Saturation of Grain Refinement during Severe Plastic Deformation of Single Phase Materials: Reconsiderations, Current Status and Open Questions
2019 Volume 60 Issue 7 Pages 1270-1282
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2019 Volume 60 Issue 7 Pages 1270-1282
Grain refinement of materials by severe plastic deformation, investigation and understanding of their properties and phenomena has been a subject of intensive research over the last three decades. Along with the invention and development of these processes it has been recognized, that grain refinement is not indefinite but stagnates for single phase materials. Accordingly, the minimum grain sizes achievable are in the range between 50 and 500 nm. Motivated to find ways to overcome these limitations, effort has been made to understand the reasons behind. Various processes were suggested to cause saturation of grain fragmentation. While all of these assumptions and models were not based on direct observations, recently in-situ approaches allowed significant progress in understanding microstructural evolution and the principle restoration processes during severe straining. It is the aim of this work to recap important earlier findings, reconsider proposed models and to present our current understanding of the processes limiting grain refinement upon severe straining. Further it will be discussed, that similar processes generally occur during deformation of such fine scaled materials. They do not only govern saturation of grain refinement during severe deformation but more important also the mechanical response and performance of these materials. This motivates an in-depth understanding and therefore open questions as well as discrepancies between various experiments will be deliberately highlighted to stimulate further research and thus progress within this area.
Grain refinement has been proven to be an extremely efficient way to synthesize ultrahigh strength metals as well as to obtain materials with other superior properties such as superplastic forming capability at lower temperatures or exceptional physical properties like magnetic or thermoelectric properties.1–7) Different than deposition techniques, invention of severe plastic deformation (SPD) methods allowed to synthesize submicrometer or even nanocrystalline (NC) materials of sufficient size on a bulk scale.8–11) The availability of nanostructures of sufficient quantity is not only a main requirement towards potential applications but also facilitates the reliable exploration of their properties. Thanks to the vast number of studies, the property spectrum of nanostructured materials or how they change upon altering various external variables such as temperatures are today widely understood.1–3) Nevertheless, many details regarding plasticity or deformation mechanisms in such confined volumes remain uncertain or controversially debated. Solving these open questions is mandatory to establish reliable models and strategies how to improve their properties further. As an example, to date it is still not possible to model or predict the resulting saturation grain size or grain shape resulting from a SPD process. This problem, well-known in the classic hot forming community, may gain increasing importance for nanoscaled grain sizes, as properties of nanomaterials are thought to be sensitive to grain size and shape, boundary state or local chemistry.12–15) Accordingly, being able to predict the necessary process parameters to synthesize materials of desired grain size, boundary state and chemistry would allow to fabricate materials with targeted values. This ultimate goal requires an in depth understanding of the processes that occur during severe straining of metals or upon subsequent treatments. As grain refinement during SPD is not indefinite, also referred to as the saturation regime, many studies aimed to understand the processes limiting the refinement in order to develop strategies to overcome them. These studies provided a general understanding which process variables are of importance and how they change the saturation grain size. Different assumptions and models regarding the processes limiting grain refinement and explaining the occurrence of a saturation regime were proposed. Most of this early work is summarized in a comprehensive review, see Ref. 16). However, these models were not based on direct experimental observations. Progress in that direction has been obtained within the last years from in-situ observations during annealing and deformation of NC and ultra-fine grained (UFG) metals using electron microscopy techniques.17–21) These results unambiguously reveal the underlying processes and provide the basis towards a quantitative understanding, while still several questions remain to be solved to establish the framework for reliable modelling activities.
It is the aim of this work to briefly summarize findings from the past, to provide an update and to present the current understanding how saturation of grain refinement occurs during SPD in single phase materials. Earlier work and models will be critically reconsidered and the most important findings still valid will be summarized. It will be highlighted, that the processes causing saturation of grain refinement do not only take place during severe deformation but will generally occur whenever nanomaterials are deformed. They strongly impact on the mechanical response and properties of such fine scaled metals, highlighting the importance to thoroughly understand these processes. Finally, open questions and discrepancies between experiments will be deliberately highlighted to stimulate further research within this area.
When metals are deformed, only a small portion of the work spent is stored in form of lattice defects, mostly dislocations and vacancies, while the rest dissipates as heat.22) These defects are not stored randomly within the material, but rearrange themselves into typical dislocation patterns allowing them to screen their stress fields.22–25) These dislocation boundaries separate regions of high from those of low defect density, and different types of boundaries might be classified, for instance with respect to their evolution. They can be differentiated into incidental boundaries (IDBs) originating from stochastic trapping of individual dislocations and geometrically necessary ones (GNBs), which form deterministic to balance and accommodate local strain differences.26,27) However, these differences and the various notations used are ignored for simplicity throughout this work and we denote the various dislocation structures formed as dislocation cells or structures. For details the reader is referred to comprehensive earlier work.27,28) Because grain subdivision and fragmentation originates from dislocation slip, their storage and rearrangement, several factors will affect the necessary strain and thereby the velocity of grain fragmentation as well as the morphology of the cells. For instance, increasing deformation temperatures will facilitate the formation of dislocation cells and impurity atoms may promote storage of lattice defects. Moreover, the active slip systems differing for various crystal orientations influence the resulting dislocation pattern during plastic deformation. Depending on the crystal orientation with respect to the loading axis, distinctively different dislocation patterns form.29,30) Nevertheless, for metals deforming predominantly by dislocation slip, grain fragmentation will occur in a similar manner and the differences between individual metals can be expected to be negligible, compare for instance results on aluminum and nickel.31,32) Similar deformation structures as for aluminum and nickel evolved upon rolling of bcc iron, although a higher tendency for strain localization was observed.33) However, deformation mechanisms apart from dislocation slip will certainly affect grain fragmentation and cause a different structural evolution at low strains. Focusing mainly on low temperature deformation, the stacking fault energy can substantially affect the early stages of grain subdivision, as for low values mechanical twinning and planar slip are favored. Compared to fcc metals with medium to high stacking fault energies, the ones having low stacking fault energies such as austenitic steels or brass show significantly higher work hardening rates at comparable strains as twinning causes a significantly faster grain subdivision, see for instance.34,35) Additionally, these metals have a higher tendency to form macroscopic shear bands in which the intense strain accelerates grain refinement.22,34) Nevertheless, even for these materials sufficient straining, e.g. during high pressure torsion (HPT), results in continuous intersections of shear bands and twins and finally the formation of a homogenous grain structure, see Ref. 35) for details. This is similar to what is found for high stacking fault fcc and bcc metals.36,37) Thus, the stacking fault energy can provoke differences of grain fragmentation and strengthening at low strain levels, however does not affect the processes and minimum grain sizes achievable after severe strains.38–40) Comparably, while differences of the dislocation structures can exist between individual crystallites, they disappear with increasing strain, finally resulting as well in a homogenous nanostructure.41)
Independent of the material increasing strains cause alignment of the dislocation cells with respect to the strain field for instance along the rolling direction, along with a continuous decrease of their spacing and an increase of their average misorientation angle. For severe strains, the misorientation angles shift to values being larger than 15 degrees and up to 70–80% of the boundaries are of high angle type, being almost random in nature.36,41–45) Interestingly, it has been found that the misorientation distribution can be described with a single function, when scaled by its mean angle.46) This scaling behaviour is independent of the deformation mode or the applied strain27,47) and was found to be valid even for the finest grain sizes, i.e. sub-10 nm copper produced by friction.47) As the evolution of boundary misorientations can be explained and modelled based on dislocation processes48) and expected shear textures formed even in the nanoscaled copper samples,47) these results provide stunning evidence that dislocation based plasticity may prevail down to the real nanoscale. Along with the increase of the average misorientation angles with strain, the average spacing between boundaries decreases continuously but tends to stagnate and levels off reaching strains on the order of ε ∼ 10, compare Fig. 1. The necessary strains, however, depend on the deformation conditions as detailed later. At these strain levels, referred to as the steady state or saturation regime, the initial coarse grained structure is transferred into a homogenous nanostructure consisting predominantly of HAGBs. Stagnation of grain refinement has already been noticed during early observations on the structural evolution during SPD processing on various metals.36,43,49) For single phase materials grain sizes in the range of 50 to 500 nm can be synthesized. Apart from microstructural features like grain size or shape also other defect densities, texture or mechanical properties will not change any further upon additional straining. Therefore, the effect of deformation parameters on the saturation grain size was investigated to find strategies to overcome these limitations. Experiments showed that a reduction of the deformation temperature, decrease of material purity or alloying are the most important parameters to further reduce the saturation grain size, although the effect of temperature diminishes for low homologous temperatures, compare Fig. 5 and Refs. 16, 37, 39, 50–52). It should be noted, that certain alloying elements are more effective in reducing the saturation grain size than others.39,53) An extremely efficient way seems to be doping with interstitial elements. For instance, addition of just 1200 ppm carbon to high purity nickel significantly reduced the saturation grain size and almost doubled the strength level.53) While alloying can effectively reduce the stacking fault energy in certain cases, it is today accepted, that no correlation between the saturation grain size and the stacking fault energy exists,38–40) although as discussed before, differences at low strains may be present.
Microstructure of a nickel polycrystal (99.99%) deformed by HPT to different strains. Clearly, for strains larger than 10 the structural refinement saturates.
Nevertheless, twinning can substantially reduce the necessary strain to reach the saturation regime as it effectively fragments the initial grain structure.35) For these materials, the necessary strain to reach saturation can increase with temperature when twinning becomes less important, what is the opposite of the general observation of reduced strains to achieve saturation at elevated deformation temperatures.16) Apart from the pronounced effect of the deformation temperature and the purity level, at low temperatures the strain rate does not seem to affect the saturation grain size considerably.37) However, at elevated deformation temperatures strain rate was found to become more important, although still less pronounced compared to effects from deformation temperature or alloying.37) Further, the starting grain size does not affect the saturation structure. In contrast to the continuous refinement observed during deformation of specimens having micrometer sized grains, grain growth occurred during HPT of specimens with grain sizes being finer than the saturation limit.54–56) However, comparing samples with the same purity level, independent of the starting grain size, similar saturation grain sizes can be achieved.55)
In any case, when sufficient strains are applied, refinement stagnates at sizes depending on the variables discussed above. Despite that, the material can still be deformed further, while defect densities or boundary length remain constant. This requires that recovery or structural restoration processes need to become active which balance the refinement caused by the applied strain. Several processes allowing the microstructure to be in equilibrium with the refinement, and thereby explaining the phenomenon of structural saturation have been proposed.16,39,57–60) Besides, models aiming to describe grain fragmentation and the resulting saturation microstructures during severe deformation were established,61) but all of them without the knowledge of the actual processes occurring within the material. Meanwhile some of them, claiming a strong influence of the stacking fault energy on the saturation grain size,57,58) have become redundant as experiments clearly confirmed that the stacking fault energy cannot be correlated with the saturation grain size.38–40) Additionally, a change to deformation modes apart from dislocation based processes such as grain boundary sliding, suggested to cause saturation, was disproven from experiments.62) This seems reasonable, as the grain sizes that can be achieved by SPD of single phase metals are about an order of magnitude larger than those where signs of sliding were experimentally claimed.63) However, as the dependency of the saturation grain size on temperature and material purity as well as the existence of a steady state regime was found to be comparable to observations during dynamic recrystallization at high temperatures, the most widely accepted idea was that similar processes will also occur at lower deformation temperatures, albeit at reduced rates.16) Hence, the mobility of grain boundaries was suggested to be the essential parameter. Migration of boundaries could maintain the grain thickness on a constant average level, while grain subdivision was thought to arise from the formation of LAGBs in the larger, elongated grains. This fragmentation or subdivision is necessary to maintain the grain length.16) Based on these considerations, it is not surprising, that the presence of a second phase allows to refine microstructures to much smaller sizes than in case of alloyed single phase systems.64,65)
Nevertheless, the responsible processes were never directly observed and despite the knowledge of the phenomenon of saturation for almost two decades just several years ago they have been observed by direct experimental evidence.18,20) While confirming mechanically induced grain boundary migration acting as the main restoration mechanism, recent results contradict previous ideas and certain details may need to be reconsidered. The outcome of these experiments as well as further insights into boundary migration at low temperatures made in the last years will be summarized within the next chapters.
To identify the processes that allow for crystal restoration during large strain deformation, two experiments have been performed. Both used split specimens of severely cold rolled aluminum and copper, respectively.18,20) A region of interest was tracked upon further cold rolling of the UFG structures at ambient temperature. This allowed to deduce any changes of the underlying grain structure as a function of the applied strain. Unambiguously, the experiments demonstrated that in the submicron scaled structures triple junctions (TJs) and/or grain boundaries (GBs) tend to migrate during deformation and allow for local coarsening of the microstructure, necessary to maintain certain microstructural features, compare Fig. 2. Figure 2(a) shows, that in the copper samples certain grains shrink and eventually disappear during deformation such as the turquoise grain to the left or the two lamella at the top of the image. Shrinkage of certain grains allows the growing ones to compensate for the refinement caused by the applied strain. In addition to this local coarsening GBs frequently tend to form bulges which split or fragment adjacent grains. Such fragmentation events, which are eventually followed by further shrinkage of the fragmented parts are highlighted with arrows in Fig. 2(a). It should be noted that, although the same terminology is used, these grain fragmentation differs from the one during the initial stages of cold working described in the previous chapter. Comparable processes were identified during severe cold rolling of aluminum. Figure 2(b) shows the fragmentation of a lamella (yellow arrow) and local coarsening of the structure presumably initiated by the motion of the TJ indicated with the red arrow. TJs may be continuously produced by the observed fragmentation events (indicated with arrows) or formation of shear bands.20) It should be noted, that no particular crystallographic orientation was found to grow preferentially, however, the overall rolling texture was maintained.18) Additionally, growth of a particular grain at a certain stage does not imply that this grain will last to grow. Rather, the growth process seems to depend strongly on the local neighborhood and therefore, strain energy differences have been suggested to determine the direction of growth.18,66)
Results obtained on various specimens revealed that migration of grain boundaries and/or triple junctions acts as a general restoration mechanism causing fragmentation and disappearance of certain grains. Exemplary positions where such events occur are highlighted with an arrow. (a) Results from cold rolled UFG copper; (b) rolling of pure aluminum to severe strains, image taken from Ref. 20); (c) nickel (99.99%) subjected to HPT (ε = 136) and (d) coarse grained copper cold rolled to a comparably low logarithmic strain of φ = 2.4.
While these experiments were able to deduce the principle restoration mechanisms at large or severe strains, it was impossible to deduce what or if there is a predominant process, i.e. if boundaries or junctions contribute more to the overall microstructural restoration. For instance, after a fragmentation event caused by a bulging GB, further migration of the boundary would yield an identical picture than motion of the TJ generated by the bulge. Nevertheless, even arbitrary analyzed severely deformed microstructures contain similar features, as can be seen for instance on a nickel sample (99.99% purity) deformed by HPT at room temperature to saturation (Fig. 2(c)). This emphasizes that the results of the split specimens were really capturing the dominant restoration mechanisms. Additionally, these restoration processes seem to occur generally, independent of the deformation process and the material, compare Figs. 2(a)–(c). Interestingly, the same processes can be captured already at even smaller strains applied. As shown in Fig. 2(d), similar features as observed after severe strains can be found in recrystallized coarse grained copper, cold rolled to a comparably low strain of 2.4. Again, grain fragmentation due to migrated or bulged boundaries is clearly visible. Similar findings at relatively low strain levels were also made upon rolling of aluminum in the mentioned study, evidencing also the role of junctions at low strain levels.20) This is in line with earlier findings, suggesting that during rolling already for strains larger than one a net removal of boundaries occurs.67) We can therefore conclude that structural restoration starts already at relatively low strains and is not occurring solely in the saturation regime. This consequently affects structural evolution and strengthening rates, and their reduction with strain is a direct consequence of the continuous boundary removal.20)
Accordingly, in the saturation regime, nucleation of new grains or grain fragmentation by the formation of LAGBs16) and a continuous increase of their misorientation as proposed earlier does not necessarily have to take place. This can be ruled out by analyzing the results from the split specimens. These datasets show that the LAGBs, frequently found in the larger grains, do not necessarily induce grain fragmentation, see Fig. 3(a). No continuous increase of their misorientation angle with strain could be measured. As can be seen from the investigated nickel sample (99.99% purity) processed by HPT to saturation and deformed further by an increment of ε = 0.30 (Fig. 3(a)), no clear trend can be identified. While for some LAGBs the misorientation angle increased with strain, it remained constant for others or even decreased. This is in line with recent in-situ experiments on UFG copper samples subjected to low cycle fatigue bending. In this study it was found that the misorientation angle of a LAGB will only change if the surrounding grain structure changes, for instance if adjacent grains shrink or disappear.19) Taken as a whole, it seems that the LAGBs are stored within the grains for geometric reasons. They realize a certain misorientation gradient along the grain, presumably required to account for the varying constraints of their neighborhood.
(a) Microstructural evolution of pure nickel samples subjected to HPT at ambient temperature (ε ∼ 100) during an additional strain increment of Δε = 0.30. Grain fragmentation events typically observed are circled. Misorientation angles of selected LAGBs are indicated before and after the applied additional strain increment. (b) Recovery annealing of the same nickel sample leaves the LAGBs unchanged, confirming their geometrically necessary character. Please note the different scale bars.
To prove if the LAGBs can be considered as geometrically necessary boundaries, the mentioned HPT deformed nickel samples (Fig. 3(a)) were annealed below their recrystallization temperature (Fig. 3(b)), i.e. at the maximum temperature possible where just defect recovery occurs. Recovery removes redundant dislocations, while geometrically necessary ones will remain until recrystallization appears, as otherwise mechanical work would be required.22) To do so, the nickel samples were annealed at a temperature of 413 K for 30 minutes. At this temperature, the UFG structure already shows a noticeable reduction in hardness due to defect annihilation.45) However, as can be seen from Fig. 3(b) the LAGB structure remained unchanged. This suggests, that the LAGBs that remain or build up in submicron sized grains should be treated as predominantly geometrically necessary boundaries but they are not responsible for inducing grain fragmentation.
To summarize, migration of GBs and/or TJs causes local collapse and fragmentation of lamellae, establishing in the saturation regime a dynamic equilibrium between refinement and coarsening. These processes mainly limit the minimum grain dimensions, i.e. the dimensions along the axial direction for a HPT disk or along the normal direction in case of rolling, compare schematics in Fig. 4. The length of the grains is continuously reduced by the formation of bulges along the grain boundary (Fig. 4(b)), while the LAGBs in the grain interior does not seem to play a crucial role in these fragmentation events. Apart from this proposed grain fragmentation mechanism, strain localization within shear bands could also fragment the grain structure and possibly cause stagnation of grain refinement, as most of the strain applied is then confined within narrow zones of the sample. Such behavior was for instance observed during cryorolling of aluminum.51) However, as the focus of the manuscript is put on cases where homogenous deformation is present, the effect of strain localization is not considered in detail.
Schematics showing the principle restoration processes at the grain scale. (a) Migration of TJs causes shrinkage and eventual collapse of individual lamellae. (b) In addition to a mechanically induced motion of boundaries (not shown), bulges (macrosteps) can form at the boundary, fragmenting neighboring grains.
It should be noted, that (local) grain growth during deformation is not a phenomenon specifically occurring during large strain deformation such as SPD processing. Grain boundary migration and coarsening were also observed during deformation of various deposited nanocrystalline as well as SPD processed materials under different loading conditions, down to cryogenic temperatures, see for example Refs. 68–76). Even a conventional hardness indent can be sufficient to disrupt the nanograin structure.68,69) From the numerous studies it is evident, that especially during cyclic loading mechanically induced grain growth seems to occur preferentially compared to monotonic loading situations.73,75,77) This might be explained by the absence of a net shape change or refinement of the grains in case of cyclic loading. The occurrence of grain growth during mechanical testing strongly affects the resulting properties. For instance, growth during tensile straining resulted in improved ductility but reduced strength levels of nanocrystalline aluminum films.78) Grain growth observed upon cyclic loading caused in most cases beside a reduction of the cyclic stresses formation of shear or localization bands which drastically deteriorate the fatigue life.73,75) As not only the resulting grain structure after SPD processing, but also the mechanical response of nanostructures is affected by the boundary mobility, it is of importance to understand boundary migration at low temperatures and its influencing parameters as well as the driving forces in full detail.
3.2 Effect of deformation temperature on the saturation microstructureDealing with migration of TJs or GBs an important parameter is usually the temperature. However, as in most of the studies, migration or grain coarsening was observed at ambient or even cryogenic temperatures, diffusion based processes may not play an important role. Thus, the migration is generally termed mechanically induced, although the effect of temperature often remains uncertain. Earlier studies on bcc iron clearly showed that already above ambient temperature a pronounced thermal dependency of the saturation grain size exists.37) Similarly, a lower rate of mechanically induced grain growth was found for a reduction of testing temperatures, although the experiments were already performed at low homologous values.74,79) For any prediction regarding the migration rate it is thus of interest to understand if a pure mechanically driven regime exists at all, or if thermal effects also need to be considered at comparably low testing temperatures, though their contribution may be limited.
To shed light on this question, experiments were performed on two pure model materials, fcc nickel and bcc tantalum, respectively.52) Both materials were subjected to HPT at temperatures ranging from 77 K to 873 K for a sufficient number of rotations (ε ∼ 136) to ensure a saturation microstructure. Microstructural modifications of the samples could be excluded to occur while rising the temperature from cryogenic to ambient ones.52) Thus, measuring the grain dimensions allows conclusions about the necessary average boundary velocities at given temperature. Analysis of hardness and the minimum grain dimensions revealed constant values, if the deformation temperature was reduced below 0.1 Tm for nickel and 0.05 Tm for tantalum, respectively. This indicates the existence of a pure mechanically driven regime, see Fig. 5(a). For higher deformation temperatures already a clear thermal dependency of the grain thickness was measured, which became increasingly pronounced for nickel above ∼0.25 Tm, in line with earlier observations.37) The increase of grain thickness with increasing deformation temperature is not surprising, as migration of boundaries or junctions becomes facilitated, resulting in an increase of the restoration rate and so larger saturation grain sizes.
One may expect that along with the increased boundary migration rates, also the probability for grain fragmentation becomes enhanced. However, the microstructural analysis revealed that not only the dimensions of the short (minor) grain axis tends to increase with temperature, but the ones of the long (major) grain axis do as well, Fig. 5(b). This is in line with an earlier study on tantalum having slightly lower purity (99.95%).80) Interestingly, up to a certain deformation temperature the dimensions of the major grain axis increased more pronounced than the ones of the minor grain axis, compare Fig. 6. While the major grain axis increased by almost a factor of four increasing the deformation temperature to 673 K, the minor axis became only twice as large.80) Accordingly, the aspect ratio strongly increased with deformation temperature, reaching almost values of ten for deformation temperatures of 673 K. This is in contrast to the common observations that an increase of the deformation temperature causes a reduction of the aspect ratio.25,37,50,81) Only for temperatures being larger than 673 K, the aspect ratio of the tantalum samples reduced again. While the increase of the minor grain axis with temperature can be expected, the even faster increasing elongation of the grains comes as a surprise, as the enhanced migration rates should also promote the formation of more equiaxed structures at higher deformation temperatures.
(a) Microhardness and grain thickness (minor axis, area weighted) of tantalum (99.999%) and nickel (99.99%) deformed by HPT to saturation. For sufficiently low temperatures both quantities become thermally independent, indicating a pure mechanically dominated restoration regime. (b) Evolution of the major and minor grain axis as a function of the homologous deformation temperature. Data is taken from Ref. 52).
(a) Evolution of the long (major) and short (minor) grain axis as well as the aspect ratio (area weighted values) of tantalum (99.95%) severely deformed by HPT as a function of the deformation temperature. (b) Representative colour inverse pole figure maps at selected deformation temperatures. The dimensions of the major axis increase faster with temperature than those of the minor grain axis, causing increased aspect ratios with temperature. Displayed data is taken from Ref. 80). Please note that the scale bars of the detailed images differ slightly.
Nevertheless, the results obtained on nickel and tantalum suggest a different, but general trend that might have not been observed earlier due to the limited deformation temperature windows investigated. Although the deformation temperature range was rather wide, this unexpected results cannot be explained by a change in the dominant deformation mechanism. Microtexture analysis revealed the expected shear textures, indicating that for all deformation temperatures dislocation based plasticity prevails.45,80) Only the spread around the ideal texture components slightly increased with temperature. Further, no signs of strain localization or shear band formation, possibly explaining the reduced grain elongations at lower deformation temperatures, were found. Representative microstructures displayed in Fig. 6(b) also show similar features of grain fragmentation as discussed in the previous chapter. However, the probability for grain fragmentation as highlighted with arrows decreases with an increase in deformation temperature, and the boundaries remain comparably straight, compare Fig. 6(b).
Interestingly, the deformation temperatures leading to the largest aspect ratio were close to the ones, where upon static annealing of the severely deformed structures first signs of structural coarsening occurred.45,80) Structural coarsening of severely deformed metals initiates by thermally induced motion of TJs above a certain temperature.17) The driving force for their movement is caused by a line tension on the triple lines, because the dihedral angles of the joining grains may be far from the equilibrium value after deformation, i.e. 120 degrees assuming constant boundary energies for HAGBs.82) As a consequence, individual lamella collapse and allow adjacent ones to increase their thickness along with a reduction of the aspect ratio. This coarsening and spheroidization process by triple junction motion can thus be considered to link recovery and recrystallization.83) Due to the good agreement between the onset temperatures of structural coarsening and those where maximum aspect ratios were measured during deformation, it is reasonable to conclude that similar to the static annealing case also during deformation above a certain temperature triple junctions become mobile.80) Their motion effectively reduces the aspect ratio again at higher deformation temperatures, as the thickness of the grains can increase distinctively faster. For low deformation temperatures thermal assistance becomes more and more negligible, clearly reflected in the weak temperature dependency of the minimum grain dimensions, Fig. 5. However, the reduced grain boundary mobility seems contradictory to the reduced aspect ratio at low deformation temperatures. Reconsidering the determined structural restoration mechanisms, faster migration of the junctions or enhanced grain fragmentation rates would be required to effectively reduce the length of the grains at lower deformation temperatures. In principle, a shift from thermally towards a mechanically induced motion of junctions could occur, although more frequent motion at reduced temperatures does not seem plausible. Junctions have been observed to become easily pinned on LAGBs or dislocation arrangements within the grains.17) The fraction of such pinning points will obviously increase for lower deformation temperatures, contradictory to the need of a higher mobility at low processing temperatures. It thus seems more likely that the observed decrease of the aspect ratio at low temperatures is a consequence of grain fragmentation events occurring more frequently. Indeed, considering the mesoscopic processes of mechanically induced boundary migration can perfectly explain the observations as will be discussed in the following.
3.3 Mechanically induced boundary migration at the mesoscaleSo far we only considered the restoration processes, migration of GBs and TJs, that occur during severe plastic deformation on the grain scale. Early work on bicrystals emphasized to understand also the mechanisms on the mesoscale by showing that comparable to LAGBs, even HAGBs can move due to an applied stress field, by a coupling of dislocations building the boundary with the applied load (e.g. Refs. 84, 85)). The bicrystal experiments revealed that the boundary velocity was proportional to the shear stresses applied.84,85) Similar to LAGBs migration of HAGBs is thought to arise from the movement of the defects that build the boundary, suggesting that they can realize a shear strain upon their migration. Apart from the bicrystals, this has been confirmed by UFG aluminum samples in an in-situ TEM study.86) The ratio between the migration distance of the boundary and the thereby realized shear displacement is called the coupling factor.87) Meanwhile more general models to account for the coupled migration have been developed,88,89) revealing that migration of general boundaries involves glide motion of disconnections, a grain boundary step associated with a dislocation.88,89) Indeed, during in-situ straining of UFG aluminium samples, motion of disconnections along the grain boundaries could be observed.90,91) Disconnections were shown to move along the grain boundary, thereby allowing for growth of the grain by their step height. Homogenous nucleation of a disconnection along a grain boundary would require reasonably high stresses and was found in MD simulations to be the rate limiting step for boundary migration.90) However, the energetically costly case of homogenous nucleation may not be necessary in real polycrystals. Nucleation may occur nearby junctions92) or especially in severely deformed metals already numerous disconnections may be present within the boundary. In addition, plastic deformation by dislocation slip can serve as a further source for disconnections. They can be continuously generated by the interaction of lattice dislocations with grain boundaries and their stress, strain or thermally induced decomposition within the boundary.91,93–95) Homogenous nucleation of a disconnection along a grain boundary may thus be considered as a rare case for severely deformed metals and only a sufficient stress field is necessary to provoke their motion. However, generally their burgers vector may not lie within the boundary plane, i.e. it contains a climb component. In this case the mobility of the boundary step will be limited and a flux of vacancies is necessary to allow for migration over larger distances. Sessile disconnections or those having a low mobility will act as strong obstacles for faster ones and eventually provoke pile ups.91) Such pile ups explain the formation of huge macrosteps, build up from individual steps, as observed during in-situ straining of UFG aluminium.21) These macrosteps observed, appear similar and comparable in size to the bulges, frequently observed to induce grain fragmentation in the SPD deformed structures (e.g. Fig. 6(b)).
It is therefore not surprising that at elevated temperatures, where the mobility of individual disconnections is high, macro steps less likely form. This will obviously lead to a reduced probability for grain fragmentation and so an increasing grain length or aspect ratio during deformation, as observed (Fig. 6(a)). This enhanced step mobility will also allow the boundary to migrate over larger distances, reflected in the continuous increase of the grain thickness and its enhanced thermal dependency, compare Fig. 6(a). The strain rate dependency of the resulting saturation microstructure can be rationalized identical. As long as thermal contributions are not sufficient to promote disconnection climb, formation of macro steps and subdivision of grains will be facilitated. Their mobility and migration distance is then determined by the coupling with the applied load and neither a time nor a temperature dependency is to be expected. For elevated temperatures, where climb of steps becomes possible, an increasing time dependency can be assumed and is also observed experimentally.37)
From the discussion above we can conclude, that the microstructure resulting from severe plastic deformation at low homologous temperatures is mainly governed by the mechanically induced motion of boundaries. The mobility of the individual grain boundary steps does not only determine the grain boundary migration rate and so the resulting grain thickness (minor length), it also governs the formation of macrosteps, causing at low temperatures subsequent grain fragmentation, thus limiting the grain length. When deformation temperatures become sufficiently high, thermally induced motion of triple junctions reduces the grain aspect ratio. The maximum grain elongation for a material will therefore be observed just below temperatures where frequent TJ motion proceeds, see schematics in Fig. 7. As this rationale is not limited to a specific material, the structural evolution with increasing grain aspects at elevated processing temperatures as observed for tantalum and nickel,45,80) should be a general one.
Schematics showing the general trends of the saturation microstructure as a function of the deformation temperature. The responsible processes determining grain size and shape are indicated in the inset images.
Indeed, investigations on several other materials, HPT deformed at varying temperatures support this conclusion, see Fig. 8(a). Irrespective of the material, the grain aspect ratio peaks at slightly elevated temperatures, being in the range of 0.15–0.25 Tm for the metals investigated. Despite this general trend, the absolute values of the aspect ratio that can be obtained differ remarkably between the samples. Interestingly, from all materials investigated, the trend is most pronounced for the tantalum samples (99.95% purity). As also another bcc metal (ARMCO iron) and another high melting point material (Pt10Ru) were investigated, these peculiarities cannot serve as an explanation for the enhanced aspect ratios in case of tantalum. In fact, for all fcc metals investigated aspect ratios of only four at maximum could be measured, similar to those of iron.
(a) Aspect ratio of various metals deformed by HPT to saturation (ε > 100) at different temperatures. For comparison data obtained on tantalum upon rolling is included. All microstructures were analyzed in radial (HPT) or transverse (CR) direction. (b) Hardness of the materials as a function of the annealing temperature showing good agreement of the temperatures causing maximum aspect ratios and the first onset of structural coarsening, reflected in a decrease of hardness. The trend lines are just guides for the eye.
Although it is yet not definitely clear what causes these differences, a possible reason for it could be the varying grain boundary free volume between the materials. It is well established that for pure metals the grain boundary free volume scales with the energy of the boundary itself.96,97) Although for a certain material the boundary energies will vary from boundary to boundary, the average values for HAGBs are strongly material dependent. Especially for the refractory metals such as tantalum or tungsten rather large boundary energies of about 3 J/m2 and so enhanced grain boundary free volumes can be expected.97,98) These values are notably larger compared to iron or the fcc metals98) and would be in line with the measurements, compare Fig. 8(a). Presumably, this enhanced free volume can facilitate the movement of the disconnections. Nevertheless, this hypothesis, despite being sound and fitting the experiments, needs to be proven. Especially, as a large MD data set on nickel has not revealed any correlation between the mobility and the boundary energy or free volume, respectively.99) Similar to the observations on tantalum and nickel also for the other materials, there is reasonable agreement between the temperatures inducing structural coarsening upon static annealing and those leading to maximum aspect ratios during annealing, compare Fig. 8(b). This supports the general picture how microstructural restoration proceeds at different temperatures drawn above (Fig. 7).
Although the observed trends of the resulting microstructure and the aspect ratio were obtained solely on HPT deformed samples, it should be emphasized that the observations and explanations are not restricted to this deformation process, but are general ones. For comparison the UFG tantalum samples processed by HPT were additionally rolled at two different temperatures until again a saturation state of the microstructure was achieved (εCR ∼ 2). Clearly, the same trends as for the HPT samples are visible, although shifted to even larger values of grain aspect ratio, see Fig. 8(a). While the same restoration processes are active during rolling (Fig. 2), the deformation path can have a substantial effect on the resulting microstructure. However, the increased grain aspect ratio of the rolled tantalum samples compared to the HPT deformed ones is mainly a result of the enlarged grain length of the rolled specimens, while the grain thickness is almost identical for a given deformation temperature. Heavily rolled (873 K) tungsten sheets provide identical microstructures with enormous grain elongations.100) Interestingly, such microstructures may be one of the keys to combine high strength with exceptional damage tolerance, but also possess highly anisotropic mechanical properties.101–103) For this reason, it is of interest to understand apart from the temperature effect how the resulting grain elongation can be further adjusted. Besides temperature, alloying or doping with impurity elements may have a substantial effect on the resulting microstructure. Because the motion of TJs above some temperature seems to restrict the aspect ratio, doping or alloying could be possible ways to pin the junction movement up to even higher temperatures. However, the mobility of the disconnections may also slow down due to the presence of doping or alloying elements, promoting grain fragmentation.
To understand the effect of alloying elements on the resulting saturation microstructure, we compare the pure nickel and tantalum samples with a commercial tantalum alloy (Ta2.5W) and a nickel alloy (Ni4.5Al), both contents given in wt-%. The results of this investigation are summarized in Fig. 9. As expected, the microstructural evolution of the alloys follows a similar trend with deformation temperature as observed for their pure counterparts. However, for both alloys, the absolute values of grain elongation decreased compared to the pure reference samples. In addition, the temperature where the maximum aspect ratio can be measured, is shifted to higher temperatures for the Ni4.5Al alloy compared to the pure nickel samples. It thus seems, that the substitutional alloying elements may facilitate grain fragmentation events, as a consequence of the reduced mobility within the boundary. This would explain the reduced minor and major grain dimensions of the alloyed samples, exemplarily shown for the nickel specimens in Fig. 9(b). Nevertheless, the trend to form more equiaxed structures in the case of alloying cannot be considered conclusive so far. Detailed studies are required, as different impurity atoms or alloying elements may cause divergent trends to appear.
(a) Effect of substitutional alloying elements on the aspect ratio as a function of the homologous deformation temperature. (b) Effect of alloying on structural dimensions of HPT deformed nickel as a function of the homologous deformation temperature. Trend lines are just a guide for the eye.
Especially interstitial atoms may behave in a different way due to their enhanced mobility already at lower temperatures. These differences become obvious when comparing microstructural parameters of various tantalum samples (high and commercial purity as well as Ta2.5W) deformed by HPT to saturation at various temperatures, see Fig. 10. While at sufficiently low deformation temperatures almost no difference between the microstructures exist, for deformation above 0.15 Tm the purity level strongly affects the resulting saturation structure. Clearly, the minor grain dimensions increased most pronounced with temperature for the tantalum samples with the highest purity level. While this behavior is expected, the major grain dimensions evolved differently. For the high purity tantalum samples, identical to the nickel specimens (Fig. 9(b)), the major grain dimensions increased continuously (Fig. 9(b)). In contrast, the major grain dimensions of the tantalum alloy and the commercial purity samples (Ta 99.95%) increased only up to deformation temperatures of 673 K, but dropped and seem to level off for deformation temperatures above, see Fig. 10. This suggests that above 673 K impurity atoms reduce the boundary step mobility and promote grain fragmentation by macrostep formation. Both of these specimens were delivered from Plansee and in case of the commercial purity tantalum, chemical analysis found oxygen to be the main impurity element. Although no detailed chemical analysis of the boundaries was performed yet it seems clear that other elements than interstitials cannot cause the observed effects, as they occur at 0.2–0.25 Tm, i.e. at temperatures, where the mobility of substitutional elements can be considered to be negligible. Further studies on the effect of alloying elements on the structural evolution are therefore necessary, to provide a conclusive statement. Especially the effect of interstitial elements needs to be investigated in detail, which have apart from their possible effect in tantalum also enormous effects in nickel.53)
Microstructural evolution of tantalum samples having different purity levels and a Ta2.5W alloy HPT deformed at different temperatures.
As discussed before, coupled motion of disconnections plays a major role for low temperature motion of grain boundaries. Therefore, the absence of correlations between parameters such as misorientation angle or crystallographic orientation and the coarsened grains in most studies may not be surprising. The coupling with applied stress fields and the clear correlation of the boundary velocity with the applied shear stress as found in bicrystal experiments, led to the conclusion that grain boundary migration is facilitated in nanomaterials due to their enhanced stress levels. Carefully designed straining experiments on NC films point out into the same direction, showing pronounced grain growth in regions of high shear stresses.72) However, several studies clearly show, that coarsening is amplified in regions where plastic strains are enlarged. For instance, grain coarsening was observed ahead of a crack in a nanocrystalline aluminum film.71) The grain size in the vicinity of the crack tip scaled linearly with the crack opening, which scales with the strain. As the equivalent stress cannot exceed the yield stress, grain growth seems to be promoted by the applied strain rather than the stress. Further, a study focusing on grain coarsening during tensile straining of nanogradient copper revealed the largest grain sizes in the necking region, close to the fracture surface, i.e. the highly strained regions. Similar results were obtained when analyzing grain coarsening during cyclic loading of nanostructured samples. To avoid fracture of the sample and to allow investigations of the microstructural evolution up to infinite number of cycles, the cyclic loading was realized directly in a HPT device.75) After transferring the initially coarse grained nickel structure into a UFG one, the monotonic torsional straining was stopped and the sample was twisted by an angle of five degrees forth and backwards. Already after 50 cycles, cyclic strain localized in a wedge shaped shear band that formed due to the local coarsening of the UFG structure, see Fig. 11. Within this shear band the grain size (HAGBs) increased already after 50 cycles by almost a factor of five, while outside this region grain coarsening was negligible.75) In line with the observed coarsening, hardness values measured within the shear band were already reduced by about 20% after 50 cycles compared to the ones after monotonic HPT. As a consequence, the applied shear stresses during cyclic loading are reduced compared to the initial material but also compared to the regions outside the shear band while the plastic strain is concentrated there. Again, on first view these results suggest, that not the applied stress but rather the plastic strain promotes migration of the boundaries in such fine grained specimens. However, on a closer look the mentioned results may not be contradictory at all.
Results on UFG nickel subjected to cyclic HPT (5 deg twist angle) for 50 cycles. Grain coarsening caused strain localization within a wedge shaped band while outside the band pronounced grain coarsening was absent. Inside the coarsened region significantly lower hardness values were measured. Data is taken from Ref. 75).
Obviously, all experiments were conducted under slightly different conditions. For instance, the bicrystal experiments were conducted at shear stresses lower than the critical resolved ones.84) Thus in these experiments no or at least only a negligible amount of lattice dislocations will be involved. Under such conditions, only preexisting boundary steps can migrate due to the coupling with the applied stress field or they have to be nucleated. On the other hand, in the experiments emphasizing the role of strain, the samples were plastically deformed, what involves at least for these grain sizes still slip of lattice dislocations. These dislocations need to be accommodated at the boundaries and can cause the formation of disconnections, as experimentally observed.91) The incoming flux of dislocations eventually generates sufficient numbers of disconnections which only have to move under the applied load, while in just slightly strained regions fewer disconnections are present. This idea is supported further by the cyclic HPT experiments presented above.75) While after monotonic HPT the sample comprises the typical shear texture, different crystallographic orientations were preferentially found in the coarsened grains within the shear bands after cyclic HPT, see Fig. 12. These orientations can realize the cyclic shear with a single or at least two coplanar slip systems, in contrast to the orientations outside the shear band, necessitating the activation of non-coplanar slip systems.75,104) The activation of a single or two coplanar slip systems can be considered to facilitate dislocation-boundary interactions and so its movement, while non-coplanar systems may easily cause interactions between dislocations resulting in reduced disconnection formation rates at the boundary.75)
Inverse Pole Figures (IPF) of the initial UFG microstructure (a) and the ones outside (b) and inside the shear band (c) that developed during cyclic HPT (same parameters as in Fig. 11). Clearly, the preferred crystallographic orientations differ between these regions. Data taken from Ref. 75).
Heavy plastic deformation of coarse grained single phase metals and alloys results in the formation of dislocation cells and cell blocks, which are finally transformed into a UFG or NC grain structure. This grain refinement saturates for strains between 10 and 30, hence a dynamic equilibrium between the generated deformation induced defects (vacancies, dislocations and boundaries) and restoration mechanisms is required. The present work aimed to summarize our current understanding of these restoration processes that limit grain refinement, focusing especially on low homologous processing temperatures. Based on experimental evidence migration of junctions and boundaries have been identified to determine the resulting microstructure, with the role of junctions becoming important at higher temperatures. Their velocity determines the amount of restoration, which balances in the saturation regime on average the applied refinement and determines the resulting grain size and shape. Grains tend to increasingly elongate with rising deformation temperature, especially in intermediate temperature regimes. This finding is a direct consequence of the enhanced mobility of disconnections within the boundary. The motion of these boundary steps due to their coupling with mechanical stresses can be considered as the elementary process for boundary migration at low homologous temperatures. Although they are moving due to the applied load, their multiplied generation in highly strained regions seem to accelerate grain growth.
Despite this improvement of our knowledge and identification of basic processes, predictions or modelling of resulting grain structures after SPD processing still remains challenging. While temperature or strain rate effects can be rationalized, our current understanding about the role of impurity or alloying elements, even if present in traces, is extremely limited. To our opinion it is thus of extreme importance to focus on the role of impurity and alloying elements and understand how they affect grain boundary and triple junction mobility at comparably low homologous temperatures (<0.35 Tm). In addition, the reason for the microstructural differences occurring between various elements despite being processed at the same homologous temperature need to be rationalized. This will not only allow to predict resulting microstructures after SPD processing. As it has been shown that boundary migration can generally occur upon mechanical loading of fine scaled structures, this knowledge is also of importance to predict and tune mechanical properties of nanostructured materials.
Financial support by the European Research Council under ERC Grant Agreement No. 340185 USMS and the Austrian Science Fund (FWF) within project number P24429-N20 is gratefully acknowledged.
