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Nomenclature for strain-induced boundaries in hot and cold working
Materials Science and Engineering A 462 (2007) 37–44
Nomenclature for strain-induced boundaries in hot and cold working H.J. McQueen a,∗ , S. Spigarelli b a
Mechanical and Industrial Engineering, Concordia University, Montreal, Que. H3G 1M8, Canada b iNFM/Department of Meccanica, University of Politecnica delle Marche, Ancona I-6013, Italy Received 13 October 2005; received in revised form 20 March 2006; accepted 11 April 2006
Abstract Recent advances in the analysis of strain-induced boundaries in cold working have led to a strong evolution in understanding of their nature and in nomenclature. This has impacted on the hot working domain, instigating a re-examination of microstructural behavior and pressure to revise the terminology. While hot working involves high strain rates and strains, it shares with creep the development of a steady state regime at relatively low strains. The development of substructure and response to Taylor polycrystalline constraints have essential differences from those in cold working, so the different boundary character warrants retention of their traditional names. © 2006 Elsevier B.V. All rights reserved. Keywords: Strain-induced boundaries; Hot working; Cold working; Creep; Dynamic recovery; Dynamic recrystallization
1. Introduction Boundaries induced by straining in various modes and at various temperatures have been described by different nomenclature although they have many features in common. In the course of an effort to reach a concordance of the names and phenomena, it was concluded that there were significant differences in behavior, dependent on temperature T and strain rate ε˙ , that are exhibited prominently in the flow curves. The existence of real differences in the phenomena indicates that exact correspondence cannot be established. The present discussion proceeds to sort these things out with the objective of clarifying the ranges of behavior thus enhancing transfer of information between fields [1–3]. Brief simplified descriptions of the mature microstructures in cold working (20 ◦ C) and in hot working (≥0.5TM , melting point K) are given, so that the two domains can be critically compared in sequence. Al is used as the primary subject because it undergoes no changes in phase with temperature nor in restoration mechanisms with strain. Determination of microstructure evolution with strain from a series of specimens is always hampered by variations in the prior grain size and orientation. Boundaries of any origin may be referred to as low angle (LAB < 14◦ ) or high (HAB > 15◦ ).
∗
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0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.04.151
Transmission electron microscopy (TEM) of cold worked metal reveals, according to Hansen and Hughes [1,4–6], at a scale of about 0.5 m, incidental dislocation boundaries (IDB) (also called cell walls, CW) that continually rearrange to maintain cells constant in size and almost equal in all directions. At spacings of 5 m, there are more permanent boundaries than the IDB; as misorientation Ψ increases with strain, these boundaries are named geometrically necessary boundaries (GNB) (also known as block walls BW) [7–9]. At a spacing of 50–100 m there are transition boundaries (TB) between deformation bands that are large regions of crystals slipping on symmetrical sets of slip systems [10–12]; as ε rises, the regions continually rotate relative to each other so that TB are permanent and rise in misorientation until they are almost indistinguishable from the original grain boundaries (Table 1). At high strains some block walls, TB and GB have become almost parallel to the elongation direction and are known as layer or lamellar boundaries with the lamellae containing cells, possibly only one layer [1]. In hot working (∼400 ◦ C) for Al, steady state sub-boundaries (SGB) are spaced at 5 m and saturate at Ψ ≈ 4◦ . They continually rearrange to maintain equiaxed subgrains that contain the Frank Network of dislocations with a constant spacing (ρi−0.5 , ρi dislocation length per unit volume) at about 0.5 m [13–18]. All dislocation walls that produce a misorientation must have a geometrically necessary array of dislocations. However, they may have additional dislocations which are paired at some distance with those having opposite Burgers vectors; such dipoles
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Table 1 Strain-induced boundaries Functional name Cold working 1. Cell walls (CW) (LAB < 14◦ , low angle) 2. Block walls (BW) (LAB or HAB) 3. Transition boundaries (TB) of deformation bands (HAB > 15◦ , high angle) Hot working 1. Subgrain boundaries (SGB) . . . (LAB) 2. No BW 3. Transition boundaries (TB) as for cold working
Other designation
Life
Misorientation
Spacing (m)
IDB GNB Layer boundaries (LB) at high ε
Transitory Semi-permanent Permanent
Rising slowly Rising quickly Rising very quickly
0.5 5 50
Transitory
Saturates
Permanent
Rising very quickly
LB at high ε
5 50
All types have a geometrically necessary dislocation component; quickly all have a redundant component (dipoles) less as T rises. IDB: incidental dislocation boundaries; GNB: geometrically necessary boundaries.
gradually annihilate through climb and cross slip in dynamic recovery (DRV). Similar to cold working, the TB are permanent boundaries but block walls are absent (Table 1) [2,3,13,17,18]. The GB become serrated through reaction with SGB so are fully distinguishable only by diffraction.
2. Comparison of hot and cold working flow curves In cold working of Al (Fig. 1), the flow curves at ε˙ = 1 s−1 reach a steady state at a high strain somewhat dependent on the deformation mode [13,17]. On the other hand at 400 ◦ C, the flow curve attains the steady state regime after a short transient that is at least one order smaller than that in cold working. At point σ X , εX on the hot working transient the dislocation density is the = σ , ε at 20 ◦ C where the rate of same as at the point σσX X σX accumulation is much higher because of the reduced rate of DRV. , ε = ε the stress is much higher. As a result at the point σεX X εX at 20 ◦ C is much At εS4 (steady state starts 400 ◦ C) the stress σεS4 higher than σ S4 and the rate of accumulation is high compared to nil at 400 ◦ C [13,17]. The high dislocation accumulation rates are associated with high strain hardening rates (θ = dσ/dε) (Fig. 1b).
The constant steady state dislocation density, that is related to S dependent on T and ε˙ , is associated with a subgrain size d (or spacing w = 0.787d) with internal density ρi (spacing ρi−0.5 ) and link length or dislocation spacing S (S = Ψ /b) in the SGB. The dependence of these spacings on σ S /G (G shear modulus) is independent of strain and of deformation mode (not entirely) [13,16,17]. These subgrains remain equiaxed up to very high strains in grains that are elongating [15]. As observed by various means [16,18], the SGB migrate, merge and annihilate, as well as decomposing (unraveling) and reforming (reknitting). 3. Taylor constraints The flow curves do not directly show what is happening with respect to slip systems selected by Taylor requirements. For plastic stability, grains in a work piece should slip on five systems to permit them to change shape in the same manner as the piece as a whole [10–12]. However, if a grain breaks up into several deformation bands with different systems, possibly only two or three are needed in each; the division process is dependent on the grain size, the grain orientation and stress concentrations from neighbors slipping differently under the same rules. This
= σ , ε = ε ) and (b) θ–σ with insert showing rate of dislocation rise ρ ˙ + or decline ρ˙ − vs. σ/G, illustrating effects of DRV Fig. 1. Schematic curves (a) σ–ε (σσX X εX X at different temperatures [17]. At 400 ◦ C 0.1 s−1 , transient to steady state is about ε = 0.2 defining εt for substructure to rearrange completely [13] compared to 20 for 20 ◦ C [17,24].
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process is very similar in both hot and cold working but the constraints are somewhat reduced as T rises as will be explained [13,17]. As strain increases, the deformation bands rotate relative to each other so that the permanent TB between them rise in misorientation Ψ , thus being very strong GNB [10,13,17]. Such boundaries studied in single crystals at 20 ◦ C consist of several layers of small cells with dislocations walls of about 5◦ each [19,20]. They have been shown to be important sites for nucleation during static recrystallisation. In hot working, the TB are usually not thick cellular layers but appear similar to SGB; they may be identifiable in TEM by differences in contrast across them and certainly by selected area diffraction (SAD). The TB are generally too far apart to have much influence on strain hardening as was documented before 1960 [10–12] when they were much studied by many techniques until TEM made possible observation of the finer substructure [21,22]. Deformation textures were studied macroscopically for years by X-ray diffraction. Theory related their formation to the rotations of the lattice according to the rules that Taylor had proposed for different grain orientations. The dimensions of the rotating regions were not amenable to direct observations. Some limited checks of macro-texture by diffraction in the TEM roughly agreed with the X-ray measurements [23], the determinations were too tedious to conduct enough for statistical correlation. With the introduction of Kikuchi pattern indexing by automatic computer analysis, the orientations of regions down to 2 m could be determined in association with spatial distribution [1,23]. 4. Cold working substructures In the early TEM studies of cold work substructures, the focus was on the cell size. Much research established that cells developed from tangles at strains of about 0.2 and then became smaller and somewhat elongated as strain increased further. It was shown that both the transverse and longitudinal direction diminished to saturation at an aspect ratio of about 1.2 [7,24,25]. With further strain, the density of dislocations in the walls and their thickness increased; however the complexity of these arrays defied analysis for many years (Fig. 2) [26]. Because of
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the limited field of view in TEM, deformation bands and TB were not readily observed or thought to have much significance. Usually, the orientations of substructure were not determined to a sufficient degree to develop an understanding of microtextures. In more careful observations, parallel microbands cut through the substructure from operation of a secondary set of slip systems that are brought by lattice rotation into an orientation highly stressed by the shaping mode [1,4–9]. Once the new dislocations cut through the cells created by the primary system, many others follow creating a band of concentrated strain [27–31]. Since these often consist of several layers of high dislocation density, they were initially named Dense Dislocations Walls. Further rotations cause new sets of microbands which intersect the first set creating blocks of cells (about 10 cells on each edge) hence the name Block Walls (BW). In cyclic extrusion compression, microbands gradually penetrate across many grains and lead to a steady state in stress and cell size (Fig. 3) [28,29]. The focus of TEM observation has thus become the character of the walls and their origin, the cells being considered the same as earlier. The simple cell walls keep rearranging while storing a limited density of dislocations hence the name incidental dislocation boundaries (IDB). The block walls have greater permanence and attain greater misorientations hence the name geometrically necessary boundaries [4,5]. When the misorientations were measured as a function of strain, the average values of both GNB and IDB increased and so did the breadths of the distributions. When the angles were normalized by the average, the distributions became independent of strain. The average misorientation rose with strain to some power: 0.7 for GNB (BW) and 0.4 for IDB (CW) [4,5]. Theories of strain hardening have been based on the increase in Ψ of GNB. The CW continually rearrange, maintaining a low cell aspect ratio as mentioned earlier. The BW are more permanent and hence rotate with the lattice moving towards being parallel with the elongation direction; as their misorientation increases they become similar to GB (Table 1). At very high strains, the structure becomes lamellar possibly only one cell thick; the crossing cell walls are low misorientations [1]. Each layer has rotated to an orientation that is close to one of the components in the
Fig. 2. TEM microstructure for Al 98.7 at ε = 4 produced by four passes (route C) through a 90◦ ECAP die, resulting in (a) very elongated block walls mainly HAB with some transverse HAB and finer cells with LAB, and (b) cells of similar orientation highlighted in dark field from one diffraction spot (500 nm bar). The HAB fraction is 0.6 with mean angle 40◦ and LAB fraction 0.4 averaging 3◦ (courtesy of Cabibbo et al. [26]).
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Fig. 3. TEM structure of Al 99.99 at ε = 1.7 produced by two passes in cyclic extrusion compression resulting in equiaxed cells intersected by micro bands (indicated by the lines), thus starting a structure of block walls. The spacing is about 1.4 m and with LAB (<10◦ ) fraction 0.90; after ε = 60, LAB (<15◦ ) fraction reduced to 0.35 (courtesy of Richert et al. [28,29]).
macro-texture; these elements of micro-texture appear to be in random order. The boundaries now called lamellar (LB), have high Ψ and are indistinguishable from the original grain boundaries; the number of such boundaries is much greater than one would expect from the plastic straining of the grains [1,23]. The final misorientations are much higher than what would have accumulated in the final number of strain-induced boundaries by the dislocation mechanisms and are in agreement with those predicted by Taylor theory [4–6]. It is clear that not all GNB observed at intermediate strains became layer bands so some must have merged with neighbors possibly with the misorientations being additive. Moreover, in rolling after each sizeable pass, shear bands repeatedly appear near a fixed angle to the rolling direction in grains with slip systems suitably oriented to the stress state [4–6,27,30,31]. Earlier microbands rotate toward the rolling plane as grains elongate and may rearrange to form blocks or layer bands. There are two features of early substructure that can be related to polycrystal constraints. The cell structures form first near the GB and tend to remain smaller and to have higher misorientations than those in the central portions of grains [32,33]. Thus, GB act as strong barriers as observed in Hall–Petch grain size strengthening; they decrease in effectiveness as the strain increases [34,35]. At high T, grain size strengthening becomes negligible. The substructures after rolling have been separated into three categories according to cell dimensions and density of the walls that are dependent on the grain orientation represented as zones on a stereographic triangle aligned with the rolling axes [1,8,32,33]. At high T, this behavior has been noticed as variations in subgrain size.
5. High temperature deformation The marked feature of high temperature deformation (T > 370 ◦ C, ∼0.65TM for Al) is the development of a steady state regime after a short transient of low strain hardening (Fig. 1) [1,2,13–18,21,23,36–39]. Over a broad range of T and ε˙ (strain rate), subgrains develop within the original grains. (The special case in which flow softening occurs with the formation of new grains is discussed at the end.) Extensive evidence confirms that the subgrain size, the link length in the walls and the link length in the Frank network in the subgrains are tied to the flow stress σ (normalized by the shear modulus G) that is in turn dependent on ε˙ through power or exponential functions and on T in an Arrhenius function [13,16,26,37]. A primary concern has been how the mobile dislocations passed through the substructure with an activation energy Q, equaling that for dislocation climb hence for vacancy migration [36]. One school of thought ignored the subgrain boundaries (SGB) and concluded that reactions with the Frank net defined the strength [36,37]. However, another school has proposed theories linking the strength to interactions of mobile dislocations with the SGB as well [16,37–39]. Notably in the creep domain at low strain rates (<10−4 s−1 ), the SGB were recognized as tilt, twist or complex walls composed of regular arrays of dislocations with great similarity to those from annealing after cold working. The initial stage of static recovery (SRV) is related to dipole annihilation and the second to SGB rearrangement [40,41]. Due to the low densities, the misorientations could be related to the dislocation spacing; thus the SGB were clearly thought to be geometrically necessary (Table 1) [36–38]. In tensile creep experiments the
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true strain seldom exceeds unity so the evolution of substructure was not extensively studied. Nevertheless in the case of Al (and of ␣-Fe), the T dependence of stress was found to extend into hot working with correlation through the Zener–Hollomon parameter (Z = ε˙ exp(Q/RT )) [13–16,21,40]. Moreover, at the higher strains and strain rates, the above characteristic substructure dimensions depended on σ/G in a consistent manner with those in creep [2,13,16]. Under the conditions of 400 ◦ C (0.7TM ) 1 s−1 for the flow curve in Fig. 1, the microstructural behavior is fully consistent with that in creep; this is certainly true for lower Z [13,16,17]. However, as Z increases and T declines below 300 ◦ C for Al, a gradual densification of substructure matches the change in mechanical properties as shown by the higher plateau starting at higher ε for 250 ◦ C (0.56TM , Fig. 1). A clear demonstration of substructure differences in hot, warm and cold rolling are experiments on 3003 and 3004 alloys at reductions up to 80% (ε = 1.86) over temperatures from 20 to 520 ◦ C [42]. For subgrains measured in TEM, the size had an inverse relationship to log Z and their character became more irregular and elongated in the warm range. The inclination of their axis of elongation to the rolling direction declined from 35◦ to 25◦ (48% reduction) to only 6◦ at 300 ◦ C (83% reduction). While planar inhomogeneities, such as microbands, were observed (with decreasing frequency with rising T), their volume fraction rise negligibly with strain [42] in contrast to a linear increase reported in cold rolling [43]. For Al, at 400 ◦ C 1 s−1 , the transient to steady state is quite short (ε ≈ 0.3) and the strain in the plateau can exceed 100 in torsion [15,17,19,23]. In hot working, the study of high ε is important to provide data commensurate with rolling ( ε ≈ 3) and extrusion (ε > 6). Even optical microscopy showed that subgrains were present in the elongated original grains [21]. Examination with TEM and SEM (Fig. 4) confirmed that the subgrains maintained their characteristic spacings but also remained equiaxed throughout such straining at constant stress (Fig. 5) [13–18,22,44–47]. Careful observations in hot working and creep, such as high voltage TEM of in situ strain, showed that the substructure constantly rearranged by the SGB migrating, merging with neighbors, annihilating, decomposing (unraveling) and reforming (reknitting) [2,13,23,38,48]. Such mechanisms were shown also to operate during the transients associated with changes in T, ε˙ or σ. The SGB are thus not permanent and hence are more similar to the cell walls or IDB in cold working than to block walls or GNB [12,13,17]. 6. Block walls not observed The Taylor theory for polycrystals is expected to apply during hot working; the textures formed in the various processes are about the same as in cold working [23,49,50]. Deformation bands form with transition boundaries; they have also been observed in creep although textures have seldom been studied because of the low strains [51]. While in the cold working transition boundaries between the bands consist of several layers of fine cells with cumulative misorientations of over 20◦ , the TB in hot working appear much like SGB in TEM, but can be defined
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Fig. 4. SEM images of 6060 alloy deformed in torsion at Z = 1.5E11 (400 ◦ C 0.1 s−1 ): (a) ε = 4 elongated grains with serrated GB and width of about three subgrains, (b) ε = 20 shortened grains with width and subgrains similar to (a). With rising strain more subgrains adjacent to GB, hence more HAB and less LAB facets [46].
by tilting to expose the dislocation arrays or by diffraction patterns. TB as described above have been observed in torsion tests on Al single crystals [52]. In high strain torsion where the original GB are elongated to become parallel to each other (almost normal to the torsion axis), additional lamellar boundaries are found between the initial GB with their origin as TB [23]. Extensive observations of the substructure at strains of 4 and higher demonstrate the absence of microbands or block walls [16]. This is consistent with the polycrystal constraints being reduced at high T because of ease of GB sliding, of cross slip and climb and of additional slip planes {1 1 0} in Al [53]. However, the most significant reason is probably the rearrangement of the substructure that is expected to be completed in every strain interval εt equaling the initial strain hardening transient (consistent with the transients for a tenfold change in ε˙ , Fig. 1) [13,16,54]. As the lattice rotates and new systems begin to operate, they do not form narrow microbands in which there is intense slip. The dislocations from the new system disperse by cross slip and climb and gradually replace the SGB of the previous system as they decompose or annihilate. This type of rearrangement has not been positively confirmed because the grains of the same orientation have not been studied under increasing ε. Changes of strain path at high T provide some evidence for decomposition of pre-existing substructures [55]. In the warm working range as T falls from 250 to100 ◦ C (0.5TM ), diminished ability to rearrange leads to increased HAB segments and finally to a BW network [13,17]. 7. Grains: texture and boundaries The torsion textures have been studied to extreme strains in both Al and in ␣-Fe in which discontinuous dynamic
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Fig. 5. OIM structure of Al 99.9 at (a) ε = 0.5 and (b) net ε = 0 produced in Al by torsion at 400 ◦ C 0.1 s−1 to 0.5 and reversal to 0 with the stress remaining steady. The grains are reversed from elongated to approximately equiaxed with fraction of GB > 15◦ declining from 0.439 to 0.315. The SB (1–5◦ ) fraction increased from 0.516 to 0.646 as a result of less subgrains being in contact with the GB (courtesy of Avramovic-Cingara et al. [47]). Earlier tests showed that as rose from 0.2 to 4, LAB (0.5–5◦ ) declined from 0.861 to 0.577 while HAB rose from 0.127 to 0.402. The fraction of 5–14◦ boundaries rise only from 0.012 to 0.022 throughout, indicating that SB did not march upward in angle. TEM showed that OIM missed many SB [16,47].
recrystallisation dDRX do not take place [23,57,58]. The microtexture from STEM Kikuchi patterns gave very close agreement with macro-texture from X-ray measurements [23]. The texture formation causes softening because grains possessing the most intense component have a lower Taylor factor. Such grains have larger subgrain size compared to those retaining the low strain texture component. The local boundary migrations associated with the absorption of SGB (Fig. 4) progress more into the grains with denser substructure; the soft texture is thereby intensified [23,46,56–60]. In hot working the grain boundaries have moderate mobility that permits them to migrate to reduce energy at triple junctions with SGB (Fig. 4) [45,61,62]. The result is serrations with wavelength and amplitude approximating the subgrain size [15–17,23]; in contrast the GB in cold working remain smooth almost flat at high strains [1]. The serrations are not permanent since the grain boundaries are lengthening while the SGB rearrange to keep the subgrains constant in size and equiaxed [62]. The serrations make it difficult to observed GB in TEM; they can be distinguished only by tilting or by diffraction. When the grains are strained to the point that their thickness is only 2–3 subgrain diameters, the serrations on neighboring GB meet pinching off the grain (causing perforations in three dimensions) (Fig. 4) [15,17,23,45]. As the impinged GB region enlarges by migration of the triple junction towards equilibrium angles, the mechanism leaves the neighboring grains thicker. Several independent observations have confirmed that the thickness never becomes less than the subgrain diameter (Fig. 6) [63]. The small grains created by DRV and grain geometry (grain refining DRV) are somewhat similar to DRX grains in Cu [60] so it was called geometric DRX (gDRX) [23]. This mechanism can start at low strains in the grains that occupy the acute angle at triple junctions, this tends to shorten and thicken the grains [13,17,56]. For a given initial grain size, the mechanism pro-
ceeds at lower strains for a lower Z that gives rise to larger subgrains (Fig. 6) [16,17,62,64]. As the grains elongate, the surface area of GB and TB become much greater. The number of equiaxed subgrains of constant size in contact with GB or TB greatly increases (Fig. 5) [13,17,23,47,65]. When serrated lamellar boundaries are separated by only 2 or 3 subgrains, most cells have as many as 1/3 to 1/2 of their facets high angle boundaries; such cells are referred to as HAB-subgrains since they are hard to distinguish from grains [13,23,65]. When observed by optical or SEM-EBS, the original elongated grains are no longer distinguishable; there
Fig. 6. In torsion at four values of Z for 6060 alloy (100 m initial grain size) by Pettersen et al. [71], the axial width of the grains ceased to decline as it approached the subgrain size, e.g., for Z = 7E11 (482 ◦ C 10 s−1 ) final grain width 10 m for SEM subgrain size 4.5 m. Previously in Al 99.7 at Z = 1.5E11 (400 ◦ C 0.2 s−1 ) (Solberg et al. [23]), 100 m grains stabilized from ε = 3 to 60 (changed ε scale) with thickness near 25 m (STEM) for 8 m SEM subgrains (* sizes averaged over ε = 3, 10, 20,40, 60) with mixture of LAB and HAB, whereas 2000 m grains continually decreased over that range with well defined subgrains [23].
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is only a field of equiaxed HAB-subgrains about the same size as the subgrains at the beginning of steady state (or slightly larger due to change of texture) [13,56,65]. When high and low angle boundaries are defined by orientation image microscopy, the fraction of low and high angle boundaries remain constant because of the above impingement (pinching off) mechanism [66]. The size of the crystallites are controlled by stress fields of the SGB and the Frank network while the GB serve as sinks [65]. The phenomena just described is quite different from dDRX in which rapid migration of GB yield a grain size that is 10 times the subgrain size for Cu or austenitic stainless steel [60,65,67]. 8. Discontinuous dynamic recrystallization While in cold working the behavior of Cu, Ni and ␥-Fe with low stacking fault energy (SFE) have many similarities to Al over large strains (up to ε ≈ 4), in hot working strong differences arise from what has been described for Al. Before the strain hardening transient is completed new grains are nucleated that decrease the strain hardening until it becomes negative; the flow curve reaches a peak and work softens as the first cycle of dDRX is completed [60,67–69]. As a result of high plastic flow iniating small subgrains with high Ψ near the GB, the GB develop strong serrations. Some of these transform into nuclei, regions of low dislocation with mobile high angle boundaries, (possibly the SGB across the serration neck) that are able to migrate under the driving force of the stored dislocation substructure energy. In creep below 10−5 s−1 , dDRX does not occur in commercial purity Al, Cu, Ni or ␥-Fe because the dislocation substructure has too low a density to produce nuclei [68–70]; this is similar to the absence of static recrystallization during annealing after creep. The new grains nucleate as necklaces along original boundaries but cease growing as the substructure induced within them reduce the differential energy driving force [68,69]. New necklaces form and grow until the old grains have a characteristic size defined by Z (T,˙ε) or by σ. Because of the rebuilt substructure, nucleation again takes place within the new grains but now randomly distributed throughout the volume so that a steady state is established in which dDRX occurs repeatedly [60,67–69]. The grain size remains constant about 10 times the subgrain diameter [67] in contrast to gDRX where the crystallite size is the same as the characteristic subgrain size. The flow stress is related to the subgrain size in the same way both before the peak and in the constant stress regime [67,68]. The steady state flow stress is about 20% lower than what would be the result from DRV alone; this is due to the elimination of finer cell sizes and dense walls that would develop without dDRX. The texture in dDRX is not a static recrystallisation texture because the nuclei are being deformed back towards the matrix texture before their formation [60]. Moreover, the strain to the peak is rather low (<1) so that an intense texture cannot develop as in cold working. Although high strains are possible in steady state, the texture remains the same as that at its start. In Cu and Al, the texture are similar at low strains but then the Al one intensifies as described earlier [56,60].
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9. Conclusions The strain-induced boundaries in hot working and creep have significant difference from those in cold working even when they perform similar structural functions. The subgrain boundaries are transitory, rearranging like cell walls but exhibit greater spacing, more regular arrays of dislocations and saturate in misorientation. In hot working as distinct from cold working, there is no formation of block walls that exhibit considerable persistence and rise in misorientation. In both hot and cold working, the permanent transition boundaries between deformation bands rise in length and misorientation with strain. Designation of one type as GNB is confusing since all strain-induced boundaries create misorientations. Classification by degree of persistence or ability to rearrange would be more useful. References [1] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D. Juul-Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Mater. Sci. Eng. 238 (1998) 219–274. [2] H.J. McQueen, M.E. Kassner, Mater. Sci. Eng. A, in press. [3] H.J. McQueen, E. Evangelista, M. Cabibbo, Mater. Sci. Eng. A, TMS’06, submitted for publication. [4] N. Hansen, D. Juul-Jensen, in: T.G. Langdon, et al. (Eds.), Hot Working of Al Alloys, TMS AIME, Warrendale PA, 1991, pp. 3–20. [5] D.A. Hughes, Y.L. Liu, in: T.G. Langdon, et al. (Eds.), Hot Working of Al Alloys, TMS AIME, Warrendale PA, 1991, pp. 21–30. [6] D.A. Hughes, A. Godfrey, T.R. Bieler, et al. (Eds.), Hot Deformation of Al Alloys II, TMS AIME, Warrendale, PA, 1998, pp. 23–36. [7] F. Schuh, M. Von, Heimendahl, Z. Metall. 65 (1974) 346. [8] B. Bay, N. Hansen, D.A. Hughes, D. Kuhlmann-Wilsdorf, Acta Metal. Mater. 40 (1992) 205–219. [9] D.A. Hughes, N. Hansen, in: J.J. Jonas, et al. (Eds.), Advances in Hot Deformation Textures and Microstructures, TMS-AIME, Warrendale, PA, 1995, pp. 427–444. [10] C.S. Barrett, L.H. Levenson, Trans. AIME 137 (1990) 112–127. [11] D. Kuhlman-Wilsdorf, Acta Mater. 47 (1999) 1697–1712. ´ [12] B. Jaoul, Etude de la Plasticit´e et Application aux M´etaux, Dunod, Paris, 1965. [13] H.J. McQueen, W. Blum, Mater. Sci. Eng. A290 (2000) 95–107. [14] H.J. McQueen, in: T.G. Langdon, H.D. Merchant (Eds.), Hot Deformaton of Aluminum Alloys, TMS-AIME, Warrendale, PA, 1991, pp. 31–54. [15] H.J. McQueen, E. Evangelista, M.E. Kassner, Z. Metall. 82 (1991) 336–345. [16] W. Blum, Q. Zhu, R. Merkel, H.J. McQueen, Mater. Sci. Eng. A205 (1996) 23–30. [17] H.J. McQueen, W. Blum, in: T. Sato (Ed.), Al Alloys Physical and Mechanical Properties, ICAA6, Japan Inst. Metals, 1998, pp. 99–112. [18] I. Poschmann, H.J. McQueen, Mater. Sci. Technol. 14 (1998) 1101–1108. [19] P.J. Wilbrandt, P. Haasen, Z. Metall. 71 (1980) 273–278, 385–395. [20] A. Berger, P.J. Wilbrandt, P. Haasen, Acta Metall. 31 (1983) 1433–1443. [21] H.J. McQueen, E. Evangelista, N. Jin, M.E. Kassner, Metall. Trans. 26A (1995) 1757–1766. [22] H.J. McQueen, D.G. Sanders, in: D.C. Dunand (Ed.), Superplasticity and Superplastic Forming, ASM International, Metals Park, OH, 2001, pp. 154–163. [23] J.K. Solberg, H.J. McQueen, N. Ryum, E. Nes, Philos. Mag. 60 (1989) 447–471, 473–485. [24] J. Gil-Sevilano, P. van Houtte, E. Aernoudt, Prog. Mater. Sci. 25 (1980) 69–412. [25] A.W. Thompson, Metall. Trans. 8A (1977) 833–842. [26] M. Cabibbo, E. Evangelista, H.J. McQueen, Mater. Sci. Eng. A, submitted for publication.
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Nomenclature for strain-induced boundaries in hot and cold working H.J. McQueen a,∗ , S. Spigarelli b a
Mechanical and Industrial Engineering, Concordia University, Montreal, Que. H3G 1M8, Canada b iNFM/Department of Meccanica, University of Politecnica delle Marche, Ancona I-6013, Italy Received 13 October 2005; received in revised form 20 March 2006; accepted 11 April 2006
Abstract Recent advances in the analysis of strain-induced boundaries in cold working have led to a strong evolution in understanding of their nature and in nomenclature. This has impacted on the hot working domain, instigating a re-examination of microstructural behavior and pressure to revise the terminology. While hot working involves high strain rates and strains, it shares with creep the development of a steady state regime at relatively low strains. The development of substructure and response to Taylor polycrystalline constraints have essential differences from those in cold working, so the different boundary character warrants retention of their traditional names. © 2006 Elsevier B.V. All rights reserved. Keywords: Strain-induced boundaries; Hot working; Cold working; Creep; Dynamic recovery; Dynamic recrystallization
1. Introduction Boundaries induced by straining in various modes and at various temperatures have been described by different nomenclature although they have many features in common. In the course of an effort to reach a concordance of the names and phenomena, it was concluded that there were significant differences in behavior, dependent on temperature T and strain rate ε˙ , that are exhibited prominently in the flow curves. The existence of real differences in the phenomena indicates that exact correspondence cannot be established. The present discussion proceeds to sort these things out with the objective of clarifying the ranges of behavior thus enhancing transfer of information between fields [1–3]. Brief simplified descriptions of the mature microstructures in cold working (20 ◦ C) and in hot working (≥0.5TM , melting point K) are given, so that the two domains can be critically compared in sequence. Al is used as the primary subject because it undergoes no changes in phase with temperature nor in restoration mechanisms with strain. Determination of microstructure evolution with strain from a series of specimens is always hampered by variations in the prior grain size and orientation. Boundaries of any origin may be referred to as low angle (LAB < 14◦ ) or high (HAB > 15◦ ).
∗
Corresponding author. Tel.: +1 514 848 2424x3145; fax: +1 514 848 3175. E-mail address: [email protected] (H.J. McQueen).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.04.151
Transmission electron microscopy (TEM) of cold worked metal reveals, according to Hansen and Hughes [1,4–6], at a scale of about 0.5 m, incidental dislocation boundaries (IDB) (also called cell walls, CW) that continually rearrange to maintain cells constant in size and almost equal in all directions. At spacings of 5 m, there are more permanent boundaries than the IDB; as misorientation Ψ increases with strain, these boundaries are named geometrically necessary boundaries (GNB) (also known as block walls BW) [7–9]. At a spacing of 50–100 m there are transition boundaries (TB) between deformation bands that are large regions of crystals slipping on symmetrical sets of slip systems [10–12]; as ε rises, the regions continually rotate relative to each other so that TB are permanent and rise in misorientation until they are almost indistinguishable from the original grain boundaries (Table 1). At high strains some block walls, TB and GB have become almost parallel to the elongation direction and are known as layer or lamellar boundaries with the lamellae containing cells, possibly only one layer [1]. In hot working (∼400 ◦ C) for Al, steady state sub-boundaries (SGB) are spaced at 5 m and saturate at Ψ ≈ 4◦ . They continually rearrange to maintain equiaxed subgrains that contain the Frank Network of dislocations with a constant spacing (ρi−0.5 , ρi dislocation length per unit volume) at about 0.5 m [13–18]. All dislocation walls that produce a misorientation must have a geometrically necessary array of dislocations. However, they may have additional dislocations which are paired at some distance with those having opposite Burgers vectors; such dipoles
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Table 1 Strain-induced boundaries Functional name Cold working 1. Cell walls (CW) (LAB < 14◦ , low angle) 2. Block walls (BW) (LAB or HAB) 3. Transition boundaries (TB) of deformation bands (HAB > 15◦ , high angle) Hot working 1. Subgrain boundaries (SGB) . . . (LAB) 2. No BW 3. Transition boundaries (TB) as for cold working
Other designation
Life
Misorientation
Spacing (m)
IDB GNB Layer boundaries (LB) at high ε
Transitory Semi-permanent Permanent
Rising slowly Rising quickly Rising very quickly
0.5 5 50
Transitory
Saturates
Permanent
Rising very quickly
LB at high ε
5 50
All types have a geometrically necessary dislocation component; quickly all have a redundant component (dipoles) less as T rises. IDB: incidental dislocation boundaries; GNB: geometrically necessary boundaries.
gradually annihilate through climb and cross slip in dynamic recovery (DRV). Similar to cold working, the TB are permanent boundaries but block walls are absent (Table 1) [2,3,13,17,18]. The GB become serrated through reaction with SGB so are fully distinguishable only by diffraction.
2. Comparison of hot and cold working flow curves In cold working of Al (Fig. 1), the flow curves at ε˙ = 1 s−1 reach a steady state at a high strain somewhat dependent on the deformation mode [13,17]. On the other hand at 400 ◦ C, the flow curve attains the steady state regime after a short transient that is at least one order smaller than that in cold working. At point σ X , εX on the hot working transient the dislocation density is the = σ , ε at 20 ◦ C where the rate of same as at the point σσX X σX accumulation is much higher because of the reduced rate of DRV. , ε = ε the stress is much higher. As a result at the point σεX X εX at 20 ◦ C is much At εS4 (steady state starts 400 ◦ C) the stress σεS4 higher than σ S4 and the rate of accumulation is high compared to nil at 400 ◦ C [13,17]. The high dislocation accumulation rates are associated with high strain hardening rates (θ = dσ/dε) (Fig. 1b).
The constant steady state dislocation density, that is related to S dependent on T and ε˙ , is associated with a subgrain size d (or spacing w = 0.787d) with internal density ρi (spacing ρi−0.5 ) and link length or dislocation spacing S (S = Ψ /b) in the SGB. The dependence of these spacings on σ S /G (G shear modulus) is independent of strain and of deformation mode (not entirely) [13,16,17]. These subgrains remain equiaxed up to very high strains in grains that are elongating [15]. As observed by various means [16,18], the SGB migrate, merge and annihilate, as well as decomposing (unraveling) and reforming (reknitting). 3. Taylor constraints The flow curves do not directly show what is happening with respect to slip systems selected by Taylor requirements. For plastic stability, grains in a work piece should slip on five systems to permit them to change shape in the same manner as the piece as a whole [10–12]. However, if a grain breaks up into several deformation bands with different systems, possibly only two or three are needed in each; the division process is dependent on the grain size, the grain orientation and stress concentrations from neighbors slipping differently under the same rules. This
= σ , ε = ε ) and (b) θ–σ with insert showing rate of dislocation rise ρ ˙ + or decline ρ˙ − vs. σ/G, illustrating effects of DRV Fig. 1. Schematic curves (a) σ–ε (σσX X εX X at different temperatures [17]. At 400 ◦ C 0.1 s−1 , transient to steady state is about ε = 0.2 defining εt for substructure to rearrange completely [13] compared to 20 for 20 ◦ C [17,24].
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process is very similar in both hot and cold working but the constraints are somewhat reduced as T rises as will be explained [13,17]. As strain increases, the deformation bands rotate relative to each other so that the permanent TB between them rise in misorientation Ψ , thus being very strong GNB [10,13,17]. Such boundaries studied in single crystals at 20 ◦ C consist of several layers of small cells with dislocations walls of about 5◦ each [19,20]. They have been shown to be important sites for nucleation during static recrystallisation. In hot working, the TB are usually not thick cellular layers but appear similar to SGB; they may be identifiable in TEM by differences in contrast across them and certainly by selected area diffraction (SAD). The TB are generally too far apart to have much influence on strain hardening as was documented before 1960 [10–12] when they were much studied by many techniques until TEM made possible observation of the finer substructure [21,22]. Deformation textures were studied macroscopically for years by X-ray diffraction. Theory related their formation to the rotations of the lattice according to the rules that Taylor had proposed for different grain orientations. The dimensions of the rotating regions were not amenable to direct observations. Some limited checks of macro-texture by diffraction in the TEM roughly agreed with the X-ray measurements [23], the determinations were too tedious to conduct enough for statistical correlation. With the introduction of Kikuchi pattern indexing by automatic computer analysis, the orientations of regions down to 2 m could be determined in association with spatial distribution [1,23]. 4. Cold working substructures In the early TEM studies of cold work substructures, the focus was on the cell size. Much research established that cells developed from tangles at strains of about 0.2 and then became smaller and somewhat elongated as strain increased further. It was shown that both the transverse and longitudinal direction diminished to saturation at an aspect ratio of about 1.2 [7,24,25]. With further strain, the density of dislocations in the walls and their thickness increased; however the complexity of these arrays defied analysis for many years (Fig. 2) [26]. Because of
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the limited field of view in TEM, deformation bands and TB were not readily observed or thought to have much significance. Usually, the orientations of substructure were not determined to a sufficient degree to develop an understanding of microtextures. In more careful observations, parallel microbands cut through the substructure from operation of a secondary set of slip systems that are brought by lattice rotation into an orientation highly stressed by the shaping mode [1,4–9]. Once the new dislocations cut through the cells created by the primary system, many others follow creating a band of concentrated strain [27–31]. Since these often consist of several layers of high dislocation density, they were initially named Dense Dislocations Walls. Further rotations cause new sets of microbands which intersect the first set creating blocks of cells (about 10 cells on each edge) hence the name Block Walls (BW). In cyclic extrusion compression, microbands gradually penetrate across many grains and lead to a steady state in stress and cell size (Fig. 3) [28,29]. The focus of TEM observation has thus become the character of the walls and their origin, the cells being considered the same as earlier. The simple cell walls keep rearranging while storing a limited density of dislocations hence the name incidental dislocation boundaries (IDB). The block walls have greater permanence and attain greater misorientations hence the name geometrically necessary boundaries [4,5]. When the misorientations were measured as a function of strain, the average values of both GNB and IDB increased and so did the breadths of the distributions. When the angles were normalized by the average, the distributions became independent of strain. The average misorientation rose with strain to some power: 0.7 for GNB (BW) and 0.4 for IDB (CW) [4,5]. Theories of strain hardening have been based on the increase in Ψ of GNB. The CW continually rearrange, maintaining a low cell aspect ratio as mentioned earlier. The BW are more permanent and hence rotate with the lattice moving towards being parallel with the elongation direction; as their misorientation increases they become similar to GB (Table 1). At very high strains, the structure becomes lamellar possibly only one cell thick; the crossing cell walls are low misorientations [1]. Each layer has rotated to an orientation that is close to one of the components in the
Fig. 2. TEM microstructure for Al 98.7 at ε = 4 produced by four passes (route C) through a 90◦ ECAP die, resulting in (a) very elongated block walls mainly HAB with some transverse HAB and finer cells with LAB, and (b) cells of similar orientation highlighted in dark field from one diffraction spot (500 nm bar). The HAB fraction is 0.6 with mean angle 40◦ and LAB fraction 0.4 averaging 3◦ (courtesy of Cabibbo et al. [26]).
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Fig. 3. TEM structure of Al 99.99 at ε = 1.7 produced by two passes in cyclic extrusion compression resulting in equiaxed cells intersected by micro bands (indicated by the lines), thus starting a structure of block walls. The spacing is about 1.4 m and with LAB (<10◦ ) fraction 0.90; after ε = 60, LAB (<15◦ ) fraction reduced to 0.35 (courtesy of Richert et al. [28,29]).
macro-texture; these elements of micro-texture appear to be in random order. The boundaries now called lamellar (LB), have high Ψ and are indistinguishable from the original grain boundaries; the number of such boundaries is much greater than one would expect from the plastic straining of the grains [1,23]. The final misorientations are much higher than what would have accumulated in the final number of strain-induced boundaries by the dislocation mechanisms and are in agreement with those predicted by Taylor theory [4–6]. It is clear that not all GNB observed at intermediate strains became layer bands so some must have merged with neighbors possibly with the misorientations being additive. Moreover, in rolling after each sizeable pass, shear bands repeatedly appear near a fixed angle to the rolling direction in grains with slip systems suitably oriented to the stress state [4–6,27,30,31]. Earlier microbands rotate toward the rolling plane as grains elongate and may rearrange to form blocks or layer bands. There are two features of early substructure that can be related to polycrystal constraints. The cell structures form first near the GB and tend to remain smaller and to have higher misorientations than those in the central portions of grains [32,33]. Thus, GB act as strong barriers as observed in Hall–Petch grain size strengthening; they decrease in effectiveness as the strain increases [34,35]. At high T, grain size strengthening becomes negligible. The substructures after rolling have been separated into three categories according to cell dimensions and density of the walls that are dependent on the grain orientation represented as zones on a stereographic triangle aligned with the rolling axes [1,8,32,33]. At high T, this behavior has been noticed as variations in subgrain size.
5. High temperature deformation The marked feature of high temperature deformation (T > 370 ◦ C, ∼0.65TM for Al) is the development of a steady state regime after a short transient of low strain hardening (Fig. 1) [1,2,13–18,21,23,36–39]. Over a broad range of T and ε˙ (strain rate), subgrains develop within the original grains. (The special case in which flow softening occurs with the formation of new grains is discussed at the end.) Extensive evidence confirms that the subgrain size, the link length in the walls and the link length in the Frank network in the subgrains are tied to the flow stress σ (normalized by the shear modulus G) that is in turn dependent on ε˙ through power or exponential functions and on T in an Arrhenius function [13,16,26,37]. A primary concern has been how the mobile dislocations passed through the substructure with an activation energy Q, equaling that for dislocation climb hence for vacancy migration [36]. One school of thought ignored the subgrain boundaries (SGB) and concluded that reactions with the Frank net defined the strength [36,37]. However, another school has proposed theories linking the strength to interactions of mobile dislocations with the SGB as well [16,37–39]. Notably in the creep domain at low strain rates (<10−4 s−1 ), the SGB were recognized as tilt, twist or complex walls composed of regular arrays of dislocations with great similarity to those from annealing after cold working. The initial stage of static recovery (SRV) is related to dipole annihilation and the second to SGB rearrangement [40,41]. Due to the low densities, the misorientations could be related to the dislocation spacing; thus the SGB were clearly thought to be geometrically necessary (Table 1) [36–38]. In tensile creep experiments the
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true strain seldom exceeds unity so the evolution of substructure was not extensively studied. Nevertheless in the case of Al (and of ␣-Fe), the T dependence of stress was found to extend into hot working with correlation through the Zener–Hollomon parameter (Z = ε˙ exp(Q/RT )) [13–16,21,40]. Moreover, at the higher strains and strain rates, the above characteristic substructure dimensions depended on σ/G in a consistent manner with those in creep [2,13,16]. Under the conditions of 400 ◦ C (0.7TM ) 1 s−1 for the flow curve in Fig. 1, the microstructural behavior is fully consistent with that in creep; this is certainly true for lower Z [13,16,17]. However, as Z increases and T declines below 300 ◦ C for Al, a gradual densification of substructure matches the change in mechanical properties as shown by the higher plateau starting at higher ε for 250 ◦ C (0.56TM , Fig. 1). A clear demonstration of substructure differences in hot, warm and cold rolling are experiments on 3003 and 3004 alloys at reductions up to 80% (ε = 1.86) over temperatures from 20 to 520 ◦ C [42]. For subgrains measured in TEM, the size had an inverse relationship to log Z and their character became more irregular and elongated in the warm range. The inclination of their axis of elongation to the rolling direction declined from 35◦ to 25◦ (48% reduction) to only 6◦ at 300 ◦ C (83% reduction). While planar inhomogeneities, such as microbands, were observed (with decreasing frequency with rising T), their volume fraction rise negligibly with strain [42] in contrast to a linear increase reported in cold rolling [43]. For Al, at 400 ◦ C 1 s−1 , the transient to steady state is quite short (ε ≈ 0.3) and the strain in the plateau can exceed 100 in torsion [15,17,19,23]. In hot working, the study of high ε is important to provide data commensurate with rolling ( ε ≈ 3) and extrusion (ε > 6). Even optical microscopy showed that subgrains were present in the elongated original grains [21]. Examination with TEM and SEM (Fig. 4) confirmed that the subgrains maintained their characteristic spacings but also remained equiaxed throughout such straining at constant stress (Fig. 5) [13–18,22,44–47]. Careful observations in hot working and creep, such as high voltage TEM of in situ strain, showed that the substructure constantly rearranged by the SGB migrating, merging with neighbors, annihilating, decomposing (unraveling) and reforming (reknitting) [2,13,23,38,48]. Such mechanisms were shown also to operate during the transients associated with changes in T, ε˙ or σ. The SGB are thus not permanent and hence are more similar to the cell walls or IDB in cold working than to block walls or GNB [12,13,17]. 6. Block walls not observed The Taylor theory for polycrystals is expected to apply during hot working; the textures formed in the various processes are about the same as in cold working [23,49,50]. Deformation bands form with transition boundaries; they have also been observed in creep although textures have seldom been studied because of the low strains [51]. While in the cold working transition boundaries between the bands consist of several layers of fine cells with cumulative misorientations of over 20◦ , the TB in hot working appear much like SGB in TEM, but can be defined
41
Fig. 4. SEM images of 6060 alloy deformed in torsion at Z = 1.5E11 (400 ◦ C 0.1 s−1 ): (a) ε = 4 elongated grains with serrated GB and width of about three subgrains, (b) ε = 20 shortened grains with width and subgrains similar to (a). With rising strain more subgrains adjacent to GB, hence more HAB and less LAB facets [46].
by tilting to expose the dislocation arrays or by diffraction patterns. TB as described above have been observed in torsion tests on Al single crystals [52]. In high strain torsion where the original GB are elongated to become parallel to each other (almost normal to the torsion axis), additional lamellar boundaries are found between the initial GB with their origin as TB [23]. Extensive observations of the substructure at strains of 4 and higher demonstrate the absence of microbands or block walls [16]. This is consistent with the polycrystal constraints being reduced at high T because of ease of GB sliding, of cross slip and climb and of additional slip planes {1 1 0} in Al [53]. However, the most significant reason is probably the rearrangement of the substructure that is expected to be completed in every strain interval εt equaling the initial strain hardening transient (consistent with the transients for a tenfold change in ε˙ , Fig. 1) [13,16,54]. As the lattice rotates and new systems begin to operate, they do not form narrow microbands in which there is intense slip. The dislocations from the new system disperse by cross slip and climb and gradually replace the SGB of the previous system as they decompose or annihilate. This type of rearrangement has not been positively confirmed because the grains of the same orientation have not been studied under increasing ε. Changes of strain path at high T provide some evidence for decomposition of pre-existing substructures [55]. In the warm working range as T falls from 250 to100 ◦ C (0.5TM ), diminished ability to rearrange leads to increased HAB segments and finally to a BW network [13,17]. 7. Grains: texture and boundaries The torsion textures have been studied to extreme strains in both Al and in ␣-Fe in which discontinuous dynamic
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Fig. 5. OIM structure of Al 99.9 at (a) ε = 0.5 and (b) net ε = 0 produced in Al by torsion at 400 ◦ C 0.1 s−1 to 0.5 and reversal to 0 with the stress remaining steady. The grains are reversed from elongated to approximately equiaxed with fraction of GB > 15◦ declining from 0.439 to 0.315. The SB (1–5◦ ) fraction increased from 0.516 to 0.646 as a result of less subgrains being in contact with the GB (courtesy of Avramovic-Cingara et al. [47]). Earlier tests showed that as rose from 0.2 to 4, LAB (0.5–5◦ ) declined from 0.861 to 0.577 while HAB rose from 0.127 to 0.402. The fraction of 5–14◦ boundaries rise only from 0.012 to 0.022 throughout, indicating that SB did not march upward in angle. TEM showed that OIM missed many SB [16,47].
recrystallisation dDRX do not take place [23,57,58]. The microtexture from STEM Kikuchi patterns gave very close agreement with macro-texture from X-ray measurements [23]. The texture formation causes softening because grains possessing the most intense component have a lower Taylor factor. Such grains have larger subgrain size compared to those retaining the low strain texture component. The local boundary migrations associated with the absorption of SGB (Fig. 4) progress more into the grains with denser substructure; the soft texture is thereby intensified [23,46,56–60]. In hot working the grain boundaries have moderate mobility that permits them to migrate to reduce energy at triple junctions with SGB (Fig. 4) [45,61,62]. The result is serrations with wavelength and amplitude approximating the subgrain size [15–17,23]; in contrast the GB in cold working remain smooth almost flat at high strains [1]. The serrations are not permanent since the grain boundaries are lengthening while the SGB rearrange to keep the subgrains constant in size and equiaxed [62]. The serrations make it difficult to observed GB in TEM; they can be distinguished only by tilting or by diffraction. When the grains are strained to the point that their thickness is only 2–3 subgrain diameters, the serrations on neighboring GB meet pinching off the grain (causing perforations in three dimensions) (Fig. 4) [15,17,23,45]. As the impinged GB region enlarges by migration of the triple junction towards equilibrium angles, the mechanism leaves the neighboring grains thicker. Several independent observations have confirmed that the thickness never becomes less than the subgrain diameter (Fig. 6) [63]. The small grains created by DRV and grain geometry (grain refining DRV) are somewhat similar to DRX grains in Cu [60] so it was called geometric DRX (gDRX) [23]. This mechanism can start at low strains in the grains that occupy the acute angle at triple junctions, this tends to shorten and thicken the grains [13,17,56]. For a given initial grain size, the mechanism pro-
ceeds at lower strains for a lower Z that gives rise to larger subgrains (Fig. 6) [16,17,62,64]. As the grains elongate, the surface area of GB and TB become much greater. The number of equiaxed subgrains of constant size in contact with GB or TB greatly increases (Fig. 5) [13,17,23,47,65]. When serrated lamellar boundaries are separated by only 2 or 3 subgrains, most cells have as many as 1/3 to 1/2 of their facets high angle boundaries; such cells are referred to as HAB-subgrains since they are hard to distinguish from grains [13,23,65]. When observed by optical or SEM-EBS, the original elongated grains are no longer distinguishable; there
Fig. 6. In torsion at four values of Z for 6060 alloy (100 m initial grain size) by Pettersen et al. [71], the axial width of the grains ceased to decline as it approached the subgrain size, e.g., for Z = 7E11 (482 ◦ C 10 s−1 ) final grain width 10 m for SEM subgrain size 4.5 m. Previously in Al 99.7 at Z = 1.5E11 (400 ◦ C 0.2 s−1 ) (Solberg et al. [23]), 100 m grains stabilized from ε = 3 to 60 (changed ε scale) with thickness near 25 m (STEM) for 8 m SEM subgrains (* sizes averaged over ε = 3, 10, 20,40, 60) with mixture of LAB and HAB, whereas 2000 m grains continually decreased over that range with well defined subgrains [23].
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is only a field of equiaxed HAB-subgrains about the same size as the subgrains at the beginning of steady state (or slightly larger due to change of texture) [13,56,65]. When high and low angle boundaries are defined by orientation image microscopy, the fraction of low and high angle boundaries remain constant because of the above impingement (pinching off) mechanism [66]. The size of the crystallites are controlled by stress fields of the SGB and the Frank network while the GB serve as sinks [65]. The phenomena just described is quite different from dDRX in which rapid migration of GB yield a grain size that is 10 times the subgrain size for Cu or austenitic stainless steel [60,65,67]. 8. Discontinuous dynamic recrystallization While in cold working the behavior of Cu, Ni and ␥-Fe with low stacking fault energy (SFE) have many similarities to Al over large strains (up to ε ≈ 4), in hot working strong differences arise from what has been described for Al. Before the strain hardening transient is completed new grains are nucleated that decrease the strain hardening until it becomes negative; the flow curve reaches a peak and work softens as the first cycle of dDRX is completed [60,67–69]. As a result of high plastic flow iniating small subgrains with high Ψ near the GB, the GB develop strong serrations. Some of these transform into nuclei, regions of low dislocation with mobile high angle boundaries, (possibly the SGB across the serration neck) that are able to migrate under the driving force of the stored dislocation substructure energy. In creep below 10−5 s−1 , dDRX does not occur in commercial purity Al, Cu, Ni or ␥-Fe because the dislocation substructure has too low a density to produce nuclei [68–70]; this is similar to the absence of static recrystallization during annealing after creep. The new grains nucleate as necklaces along original boundaries but cease growing as the substructure induced within them reduce the differential energy driving force [68,69]. New necklaces form and grow until the old grains have a characteristic size defined by Z (T,˙ε) or by σ. Because of the rebuilt substructure, nucleation again takes place within the new grains but now randomly distributed throughout the volume so that a steady state is established in which dDRX occurs repeatedly [60,67–69]. The grain size remains constant about 10 times the subgrain diameter [67] in contrast to gDRX where the crystallite size is the same as the characteristic subgrain size. The flow stress is related to the subgrain size in the same way both before the peak and in the constant stress regime [67,68]. The steady state flow stress is about 20% lower than what would be the result from DRV alone; this is due to the elimination of finer cell sizes and dense walls that would develop without dDRX. The texture in dDRX is not a static recrystallisation texture because the nuclei are being deformed back towards the matrix texture before their formation [60]. Moreover, the strain to the peak is rather low (<1) so that an intense texture cannot develop as in cold working. Although high strains are possible in steady state, the texture remains the same as that at its start. In Cu and Al, the texture are similar at low strains but then the Al one intensifies as described earlier [56,60].
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9. Conclusions The strain-induced boundaries in hot working and creep have significant difference from those in cold working even when they perform similar structural functions. The subgrain boundaries are transitory, rearranging like cell walls but exhibit greater spacing, more regular arrays of dislocations and saturate in misorientation. In hot working as distinct from cold working, there is no formation of block walls that exhibit considerable persistence and rise in misorientation. In both hot and cold working, the permanent transition boundaries between deformation bands rise in length and misorientation with strain. Designation of one type as GNB is confusing since all strain-induced boundaries create misorientations. Classification by degree of persistence or ability to rearrange would be more useful. References [1] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D. Juul-Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Mater. Sci. Eng. 238 (1998) 219–274. [2] H.J. McQueen, M.E. Kassner, Mater. Sci. Eng. A, in press. [3] H.J. McQueen, E. Evangelista, M. Cabibbo, Mater. Sci. Eng. A, TMS’06, submitted for publication. [4] N. Hansen, D. Juul-Jensen, in: T.G. Langdon, et al. (Eds.), Hot Working of Al Alloys, TMS AIME, Warrendale PA, 1991, pp. 3–20. [5] D.A. Hughes, Y.L. Liu, in: T.G. Langdon, et al. (Eds.), Hot Working of Al Alloys, TMS AIME, Warrendale PA, 1991, pp. 21–30. [6] D.A. Hughes, A. Godfrey, T.R. Bieler, et al. (Eds.), Hot Deformation of Al Alloys II, TMS AIME, Warrendale, PA, 1998, pp. 23–36. [7] F. Schuh, M. Von, Heimendahl, Z. Metall. 65 (1974) 346. [8] B. Bay, N. Hansen, D.A. Hughes, D. Kuhlmann-Wilsdorf, Acta Metal. Mater. 40 (1992) 205–219. [9] D.A. Hughes, N. Hansen, in: J.J. Jonas, et al. (Eds.), Advances in Hot Deformation Textures and Microstructures, TMS-AIME, Warrendale, PA, 1995, pp. 427–444. [10] C.S. Barrett, L.H. Levenson, Trans. AIME 137 (1990) 112–127. [11] D. Kuhlman-Wilsdorf, Acta Mater. 47 (1999) 1697–1712. ´ [12] B. Jaoul, Etude de la Plasticit´e et Application aux M´etaux, Dunod, Paris, 1965. [13] H.J. McQueen, W. Blum, Mater. Sci. Eng. A290 (2000) 95–107. [14] H.J. McQueen, in: T.G. Langdon, H.D. Merchant (Eds.), Hot Deformaton of Aluminum Alloys, TMS-AIME, Warrendale, PA, 1991, pp. 31–54. [15] H.J. McQueen, E. Evangelista, M.E. Kassner, Z. Metall. 82 (1991) 336–345. [16] W. Blum, Q. Zhu, R. Merkel, H.J. McQueen, Mater. Sci. Eng. A205 (1996) 23–30. [17] H.J. McQueen, W. Blum, in: T. Sato (Ed.), Al Alloys Physical and Mechanical Properties, ICAA6, Japan Inst. Metals, 1998, pp. 99–112. [18] I. Poschmann, H.J. McQueen, Mater. Sci. Technol. 14 (1998) 1101–1108. [19] P.J. Wilbrandt, P. Haasen, Z. Metall. 71 (1980) 273–278, 385–395. [20] A. Berger, P.J. Wilbrandt, P. Haasen, Acta Metall. 31 (1983) 1433–1443. [21] H.J. McQueen, E. Evangelista, N. Jin, M.E. Kassner, Metall. Trans. 26A (1995) 1757–1766. [22] H.J. McQueen, D.G. Sanders, in: D.C. Dunand (Ed.), Superplasticity and Superplastic Forming, ASM International, Metals Park, OH, 2001, pp. 154–163. [23] J.K. Solberg, H.J. McQueen, N. Ryum, E. Nes, Philos. Mag. 60 (1989) 447–471, 473–485. [24] J. Gil-Sevilano, P. van Houtte, E. Aernoudt, Prog. Mater. Sci. 25 (1980) 69–412. [25] A.W. Thompson, Metall. Trans. 8A (1977) 833–842. [26] M. Cabibbo, E. Evangelista, H.J. McQueen, Mater. Sci. Eng. A, submitted for publication.
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