2019 Volume 60 Issue 7 Pages 1230-1242
Processing of metallic materials by Severe Plastic Deformation (SPD) leads to the formation of many lattice defects (e.g., vacancies, dislocations, twin faults and grain boundaries). In this paper, the characteristic features of the defect structure in SPD-processed bulk metallic materials are overviewed. The influence of the material properties, such as the melting point, stacking fault energy and solute content, as well as the SPD-processing conditions (e.g., SPD route and applied hydrostatic pressure) on the type and densities of defects is discussed in detail. In addition, the effect of lattice defects on the mechanical strength of SPD-processed materials is oveviewed.
Fig. 2 The maximum dislocation density as a function of the melting point (Tm) and SFE for pure fcc metals processed by ECAP at RT. The solid and dashed arrows indicate that the higher the melting point and the lower the SFE, respectively, the larger the saturation dislocation density.
Severe Plastic Deformation (SPD) techniques are often applied to achieve high strength in bulk metallic materials.1,2) The most frequently used SPD methods are equal channel angular pressing (ECAP),3) high pressure torsion (HPT),4) multidirectional forging (MDF),5) twist extrusion (TE)6) and accumulative roll bonding (ARB).1) The elevated yield strength obtained after SPD-processing can be attributed mainly to the high density of lattice defects such as dislocations, twin faults and grain boundaries.7) Therefore, the study of the evolution of defect structure during SPD is necessary for the understanding of the mechanical performace of ultrafine-grained (UFG) materials.
In the last two decades, numerous experiments and model calculations were carried out for the determination of the type and amount of lattice defects in SPD-processed metals and alloys.8,9) The evolution of vacancy concentration, density and character of dislocations, and misorientation distribution of grain boundaries was investigated as a function of imposed strain using different methods of SPD.7) In addition, the effect of fundamental properties of materials, such as melting point, stacking fault energy and purity level, on lattice defect structure was also studied in the literature.10–13) These investigations contributed to a deeper understanding of the correlation between the processing conditions, lattice defect structure and mechanical performance of SPD-processed metals and alloys. This knowledge enables to achieve the desired mechanical and functional properties of bulk UFG materials by tailoring the defect structure with an appropriate selection of SPD conditions. This process can be referred to as “defect structure engineering”.
In this paper, the defect structure in SPD-processed bulk materials is overviewed. The effects of the processing conditions and the properties of materials on the type and density of lattice defects are summarized. Separate sections are devoted to vacancies, dislocations, twin faults and grain boundaries formed during SPD. In addition, the correlation between the lattice defect structure and the mechanical strength of SPD-processed metals and alloys is discussed.
SPD-processing of metallic materials usually produces a high concentration of excess vacancies. Excess vacancies are formed by non-conservative motion (e.g., climb) of dislocations during plastic deformation. In addition, the vacancies formed during SPD tend to form clusters as the energy of these vacancy agglomerates is lower than the sum of the energies of the constituent individual vacancies.14) The vacancy concentration and the cluster size in SPD-processed materials were studied by different methods such as (i) electrical resistivity (ER) measurements, (ii) positron annihilation spectroscopy (PAS) and (iii) differential scanning calorimetry (DSC). The most serious challenge in the application of these methods is the separation of the contributions of vacancies and other lattice defects such as dislocations and grain boundaries. This separation is often carried out by the measurement of the density of other defects using independent methods, such as the determination of the dislocation density by X-ray line profile analysis (XLPA).15) Nevertheless, all experimental methods showed that SPD-processing at RT yielded a very high excess vacancy concentration with the value of 10−4–10−3.16–21) This value is 17–18 orders of magnitude higher than the equilibrium vacancy concentration at RT. In thermal equilibrium, similar high vacancy concentration can only be obtained at temperatures close to the melting point.
Experiments on face-centered cubic (fcc) metals, such as Cu and Ni, revealed that the vacancy concentration increased monotonously with increasing the strain applied during SPD.17,20) The maximum vacancy contentration obtained in Cu processed by ECAP at RT was ∼4 × 10−4.16) Smaller vacancy concentrations between 10−5–10−4 were determined in Ag and Cu–0.18% Zr alloy samples after 4–8 passes of ECAP at RT.19,21) HPT processing on Cu and Ni resulted in a much higher vacancy concentration of 1–2 × 10−3 than that obtained for the ECAP-processed counterparts.17,20) The larger amount of vacancies observed for HPT-processing can be explained by the very high hydrostatic pressure in the sample which hinders the migration of vacancies to sinks.
PAS experiments revealed that more than 90% of vacancies are clustered in SPD-processed fcc metals.17) These vacancy agglomerates contain 4–9 vacancies in HPT-processed Cu.20) For Al deformed by HPT at RT, the average number of vacancies in the agglomerates reached 40.22) At the periphery of the HPT disk, the vacancy concentration and the cluster size were usually larger than in the center. In fcc materials, the three-dimensional vacancy agglomerates may collapse into two-dimensional clusters on close-packed {111} planes which are bounded by small Frank-type dislocation loops with the Burgers vector 1/3⟨111⟩. These dislocation loops are sessile and contribute to hardening of SPD-processed metallic materials. With decreasing the stacking fault energy (SFE) the formation of these two-dimensional vacancy agglomerates on {111} planes is energetically more favorable. For instance in Ag with very low SFE (∼16 mJ/m2), four passes of ECAP at RT resulted in the formation of many Frank-loops with the diameters between 3 and 14 nm and a volume density of ∼2 × 1022 m−3.21) In general, in SPD-processed Cu and Ag samples single vacancies were not detected while in Ni with high SFE single/double vacancies have a fraction of 10% in the total vacancy concentration.17)
Similar high vacancy concentration and cluster size were observed in body-centered cubic (bcc) and hexagonal close-packed (hcp) metals and alloys processed by SPD.23–28) For instance, after 1/4 turn of HPT in an interstitial-free steel the vacancy clusters comprise of 9 vacancies which value was enhanced to 14 when the number of turns increased to five.24) Similar result was obtained for pure Fe and W.25,27) In 316L steel, the vacancy concentration increased to about 5 × 10−4 after 10 turns of HPT.26) In Ti–6Al–7Nb alloy processed by 1/4 turn of HPT, the average number of vacancies in the clusters was four and the vacancy concentration was estimated as 3 × 10−5.28) This material comprised an hcp α-titanium alloy and a bcc β-phase. The concentration and cluster size of vacancies in SPD-processed materials are summarized in Table 1. It should be noted that the vacancy concentration in SPD-processed materials is often higher than the upper detection limit of PAS (∼5 × 10−5), therefore in these cases only the cluster size was determined by this method. Vacancy concentrations higher than this limit were determined by DSC or the combination of PAS and other methods.
Characterization of dislocation structure in SPD-processed materials can be carried out with good statistics using indirect methods such as PAS and XLPA. Detailed description of these techniques can be found in Refs. 15, 22. Generally, the dislocation density increases with increasing strain imposed during SPD.7) As an example, Fig. 1 shows the evolution of the dislocation density for Cu and AM60 Mg alloy processed by ECAP at RT and 220°C, respectively.29,30) Saturation of the dislocation density was achieved even after 2–3 passes of ECAP which corresponds to an equivalent strain of about 2–3. For Cu, this maximum dislocation density value (∼21 × 1014 m−2) remained practically unchanged up to 10 passes, then after 15 ECAP passes the dislocation desity decreased to ∼15 × 1014 m−2, corresponding to a reduction of 30%. Further change in the dislocation density was not observed up to 25 passes of ECAP. The decrease of the dislocation density between 10 and 15 passes can be attributed to the relaxation of the microstructure at high strains. Namely, a dynamic recovery of the dislocation structure might occur which included the rearrangement and annihilation of dislocations.29)
The evolution of the dislocation density as a function of the number of passes for Cu processed by ECAP at RT as well as AM60 Mg alloy processed by ECAP and MDF at 220°C.
For AM60 Mg alloy processed by ECAP at 220°C, the maximum dislocation density was much smaller while the decrease of the density of dislocations occurred at lower number of passes (after 2 passes) than in the case of Cu (see Fig. 1). This can be explained by the much higher homologous temperature of ECAP for AM60 alloy (0.53) as compared to Cu (0.22). The higher homologous temperature facilitates recovery and recrystallization during SPD. Indeed, former studies31,32) have shown that dynamic recrystallization has a significant role in grain refinement of Mg alloys SPD-processed at elevated homologous temperatures. Dynamic recrystallization in ECAP-processed AM60 alloy between 2 and 4 passes resulted in a large decrease of the dislocation density from ∼5.6 × 1014 m−2 to ∼0.7 × 1014 m−2 which corresponds to a reduction of 87%. This value is much higher than that for Cu processed by ECAP at the homologous temperature of 0.22 as in the latter sample only dynamic recovery occurred at high strains of SPD. It should be noted that no or only negligible reduction in the dislocation density was observed after the saturation for HPT-processed materials.33,34) This difference can be explained by the supression of dynamic recovery and recrystallization due to the high pressure applied during HPT.
The saturation (or maximum) dislocation density depends on the material characteristics such as the initial microstructure before SPD, SFE, solute concentration and secondary phase content, as well as the conditions of SPD-processing such as homologous temperature and method of SPD.7) If SPD-processing is carried out at RT, the dependence of the dislocation density on the homologous temperature can be depicted as a dependence on the melting point. The higher the melting point of the as-processed material, the more difficult the annihilation of dislocations, leading to a higher dislocation density.35) At the same time, SFE also significantly influences the maximum dislocation density since the lower SFE increases the splitting distance between partials in dissociated dislocations, thereby hindering annihilation of dislocations by cross slip and climb.36) The effects of melting point and SFE on saturation dislocation density are illustrated in Fig. 2, where the maximum dislocation density was plotted as a function of the melting point and SFE for pure fcc metals processed by ECAP at RT. The solid and dashed arrows indicate that the higher the melting point and the lower the SFE, respectively, the larger the saturation dislocation density. The lowest and highest dislocation densities were achieved in Al and Ag, respectively. For a given material, the increase of the temperature of SPD-processing yields a reduction of the maximum achievable dislocation density. For instance, if temperature of ECAP increased from 220°C to 250°C (this corresponds to the change of the homologous temperature from 0.53 to 0.57), the maximum dislocation density in AX41 Mg alloy decreased from ∼2.5 × 1014 m−2 to ∼0.9 × 1014 m−2.37) The plateau dislocation density achieved at high numbers of passes was also smaller for the higher processing temperature (∼0.7 × 1014 m−2 and ∼0.4 × 1014 m−2 for 220°C and 250°C, respectively).
The maximum dislocation density as a function of the melting point (Tm) and SFE for pure fcc metals processed by ECAP at RT. The solid and dashed arrows indicate that the higher the melting point and the lower the SFE, respectively, the larger the saturation dislocation density.
The annihilation of dislocations during SPD-processing is also hindered by the solute alloying elements and the secondary phase particles in the matrix. Therefore, the saturation dislocation density usually increases with increasing solute concentration as shown for Ni(Mo,Al,Fe) alloys processed by HPT at RT and Al(Mg) samples deformed by ECAP at RT in Fig. 3. The data were taken from Refs. 10, 38. For both cases, the alloying effect on dislocation density was enhanced for higher solute contents, and a large increment in the dislocation density was observed only above the solute concentration of 1 wt.%. The addition of secondary phase particles also resulted in an enhancement of the dislocation density in SPD-processed materials. As an example, Fig. 4 shows that the saturation dislocation density in Cu processed by HPT at RT increased from ∼43 × 1014 m−2 to ∼111 × 1014 m−2 due to the addition of 3 vol% carbon nanotubes (CNTs).39) The mechanism of this effect is similar to that of solute atoms, i.e., CNTs hindered the annihilation of dislocations during HPT, thereby yielding a much higher dislocation density in the saturation state. It should be noted that the Cu-CNT composite was consolidated from a blend of Cu and CNT powders using HPT technique. Therefore, the saturation dislocation density obtained for the consolidated UFG Cu sample differs slightly from the value determined for a specimen processed from bulk coarse-grained Cu by HPT at RT (∼37 × 1014 m−2). However, taking the uncertainties of these values into account the dislocation densities obtained in UFG Cu samples processed from bulk material and powder by HPT agree within the experimental error.
The saturation dislocation density versus the solute concentration for Ni(Mo,Al,Fe) alloys processed by HPT at RT and Al(Mg) samples deformed by ECAP at RT.
The effect of the addition of 3 vol% carbon nanotubes (CNTs) on the saturation dislocation density and twin fault probability in Cu processed by HPT at RT.
As it was shown above, alloying effect on dislocation density was enhanced with increasing solute concentration. If concentrations of solute and solvent element are equal in a multicomponent material with a number of constituents higher than three, a high entropy alloy (HEA) is obtained.40) The dislocation density in some HEAs processed by HPT at RT was studied by XLPA41–43) and the saturation values are summarized in Table 2. It was revealed that the dislocation density increased monotonously with increasing shear strain and then saturated with the value of ∼200 × 1014 m−2 at a strain of ∼40 for most of HEAs, irrespectively of their crystal structure and composition. This dislocation density is very high among the values obtained for conventional metals and alloys processed by HPT (see Table 2). It should be noted, however, that in fcc CoCrFeMnNi HEA processed by HPT at RT the saturation dislocation density was only slightly higher ((194 ± 20) × 1014 m−2) than the value obtained for pure fcc Ag ((154 ± 16) × 1014 m−2). The similar dislocation densities in the highly alloyed HEA and the pure Ag can be explained by the very close and low SFE in the two materials (∼19 mJ/m2). As we discussed above, the low SFE hinders the annihilation of dislocations during HPT, resulting in a high saturation value of dislocation density. It seems that the low SFE of CoCrFeMnNi HEA is a deterministic factor while the alloying effect is marginal in the evolution of the dislocation density during HPT. It is also noted that a very high saturation dislocation density also formed in a traditional 316L steel sample ((143 ± 10) × 1014 m−2) where the SFE is similarly low (∼19 mJ/m2) as for CoCrFeMnNi HEA.50)
Beside the properties of materials (e.g., melting point, SFE and solute content), the method of SPD may also influence the dislocation density. As an example, Fig. 5 shows the saturation dislocation density in pure Cu obtained by different methods of SPD at RT.47,48) The values are also listed in Table 2. The lowest dislocation density with the value of ∼10 × 1014 m−2 was obtained by MDF and TE. A two times higher dislocation density was achieved by ECAP and equal channel angular rolling (ECAR). Similar difference between the dislocation densities obtained by ECAP and MDF was observed for AM60 Mg alloy processed by SPD at 220°C.30) In the former and latter cases, the maximum dislocation density values were ∼5.6 × 1014 m−2 and ∼1.8 × 1014 m−2, respectively, as shown in Fig. 1. It is worth to note, that for ECAP the processing route (e.g., A, BC and C) only slightly influences the evolution and the saturation value of the dislocation density, as it was shown for AX41 Mg alloy processed by ECAP at 220°C.51) At the same time, the fractions of basal, prismatic and pyramidal dislocations in AX41 alloy depended considerably on the route of ECAP which can be explained by the different textures formed during the various processing routes. The highest dislocation density was usually obtained by HPT-processing as the large hydrostatic component of the applied stress field hinders diffusion during HPT, thereby retarding the annihilation of dislocations. For instance, in copper processed by HPT the saturation dislocation density was about ∼40 × 1014 m−2 (see Fig. 5 and Table 2).47)
The saturation dislocation density in pure Cu obtained by different methods of SPD at RT. MDF: multi-directional forging, TE: twist extrusion, ECAR: equal channel angular rolling, ECAP: equal channel angular pressing, HPT: high pressure torsion.
In general, the difference between the dislocation densities obtained on the same material by various SPD methods can be explained by the different deformation conditions, such as the imposed strain, strain rate, hydrostatic pressure and degree of non-monotony of deformation. The latter feature of SPD can be characterized by the ratio of the length of the strain trajectory and the spacing between the starting and end points of deformation in the five-dimensional space of the independent deviatoric strain tensor components.52,53) The larger the value of this ratio, the higher the degree of non-monotony of deformation. The higher degree of non-monotony for ECAP compared to MDF might have contributed to the larger maximum dislocation density in ECAP-processed Cu and AM60 alloy. It should be noted, however, that the dislocation density is usually measured after SPD-processing, therefore its value may differ from the dislocation density under loading. For instance, in the case of HPT when the pressure is released a large fraction of dislocations may be annihilated due to the accelerated diffusion.54) This effect may be more significant for materials with high SFE as the low value of SFE can hinder the annihilation of dislocations after SPD-processing. Indeed, for Al alloys with high SFE the saturation dislocation density measured after HPT at RT was practically the same as the value obtained after ECAP at RT (see for example Al–1%Mg alloy in Table 2).7,10,49) At the same time, the grain size in these Al alloys was smaller after HPT than for ECAP-processing, indicating the effect of the different loading conditions in the two SPD techniques.
The initial state of the material also influences the evolution of the dislocation density during SPD. It has been shown recently55) that if the same ECAP-processing at 220°C was applied on as-cast and extruded states of an AX41 Mg alloy, the maximum dislocation density was achieved after two passes for the as-cast material while in the case of the extruded sample the highest dislocation density was obtained even after one pass of ECAP. On the other hand, the maximum dislocation density achieved by ECAP was practically the same (∼2.5 × 1014 m−2) for both initial states. For the as-cast and extruded AX41 specimens, the dislocation density was reduced considerably after two passes and one pass, respectively, and the decrease of the dislocation density was faster for the extruded sample. This reduction in the dislocation density was similar to the trend shown for AM60 Mg alloy in Fig. 1.
In addition to the dislocation density, the arrangement of dislocations and the population of the different slip systems can also be determined by the method of XLPA.15) The former feature can be characterized by a dimensionless dislocation arrangement parameter (denoted as M) which has a smaller value if dislocations in the studied sample are arranged into low-energy configurations such as dipoles or low angle grain boundaries (LAGBs). The dislocation arrangement parameter usually decreases with increasing strain imposed during ECAP and saturates at low numbers of passes, similar to the dislocation density.34,48) For HPT-processed materials, the saturation of parameter M occurred also at low imposed strains and only marginal changes were observed with increasing numbers of revolutions or distance from disk center.24,38) As an example, Fig. 6 shows the values of the dislocation arrangement parameter for two Ni alloys with different solute concentrations. It is evident that although the value of M only slightly changes along the disk radius and with increasing number of turns, the dislocation arrangement parameter is much larger for the alloy with a higher solute content. This difference can be explained by the pinning effect of solute atoms on dislocations which hinders their rearrangement into low-energy configurations. The influence of low SFE on the arrangement of dislocations is similar to the effect of alloying, i.e., the lower the SFE, the higher the value of M. This was demonstrated for Cu–Zn alloys where the reduction of SFE with increasing Zn content resulted in a higher degree of dislocation dissociation which impeded rearrangement of dislocations, thereby leading to a larger value of M.11)
The values of the dislocation arrangement parameter (M) at the center, half-radius and periphery of HPT processed disks for two Ni alloys with different solute concentrations.
Significant amount of stacking and twin faults in SPD-processed materials was observed if the value of SFE is smaller than 40 mJ/m2.7) The lower SFE is accompanied by a smaller twin fault energy which facilitates the nucleation of twins. During SPD, twin faults are usually formed at dislocation glide obstacles such as Lomer-Cottrell locks and grain boundaries. At these locations, the high stresses can exceed the critical value necessary for twin nucleation. The amount of twin faults can be characterized quantitatively by the twin fault probability. This quantity is usually determined by XLPA and gives the fraction of twinned crystal planes among the possible planes of twinning (e.g., these are planes {111} in fcc crystals).15) The twin fault probability is given in percentage. It was found that the value of twin fault probability usually increases with increasing strain applied during SPD.7) This effect can be explained by the increase of the number of nucleation sites since both the dislocation density and the grain boundary area increase during deformation. The evolution of twin fault probability as a function of number of ECAP passes was carefully studied in Ag with two different degrees of purity (4N5 and 4N).56) The saturation of twin fault probability in silver occurred between 4 and 16 passes of ECAP. For 4N purity silver, the saturation was observed earlier and with a smaller twin fault probability value since for high numbers of ECAP passes the impurities were segregated at grain boundaries, thereby hindering twin nucleation. The saturation twin fault probability values for 4N5 and 4N purity silver samples processed by ECAP at RT are shown in Fig. 7. HPT-processing of 4N purity Ag at RT resulted in an enhanced twin fault probability (2.1 ± 0.2%) compared to the ECAP-processed sample with the same impurity level (0.8 ± 0.1%).56) This can be explained by the much higher dislocation density in the HPT-processed sample which might result in a higher density of twin nucleation sites.
The saturation twin fault probability values for 4N5 and 4N purity silver samples processed by ECAP at RT and for a 4N purity silver processed by HPT at RT.
In addition to low SFE, small grain size also increases the probability of twinning in SPD-processed fcc materials.7) This effect can be explained by the increase of equilibrium splitting distance between partials of dissociated dislocations with decreasing grain size.57) The extension of stacking faults between partials on neighboring {111} planes in fcc crystals can result in the formation of twin lamellas. Figure 8 illustrates the combined effect of SFE and grain size for UFG fcc metals and alloys processed by ECAP and HPT at RT.11,25,41,45,46,58) The dashed and solid arrows indicate that twin fault probability increases with decreasing SFE and grain size, respectively. The points in Fig. 8 represent both pure metals and alloys. It is well known that alloying may cause reduction of SFE. For instance, the additon of 30% Zn or 16% Al to Cu yields a decrease of SFE from ∼60 to ∼10 or 6 mJ/m2, respectively.11,58) Therefore, alloying can result in a simultaneous reduction of grain size, increase of dislocation density and enhancement of twin fault probability. There is a mutual influence between these effects as the high dislocation density and the small grain size may increase the probability of twinning while twin fault formation may contribute to grain refinement. It is noted that beside alloying, the addition of CNTs to Cu can also result in a significant twinning during HPT. For instance, 3 vol% CNT addition yielded a saturation twin fault probability of ∼1.1% in copper processed by HPT at RT while twinning was not observed in pure Cu deformed under the same conditions (see Fig. 4).39) In Fig. 8, the value of the twin fault probability for an fcc CoCrFeMnNi HEA processed by HPT at RT was also plotted. In this material, a very high twin fault probability of ∼2.7% was achieved due to the combination of low SFE (∼19 mJ/m2) and very small grain size (∼27 nm).41)
The effect of SFE and grain size on the twin fault probability of UFG fcc metals and alloys processed by ECAP and HPT at RT. The solid and the dashed arrows indicate that the smaller the grain size and the SFE, respectively, the larger the saturation twin fault probability.
During SPD-processing, the stored energy is reduced if dislocations are rearranged into low-energy configurations such as dipolar walls or LAGBs. Therefore, in the very early stage of SPD when the coarse grains are not refined yet, the fraction of LAGBs increases (i.e., the fraction of high angle grain boundaries (HAGBs) decreases) as shown in Fig. 9 for an as-cast AX41 alloy processed by ECAP at 220°C.55) HAGBs are defined as boundaries with misorientations higher than 15° and its fraction is usually determined by electron backscatter diffraction technique (EBSD). It should be noted that in this overview the boundaries other than HAGBs are taken as LAGBs. At the same time, in some works LAGBs are defined as grain boundaries with misorientations smaller than 5° while misorientations between 5° and 15° are related to medium angle grain boundaries. Nevertheless, for high strains of ECAP a large amount of HAGBs forms due to grain refinement. Therefore, after 1 pass of ECAP the fraction of HAGBs started to increase with increasing number of passes as illustrated in Fig. 9 for pure Al, Al–1 wt.% Mg and AX41 alloys processed by ECAP.55,59,60) It is noted that for Al and Al–1 wt.% Mg alloy the HAGB fraction of the initial sample was not measured, therefore its reduction in the beginning of ECAP was not detected. Moreover, if the initial material was pre-deformed before SPD (e.g., by extrusion or rolling), significant decrease of HAGB fraction was not observed since it had already been occurred during pre-deformation.38,55) The saturation HAGB fraction was achieved between 4 and 12 passes of ECAP with the value of 60–80% (see Fig. 9). For HPT-processed metals and alloys, the fraction of HAGBs saturated at the disk periphery after about 5 turns.24,49) The saturation HAGB fraction is usually higher for HPT than for the ECAP-processed counterparts, as shown in Fig. 10 for IF steel and Al–1 wt.% Mg alloy with bcc and fcc structures, respectively. It should be noted that even after the saturation of HAGB fraction in SPD-processed materials, the fraction of LAGB is still higher than in a random misorientation distribution (Mackenzie distribution) as illustrated this phenomenon for fcc materials in Fig. 11.3) This effect can be attributed to the large amount of dislocations arranged into LAGBs inside the grains. Accordingly, the experimentally determined fraction of HAGBs in SPD-processed materials (60–80%) is smaller than the theoretical value characteristic for random misorientation distribution (89.3%).4) It should be noted that there is a lower detection limit of about 0.1° in the determination of misorientation using EBSD technique.61) In addition, the grain boundary misorientation distribution is usually determined only for angles higher than 2°. Therefore, LAGBs with misorientations smaller than this limit are missing from the experimentally determined LAGB fraction. Thus, the difference between the real HAGB fraction for SPD-processed materials and the theoretical value for random misorientation distribution may be even higher than the value estimated from the EBSD measurements.
The evolution of HAGB fraction as a function of number of ECAP passes for AX41 alloy processed at 220°C, as well as for Al and Al–1 wt.% Mg alloy processed at RT.
Comparison of the saturation values of HAGB fraction obtained by ECAP and HPT at RT for IF steel and Al–1 wt.% Mg alloy with bcc and fcc structures, respectively.
A schematic comparing a grain boundary misorientation distribution obtained for SPD-processed fcc materials (solid line) with a random distribution (dashed curve).
The processing temperature of SPD may influence the fraction of HAGBs. It was found that the saturation HAGBs fraction remained unchanged or decreased with increasing the temperature of SPD.62–64) The higher fraction of LAGBs at higher SPD-processing temperatures can be explained by the easier arrangement of dislocations into LAGBs due to the higher thermal activation. The solute content of alloys only slightly influences the saturation value of HAGB fraction. For instance, in both pure Al and Al–1 wt.% Mg alloy processed by ECAP at RT the saturation HAGB fraction was about 60–70%.59,60) For Ni–1.3 wt.% (Mo,Al,Fe) and Ni–8.6 wt.% (Mo,Al,Fe) alloys processed by HPT at RT, the saturation HAGB fraction was about 70%, irrespectively of the solute content.38) At the same time, the rate of the evolution of HAGB fraction with increasing strain is lower for higher alloying element concentrations in both Al and Ni alloys,59,60) suggesting that solute atoms hinders the evolution of LAGBs into HAGBs during SPD. This is also valid for the average grain boundary misorientation. For instance, the increase of the average misorientation for pure Al processed by ECAP at RT was faster as a function of number of passes than that for Al–1 wt.% Mg alloy, however the saturation values were the same (about 30°) for both materials. It seems that SFE has no considerable effect on the saturation value of the fraction of HAGBs since for both pure Al and Cu processed by ECAP at RT the HAGB fraction was about 70% although the SFE is much smaller for Cu.59,65)
As it was discussed above, the fraction of HAGBs may be overestimated by EBSD since a significant portion of LAGBs is not detected due to detection limit of misorientation angle. At the same time, the total amount of HAGBs determined by EBSD is not infleunced by this detection limit. Considering a simple model of materials with uniform cubic grains, the area of HAGBs in a unit volume (AHAGB) can be expressed by the grain size (D) estimated by EBSD as AHAGB = 3/D. Here, the grain size is determined as the average size of the areas bounded by HAGBs in the EBSD images. It should be noted that if the grain size is determined by TEM, the calculated value of AHAGB may be overestimated as in a usual TEM image the misoriention is not measured, i.e., boundaries with misorientations smaller than 15° may also be taken as HAGBs. For instance, for an UFG Ni processed by ECAP at RT the grain size determined by TEM (240 nm) was close to the grain size obtained by EBSD using a lower misorientation limit of 5° (230 nm).66)
For bulk SPD-processed metallic materials, the value of AHAGB monotonously increases with increasing imposed strain, i.e., the non-monotonous evolution of HAGB fraction shown in Fig. 9 was not observed for AHAGB. The saturation value of the area of HAGBs in a unit volume was obtained between 106 and 108 m−1 which correspond to the grain size of about 3 µm and 30 nm, respectively. It was found in numerous papers10,12,13,37,67–71) that the minimum grain size achievable by SPD depends considerably on the homologous temperature of deformation, solute content and secondary phase fraction of SPD-processed metallic materials. Therefore, the saturation value of the area of HAGBs in a unit volume is also influenced by these properties. Namely, the lower the homologous temperature of SPD, as well as the higher the solute and secondary phase contents of the material, the higher the saturation value of AHAGB.7,13,39,69) Figure 12 illustrates the effect of solute content for Ni(Mo,Al,Fe) alloys processed by HPT at RT and Al(Mg) samples deformed by ECAP at RT. These data were obtained on the same samples as used for the study of the evolution of the dislocation density in Fig. 3. The addition of secondary phase particles to the matrix before SPD also increases the saturation value of AHAGB. For instance, 3 vol% CNT addition to Cu processed by HPT at RT yielded an increase of HAGB area from ∼2 × 107 m−1 to ∼4 × 107 m−1.39)
The saturation HAGB area in a unit volume versus the solute concentration for Ni(Mo,Al,Fe) alloys processed by HPT at RT and Al(Mg) samples deformed by ECAP at RT.
Considerable influence of SFE on the HAGB area (i.e., on the grain size) was not detected which behavior significantly differs from the effect of SFE on the dislocation density (see the dashed arrow in Fig. 2). Although, low SFE hinders the annihilation of dislocations during SPD-processing, resulting in a higher saturation value of dislocation density, the re-arrangement of dislocations into grain boundaries is also impeded by the low SFE. Thus, finally the higher saturation dislocation density was not accompanied by a smaller grain size, i.e., a higher saturation value of AHAGB. For instance, in pure Ag with very low SFE (19 mJ/m2) the saturation value of AHAGB was 1.5 × 107 m−1 (corresponding to the minimum grain size of 200 nm) after ECAP at RT,36) and similar values were obtained for Au, Cu and Ni with significantly higher SFE values (38, 62 and 125 mJ/m2, respectively).66,72,73) Very high saturation values of AHAGB (∼108 m−1) was achieved in HPT-processed HEAs (e.g., in CoCrFeMnNi,41) Al0.3CoCrFeNi,74) CoCrFeNiMnTi0.175) and AlNbTiVZr0.576)) which corresponds to a grain size value of 25–30 nm.
The method of SPD usually has only a minor influence on the saturation area of HAGBs in a unit volume, except HPT-processing. Indeed, the saturation value of AHAGB in Cu was about 1.5 × 107 m−1 (corresponding to a grain size of ∼200 nm), irrespectively of the SPD processing method (ECAP, ECAR, TE or MDF) performed at RT.47,48) A very small difference between the saturation HAGB areas (i.e., between the minimum grain sizes) was also observed in AM60 Mg alloy processed by ECAP and MDF at 220°C.30) At the same time, HPT-processing may result in a considerably higher HAGB area (i.e., smaller grain size) as compared to ECAP, especially for high SFE materials. Indeed, in commercially pure Al and Al–Mg alloys processed by HPT at RT the HAGB area was about two times higher than that obtained after ECAP.10,49,77) On the other hand, in Ag with low SFE HPT did not yield a significantly higher saturation HAGB area compared to that obtained by ECAP-processing.45) For copper with medium SFE, HPT-processing resulted in a slightly higher maximal AHAGB (∼1.9 × 107 m−1, corresponding to a minimum grain size of ∼160 nm) than the saturation value for ECAP (∼1.5 × 107 m−1).47) It seems that the lower the SFE, the less effective the HPT-processing in the increase of HAGB area despite the much higher saturation dislocation density as compared to ECAP (see section 3). This effect may be caused by the hindering effect of low SFE on the rearrangement of dislocations into boundaries, therefore the HAGB area was not different in the HPT sample even if the dislocation density was much larger compared to the ECAP-processed counterpart. It should be noted, however, that in SPD-processed silver the grains contained a high amount of twin faults. These defects can be considered as special HAGBs, therefore their contribution to the total HAGB area must be taken into account. Considering a uniform grain size with cubic shape in a model fcc material with low SFE, the area of twin faults in a unit volume can be obtained as β/(100 × d111) where β is the twin fault probability in percentage and d111 is the spacing between the neighboring lattice planes {111}.21) Using the saturation values of β obtained for 4N purity Ag processed by ECAP and HPT (see Fig. 7), the contributions of twin faults to HAGB area is about 3 × 107 and 9 × 107 m−1, respectively. Adding these values to the area of other HAGBs (∼1.5 × 107 m−1), the saturation value of the total HAGB area for HPT is ∼11.5 × 107 m−1 which is much higher than that for ECAP (∼4.5 × 107 m−1), similar to high SFE fcc metals (see above).
Numerous studies have shown that the correlation between the yield strength and the grain size for UFG materials obeyed the Hall-Petch formula; however the Hall-Petch slope is slightly lower than that for the coarse-grained counterparts.33,78–81) There are other investigations which applies an additional Taylor term beside the Hall-Petch term for taking the hardening effect of dislocations into account.41,82–85) Twin faults inside the grains formed during SPD-processing also have a contribution to the strength. The hardening effect of twin faults can also be described by a Hall-Petch term in which the grain size is substituted by the twin boundary spacing.86) It was shown that the same Hall-Petch constant can be used for both grain size and twin boundary spacing.87) In practice, the strengthening of grains and twin faults can be handled with a single Hall-Petch term in which the lesser of the values of the grain size and the twin boundary spacing shall apply.41) As both Hall-Petch and Taylor equations are well-known relationships between the yield strength and the microstructural parameters, therefore they are not discussed here. Rather, special effects of the defect structure on the strength of SPD-processed materials, such as the influence of dislocation arrangement and grain boundary misorientation on the yield strength, are presented in the next paragraphs.
It has been shown for ECAP-processed fcc metals that the strengthening effect of dislocations depends on the number of passes and the value of SFE of the material.7,29) The common reason of these effects is that the arrangement of dislocations depends on both the imposed strain and SFE. With increasing strain of SPD, dislocations are arranged into low energy configurations, such as LAGBs and dipolar walls, and this clustered dislocation structure has a higher strengthening effect than that of a randomly distributed dislocation ensemble.88) As a consequence, the value of parameter α in the Taylor equation increased with increasing the number of ECAP passes.7,29) This parameter characterizes the hardening of a unit dislocation density. It was also revealed that the lower the SFE, the smaller the value of α as the high degree of dislocation dissociation hinders the clustering of dislocations.29)
It is generally believed that SPD-processing results in hardening while annealing after SPD leads to softening of materials. At the same time, there are several examples in the literature which revealed opposite trends.89–91) For instance, it was shown that moderate annealing in UFG or nanocrystalline materials may yield a considerable strengthening of the sample.8,89–94) This effect is referred to as annealing-induced hardening and not related to the strengthening caused by precipitation during annealing of SPD-processed supersaturated solid solutions. For UFG Ni–1.3 wt.% (Mo,Al,Fe) processed by HPT at RT, annealing to 600 K resulted in an increase of the yield strength by 19% from 970 to 1160 MPa.91) Simultaneously, the ultimate tensile strength increased by 13% from 1140 to 1290 MPa. This hardening cannot be explained by precipitation or grain growth as the alloy remained solid solution and the grain size was the same (∼180 nm) before and after the heat treatment. At the same time, the dislocation density decreased from 27 ± 3 × 1014 m−2 to 17 ± 2 × 1014 m−2 and the dislocation arrangement parameter also decreased significantly. These changes suggest a recovery of the dislocation structure, including dislocation annihilation and the rearrangement of the remaining dislocations into a more clustered configuration. The latter phenomenon is also confirmed by the increase of LAGB fraction during annealing as revealed by EBSD experiments.91) As it was mentioned in the previous paragraph, the hardening effect of a more clustered dislocation structure is higher which may overwhelm the softening caused by the decrease of the dislocation density. It should also be noted that the decrease of the dislocation density during annealing does not necessarily yield a decrease of the yield strength. Rather, if mobile dislocations are annihilated, the subsequent plastic deformation becomes more difficult.89) Therefore, the annihilation of mobile dislocations during the heat treament of the HPT-processed Ni–1.3 wt.% (Mo,Al,Fe) alloy might have also contributed to the observed hardening. In addition, the relaxation of non-equilibrium HAGBs during annealing may yield a more difficult emission of dislocations from the boundaries and this effect may also result in hardening.8) It should be noted that the annealing-induced hardening effect can only be observed after heat treatments at moderate temperatures, corresponding to the homologous temperature of about 0.35. If the temperature of annealing increased to about 0.45, softening occurred due to the annihilation of dislocations in LAGBs and grain growth.
The increase of solute content in SPD-processed materials reduced the effect of annealing-induced hardening since solute atoms hinder the rearrangement of dislocations into LAGBs. Therefore, in HPT-processed Ni–8.6 wt.% (Mo,Al,Fe) alloy annealing resulted only in a 2.4% increase of the yield strength from 1367 to 1400 MPa.91) It should be noted that the influence of an increased solute content on the effect of annealing-induced hardening is opposite in nanocrystalline Ni alloy films. For instance, in electrodeposited Ni–Mo layers the increase in Mo content from 0.8 to 21.5 at% resulted in an enhancement of annealing-induced hardening from 20% to 125%.94) In addition, the peak hardness was achieved at higher temperatures for the samples with larger solute content. The different trends in the effect of solute concentration on the annealing-induced hardening of SPD-processed UFG and electrodeposited nanocrystalline Ni alloys were caused by the different mechanisms of plastic deformation. In nanocrystalline Ni–Mo films, the grain size varied between 3 and 25 nm. The higher the Mo content, the smaller the grain size. In all samples, the main deformation mechanism is grain boundary sliding due to the very small grain size. During annealing, the alloying elements were segregated to grain boundaries which hindered grain boundary sliding. This effect was more pronounced in alloys with higher solute contents, leading to a higher annealing-induced hardening. It is noted that strengthening caused by a heat treatment was also observed in 4N purity Al (the yield strength increased by 9%),89) i.e., alloying is not a prerequisite for the observation of this effect.
For an UFG or nanocrystalline material hardened by annealing, subsequent plastic deformation may yield a softening. This deformation-induced softening effect was demonstrated on 99.2% pure Al processed by ARB at RT.89) Annealing at 150°C for 30 min resulted in an increase of the yield strength which was fully restored by cold rolling with a thickness reduction of 15%. In these samples, the grain size was about 200 nm, therefore dislocations played a main role in plastic deformation. The cold rolling step caused an increase of the density of mobile dislocations, leading to a softening in the sample hardened formerly by annealing. It was also shown that SPD-processing can result in a smaller hardness than the value obtained on an intial well-annealed specimen of pure Al, In, Sn, Pb, Zn metals and Al–Zn alloy.67,68,95–97) These materials have low melting temperatures, therefore when their grain size was refined to the UFG regime, grain boundary sliding became a dominant deformation mechanism during hardness measurement at RT. In addition, HAGBs may act as dislocation sinks during deformation, therefore the increase of the amount of HAGBs during SPD can yield an easier annihilation of dislocations in low-melting-temperature metals with high dislocation mobility.96) Thus, softening can be observed after SPD-processing of materials with low melting points, however for Al this effect was detected only if the purity level reached 6N. In this material, for low strains of HPT (in the vicinity of the disk center) the hardness increased, but at high strains the hardness decreased despite the further grain size reduction. At shear strains higher than two, the hardness was lower than that for the initial annealed state, despite the much smaller grain size (∼20 µm in the saturation state while the grain size was higher than 1 mm in the initial state).96) For high purity Al processed by SPD, grain boundary sliding may occur even at RT,97) which might have contributed to the observed softening. This behavior resulted in an inverse Hall-Petch behavior for 6N Al processed by HPT at RT for high numbers of turns as shown in Fig. 13. It is noted that a hardness decrease due to HPT-processing was also observed for a supersaturated solid solution Al–30% Zn alloy, in which the wetting of grain boundaries with a ∼3 nm thick Zn-rich layer caused an SPD-induced softening.98)
Hall-Petch plot for 6N purity Al processed by HPT, illustrating SPD-induced softening.
In this overview, the features of defect structure formed during SPD-processing are described in detail. In addition, some special effects of lattice defects on mechanical strength of SPD-processed UFG materials are discussed.
It was found that SPD-processing at RT yielded a very high excess vacancy concentration with the value of 10−4–10−3. HPT processing resulted in a much higher vacancy concentration than that obtained by ECAP. The larger amount of vacancies observed for HPT-processing can be explained by the very high hydrostatic pressure in the sample which hinders the migration of vacancies to sinks. It was revealed that more than 90% of vacancies are clustered in SPD-processed fcc metals. These vacancy agglomerates contain 4–40 vacancies.
Generally, the dislocation density increases with increasing strain imposed during SPD. Saturation of the dislocation density was achieved after 2–3 passes of ECAP which corresponds to an equivalent strain of about 2–3. Further straining resulted in a decrease of dislocation density due to relaxation of microstructure at high strains. Finally, the dislocation density reached a plateau value. The maximum dislocation density depends on the material characteristics such as the initial microstructure before SPD, SFE, solute concentration and secondary phase content, as well as the conditions of SPD-processing such as homologous temperature and method of SPD. The dislocation densities for HEAs were very high among the values obtained for conventional metals and alloys processed by HPT. The higher solute content and the lower SFE resulted in a less clustered dislocation structure.
Significant amount of stacking and twin faults in SPD-processed materials was observed if the value of SFE is smaller than 40 mJ/m2. It was found that the value of twin fault probability usually increases with increasing strain applied during SPD. In addition to low SFE, small grain size also increases the probability of twinning in SPD-processed fcc materials. In HEAs, the twin fault probability is determined mainly by the value of SFE.
In the very early stage of SPD when the coarse grains are not refined yet, the fraction of HAGBs decreases. Further SPD straining resulted in an increase of HAGB fraction. The saturation HAGB fraction was achieved between 4 and 12 passes of ECAP with the value of 60–80%. The saturation HAGB fraction is usually higher for HPT than for the ECAP-processed counterparts. The solute content of alloys only slightly influences the saturation value of HAGB fraction. Although, the low SFE hinders the annihilation of dislocations during SPD-processing, resulting in a higher saturation value of dislocation density, the rearrangement of dislocations into grain boundaries is also impeded by the low SFE. Thus, finally the higher saturation dislocation density was not accompanied by a smaller grain size. Very high saturation values of HAGB area (∼108 m−1) was achieved in HPT-processed HEAs.
The strengthening effect of dislocations depends on the number of passes and the value of SFE. Annealing-induced hardening was observed during heat-treatment of SPD-processed materials. This effect can be explained by the annihilation of mobile dislocation and the rearrangement of remaining dislocations into a more clustered configuration. The increase of solute content in SPD-processed materials reduced the effect of annealing-induced hardening since solute atoms hinder the rearrangement of dislocations into LAGBs. It was also shown that SPD-processing can result in a smaller hardness than the value obtained on an intial well-annealed specimen of pure Al, In, Sn, Pb, Zn metals and Al–Zn alloy. This deformation-induced softening can be explained mainly by the dominance of grain boundary sliding during deformation in fine-grained low-melting-temperature SPD-processed materials.
This work was financed partly by the Ministry of Human Capacities of Hungary within the ELTE University Excellence program (1783-3/2018/FEKUTSRAT).
