Deformation mechanisms and strain rate sensitivity of bimodal and ultrafine-grained copper

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Deformation mechanisms and strain rate sensitivity of bimodal and ultrafine-grained copper

J. Bach Methodology Investigation Writing – original draft Writing – review & editing Visualization , M. Stoiber Investigation Visualization , L. Schindler Investigation Visualization , ¨ H.W. Hoppel Conceptualization Methodology Investigation Writing – review & editing Visualization Supervision ¨ M. Goken Conceptualization Writing – review & editing Supervision Project administration PII: DOI: Reference:

S1359-6454(19)30883-3 https://doi.org/10.1016/j.actamat.2019.12.044 AM 15740

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Acta Materialia

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18 April 2019 20 December 2019 23 December 2019

Please cite this article as: J. Bach Methodology Investigation Writing – original draft Writing – review & editing V M. Stoiber Investigation Visualization , L. Schindler Investigation Visualization , ¨ H.W. Hoppel Conceptualization Methodology Investigation Writing – review & editing Visualization Supervision ¨ M. Goken Conceptualization Writing – review & editing Supervision Project administration , Deformation mechanisms and strain rate sensitivity of bimodal and ultrafine-grained copper, Acta Materialia (2020), doi: https://doi.org/10.1016/j.actamat.2019.12.044

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Deformation mechanisms and strain rate sensitivity of bimodal and ultrafine-grained copper J. Bach, M. Stoiber, L. Schindler, H. W. Höppel* and M. Göken Institute I: General Materials Properties, Department of Materials Science and Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg FAU, Martensstr. 5, 91058, Erlangen, Germany

*Corresponding author:

Email: [email protected]; Phone: +49 9131 85 27503; Fax: +49 9131 8527504

Graphical abstract Materials with ultrafine grain size in the range from 100 nm to 1 µm exhibit very high strength paired with a satisfactory ductility when compared to their coarse grained (CG) counterparts. Although this typical behavior is already well known, the dominating deformation mechanisms are still controversially discussed in literature. One idea to explain the deformation behavior of ultrafine-grained metals is that deformation is mainly triggered by grain boundary sliding. Another explanation is that deformation in ultrafine-grained materials is controlled by the thermally activated dislocation annihilation of dislocations at grain boundaries. To gain deeper insights to the relevant deformation mechanisms in UFG metals a systematic study was conducted where the deformation behavior of UFG and bimodal copper (consisting of UFG and CG grains) is compared to the behavior of their CG counterparts. The UFG microstructure was obtained by equal channel angular pressing (ECAP). To achieve a bimodal or coarsened microstructure, specimens were annealed at 125 °C or, respectively, 140 °C subsequent to the ECAP-process. Mechanical characterization and investigation on the strain-rate sensitivity were done by compression strain-rate jump tests at room-temperatures and elevated temperatures. It turned out clearly that the degree of bimodality determines the dominant deformation mechanism and the strain-rate sensitivity. In the UFG-state thermally activated annihilation of dislocations at the grain boundaries govern the mechanical behavior. For the bimodal microstructure the annihilation of dislocation at the interface of coarsened grains to the surrounding ultrafine-grained matrix define the mechanical behavior. For the fully coarsened state plastic deformation is mainly governed by dislocation interaction in the grain interior. Annihilation at grain boundaries plays only a minor role.

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Abstract Materials with ultrafine grain size in the range from 100 nm to 1 µm exhibit very high strength paired with a satisfactory ductility when compared to their coarse grained (CG) counterparts. Although this typical behavior is already well known, the dominating deformation mechanisms are still controversially discussed in literature. One idea to explain the deformation behavior of ultrafine-grained metals is that deformation is mainly triggered by grain boundary sliding. Another explanation is that deformation in ultrafine-grained materials is controlled by the thermally activated dislocation annihilation of dislocations at grain boundaries. To gain deeper insights to the relevant deformation mechanisms in UFG metals a systematic study was conducted where the deformation behavior of UFG and bimodal copper (consisting of UFG and CG grains) is compared to the behavior of their CG counterparts. The UFG microstructure was obtained by equal channel angular pressing (ECAP). To achieve a bimodal or coarsened microstructure, specimens were annealed at 125 °C or, respectively, at 140 °C subsequent to the ECAP-process. Mechanical characterization and investigation on the strain-rate sensitivity were done by compression strain-rate jump tests at room-temperatures and elevated temperatures. It turned out clearly that the degree of bimodality determines the dominant deformation mechanism and the strain-rate sensitivity. In the UFG-state thermally activated annihilation of dislocations at the grain boundaries govern the mechanical behavior. For the bimodal microstructure the annihilation of dislocation at the interface of coarsened grains to the surrounding ultrafine-grained matrix dominate the mechanical behavior. For the fully coarsened state plastic deformation is mainly governed by 2

dislocation interaction in the grain interior. In this regime, annihilation at grain boundaries plays only a minor role.

1. Introduction During the last decades research on nanocrystalline and ultrafine-grained (UFG) materials became very popular in the scientific community, see for example [1]. The strongly increased interest is on the one hand mainly due to the very promising mechanical properties and on the other hand to the significant improvements in the field of severe plastic deformation (SPD) [2, 3]. Related to that, the availability of UFG materials in reasonable quantities and homogeneity has strongly been improved [4]. Among the different SPD processes equal channel angular pressing (ECAP) is one of the most widely used methods to obtain very homogeneous bulk UFG metallic materials [5, 6]. For further details on the principles of ECAP-processing see [7]. Due to the strong plastic deformation applied during ECAP-processing subgrains form within the initial grains and evolve with ongoing plastic deformation, into grains with high angle grain boundaries [8,9]. Thus, after the first ECAP-passes a high degree of low angle boundaries is obtained and subsequently with increasing number of ECAP-passes, the fraction of high angle grain boundaries increases [10, 11]. The obtained grain size lies typically between 100 nm and 1 µm. As a consequence of this ultrafine grain size, materials show a significantly increased strength, partially paired also with a higher ductility [3, 12-14]. In this context, the strain rate sensitivity (SRS), i.e. the dependence of the flow stress on the applied deformation rate [15], becomes very important. For fcc materials the SRS is significantly enhanced for UFG materials. According to Hart the strain-rate sensitivity can be described by using the following equation [16]:

̇

|εpl, T

(1)

Where σ is the flow stress and ̇ is the applied strain-rate. It is essential to determine the rate sensitivity at a constant microstructure, since any microstructural changes would lead to a change of m. Although an enhanced SRS is a prerequisite for a high ductility of UFG materials, the relevant deformation mechanisms in UFG-materials are still controversially discussed. One possible explanation is that deformation in UFG-materials is mainly caused by grain boundary sliding [17,18]. Another plausible mechanism is that deformation is controlled by thermally activated 3

annihilation of dislocations at grain boundaries [8, 14]. Renk et al. [19] suggested from nanoindentation strain-rate jump-tests at different temperatures and from the analysis of the activation energies that the thermally activated annihilation of lattice dislocations at grain boundaries is the dominating mechanism controlling the enhanced rate sensitivities in nanocrystalline metals at elevated temperatures. Isaev et al. [20] concluded for UFG copper that in the temperature range of 77–200 K the plastic deformation is determined by a thermally activated mechanism of crossing the forest dislocations, whereas at temperatures above 200 K dislocation depinning from local obstacles in the grain boundaries is the determining deformation process. However, the enhanced fraction of the grain boundary volume in NC/UFG materials seems to play an important role. Due to the high fraction of grain boundary volume, dislocations are mostly stored close to or in grain boundaries, as e.g. shown by Valiev et al. for Armco iron [21]. Grain boundaries are sources and sinks for dislocations. The emission of dislocations from grain boundaries in ultrafine-grained materials was already reported by Wang et al. for copper [22] and Mompiou et al. for aluminum [23]. In this context, it has to be regarded that the grain boundary character of SPD deformed materials differs strongly from relaxed grain boundary structures which are typically for CG materials. This different grain boundary character is due to extrinsic dislocations stored at the grain boundaries [24], which are also often denoted as ―non-equilibrium‖ grain boundaries, compare Nazarov et al. [25], and a higher access volume at the grain boundaries [26]. Ovid`ko et al. [27] described theoretically also for low angle grain boundaries that these extrinsic dislocations can trigger the dislocation emission at the grain boundary. Thus, a deeper insight to the dislocation interaction at grain boundaries is the key aspect for understanding plastic deformation of UFG and bimodal materials with a rather high fraction of the grain boundary volume.

Bimodal grain size distributions consisting of coarser grains and grains in the ultrafinegrained regime have been first reported by Wang et al. [28] and Höppel et al. [29]. The latter paper showed that a bimodal microstructure with a particular amount of coarser grains embedded in an UFG matrix in copper is beneficial for the fatigue life in strain controlled fatigue tests. It was also discussed that the coarse grains mainly carry the plastic deformation and thus play a major role for the onset of localized damage during cyclic loading. Besides others, the very positive effect of a bimodal microstructure on the ductility in monotonic tensile tests has been intensively reported by Ma and Wang [22, 28, 31]. Qian et al. [32] reported for bimodal nickel an improved fatigue crack growth resistance. The positive effect 4

on the ductility of a bimodal grain-structure was also reported by Schuh et al. [33] for nanocrystalline compositionally complex alloys of the CoCrNi-family. As already mentioned earlier, fcc-UFG/NC materials often show a pronounced strain-rate sensitivity. Gray et al. [34] were one of the first authors who reported that UFG fcc materials, like copper, show an increased SRS. Wie et al. [35] showed for copper that SRS depends on the grain size and that the SRS is only increased below a critical grain size. In this context, it is also reported for UFG copper that SRS depends on the number of ECAP-passes [36]. Thus, there is an interplay between the grain boundary character (high/low angle boundaries), an increasing testing temperature leading to enhanced SRS and an increasing mean grain size leading to a reduced SRS. This is also shown in [36], where compression strain rate jump tests for UFG copper were performed at different temperatures between RT and 150 °C for 4 and 8-ECAP passes. It was found that SRS is significantly higher for the 8-pass material compared to the 4-pass material. For the N8-material SRS was strongly increasing with raising the testing temperature up to 125 °C albeit the grain structure changes from UFG to a bimodal one. At 150 °C a sudden drop in SRS was obtained as the grain structure was then completely coarsened to the CG regime [36]. The role of ultrafine and conventionally grained layers and their contributions to the enhanced SRS was also investigated by Ruppert et al. [37]. The authors investigated the local and global SRS-behaviour of layerwise bimodal Allaminates, produced by Accumulative Roll Bonding. It was also concluded, that thermally activated annihilation of dislocations at the interfaces between CG and UFG layers is the dominant time-dependent deformation mechanism.

Although bimodal structures have been first reported for more than a decade ago, compare [29], there is no systematic investigation of the influence of the degree of bimodality on the mechanical properties and in particular on the SRS. In this work the deformation behavior of copper with a fully ultrafine-grained, a partly coarsened bimodal and an almost fully coarsened microstructure is systematically investigated using compression strain rate jump tests. The obtained mechanical properties combined with a microstructural characterization of the different conditions allow drawing a clear picture of the dominating deformation mechanisms in those microstructures.

2. Experimental Oxygen free high-conductivity (OFHC) Cu of 99.99 % purity was used. Bars with a square cross section with edge length of 15 mm and length of 90 mm were processed by ECAP at the 5

Institute of Materials Science and Engineering, Prof. M. Wagner, at the University of Chemnitz. The bars were deformed using Route Bc (rotation of 90° around the extrusion axis). Samples after 4 and 8 ECAP passes (also denoted as N4 or, respectively, N8) were investigated. After the ECAP-process cylindrical samples with a diameter of 4 mm and a height of 4.7 mm were cut from the bars. The specimens were then annealed at 125 °C or, respectively, at 140 °C for up to 60 minutes.

The Vickers hardness HV3 was measured using a KBW 10-V hardness measurement system from KB Prüftechnik GmbH. Compression tests were performed at a universal testing machine Instron 4505 equipped with a Hegewald & Peschke control software. Compression tests carried out at 21 °C, 75 °C or, respectively, 100 °C for samples heat treated at 125 °C in a strain rate range from 10-3 s-1 to 10-5 s-1, see Figure 1. All tests at elevated temperatures have been started only 20 minutes after the testing temperature was reached in order to ensure thermally stable conditions during the tests.

Figure 1: Sequence of strain-rate jumps during compression tests. Strain-rates are given at the deformation intervals.

In addition, another set of specimens were heat treated at 140 °C and compressed at 75 °C with the same setup as specimens heat treated at 125 °C. The strain rate sensitivity was determined in all tests by analyzing the strain-rate jump from 10-5 s-1 to 10-4 s-1 at approximately 20 % of true strain. By this procedure it is ensured that the strain rate sensitivity is determined at the condition of stable dislocation arrangements. However, the analysis could also be made at other strain-rate increments. In order to ensure comparable and stable microstructural conditions we selected only the last strain-rate jump increment from 10-5 s-1 to 10-4 s-1 at approximately 20 % of true strain for further analysis. In 6

order to ensure that the obtained SRS-values reflect for the differences for stable microstructural conditions (dislocation structures) the SRS has been calculated by either backextrapolation of the quasi-saturation stress or by back-extrapolation considering constant strain hardening behavior. Thus, the correlated stress levels 2 (lower stress value) were determined at the strain when the strain rate jump has been applied. Figure 2 shows schematically the two different principal cases.

Figure 2: Scheme how stress interval σ1 – σ2 was determined back-extrapolation from a) quasi stationary stress or b) from strain intervals with constant hardening behavior.

For the microstructural characterization the specimens were ground and polished to 1 µm and in a final step electrolytically polished. For this the electrolyte D2 from Struers was used at a voltage of 15 V for 5 – 10 seconds. The microstructure was investigated with a scanning electron microscope Crossbeam 1540 EsB from Zeiss, using a quadrant backscatter detector. Electron backscatter diffraction (EBSD) measurements were done using an EBSD-detector from Oxford Instruments.

3. Results 3.1 Hardness The specimens that have been subjected to 8 ECAP passes show a distinct decrease in hardness with increasing annealing time at 125 °C. Starting from 146 HV3 after ECAP pressing the hardness decreases only slightly within the first 10 minutes of annealing, but then deteriorates rapidly between 10 and 30 minutes down to about 90 HV3 and further decreases weakly to 81 HV3 after 60 min of annealing, see Figure 3. It is also worth to note that the scatter of the measurements differs significantly for the specimens annealed at the one hand side for 0 min or 60 min and on the other hand for annealing times between 10 min and 45 min. The latter conditions show an unusual large scatter in comparison to the measurements at 0 or 60 minutes. This unusual scatter of the hardness data can be explained by a bimodal grain size distribution that develops during annealing times of 10 minutes or longer, compare Figure 3 and Figure 7. As the monomodal grain size distribution spreads into a distribution for the coarsened and one for the ultrafine grained grains with increasing annealing time a 7

stronger scatter of the hardness data is obtained. The degree of the remaining UFG-grains reduces with increasing annealing time, see Figure 3. Thus, after an annealing time of 20 minutes approximately 60 % of the grains are still in the ultrafine-grained regime. This fraction reduces further to 25-30% after an annealing time of 45 minutes. In the case for 0 min or, respectively, 60 minutes of annealing, either a homogenous UFG or CG microstructure can be found, resulting also in the small scatter of the hardness data, see Figure 3 and Figure 7a) and d).

Figure 3: Evolution of the hardness for copper with 4 or, respectively, 8 ECAP-passes for annealing times from 0 min to 60 min at 125 °C. The fractions of grains in the ultrafine grained regime, i.e. smaller than 1 µm, are plotted on the second Y-axis for the 8 ECAP-passes specimens

For the material that has been subjected to 4 ECAP-passes the initial hardness is rather similar compared to the material subjected to 8 passes. However, the hardness evolution with increasing annealing time differs strongly to that of the specimens subjected to 8 passes. The hardness decreases from 148 HV3 to 135 HV3 after 20 min annealing at 125 °C. Up to an annealing time of 45 minutes the hardness is more or less constant. After 60 min the hardness drops to a value of 126 HV3, Figure 3. Again, a strong scatter of the hardness data is visible, 8

caused by the onset of the evolution of a bimodal microstructure. It should also be pointed out, that the coarser grains are much more inhomogenously distributed for the 4-pass specimens and the few CG grains are rather large, both compared to the 8-pass specimens.

3.2 Compression strain rate jump tests Compression strain rate jump tests allow to gain an in depth insight to the deformation behavior and the influence of the microstructure on to. Thus, compression tests have been performed at strain rates between 10-3 s-1 to 10-5 s-1 at RT, 75 °C or 100 °C, in order to prove also for the deformation behavior at elevated temperatures. Figure 4 shows the stress-strain behavior of the compression strain rate jump tests for the N4 conditions on the left (Figure 4a, c, e) and for the N8 specimens on the right (Figure 4b, d, f) after annealing at 125 °C for different time increments (0 min – 60 min). For the N4-specimen tested at RT (Figure 4a) it is visible that the stress-strain response for the material annealed for 10 min or, respectively, 20 min is rather unaffected compared to the as-ECAPed condition. The condition annealed for 45 minutes exhibit a reduced yield-stress but, due to strain hardening, the flow stress increases with plastic straining and reaches almost the level of the specimens annealed for 10 and 20 minutes. On the other hand, the specimen annealed for 60 minutes exhibits a more strongly reduced yield strength and does not show pronounced strain hardening during the complete test. In addition, the strain rate sensitive behavior is decreased. At a testing temperature of 75 °C (Figure 4c), the stress-strain behavior of all conditions is almost identical. Only small differences in the reached stress levels are visible. In contrast, at a testing temperature of 100 °C (Figure 4e) the stress-strain-behavior of the conditions 0 min, 10 min and 20 min is rather similar, showing only slight differences in the yield strengths, which level out during further plastic straining. For the conditions annealed for 40 min or, respectively, 60 min, the yield strengths are reduced more strongly and strain hardening becomes more pronounced. A detailed look at the tests performed at 75 °C and 100 °C reveal that for the pure UFG-structures small softening during plastic straining is visible. This strain softening at elevated temperatures is already described in [40] for UFG Cu.

Regarding the N8 material, a deformation behavior either typical for ultra-fine grained or coarse grained microstructures is obtained, depending on the annealing time, see Figure 4b. The untreated as-ECAPed (0 min) UFG microstructure shows a high yield strength and nearly no further strain hardening after about 2 % of plastic straining. However, a slight decrease in strength with increasing plastic strain after more than about 15 % of strain can be noticed, 9

indicating some structural instabilities. EBSD-measurements confirmed that the grain size did not change during testing. In addition, a pronounced dependence of the flow stress on the deformation rate when tested at room temperature is apparent. This behavior is typical for single-phase (type I) fcc-materials with an UFG microstructure, compare for example [19, 43]. A short annealing treatment at 125 °C for 10 minutes does not change the observed behavior significantly.

By an annealing treatment of 20 minutes or longer the deformation behavior changes significantly. The yield strengths are significantly reduced and strain hardening becomes very pronounced. The pronounced dependence of the flow stress on the deformation rate strongly diminish with increasing annealing time. When the testing temperature is increased to 100 °C, a very similar deformation behavior is obtained compared to the results obtained at RT. However, the yield strengths are lower and the flow stresses are much stronger dependent on the applied deformation rates, compare Figure 4f). At a testing temperature of 75 °C, Figure 4d), the deformation behavior is also rather similar to what is known from the other tests performed at RT and 100 °C: The tests performed on samples which were in the as-received condition or annealed for 10 min exhibit after a certain amount of plastic strain a steady state behavior with constant flow stresses for all strain-rate intervals, except for the lowest strain rate. The flow stress depends more strongly on the strain rate than in tests that are carried out at room temperature. Both conditions show a deformation behavior typical for UFG materials. The specimens, which were annealed for 30 minutes (not displayed in Figure 4d), 45 minutes or, respectively, 60 minutes, exhibit a strongly reduced yield strength and pronounced strain hardening during all deformation intervals. This behavior is well known for CG materials. In contrast, the deformation behavior of the condition annealed for 20 min is rather untypical for either UFG or CG microstructures: A high yield strength and only very small strain hardening are observed and the dependence of the flow stresses on the strain rate is almost negligible. In order to prove for this unusual behavior, another annealing heat-treatment at 140°C for different time increments has been performed in addition. The results of the compression strain rate jump tests for these conditions at 75 °C testing temperature are shown in Figure 4g. Similarly to the behavior of the specimens annealed at 125 °C a strong dependence of the flow stress on the strain rate for 0 min or the short annealing time of 5 min, with nearly no strain hardening through the whole experiment (UFG behavior) is obtained. On the other hand, for longer annealing times (20 min and more) pronounced strain hardening is observed (CG behavior). In contrast, the 10

deformation behavior of the specimen annealed at 140 °C for 10 min is again rather untypical for either UFG or CG microstructures and is rather comparable to the behavior obtained for the specimen annealed at 125 °C for 20 min. For both conditions, the flow stress is almost insensitive to the applied strain rates and no strain hardening or softening was observed during the complete tests.

The observed overall mechanical behavior has to be discussed in view of the changes in the microstructure. With increasing annealing time the amount of coarsened grains increases, see Figure 3. While the short-time annealing and the small amount of coarser grains of less than 15 percent (after 10 minutes annealing) does not change the mechanical behavior significantly, a strongly increasing amount of coarse grains affect the mechanical behavior tremendously: The yield strength is lowered and strain hardening is way more pronounced when the fraction of CG-grains increases further. Moreover, the strain rate sensitivity of the material becomes smaller with increasing amount of CG-grains. Pronounced differences are also prevalent between the N4 and the N8 specimens. As already visible in Figure 3, the hardness of the N4-specimens decreases not very strongly with increasing annealing time. In contrast, for the N8-specimens the hardness drops significantly with increasing annealing time and amount of CG-grains. This behavior is also displayed by the compression tests. For all testing temperatures, the N4 specimens show only a small decrease of the flow stresses with increasing annealing time when compared to the N8 specimens. For the latter specimens, a pronounced decrease of the yield strengths and the flow stresses and a strong increase of strain hardening is observed for all annealing times except for the annealing for 20 min at 125 °C and 10 min at 140 °C. As already mentioned above, during annealing treatment the coarse grains became rather inhomogeneously distributed and larger for the N4 material both compared to the N8 counterparts. Thus, in the following we mainly focus on the behaviour of the N8 material.

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Figure 4: Compression strain rate jump tests performed on a),c),e) N4 material and 12

b),d),f),g) on N8 material at different testing temperatures. Different conditions annealed at a)-f) 125 °C and g) at 140 °C for various time-increments were selected. For reasons of clarity, the graphs for an annealing time of 30 minutes is omitted for all conditions. In order to understand the obtained mechanical behavior of the N8 material better, Figure 5a shows the amount of strain hardening with increasing annealing time. The amount of strain hardening stress was calculated by the flow stress taken at 20 % of plastic strain minus the 0.2 % yield stress, both determined at a strain rate of 10-4 s-1. In Figure 5b the same (selected) graphs from Figure 5a are plotted but in addition the fraction of the coarse grains is shown and regimes of different deformation mechanisms are displayed. For the tests performed at RT and 100 °C S-type curves are obtained which clearly exhibits that as long the amount of CG fraction is small (less than 15 %) strain hardening is not very pronounced (regime I: UFG dominated). As it is expected, the strain hardening is higher for the RT experiments and lower for the experiments performed at 100 °C. With increasing annealing time and further increasing CG-fraction, strain hardening increases strongly (regime II: dominated by the degree of bimodality) and, within the scatter of the data, saturates at values that are about three times higher than for the UFG dominated conditions (0 min, 10 min), when the CGfraction equals  60 % (regime III: CG dominated).

Figure 5: Amount of strain hardening vs. annealing-time at 125 °C. a) data for testing temperatures at RT, 75 °C and 100 °C. b) selected graphs from a) but in addition the CG-fraction is displayed on the right Y-axis. Also regimes of different deformation mechanisms are indicated: regime I: UFG dominated, regime II: dominated by the degree of bimodality, regime III: CG dominated.

However, the behaviour for the specimens tested at 75 °C is different, see Figure 5a. As the testing temperature lies between RT and 100 °C, it is also expected that the strain hardening 13

curve should lie in-between. For the as ECAPed- (0 min) and the 10 min annealed conditions the amount of strain hardening fits to the expectation. This holds also for annealing-times of 30 minutes and longer. Contrarily, the specimen annealed for 20 min and tested at 75 °C shows a tremendous drop in strain hardening below the value that is obtained for the specimen annealed for 10 minutes and tested at 100 °C. In this context it has to be mentioned that due to the already described softening during compression testing at 75 °C for the as ECAPedmaterial (0 min) the maximum stress level obtained at a strain rate of 10-4 s-1 at 6 % plastic strain was taken to calculate for the amount of strain hardening. The data one would obtain at 20 % plastic strain for the 0 min condition is also displayed in brackets in Figure 5a).

3.3 Strain rate sensitivity Based on the results of the compression strain-rate jump test also the strain rate sensitivity (SRS) was determined. It turns out that the different microstructural configurations (fully ultrafine-grained, bimodale, CG microstructure) and the testing temperature are most important for the deformation behaviour. Comparing the as-ECAPed conditions, SRS for the N8 specimen is signifcantly higher than the value for the N4 specimen. This holds not only for the experiments performed at RT but also for the tests at 75 °C and 100 °C. Expectingly, the SRS values increase with increasing testing temperature, compare Figure 6a. An annealing treatment at 125 °C leads to a slight decrease of the SRS after 10 minutes annealing time and a pronounced decrease after 20 minutes, when the tests for the N8 material at a testing temperature of 100°C are regarded. The SRS values decrease further with increasing annealing-time. The behaviour at RT is qualitatively similar but the relative decrease in SRS is much less pronounced. The N4 condition shows an evolution of the SRS value at 100 °C testing temperature which is rather close to the behaviour of the N8 specimen at RT. However, when the tests performed at 75 °C are regarded, some significant differences can be observed for the N8 material, see Figure 6b. Similar to the behaviour for a testing temperature at 100 °C the SRS-values slightly decrease when the specimen is annealed at 125 °C for 10 minutes. Surpringsingly, after 20 minutes annealing at 125 °C the strain rate sensitivity drops strongly from 0.062 down to 0.006 and increases again to 0.029 for specimens annealed for 30 minutes. Further annealing leads again to a decrease in the SRS down to a value of 0.016, Figure 6b. A similar trend is observed for the specimens annealed at 140 °C and tested at 75 °C. For very short annealing times (up to 5 minutes) a small decrease in strain rate 14

sensitivity is visible. Subsequently, a strong decrease in strain sensitivity down to a minimum value of 0.01 is obtained when the sepecimen is annealed for 10 minutes, SRS increases again up to 0.031 by annealing for 20 minutes. Again, further annealing leads to a decrease of SRS down to 0.02 after 60 minutes of annealing (For a comprehensive view of the obtained SRS values see TableA1 in the appendix.).

Figure 6: Strain rate sensitivity for different a) numbers of ECAP-passes, testing temperatures and annealing times at 125 °C and b) for 8 ECAP-passes and different annealing times at 125 °C and 140 °C, tested at 75 °C.

3.4 Microstructure and grain growth behavior After 8 ECAP-passes, a homogenous ultrafine-grained microstructure with globular grains, see Figure 7 a), b), has been obtained. 20 minutes of annealing treatment at 125 °C lead already to a bimodal microstructure, see Figure 7c). The coarsened grains are in the range from 5 µm to 10 µm and are embedded in an ultrafine matrix. After 60 minutes of annealing the microstructure is coarsened by 92 %, Figure 7 d, see also Figure 5 b)). The specimens subjected to 4 ECAP-passes show a completely different behavior (not displayed here): The microstructure after ECAP processing is also ultrafine-grained. After annealing at 125 °C for 20 minutes, some grains show an abnormal grain growth. Those grains are much larger than the coarsened grains in the N8 material and are also not so evenly distributed across the specimen. Even after an annealing time of 60 minutes most of the grains are in the ultrafine grain size regime for the 4 ECAP pass material.

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Figure 7: Microstructure of copper after 8 ECAP-passes and annealing at 125 °C for a) 0, b) 0 (detail), c) 20 and d) 60 minutes.

Increasing the annealing temperature to 140 °C, first isolated coarsened grains are found after 5 minutes in the case of the N8 material. After 10 minutes a bimodal structure develops, which is comparable to the specimens annealed at 125 °C for 20 min. After 20 minutes at 140 °C the grain structure has nearly completely coarsened, see Figure 8 a), b) and c). Electron backscatter diffraction (EBSD) measurements revealed for specimens which were annealed for 10 minutes at 140 °C that the grains coarsened show no preferred crystallographic orientations, see Figure 8d).

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Figure 8: Microsturcture of copper (N = 8) after annealing at 140 °C for a) 5, b) 10 and c) 20 minutes and d) EBSD image after 10 min annealing.

4. Discussion

4.1 Hardness The evolution of hardness with increasing annealing time clearly showed a higher thermal stability for specimen processed for 4 ECAP-passes, when compared to the samples processed for 8 ECAP passes. For the latter case, the hardness starts to drop strongly when the specimens are annealed at least for more than 10 minutes at 125 °C and declines by about 44 % during further annealing. In contrast, the specimen subjected to only 4 ECAP-passes shows only a decrease in hardness of 15 % after 60 minutes annealing. This behavior is correlated to a strong increase of the grain size during the annealing process in the material processed for 8 ECAP passes, see Figure 7 a, c and d. In contrast, grain coarsening in the material after 4 ECAP-passes is rather inhomogeneous and not so pronounced. When the SEM-images of the initial states are regarded, the grain size for both conditions appear to be 17

nearly the same. It is well known that the amount of high angle grain boundaries increases during further ECAP-processing from 4 to 8 passes although the grain size and the strength of the materials does not change significantly. The evolution of the misorientation has been investigated on aluminum by Saxl et al. [38] and on copper by Molodova et al. [39], both showing a strong increase of the amount of high angle grain boundaries (HAGB) with increasing number of ECAP-passes. From earlier own investigations on the same material it is known that with increasing number of ECAP-passes the misorientation between the grains is increasing although the grain size and the resulting deformation resistance is unaffected. For the N4 material the low angle grain boundary fraction is about 80 %, whereas for the N8 material it amounts to approximately 50 % [36]. Thus, the strong differences in the coarsening behavior and the thermal stability are most likely a consequence of the character of the grain boundaries. It is also evident that a higher amount of HAGBs leads to a stronger coarsening of the ECAPed material and that the grain boundary mobility of HAGB has to be higher than that of LAGBs.

4.2 Strain rate sensitivity Another aspect that seems to be governed by the character of the grain boundaries, is the strain-rate sensitivity. For both conditions (N4 and N8) a dependence of the flow stress on the applied strain-rate was obtained, compare Figure 4. However, it also turns out that the strain rate sensitivity is more pronounced for the material processed for 8 ECAP-passes. This behavior can be again explained by the higher amount of high angle grain boundaries, implying that, according to Blum and Zheng [8], the relevant time-dependent deformation process in UFG materials is the thermally activated annihilation of dislocations at the grain boundaries. Diffusion of dislocations along grain boundaries appears to be easier in the material with a higher amount of HAGBs. The eased climbing processes along the HAGBs leads to dislocation annihilation with other dislocations stored at the grain boundary. This process determines the steady state flow stress often observed in ultrafine grained materials, and accounts also for the small strain hardening, compare Figure 5. With increasing testing temperature the strain-rate sensitivity of both ECAP-conditions becomes stronger. For Cu processed for 8 ECAP-passes m is two times higher at a test temperature of 100 °C compared to the SRS measured at room temperature. Therefore, the annihilation processes of dislocations at grain boundaries are more pronounced at elevated temperatures [19,36]. In this context, it should be pointed out that even at 100 °C the ultrafine grains of the heat-treated conditions remain stable during the compression tests. However, for 18

the as-ECAPed condition, slight strain induced coarsening takes place, see also Bach et al. [40]. However, as the SRS analysis was always taken at  20 % total strain the contribution of strain induced coarsening of the UFG-grains can be disregarded. At this point, we would like to remind, that the material, except for the as-ECAPed-conditions was heat-treated prior to testing at 125°C or, respectively, at 140°C for different annealing times. As the testing temperatures (RT, 75°C, 100°C) were always below the annealing temperature and as all tests at elevated temperatures were only started 20 minutes after the testing temperatures have been reached the first time, thus thermally driven changes during compression testing of the UFG structure are rather unlikely and have not been observed. Compared to the tests performed at 100 °C on the N8 material the tests conducted at 75 °C revealed an almost identical SRS of 0.07 in the initial UFG state. However, the SRS significantly changes when the annealed samples are considered. For a testing temperature of 75 °C the SRS sharply declines from 0.07 for the as ECAPed-condition down to 0.005 for the specimen annealed for 20 minutes at 125 °C. With further annealing the SRS increased again up to 0.029 after 30 minutes of annealing and for further annealing the value declines again to 0.02 after 60 minutes.

The different deformation behaviors during the compression strain rate jump tests described in paragraph 3.2 can be correlated to ultrafine-grained, bimodal or coarsened microstructures. In the UFG dominated states, where, according to Figure 5b, the amount of coarser grains is not larger than 15%, deformation is mainly controlled by the thermally activated annihilation of the dislocations at the boundaries of the ultrafine grains. As described earlier by Blum and Zheng [8] in this regime the time-depending step is the thermally-activated annihilation of dislocations at the grain boundaries. Consequently, the recovery rate is directly related to this process. According to Figure 5, the amount of strain hardening is low in UFG dominated microstructures, thus recovery has to be rather effective in these structures. However, it also becomes obvious that the recovery rate does not completely equilibrate the deposition rate of new dislocations, otherwise strain hardening would not be observed. When the long term annealed conditions (30 min, 45 min, 60 min) are regarded, the CG-fraction increases to 64 %, 72 % or, respectively, 92 %, which indicates that the remaining UFG-grains are isolated islands in a matrix with coarse grains. Consequently, the yield strength is significantly reduced and strain hardening is strongly pronounced. Thus, it becomes obvious that in the CG dominated regime the recovery rate is strongly diminished. By a simple calculation one can estimate the grain boundary volumes for the different states. Assuming a 19

grain boundary thickness of 1 nm, an UFG-grain size of 200 nm and a CG-grain size of 2 µm one obtains a grain boundary volume of 2 % for the UFG condition or, respectively,  2 ‰ for the CG condition. In other words, the grain boundary volume is one order of magnitude smaller than in the UFG condition and thus, the recovery rate cannot be as high as in the UFG regime. Consistently, the amount of strain hardening in the CG regime is by a factor of  3 higher than in the UFG regime, see Figure 5, which implies, derived from the well-known Taylor equation, that the recovery rate has to be roughly 9 times smaller in the CG regime than in the UFG regime. Interestingly, the roughly 9 times smaller recovery rate in the CG condition fits pretty well to the by one order of magnitude smaller grain boundary volume. Thus, this simple semi-quantitative estimation strongly support the proposed mechanism of thermally activated annihilation of dislocations at the grain boundaries. By an annealing time of 20 min at 125 °C a microstructure consisting of 40% of coarser grains and 60 % of UFG grains is obtained. Thus, the coarse grains are embedded in an UFG matrix. In this regime of bimodality the strain rate sensitivity at RT is only slightly reduced, Figure 6a. However, at RT the amount of strain hardening, Figure 5a, is as high as for the CG-regime, indicating, that recovery at this low temperature is not efficient enough to equilibrate the deposition of new dislocations. We can also derive therefrom that the predominant amount of dislocation sources have to be active in the coarsened grains, otherwise we will not observe the same amount of strain hardening as it was found for the CG-dominated regime. Due to the prevailing localization of plastic deformation in the coarse grains and due to the low testing temperature the generation rate (in the coarse grains) of new dislocations is significantly higher than the recovery rate at the CG/UFG grain boundaries. At 100 °C testing temperature the SRS drops from 0.07 for the as-ECAPed condition to 0.05 after 20 min of annealing at 125 °C. However, the amount of strain hardening, Figure 5a, is not as high as it is for the CG dominated regime. This behavior can in principal be explained by either a strongly increased recovery rate at the elevated testing temperature, or by a more homogenously distribution of plastic deformation between the coarse and ultra-fine grains.

At a testing temperature of 75 °C and an annealing time of 20 min at 125 °C the SRS significantly drops from 0.07 for the as-ECAPed condition down to 0.005, Figure 6b. Also the amount of strain hardening is significantly reduced, when compared to the data obtained for the UFG regime (0 min, 10 min) and also to the data obtained for a testing temperature at 100 °C, Figure 5a. Thus, it is evident that for this particular microstructural arrangement and 20

testing conditions the recovery rate almost fully equilibrates the generation rate of dislocations. In this context it has to be pointed out, that for all other conditions (0 min, 10 min, 30 min, 45 min, 60 min) the data points in Figure 5a completely fulfil our expectations, that with increasing temperature the amount of strain hardening decreases and that the amount of strain hardening is different to the CG and UFG dominated regimes. However, for the 20 min annealed condition the amount of strain hardening is rather unexpected. The same holds for the SRS data in Figure 6b. As this abnormal behavior of the SRS data has been repeatedly observed also for the condition annealed at 140 °C, it becomes clear that there are some particularities that account for the observed behavior.

Taking into account all of the above described findings a rather likely explanation for the observed behavior is that there is an interplay of an increased recovery due to thermally activated annihilation at the grain boundaries on the one side and a different amount of localization of plastic deformation in coarse and ultra-fine grains on the other side. In more detail the following picture can be drawn: In the UFG dominated regime, a relatively high SRS is obtained which is due to the relative high ratio of grain boundary volume to grain interior volume and the small grain size. Thus, annihilation of dislocations at the grain boundaries can easily take place and consequently for different strain rates different flow stresses are measured, see also [19,35,40]. In UFG microstructures grain boundaries act as sinks and sources for dislocations [41] and due to the homogenous grain structure, plastic deformation is homogenously distributed. Thus, the obtained strain-rate dependent different flow stresses are the consequence of an equilibrium of dislocation formation and annihilation at HAGBs. As mentioned above, for annihilation processes thermally activated climb of dislocations along the grain boundary is necessary. As this process is time-dependent different flow stresses develop for different strain rates and a high strain-rate sensitivity is found for the UFG structure. Consequently, due to the eased recovery of dislocations at the grain boundaries and the high amount of grain boundary volume in the UFG regime, the amount of strain hardening in this regime is also small. It is also evident and meets the expectations that with increasing testing temperature the recovery rate increases. The described behavior holds for all testing temperatures in the UFG dominated regime.

For the CG dominated regime, where the microstructure mainly consists of grains in the micrometer range, the deformation behavior changes significantly. The plastic deformation 21

localizes predominantly at the coarse grains. As the number of adjacent grains and thus the grain boundary volume is significant smaller compared to the UFG dominated regime the number of potential annihilation sites for dislocations is significantly reduced and thus recovery is not as efficient as in regime I. Therefore, pronounced work hardening is observed, indicating that the rate for generation of dislocations is much higher than the recovery rate. The amount of piled-up dislocations is determined by the generation of dislocations, which again is influenced by the applied strain-rate. This leads to the observed small strain-rate sensitivity in this regime and pronounced strain hardening during further straining. As for regime I, the described behavior for regime III holds for all testing temperatures.

In regime II the situation becomes more complicated: In this regime, the microstructure consists of grains larger than 1 µm by a fraction of between 15% and 60 % embedded in an UFG matrix. Those larger grains are evenly distributed across the sample and are always surrounded by an ultrafine-grained matrix, see Figure 7c and Figure 8b. In this microstructural configuration we have also to account for the differences in the homogeneity of plastic deformation. Table 1 shows the differences in the yield strengths for the various testing temperatures for the conditions with a solely UFG-structure (0 min) and for an almost purely CG structure (60 min). At RT the differences in yield strength between the CG and the UFG conditions is very pronounced. Although these data reflect only the macroscopic yield strength one can consider the data to estimate the local differences in the yielding behavior for the UFG and CG grains for the bimodal structures. From Table 1 it becomes obvious that at RT a strong localization of plastic deformation to the coarse grains is to be expected. The UFG grains, of course, have also to adapt by plastic deformation in order to keep the integrity of the material, but due to the huge difference in local yield stress, it is rather likely that plastic deformation is highly localized to the CG-grains. Thus, although the mechanism of thermally activated annihilation of dislocations at the grain boundaries is parent for the obtained strain rate dependent deformation behavior, the localization of the plastic deformation is so strongly pronounced that the recovery process cannot balance the dislocation generation rate. Consequently, for these conditions the material exhibits a SRS value that fits in line with the data obtained for regime I and regime III, compare Figure 6a. As a consequence of this behavior, also the amount of strain hardening (Figure 5a) is at the same level as it is found for the CG dominated regime. In line with these findings and as a direct consequence of the high localization of the plastic deformation at the CG grains, which are in this regime always embedded in an UFG-matrix, it has to be considered that the pile-up 22

stress at the grain boundary has to be as high as the yield stress of the neighboring UFGgrains is. Otherwise, a macroscopic uniform deformation is not possible. Thus, it is likely that additional dislocations are stored at the grain boundaries in order to keep the compatibility of the material. Recovery processes at the grain boundaries might also be affected by this. With increasing testing temperature to 75 °C the difference between the yield strength of the UFG and CG condition, Table 1, stays almost the same. Thus, plastic deformation starts to be mainly localized to the coarse grains and the UFG-grains are deforming by intense pile-up stresses for reasons of compatibility, as already discussed for the behavior at RT. This localization of the plastic deformation to the coarse grains leads to a pile-up of the dislocations at the grain boundaries. Consequently, the dislocation source will have to overcome an additional back stress from the pile-up. If the recovery rate of the dislocations at the grain boundaries is as high as the generation rate of new dislocations, which is driven by the pile-up back stress, a steady-state like, rate insensitive deformation behavior with no hardening will be obtained. Thus, a direct coupling between the dislocation generation rate and the recovery rate via a pile-up-source stress interaction is likely to govern the deformation behavior. Obviously, this is exactly what we have observed. Although plastic deformation is localized in the coarse grains, the amount of strain hardening, Figure 5a, is lowest. Due to the elevated temperature, recovery at the grain boundaries is enhanced compared to the RT-tests. For this particular condition, the flow stress becomes almost insensitive to the strain rate and strain hardening is strongly diminished, as the rate of generation of new dislocations in the coarse grains is almost completely equilibrated by the recovery rate. This behavior is also strongly supported by the test performed at 75 °C on the material annealed at 140 °C for 10 min. The question may come up, why is then a reduced SRS with increasing temperature not observed for the UFG states? In our opinion, the relevant point is that the deformation mechanisms are changing. In the UFG regime the grain boundaries act as sources and sinks for dislocations. This behaviour is already known from literature [23,27]. With increasing CG-fraction, plastic deformation mechanism changes. Plastic deformation is more localized to the CG-grains, which are compared to the UFG-regions softer by about a factor of 2.4. They start to plastically deform and pile-ups will form, until the pile-up stress is as high as the yielding point of the surrounding UFG grains and those grains will subsequently plastically deform in order to keep the compatibility. However, the dislocation sources in the CG-grains have to be more active to reach the necessary pile-up stresses in order to foster the plastic deformation in the UFG grains. The observed low strain hardening behaviour and the low 23

SRS value for the bimodal condition tested at 75°indicate that for this condition, thermally activated annihilation of dislocations at the grain boundary is not a dominating deformation mechanism. We assume, that due to the particular arrangement and the high differences in the yield stresses of the UFG and CG grains, this mechanism starves as there are not enough annihilation partners at the boundary available. However, at 100 °C, the differences in the yield stresses of the CG and UFG-conditions are way more smaller (see Table 1: only 1.8 the YS of CG). Thus plastic deformation becomes less localized to the CG-grains and consequently, the UFG grains will more easily contribute to the plastic deformation. As in UFG-structures, the grain boundaries act as sources and sinks for dislocations, there will be a higher probability for dislocations entering the grain boundary to find an appropriate annihilation partner within climbing distance.

Table 1: Yield stresses and differences in yield stresses for the UFG condition (0 min) and the long-term annealed (60 min) CG-condition at different testing temperatures. Testing

YS / MPa YS / MPa YS / MPa

temperature /°C

UFG

CG

21 (RT)

377

182

195

75

352

149

203

100

267

148

119

From Figure 6a and b (and from Table A1 in the Appendix) it becomes evident, that at a testing temperature of 100°C recovery is not further enhanced when compared to the behavior at 75°C, as the SRS values at 75°C, or, respectively, 100°C for the as-ECAPed condition are exactly the same. Thus, one would expect that the mechanical behavior at 100 °C would generally be similar to that at 75°C but at a lower stress level. However, these considerations do not fit to what we have obtained from our experiments. At this point, again the different localization of plastic deformation has to be taken into account. From Table 1 we can deduct, that the difference between the yield stress of the UFG and CG-conditions at 100°C is significantly reduced to 60 % of the values obtained for 75 °C or, respectively, 21 °C testing temperature. Thus, it is assumed that at the highest testing temperature the pile-up stress necessary to transform the plastic deformation form the CG-grains to the UFG-grains is significantly smaller. Thus, UFG-grains will contribute more strongly to plastic deformation and the dislocation generation is more homogenously distributed between the coarse and 24

ultra-fine grains. The obtained amount of strain hardening for the specimen annealed for 20 min at 125 °C also supports this suggestion. If plastic deformation would be still mainly localized only to the coarse grains, the amount of strain hardening, Figure 5a, shall be then as high as for the CG dominated regime and the behavior should be similar to that obtained for a testing temperature of 21°C. This is not the case. The amount of strain hardening for this microstructural configuration lies fairly well in between the data for the UFG and CG dominated regime. Due to the more homogenous deformation and the reduced pile-up stresses to the dislocation sources in the CG-grains the equilibrium between the pile-up back stress driven generation of new dislocations in the coarse grains and the recovery rate observed for the testing temperature at 75°C is unsettled at a testing temperature of 100 °C. In addition, the ultrafine-grains also contribute to the plastic deformation, where the grain boundaries act as dislocation sources and sinks, compare also [23,27]. Bringing all the observations together, it can be concluded, that thermally activated annihilation of dislocations at the grain boundaries is the dominating deformation mechanism not only for UFG but also for bimodal grain structures. However, for the bimodal structures one has also take into account that depending on the temperature the particular UFG and CG fractions differently contribute to plastic deformation.

Grain boundary sliding as mechanism for the deformation of the investigated microstructures could explain the high SRS for the homogeneous ultrafine-grained microstructure and small SRS observed in the completely coarsened microstructure. However, the absence of a dependence of the flow stress on the deformation rate in the bimodal microstructure could not be explained by grain boundary sliding. As seen in Figure 7c) and Figure 8b) the larger grains are still surrounded in an ultrafine-grained matrix. Thus, deformation should still mainly take place in the globular ultrafine-grained matrix, as grain boundary sliding should be easier in the matrix due to the high number of non-equilibrium dislocations in an ultrafine-grained microstructure [17, 42]. With a steady decrease of the fraction of ultrafine grains and an increasing fraction of larger micrometer sized grains, which interfere with the flow of the ultrafine-grained matrix, the SRS should decrease steadily. Thus, grain boundary sliding could not explain the very low SRS values for the tests conducted at 75 °C and for the specimens annealed for 20 minutes at 125 C or 10 minutes at 140 °C. Dislocation interactions at grain boundaries could explain the high SRS in fully and nearly fully ultrafine-grained microstructures. It can also explain the strong drop in SRS for bimodal microstructures and the subsequent slight increase for more homogenous but larger grained 25

microstructures. Dislocation interactions at grain boundaries can cause also grain boundary movement or grain rotation as a resulting effect, but this does not automatically imply that grain boundary sliding is the dominant deformation mechanism in ultrafine-grained and bimodal microstructure. Contrarily, thermally activated annihilation of dislocations at the grain boundaries is obviously the most important mechanism for deformation for the UFG and bimodal grain sizes investigated here. For the solely UFG-condition, the given explanations are in excellent agreement with other researchers, see for example [19,20,35,44].

5. Conclusion Due to the combination of mechanical compression strain rate jump tests with microstructural investigations on UFG, bimodal and coarse grained copper the following conclusions can be drawn: In copper an ultrafine-grained microstructure can be changed gradually from fully ultrafinegrained over a bimodal microstructure to a fully coarsened microstructure by heat treatment. Strain rate sensitivity measurements can be used to get a deeper understanding of the basic deformation mechanisms in the different microstructures. In the case of a fully ultrafine-grained microstructure dislocation formation and annihilation mainly occurs at grain boundaries. Thermally activated annihilation at grain boundaries dominated the deformation behavior, resulting in a high strain rate sensitivity with high stresses for high strain rates and low stresses for low strain rates. For a bimodal microstructure dislocation annihilation is still favorable at grain boundaries, but generation of dislocations is mainly concentrated in the coarsened grains. When coarsened grains are embedded in an ultrafine-grained matrix a constant flow stress can develop, due to a direct coupling between the dislocation generation rate and the recovery rate via a pile-upsource stress interaction. This leads to an almost strain-rate insensitivity behavior for the investigated range of strain rates between 10-5 s-1 to 10-3 s-1 due to the high annealing rate. For a completely coarsened microstructure dislocation annihilation at grain boundaries is still possible, but the grain boundary volume is one order of magnitude smaller than for the UFG dominated regime and thus, recovery at grain boundaries is strongly diminished. In this CG dominated regime, dislocation generation mechanisms and reactions in the interior of larger grain become more prominent than annihilation at grain boundaries.

26

Acknowledgement The authors gratefully acknowledge the funding of the German Research Council (DFG). Declaration of Interest Statement None.

Author Contributions: Conceptualization:H.W.H and M.G.; Methodology: H.W.H, J.B; Investigation: J.B. L. S., M.S., H.W.H; Writing—original draft preparation: J.B.; Writing—review and editing: H.W.H, J.B. M.G. Visualization: J.B. L.S.,M.S., H.W.H. ; Supervision: H.W.H., M.G. Project administration: H.W.H. M.G.

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Appendix

Table A1:

SRS for different ECAP-passes, annealing times and annealing temperatures

Annealing time in min SRS for specimens annealed at 125 °C N=4

Tested at 21 °C Tested at 75 °C Tested at 100 °C

SRS for specimens annealed at 125 °C N=8

Tested at 21 °C Tested at 75 °C Tested at 100 °C

SRS for specimens annealed at 140 °C N=8

Tested at 75 °C

0

2

5

10

15

20

25

30

45

60

0.013

---

---

0.012

---

0.011

---

0.010

0.010

0.010

0.018

---

---

0.018

---

0.016

---

0.015

0.017

0.015

0.023

---

---

0.022

---

0.018

---

0.021

0.020

0.019

0.029

---

---

0.027

---

0.021

---

0.023

0.019

0.018

0.073

---

---

0.062

---

0.006

---

0.029

0.023

0.016

0.070

---

---

0.068

---

0.049

---

0.042

0.040

0.034

0.070

0.069

0.065

0.010

0.029

0.031

0.022

---

0.022

0.019

31