major and minor texture components and in such cases large misorientations within the original grain can build up during deformation.

Both the microstructural and textural evolution leads to the formation of dislocation boundaries in which a fraction may be classified by their higher angles (> 15520”). Mechanisms for the formation of these high angle boundaries are discussed in the following.

(a) / (h)

large strains

small strains liar Boundaries (LBs)

Fig. I. Schematic drawing of deformation microstructures and grain subdivision. (a) Small to medium strain deformation, t,~ = 0.0660.80 with long microbands and dense dislocation walls (DDW) surrounding groups of cells in cell blocks; (b) large strain deformation, tvM > 1 with lamellar boundaries (LBs) parallel to the deformation direction, sandwiching in narrow slabs of cells or equiaxed subgrains.

HUGHES and HANSEN: GRAIN SUBDIVISION MECHANISMS 3873

(a) (b) n I , I I i 1 I I I I

1.0 - I I\

I

GNBs 1

0

0 5%cr W 10% cr -1 A 30% cr ‘I 50% cr

- fit

0 5% cr ?? 10% cr a A 30% cr T 50%/a

- fit

e/e,, e/e, Fig. 2. Probability density functions of the boundary misorientation angles, normalized by the average misorientation angle, scale to the same function for 5-50% cr. or 6”~ = 0.06-0.80. (a) Scaled probability density for IDB misorientation angles. The curve fit for all of the IDB data is given by equation (2) with CI = 3. (b) Scaled probability density for GNB misorientation angles. The curve fit for all of the GNB data

is given by equation (2) with IX = 2.5 [36, 521.

P(Q, &“I = we/e:“) (1)

where 6 and B are the scaling exponents and,f(x) is the scaling function which is assumed to be independent of total strain imparted to the sample; 6 and b equal one when equation (1) is subject to the scaling constraints. Equation (1) implies that if one plots &P(Q, 0,“) as a function of 0/Q,, one should find a single curve, f(Q/&), regardless of the total strain imposed on the sample. This scaling behavior is shown in Fig. 2(a) and (b) for GNBs and IDBs separately. These distributions can be described by the following empirical equation:

3.2.1. Microstructural mechanisms. A number of mechanisms based on microstructural evolution and dislocation processes have been suggested for the origin of these high angle boundaries [34, 351. These include:

(i) cell block formation in which grains start to subdivide from the beginning of deformation creating long boundaries (dense dislocation walls/microbands) in which misorientations increase steadily with increasing strain;

(ii) an origin as in (i) but with an accelerated evolution at grain boundaries and at triple junctions;

(iii) coarse slip in S-bands or shear bands that give rise to regions rotated relative to the neighboring matrix;

(iv) coalescence of boundaries at large strain.

The microstructural mechanisms, particularly (i) and (ii), are expected to produce boundaries with misorientations mainly up to 15-30”. It has been found that the distribution of the boundary misorientation angles for these dislocation mechanisms scales with the average angle of misorientation at low to medium strain according to a scaling hypothesis [36]. This scaling hypothesis allows us to predict the distribution of misorientation angles that would be created at large strain from the dislocation mechanisms. The scaling hypothesis takes the following mathematical form (an analog from Refs [37, 381) in which the probability density of misorientation angles, P(Q, 0,“) is expressed as:

tExtrapolation of IDB angles have not been included as those boundaries will contribute to the low end of the angular distribution, which is not part of the present problem.

CP .m) = r(a) X% - ’ exp( - c(x)

where x = e/Q,,, c( is a fit parameter and T(a) is the gamma function evaluated at argument M. The value c( = 3 gives a description of the scaled IDB distribution, whereas c( = 2.5 describes the distribution of GNBs.

The angular distribution which follows from equation (1) and equation (2) has been extrapolated to large strains based on an estimate of the H,, for GNBs at cold reductions (c.r.) of 70% and 90%.t This extrapolation uses an empirical 2/3 power law relationship between the average misorientation angle and the strain within the scaling regime for GNBs. H,, for GNBs at 70% and 90% c.r. is estimated to be 10” and 15”, respectively, according to Ref. [36]. This calculated distribution of angles based on the microstructural contributions shows that 99% of the boundaries are less than 30” at 70% c.r. and 45” at 90% c.r. [Fig. 3(a)]. Note that in this paper, both misorientation and disorientation are used interchangeably to mean the minimum angle that reflects the crystal symmetry. Disorientation is


the word coined to describe a misorientation calculated based on a minimum angle relationship between crystallites determined by considering all symmetry operations [39].

3.2.2. Texture mechanisms. Of equal importance to the origin of high angle boundaries are mechanisms involving grain subdivision and the evolution of a preferred texture during deformation, including:

(i) the rotation of a subdivided grain to different preferred crystal orientations during deformation;

(ii) ambiguity of slip systems for unstable crystal orientations that lead to diverging rotations within a grain.

Grains rotate to a few preferred crystal orientations that are frequently arranged along a continuous skeleton line in orientation space. Large crystal rotations are required to bring the starting texture to the final preferred texture for most deformation conditions. If a grain subdivides, the individual crystallites within a grain may also rotate towards the preferred end orientations [19]. Since the different end orientations may differ by very large misorientations, this process will thereby create very high angle boundaries. The creation of the highest angle boundaries based on texture evolution will occur only after some finite deformation when the preferred end texture is well developed. Recent analysis based on local crystallography measurements have shown this relationship between deformation induced high angle boundaries and the evolution of typical deformation textures in rolling and torsion [19, 20,401.

The high angle boundaries that form as a result of texture evolution in subdivided grains, may relate directly to the orientation of the different texture components (see Table 1) and their neighbor-neighbor relationship. This relationship has been explored for 10 components and variants (cube, brass, Goss, copper, S) of the typical rolling texture of f.c.c. metals.7 These ideal components can give rise to 44 different neighbor-neighbor relationships, each characterized by an angle/axis pair. To calculate a distribution based on these 44 permutations, it is assumed that each component has an equal probability of being a nearest neighbor of another component. Also only the exact ideal component is considered. Note that while more elaborate methods have been employed in the past to obtain angle distributions based on texture orientation distribution functions, those calculations also contain assumptions that are not relevant for the present case [e.g. 411. Thus, the present simplification is preferred for illustration. The calculated distribution of the

tThe cube component is included in this analysis because it is a major component of the initial texture. However, the rotated cube component in Table 1 is not included, since it is a minor transitionary component and not part of the deformation components.

(4 0.1 I I / 1 I

contribution from 0.08

-: 0.06 Q)

g 0.04

0.02

islocation accumulation

” 0 10 20 30 40 50 60 (b, Disorientation (deg)

texture development: equal probability of each ideal component as a nearest neighbor

0 20 40 60 Disorientation (deg.)

Fig. 3. Predictions of probability distributions for disorientation angles based on a simple composite model combining (a) microstructure mechanisms and (b) grain

subdivision and texture evolution mechanisms.

misorientation angles based on these ideal orientations are given in Fig. 3(b), and shows a range from 20 to 60”.

3.2.3. Evolution oJ‘ microstructure and texture. Comparing Fig. 3(a) and (b), it is apparent that very different distributions and ranges of angles are produced by the two types of mechanism. The microstructural mechanisms produce a peak in the distribution at low angle ranges less than l&15”, whereas the texture evolution produces a peak at the high angle range above 40”. A combination of the two distributions into a total distribution with the correct amount of each population would be needed for a complete quantitative prediction. This combination would reflect that both microstructure and texture evolve and interact with each other. Methods of combining the distributions will be addressed later in the discussion section.

The microstructural and textural evolution establish a framework for the evolution of deformation induced high angle boundaries. This framework, however, needs experimental verification which is done in the following for aluminum, nickel and tantalum deformed at medium to large strain. The experimental section is followed by a comparison of the hypothetical angular distribution with those observed experimentally, and includes the effect of material and process parameters. Finally, the effect on material properties of a relatively large number of high angle boundaries present in the deformed microstructure is discussed.


Table 1. Ideal texture components for the various deformation conditions

F.c.c. rolling

Label

Cube (D) Rotated cube (RC) s (SI, s:. SI, Sd) Copper (C, and C-1) Brass (B and B?) Goss (G) a fiber /r fiber

F.c.c. torsion B.c.c. rolling

Crystal orientation Crystal orientation jhkl] (unv)?

Crystal orientation Label (hk/)(ucw)1_ Label {hk/J<uow)i

(I li)[2ii] Cube (D) jl00}<00l> Rotated cube (RC) {ooi~(iio) Goss (G) Taylor (TI)

(O_llI;(lOO> (lll)[211]

Taylor (Tz) (l I l)[2iil Cross Taylor (CT,) (iii)[oii] Cross Taylor (CT?) (ii I)[OI I]

Fiber linkmg the sequence: BI, Sz. CI, SI. B:, Si, Cz, SI

tThe designation jhk/)(uw) refers either to the rolling plane and rolling direction. respectively, in rolling, or the shear plane and shear direction, respect&y ‘for torsion.

4. EXPERIMENT AND RESULTS

4.1. E,xperirnent

The properties of the three materials and the various deformation conditions used in this study are shown in Table 2. Thin foils for transmission electron microscopy (TEM) were made to view the samples in the longitudinal side plane for rolling or the Z-theta plane for torsion. (Z is the shear plane normal, theta is the shear direction.) Transmission electron microscopy and convergent beam diffraction analysis of these samples was performed. Orientations of individual crystallites were obtained from the convergent beam Kikuchi patterns. Crystallites as small as 40 nm could be measured with this technique. The Kikuchi patterns were analyzed using a computer method based on the techniques in Refs [IO, 421 to obtain the orientation matrices for individual crystallites. The minimum angle misorientation relationship (disorientation) between adjacent crystallites separated by dislocation boundaries was calculated by considering all 24 symmetry operations for the orientation matrices in a standard manner, The axis/angle pairs for the disorientations were also calculated. The axis/angle pairs were quantitatively

compared to axis/angle pairs for coincident site lattices. The disorientation axes were also compared to the sample axes of the adjacent crystallites. A negative or positive disorientation angle was assigned by considering whether the disorientation axis is in a left hand or right hand triangle, respectively.

Measurement errors for these Kikuchi methods include errors that arise from measuring the Kikuchi pattern itself and cumulative errors in the measured orientations due to slight overall bending in the thin foils. Errors in both the orientation and misorientation between adjacent crystallites based on pattern measurement are 0.1 to I”, as examined in Refs [lo. 421. Note that orientation angle changes due to overall foil bending are restricted by both the thick supporting sample rim and the geometry of the sample holder and microscope. Furthermore, these errors were carefully examined using single crystal thin foils measured over large distances of 500 to 1000 pm. Such careful measurement showed that cumulative errors in the orientation measurement that would develop owing to slight foil bending are only about 2’ over 100 kirn of sample [43]. Additional evidence for the goodness of TEM orientation analyses is found in Ref. [44] in which orientations in

Table 2. Average intercept spacing following deformation and observation length either in the ND for rolling or : dire&Ion for torsion

Spacmg

Material and deformation Original grain All dislocation High angle Observation condltlonst boundaries$ (pm) boundaries (pm) boundaries. H > IS’ (pm) length (pm)

Nickel (99.99%) f.c.c. 80 flrn initial grain size:

Rolhng 70% cr. (<>M = 1.4)” 32.0 0.40 0.72 13.7 Rollin 90% cr. ((,M = 2.7) 8.0 0.22 0.53 12.2 Rolling 98% cr. (fthl = 4.5) 1.6 0.16 0.37 7.7 Torsion (c.~ = 4.1) 11.5 0.17 0.34 9.6

Alummum (99.5%) f.c.c. 90 pm mitral grain sire:

Rolling 90% cr. (c,, = 2.7) 9.0 0.50 2.00 38.X Aluminum (99.8%) f.c.c. I50 x 300 pm mltial grain size:

Rolling 90% c.r. (c\~ = 2.7) 15.0 0.35 2.10 42 Tantalum (99.99%) b.c.c. 44 pm imtial grain size:

Rollmg 90% x.r: ((ih, = 2.7) 4.4 0.25 1.80 6

tGrain size is given as a Heyn intercept distance. $Calculated based on the deformation kinematics and mitral spacing. VLM iq van Mises effective strain. ‘xx IS cross rolled.


a single crystal were measured over long distances in the TEM and then compared to similar measurements using scanning electron microscopy (SEM). The errors from these effects, < 1” on misorientation and < 3” on orientation, are insignificant with respect to the range of misorientation angles and to the identification of local orientation type considered in this paper.

For the rolled nickel and aluminum (small grain), the macroscopic crystallographic texture was measured previously using neutron diffraction and plotted as an orientation distribution function (ODF) [20, 341. The macroscopic crystallographic textures for Ta, coarse grain aluminum, and torsion deformed nickel was measured using standard X-ray diffraction techniques and are reported in Refs [4547], respectively. The starting textures ranged from random to medium recrystallization textures for all materials, except the coarse grained aluminum sample which had a strong (100) TD (transverse direction) fiber. Following deformation, typical deformation textures developed in every case.

Previous extensive observations show that key dislocation structures are common to a broad range of metals, alloys and deformation modes [ 17, 28, 31, 32, 48-521. Furthermore, these key structures evolve within a common framework for microstructural evolution, which we call grain subdivision [28&32]. The observations in the present study are in general accord with this earlier work. However, new results have been obtained especially on the microstructure and local crystallography of specimens deformed at medium to large strains. These results are presented in subsections 4.24.4.

4.2. Microstructure

Similar large strain microstructures develop at large strains for this diverse group of materials and conditions. Typical for all is a composite structure of long lamellar dislocation boundaries alternating with strips of equiaxed subgrains. Examples of these structures for the three materials and three deformation modes are shown in Fig. 4(a) and (b). Sinuous strips of many fine lamellae alternate with strips of equiaxed subgrains and widely spaced lamellae. The macroscopic shape of these large strain structures reflects the direction of the imposed deformation. Thus for straight rolling and cross rolling the lamellar boundaries are nearly parallel to the rolling plane, while in torsion the lamellar boundaries are nearly parallel to the z plane which contains the shear direction. The proportion of the microstructure containing equiaxed subgrains compared to the proportion containing strips of lamellar dislocation boundaries depends on the material and the deformation mode. For example, aluminum with its higher stacking fault energy has a greater proportion of equiaxed subgrains than rolled nickel. Torsion deformed nickel has a greater proportion of equiaxed subgrains than does rolled nickel.

The type of structure found in between the lamellar boundaries also depends on the material and the strain level. For aluminum and nickel, dislocation cells are typically found in between the lamellar boundaries. These cells are arranged one to three cells deep between the lamellar boundaries and a few to many cells along their length at these large strains. Fewer cells are observed in nickel than in aluminum. For tantalum a loose network of dislocations in a Taylor-like lattice is more commonly observed in between the lamellar boundaries than are strings of equiaxed cells. In all cases a string of low angle equiaxed cells within a lamellar band is punctuated at either end by an equiaxed subgrain. These subgrains are surrounded by very high angle boundaries and are thus very like a micrometer sized grain.

The boundaries introduced by deformation in the form of dislocation boundaries or as high angle boundaries are predominantly present as a banded structure of a macroscopic orientation with respect to the specimen axes. Examples are the microband structure at low and medium strain and the lamellar structure at large strain. For such anisotropic microstructures it has been chosen to use the boundary distance or the number of boundaries measured along straight lines as the structural parameters. For example, the average intercept spacing of these boundaries along ND (normal direction) and z directions is shown in Table 2 for the various conditions.

Additionally, there are also regions filled with equiaxed subgrains (ES) or remnants of the smaller strain microband structure. The smaller strain microband structure is most prevalent in the 70% c.r. sample and is also found with a lower frequency in 90% c.r. samples. No microbands are found at 98%. The microband structure at these large strains is interpenetrated by coarse slip in S-bands. The _ 5-pm long S-bands run parallel to crystallographic slip planes and directions. Frequently, lamellar boundaries are formed in regions where S-bands intersect the microbands. It was also observed that some grains at 90% c.r. were traversed by regions of localized glide that are roughly 1-5 pm wide by 20&200 pm long. In addition to the disappearance of the small strain microstructure features, the principle change in the dislocation microstructure with increasing strain above 70% is the coalescence of dislocation boundaries.

The local orientation measurements were compared with the macroscopic textures. It was observed that both microscopically and macroscopi- tally there is a large spread about the ideal texture components with the local orientation falling within the intensity contours of the macroscopic ODFs. In such a comparison care should be taken owing to the limited number of local orientation measurements The qualitative agreement observed, however, indicates that the sampling in the convergent beam analysis is representative for the specimens.


Fig. 4(a&Caption overleaf.

4.3. Disorientations and angle/axis pairs

The distributions of the measured boundary misorientations are shown in the histograms in Fig. S(a)-(f) for all of the materials and deformation modes at strain levels above tuM = 1.4. All of these distributions include a wide range of angles from near zero to 62.8’. Significantly, these distributions also exhibit both a large peak at small angles and a

medium sized population at very high angles. The population at the very high angles is not observed at strain levels at or below tvM = 1. The rotation axes for these disorientations, plotted in the adjacent standard triangles, are generally scattered across the whole triangle and do not show strong crystallographic preferences.

The average spacing of the high angle boundaries, shown in Table 2 is always much less than the average


spacing of original grain boundaries for all materials and deformations. The spacing of the high angle boundaries is also smaller than a 30 deviation in the average grain boundary spacing, indicating that the majority of the high angle boundaries are formed by the deformation process.

The disorientations across the dislocation boundaries in adjacent crystallites are plotted against distance within a grain in Fig. 6(a)-(e). The disorientations were measured in a line either along the ND for rolling, or the z axis for torsion. All of the orientation changes shown occur sharply at a dislocation boundary. Note the alternating nature of the disorientations showing very little cumulative angle change over the distances considered. There is a very wide range of spacings for the high angle boundaries. While these boundaries are distributed continuously throughout the distances measured, some clusters of high angle boundaries as well as quieter regions with small angle changes can be seen. The wide variety of rotation axes for the lamellar boundaries (Fig. 5) indicates a varied mixture of boundary types from near twist and tilt boundaries to mixed type boundaries.

The length of these high angle boundaries was explored by following the orientations along two adjacent lamellar boundaries for a long distance of 40 Ltrn along the RD. These boundaries are part of a structure in which many high angle changes occurred perpendicular to the LBs. In contrast to a direction perpendicular to the LBs, mostly small angle changes were found within the lamellar bands (Fig. 7). High angle changes occur occasionally within a band when a small equiaxed subgrain was traversed. Of equal significance was the fact that the rotation axes within a lamellar band were more likely to be clustered about preferred axes, in contrast to the varied rotations across the bands. Note that except for the small equiaxed subgrains, one lamellar band is composed of orientations around the same Si orientation variant for 40pm (Fig. 7) while the adjacent band is composed of the B, orientation variant. Consequently a very high angle boundary is maintained between the two bands for at least 40 pm.

Different magnitudes of angle changes were found within different dislocation microstructures. Well-developed lamellar bands had larger misorientations than did regions of microbands. High angle boundaries were also frequent across the long strips of LBs formed in a microband structure due to coarse slip along S-bands or in which micro-shear bands occurred within a microband structure. An example of this effect was observed in the structure represented by the disorientation plot in Fig. 6(a).

4.4. Local texture distributions

The pattern of orientations of individual crystallites is highlighted in the previous disorientation [Fig. 6(a)-(e)] by color shading regions to reflect their association with specific ideal components. A local orientation is classified as an ideal component if it has

a disorientation of less than 15- relative to the ideal component. An orientation not within 15 of any ideal component is taken to be a random orientation. The ideal components considered throughout the paper are listed in Table 1. The complementary variants of the same ideal component were also distinguished, since these variants differ from each other by high angle rotations (e.g. 60^ about (1 11)).

The most striking features in Fig. 6(a)-(e) are the large number of high angle disorientations that accompany a very fine scale pattern of local texture components. Note that most (>2/3) of the very high angle changes, >30 , in Fig. 6(a))(e) separate two different ideal texture components. In contrast, only l/4 separate an ideal component from a random component and less than l/l5 separate two random components. Remarkably, owing to the many high angle changes, nearly all of the ideal texture components and their variants are frequently found over a distance of just a few micrometers in all these various structures. For f.c.c. rolling, the orientations can be seen to span a wide range of the x and /I’ fibers plus some random components [see especially Fig. 6(a), (b) and (d)]. These orientations are frequently arranged in space so that they alternate back and forth along the length of the c( and /r fibers. Analogously, for torsion, observed orientations span and alternate along the {l I ~)(uz~M~) and (Ml){ 110) fibers [Fig. 6(c)]; for b.c.c. rolling all of the ideal components along the {OOl}(urn~) or (111 ](uw~) fibers are found [Fig. 6(e)]. Strikingly, this trend can already be observed at a 70% c.r. (E,~ = 1.4) [Fig. 6(a)] and is maintained with increasing strain.

At these large strains the random components were scattered throughout the microstructure. Although random components could be found in regions with either S-bands or localized glide bands, the frequency of the random components was not any higher than elsewhere. In fact the localized glide bands were typified by having a normal deformation texture. e.g. copper or S.

It must be noted that texture components of a different color are not always separated by high angle boundaries in Fig. 6. This result occurs as a consequence of the texture grouping we use that is based on the classification of an orientation as ideal if it is within I5 of the ideal, combined with the fact that adjacent ideal orientations along the b fiber are only 19.4 apart.

The local measurements also show that each of the deformation texture components is composed of a very large number of small volumes with orientations scattered around the ideal orientations. An estimate of the size of such volumes for rolling shows that their average dimension in the ND direction may be l/3 to l/5 of the reduced grain size (Table 2). The dimensions in the RD and TD directions gives an average aspect ratio for the pancake shaped volumes of about 335. This average aspect ratio is somewhat misleading because of the wide distribution of lengths for the “pancake” shaped volumes. Within lamellar


0 20 40 60 Disorientation (“)

in


iii iii

0 20 40 60 0 20 40 60 Disorientation (deg.) Disorientation (“)

In 10 .!2 m” -a 8 5 p” 6

z 4 G

% 2

5 0 0 20 40 60

Disorientation (deg.)


Fig. 5. Histograms showing the distribution of the magnitude of disorientations across dislocation boundaries measured along either the normal direction for rolling or the z direction for torsion. Note that the histograms generally show two peaks in their distribution. The disorientation axes are plotted in standard triangles. Axes for 0, ISI > 35”; A, 18” < /0/ i 35”; 0,]0\ < 18”. (a) Nickel 70% cr.,(b) nickel 90% cr., (c) nickel 98% cr., (d) nickel deformed by torsion, (e) aluminum 90% c.r., smaller grain size

and (f) tantalum 90% x.r.

HUGHES and HANSEN: GRAIN SUBDIVISION MECHANISMS

_- 0 2 4 6 8 10 12 14

Distance along ND (Fm)

(b) mm~~mm 0 B, B2 C2 S1 S, S, G random

“Y

0 1 2 3 4 5 60 1 2 Distance along ND (pm)

CC) s mm mm%3 u A,’ A 2* A, A2 B1 Bz C 110 fiber111 fiber random

40 a z .2”

20

m z 0

z s: -20

a -40

-60 _

60

6 8 10 Distance along 2 axis (pm)

bands, pancake shaped volumes with aspect ratios of lo-20 are punctuated by high angle equiaxed subgrains with aspect ratios of 1. Another contribution to the wide variety of these aspect ratios is the tendency of high angle boundaries to cluster. Thus, a distribution of the individual volume elements that compose the macroscopic texture has a very large spread in size from a small fraction to a couple of pm3.

4.5. The efects of grain orientation, material purity, crystal structure, strain level and deformation mode

The formation of high angle boundaries and

Cd)

-60 __ 0 5 10 15 20 25 30

Distance along ND (Fm) .,00Dl04

(e)* m -- W? (001)[~10](001)<uvw>(111)[011] (lll)filZ] (lll)[i2l](lll)<uvw>

60

40 7 ; 20

B B g 0

‘i: 8 -20

-40

-60 0 1 2345678

Distance along ND (Km)

Fig. 6. The disorientation angles measured across dislocation boundaries in either the normal direction for rolling or the z direction for torsion show an alternating character with distance. These boundaries separate finely distributed texture components as shown by the color shading. (a) Nickel 70% cr., (b) nickel 98% c.r., (c) nickel deformed by torsion, (d) aluminum 90% c.r., smaller grain size and

(e) tantalum 90% x.r.

0 5 10 15 20 25 30 35 4u Distance along RD (pm)

sr.C-l.RD* Fig. 7. Disorientation angles measured across dislocation boundaries within a single lamellar band in the rolling direction. The color shading shows that similar texture

components are maintained within the band.


local orientations may be affected by several parameters including grain orientation, material purity, crystal structure, strain level and deformation mode.

4.5. I. Orientation effkcts. In general the high angle boundaries are distributed widely throughout the distances measured. These high angle changes occur both in the grain centers and near original grain boundaries. At the same time, there are quiet regions with only low to medium angle changes and regions with clusters of high angle boundaries. For the case of f.c.c. rolling, these quiet regions were associated with average grain orientations along the c1 fiber, including Goss and brass components [see, e.g. Fig. 6(d)]. For b.c.c. rolling these regions were primarily associated with the rotated cube orientations (see, e.g., Fig. 6(e) and Ref. [53]). In no case did these regions with low to medium angle changes extend across the whole grain width; rather they occupy fractions of a grain, even for the rotated cube orientation in tantalum. In contrast to the quiet areas, the clusters of high angle changes in f.c.c. rolling are associated with alternations primarily along the /j’ fiber including finely distributed regions with the variants of S, copper and brass plus occasionally a Goss orientation. No clear orientation effects could be identified for the case of torsion, although somewhat larger frequencies of high angle changes are associated with orientations along the (111) fiber compared to the (110) fiber.

4.5.2. Material purity and type. Similar numbers of high angle boundaries and varieties of local orientations are observed for a range of material purity from 99.999% to 99.5% (Table 2 plus Ref. [ 191). However, significantly more high angle boundaries were observed in nickel than in aluminum, consistent with a finer spacing of dislocation boundaries in nickel compared to aluminum.

4.5.3. Crystal structure. The different deformation textures that develop reflect the different crystal structures, f.c.c. or b.c.c. as expected. However, both the b.c.c. and f.c.c. metals show similar trends with respect to the number of high angle boundaries and texture components. However, the average number of texture components in b.c.c. tantalum, 24, is smaller than that for f.c.c. 2-7, at the same strain. This difference is partly related to the stability of the rotated cube grains in the tantalum and the larger number of ideal texture components for f.c.c. compared to b.c.c.

4.5.4. Grain size and shape effects. The grain sizes in this study ranged from medium-small (44 pm) to medium-large (150 p). Within this grain size range no observable effects of either the initial or deformed grain size were observed. For example, the same average spacing of high angle boundaries is observed for aluminum with two different initial grain sizes (Table 2). Both aluminum samples showed the similar varieties of high angle boundaries and local texture components. All of these suggest a minor role of the

initial grain size. It must, however, be noted that neither very large grain nor small grain specimens have been examined.

4.5.5. Strain level. The formation of most of the very high angle boundaries occurs within a very limited strain range. At strain levels between 50 and 60% c.r. (t,, = 0.8 to l), all of the observed high angle boundaries are less that 25-30”. Strikingly with increasing strain to 70% c.r. (tvM = 1.4), the maximum angle increases to 62.8’. The frequency of high angle boundaries also increases in this narrow strain range. With a further increase in strain from 70% c.r. (ttM = 1.4) to 90% c.r. (c,~ = 2.7) there is some increase in the number of very high angle boundaries. However, none occurs above 90% c.r. This development of high angle boundaries matches the overall trend for dislocation boundaries with increasing strain in this strain range. For example, Table 2 shows that the spacing of the high angle boundaries in nickel decreases with strain at a similar rate compared to the dislocation boundaries. This decrease is quite different from that of the steep decrease of the original grain boundaries during rolling (Table 2). The torsion data for the high angle and the dislocation boundary spacing match the rolling data (Table 2).

The variety of local orientations increases in tandem with the formation of the very high angle boundaries. At the very largest strains it is observed that there is a slight increase in the number of random components in the structure.

4.5.6. Deformation mode. The different deformation modes, torsion and rolling, produce different preferred textures and different macroscopic shape changes. Both modes produce an active texture evolution that includes large rotations. In spite of the differences, very similar average spacings are observed for both the high angle boundaries and the dislocation boundaries (Table 2). However, in torsion the grain shape does not become as flat as that in rolling (by a factor of 7). Consequently, the similar high angle spacings between the two types of deformation mode results in the creation of 334 high angle boundaries per grain in rolling compared to 27 in torsion, on average. The similarities in the distribution of the high angle boundaries and in the diversity of local texture components is also shown by comparing Fig. 6(b) and (c).

5. DISCUSSION

5.1. Boundary formation

The observed microstructural subdivision leads to the subdivision of the characteristic texture components into small volume elements. These observations support the hypothesis that deformation induced high angle boundaries arise from both microstructural and textural evolution.

The current experiments provide added information to that previously published on the origins of


high angle boundaries. This information includes the relative importance of each mechanism and the range of high angles created.

5. I. 1. S-bands. The S-band structure provides a very visual illustration of a mechanism by which deformation structures can develop many long high angle boundaries subdividing the original grains. At strains ranging from 50 to 90% c.r., various distributions and arrangements of S-band clusters have been observed within grains including both evenly spaced strips and groups of strips. The first arrangement would lead to evenly spaced high angle boundaries, while the latter to clusters of high angle boundaries. The observed range of angles formed by this mechanism are in the medium to higher angle range from 10 to 30” with 20” boundaries most typical. This mechanism is very common and the number of high angle boundaries that it produces is high. However, it is unlikely that very high angle boundaries greater than 40” could be produced by this mechanism alone. A similar effect is found for the observed shear bands, but their frequency in the microstructure is less than that for S-bands.

5.12. Cell blocks. Cell block formation results in high angle boundaries that are generally less than 35, as discussed in Section 5.2.

5. I .3. Coalescence ofboundaries. At large strain, a high proportion of boundaries are combined together as the number of boundaries across a grain is reduced with increasing strain. The resultant angle change across the coalesced boundaries will be quite varied and depend on either the alternating or cumulative character of their angle/axis pairs. Calculations, based on experimental data, show that high angle boundaries formed by coalescence are rare. This result is due to the great variety of boundary axes and the diversity of neighbor orientations that makes strictly cumulative misorientations uncommon [35].

5.1.4. Grain-grain interactions. The current data sets provide an estimate of the relatively modest proportion of high angle boundaries arising from grain boundary effects. Of particular importance is the torsion data [Fig. 6(c)] in which 28 high angle boundaries are spread across the distance of one grain and thus two grain boundary regions. Based on the experimental observations of grain boundary regions [54-561 and simulations [57], only 20% of these boundaries should be associated with grain boundary interactions. The remaining 80% must occur for other reasons. The high angle boundaries found in rolling also spread across the whole grain width and are not associated with the grain boundary regions. For example, the measurements in Fig. 6(a) (nickel 70% cr.), that begin on the right in the middle of an original grain and end on the far left at a grain boundary, show that the high angle boundaries are continuously distributed across the grain.

5.1.5. Special initial orientations. There is a clear orientation dependence on the formation of high angle boundaries. However, the importance of special

orientations in creating high angle boundaries depends on the starting texture of the material. While this mechanism is a potent source of high angle boundaries in polycrystals with strong starting textures such as cube, its potency diminishes with an increasingly random starting texture since fewer regions are near these special orientations. For the weakly textured materials in this study, this mechanism is only of small to moderate importance.

5.1.6. Et’olving texture. A more potent source of high angle boundaries may be found if one considers the whole of texture evolution and not just the evolution of special orientations. Large crystal rotations are required to bring the starting texture to the final preferred texture.

The above hypothesis is supported by considering crystal rotations using a Taylor model. During deformation, an initially random grain is reoriented along a path in orientation space that is defined by the rotation or reorientation velocity field in orientation space [58]. Since both the magnitude and direction of this velocity depends on location in orientation space, each part of a subdivided grain will have a somewhat different reorientation velocity and direction. While this rotation field is generally smooth, there are regions in which a small change in orientation causes a reasonably large change in the velocity. Large differences in velocity between adjacent crystallites in a grain result in the evolution of large differences in orientation and misorientation. As texture evolves, a random subdivided grain will approach regions with large velocity changes as follows.

The characteristic structure of the rotation field causes crystals of any general or random orientation to be funneled into orientation streams flowing to one end orientation. However, as the crystal volumes of a subdivided grain are swept along these reorientation streams, the volumes rotate near one or more surfaces in orientation space that separate streams with branching paths to different end orientations. Because a grain has been subdivided, it contains a range of crystal orientations, each with its own rotation rate and direction, since the latter depend on the current orientation with respect to the deformation axes. Consequently, different parts of a grain will approach these branching paths at different times and locations in orientation space. These differences will cause some parts of a grain to follow one branch while others will follow a different branch, thereby creating some very high angle boundaries when the different end orientations are reached. The initial crystal orientation and deformation mode will dictate the degree of subdivision necessary to cause this large scale splitting. For special orientations already near the surfaces in orientation space that separate branching paths, grain subdivision into regions separated by only a couple of degrees of misorientation is required. In contrast, for orientations that are farthest away from these branches, grain subdivision


into regions separated by 20” rotation angles is required, based on the 45” periodicity of these branches.

The creation of high angle boundaries based on texture evolution will occur only after some finite deformation when the preferred end texture is well developed. This delay occurs because an initially random grain will only be swept near these branches when it is near to the end orientation or fiber of orientations characteristic for the deformation.

5.2. Comparison of the hypothetical distributions of misorientation angles with experiment

The prediction based on the addition of distributions in Fig. 3 based on both microstructure and texture provides good qualitative agreement with the experimental distributions in Fig. 5. While the simplified model represented in Fig. 3 captures the main features observed, it is not meant to be quantitative. For example, the distribution peak at the small angle range occurs at a somewhat larger low angle in the predictions than in the experiments. This moderate difference is indicative of the interactions between the dislocation and the texture mechanisms which we know exist, but do not account for in the simple model. Also the contribution to the distribution from the dislocation mechanisms is based on an extrapolation of both the average angle and the scaling observed at small to moderate strains. This extrapolation is acceptable for strains below c,~ = 2.7 (90% c.r.), although it slightly over-predicts the average angle from the dislocation contribution.

From the experimental results, we know that dislocation boundaries form which subdivide the original grains and that a preferred texture evolves. Thus both dislocation processes and texture evolution occur together in the experiments. This is reflected in the distribution of misorientation data in Fig. 5, clearly showing a large peak in the distribution at lower angles and a second population at high angles. The dislocation mechanisms [Fig. 3(a)] contribute most to the peak observed at small angles, but only 1% of those boundaries contribute to the angle range greater than either 30’ or 45” at 70% and 90% c.r., respectively. The experiments show a significantly larger percentage of lo-25% for the high angles This high angle population is in a similar range to the broad peak formed by preferred texture formation in a subdivided grain [Fig. 3(b)]. The texture mechanisms contribute to only a small portion of the distribution at the lowest angle range.

Combining the two distributions in the simplified model of Fig. 3 to obtain a more quantitative prediction would require the incorporation of the grain subdivision as described by Fig. 3(a) into a crystal plasticity model. This incorporation is easiest to envision, for example, in a finite element based plasticity model. As texture evolves within subdivided grains in the polycrystal model, a fraction of high angle boundaries will grow at some of the boundaries

created by grain subdivision. Which of the boundaries becomes a high angle boundary as texture evolves will depend on the local crystal orientation and the angle/axis pair of the boundary misorientation.

The predictions based on an addition of distributions establish the essential physical background required for the development of theoretical models of misorientation distributions at large strains. These misorientation distributions, when combined with the spatial distribution of dislocation boundaries, provide the basis for quantifying dislocation structures and stored energy for inclusion into constitutive models of material deformation, texture formation and recrystallization.

5.3. Texture and texture spread

Notably, the microstructural subdivision of grains into fine crystallites having a large spread in orientations does not lead to new major texture components, indicating that Taylor-like kinematics are valid on average. Instead, subdivision creates some minor components and a spread in the texture. This spread increases the width and decreases the intensity of the texture peaks in the ODF. In the following we estimate this spread based on the microstructure. Regions separated by both high angle boundaries and low angle boundaries contribute to this spread. The local orientations reflect the effect of the microstructure on the texture. Thus, the microstructural contribution to the observed texture spread is estimated by averaging the difference (disorientation) between the measured individual orientations and the orientations of the nearest ideal texture components. Those values, shown in Table 3, are similar for all of the rolled samples and range between 11 and 13” at a 90% cold reduction. In contrast, the spread in the torsion textures, 16.9”, is much larger than those for rolling, consistent with the differences in the respective macroscopic textures. These data also show an increasing texture spread with increasing large strain. However, this may or may not be a real trend as the differences are within one standard deviation. More data would be needed to determine if this trend is correct.

Table 3. Average spread about the ideal deformation texture components due to the microstructure

Average spread Material and deformation conditions

Nickel:

(’ )

Rolling 70% cr. (c,\, = 1.4) 9.2 Rolling 90% cr. (C\M = 2.7) 10.7 Rolling 95% cr. (r,, = 3.5) 11.9 Rolling 98% c.r. (F,M = 4.5) 12.6 Torsmn (CM = 4.0) 16.9

Aluminum: Rolling 90% cr. (LM = 2.7) (99.5% purity)

12.9

Rolling 90% cr. (C.M = 2.7) (99.8% purity)

Tantalum:

13.1

Rolling 90% x.r. (fvM = 2.7) 11.0


Calculated deformation textures frequently predict much higher intensities at the peak intensity points in the ODF as well as much narrower angular spreads in intensity about those peaks than is found in experiments [59]. Smoothing factors used in recent texture simulations to reduce the sharpness of those calculated textures to the approximate levels observed in experiment, include 7.5” [.59] and 7-8” [60]. However, larger smoothing factors from 9 to 17”, based on Table 3, may be more representative for textures developing at large strains. As an additional application of the present data, the orientation spread owing to the microstructure can be introduced into polycrystal models to predict the formation of the high angle boundaries.

5.4. Effect qf material and deformation parameters

Several parameters have an effect on the formation of high angle boundaries. Strain level has a large effect that has also been previously observed [2, 31. The crystal orientation is also important and the observation of clustering of high angle boundaries at large strain indicates that some (unstable) grain orientations have a much larger tendency to become subdivided by high angle boundaries than other (stable) orientations. This also agrees with previous observations [I, 27, 521. In contrast, the deformation mode, crystal structure and material purity may have second order effects.

As regards grain size, it has been found to have no effect on the spacing between the high angle boundaries (see Table 2). This is in contrast to the observations in Refs [26, 271, where the subdivision of grains has been studied in crystallographically etched longitudinal sections of fine and very coarse grained copper cold-rolled 83%. The average layer thickness for volumes of different crystallographic orientations decreased from - 17 pm in specimens having an initial grain size of -3000 firn to -2.5 pm in specimens having an initial grain size of 40 pm. To clarify this issue experiments are under way on specimens with a larger difference in grain size than in the present study.

Finally, it is a general observation that most of the high angle boundaries are created in the strain range at which a crystallographic texture is rapidly evolving. It appears that the parameters associated with a very active texture evolution have the largest influence on the creation of the very highest angle boundaries.

5.5. &i?ect on recovery and recrystallization

In general these effects are suggested to be similar to those encountered when the original grain size is reduced. In general the high angle boundaries act as sinks for dislocations during annealing and as nucleation sites [61]. Another important effect is related to the fine distribution of texture components in the deformed microstructure which may affect the growth of grains

during recrystallization. Specific orientation relationships may result in accelerated growth, but in most cases the migration of high angle grain boundaries will be slowed down or stopped by orientation pinning. Orientation pinning arises by impingement between a growing grain and a deformed crystallite of similar orientation that leads to the replacement of a mobile high angle boundary with a much less mobile low angle boundary [61].

6. CONCLUSIONS

Deformation of metals from medium to large strain introduces significant changes in microstructure, texture and local crystallography. These changes are illustrated by experimental examples for different metals deformed by different processes. The following conclusions are drawn:

??The microstructure evolves into a lamellar structure of dislocation boundaries of small and medium angles mixed with high angle boundaries. The number of the latter is significantly larger (e.g. about 3-5 times in rolling, 27 times in torsion) than the number of original grain boundaries.

??The macro-texture evolves into a typical deformation texture containing a number of texture components. Local crystallographic measurements show that the volume fraction of the individual texture components is composed of micrometer and submicrometer sized volumes distributed throughout the deformed microstructure.

??The distribution of misorientations across lamellar boundaries has been estimated based on assumptions that those boundaries are formed by evolving grain subdivision processes, which can lead to different texture components within an original grain. The estimated distributions are in good agreement with those determined experimentally at large strain by automated Kikuchi diffraction techniques.

??The formation of high angle grain boundaries during plastic deformation leads to a deformation induced reduction in grain size. This grain refinement will have an effect both on the mechanical and on the thermal behavior of the deformed metal.

Ackno~~ledgernents-Discussions with D. Juul Jensen as well as the neutron diffraction measurement of texture are gratefully acknowledged. This work was supported by the Office of Basic Energy Sciences, U.S. of DOE, under contract No. DE-AC04-94AL85000.

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