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The dependence of recrystallization temperature and stored energy on rolling strain in polycrystalline copper
Scripta METALLURGICA et MATERIALIA
Vol. 28, pp. 197-200, 1993 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved
THE DEPENDENCE OF RECRYSTALLIZATION TEMPERATURE AND STORED ENERGY ON ROLLING STRAIN IN POLYCRYSTALLINE COPPER L. Liu and I. Baker Thayer School of Engineering, Dartmouth College, Hanover, NH 03755 (Received
November
17, 1992)
Introduction There have been several measurements of the stored energy of cold work for rolled copper [1-5]. Haessner and Hoschek [3] showed that in a high-purity (112.)[111] copper single crystal the stored energy of cold work, Ecw, increased linearly with increasing strain until a saturation stored energy of cold work, Esat, was reached at a rolling reduction of about 96%. Baker and Martin [4] also showed an approximately linear relationship between Ecw and strain up to strains of about 200% in both an internally-oxidized, high-purity (111)[1 i0] copper single crystal and a similar crystal containing A1203 particles. For the (112.)[111] crystal examined by Haessner and Hoschek [3] the increase in Ecw with increasing strain produced a concomitant decrease in recrystallization temperature, TR. However, once Esat was attained increasing the rolling strain further did not lead to a further reduction in TR [3]. Esat for the (112)[111] copper crystal was 84 J.mo1-1 and the minimum recrystallization temperature, Tmin, reached was 120oc. Measurements of Esat and Train for other orientations of copper single crystals by Haessner, Hoschek and Tolg gave values as low as 29 J.mo1-1 for Esat and as high as 300°C for Tmin for (111)[1 10] and (111)[ 112] crystals respectively [5]. The latter authors showed a rough correlation between Esat and Tmin: as Esat increased Train decreased [5]. However, some orientations clearly did not fit into this scheme: a (110)[1 i0] crystal had both one of the lowest Esat values, at 42 J.molA, and also one of the lowest Train values, at 153oc [5]. This indicates indirectly that the stored energy alone does not determine the recrystallization kinetics. In other words, as is well known, the microstructure developed during rolling is important for the subsequent recrystallization kinetics. The purpose of the present paper is to present measured values of Ecw and TR for polycrystalline copper as a function of rolling strain and to compare the results with those cited above. Exoerimental Blocks, 50mm long by 12mm wide by 7.5mm high, of 99.99% polycrystalline copper were annealed at 550oc for 36 hours under vacuum, after which a heavily-twinned 16.5 ktm grain size was obtained, Figure 1. The annealed blocks were rolled at room temperature with reductions of -0.02 mm per pass. After certain rolling reductions, specimens (three at each strain) for differential scanning calorimetry (6mm square) were cut from the blocks using a slow-speed diamond saw. Subsequently, the specimens were etched in 50% nitric acid in order to remove any surface damage which might have caused preferential recrystallization at the specimen's surface. Specimens were placed in one of the two furnaces of a Perkin Elmer DSC7 controlled by a DEC station 325C. A well-annealed copper block of similar weight was placed in the other furnace. The two furnaces were heated at 40oc min-1 and the difference in power between the two furnaces needed to maintain the beating rate was recorded as a function of temperature. When recrystallization occurred in the rolled specimen, a lower power input was required for the specimen furnace, and a peak occurred on a plot of power input versus temperature. The stored energy of deformation for weight of sample used is then the area under the peak; the recrystallization temperature is taken to be the apex of the peak.
197 0956-716X/93 $6.00 + .00 Copyright (c) 1992 Pergamon Press Ltd.
198
ROLLING STRAIN IN COPPER
Vol.
28,
Figure 1. Optical micrograph of 99.99% polycrystaUinecopper annealed at 550°C for 36 hours. Results and Discussion The stored energy of cold work is presented graphically as a function of percentage rolling in Figure 1. Data for (111)[1 i0] and (112.)[111] copper single crystals [3,4] are included for comparison. 50
i
4O 30
~
10
0
i
0
I
50
i
I
100
i
I
150
i
I
200
i
250
Strain ( % )
Figure 2. Stored Energy as a function of percentage strain for rolled polycrystalline copper (o). Each point is the average of three measurements. Also shown are data for (112)[111] (m) [3,5] and (111)[1 i0] copper single crystals (A) [4].
No.
2
Vol.
28, No.
2
ROLLING STRAIN IN COPPER
199
Owing to the limitation imposed by the highest operating temperature of the DSC, no data were obtained for strains less than 20% since recrystallization occurred above 700oc. Ignoring for the moment the datum at 20% strain, the stored energy is an approximately linear function of strain over the range shown. This is to be expected for a metal which exhibits a parabolic work hardening rate [4]. The plot for the polycrystalline copper over this range is approximately parallel to the plots for the (111)[110] and (112)[111] copper single crystals [3,4], except that it is higher. Thus the approximately linear relationship between stored energy and strain appears to be quite general over this range. The line for polycrystalline copper is, of course, higher than those of the two single crystals. This, again, is to be expected. For single crystal copper the dislocations present, to a first approximation, are statistically-stored dislocations [6]. In polycrystalline copper, in addition to the statistically-stored dislocations, geometrically-necessary dislocations are required to accommodate the strain differences at the grain boundaries [6]. Thus, the stored energy of cold work for polycrystalline copper can be written in terms of the dislocation density as Ecw = Gb2 (p s +P o ), where G is the shear modulus, b is the magnitude of the Burgers' vector of the dislocations, andps andpG are the statistically-stored and geometrically-necessary dislocations respectively. Ashby [6] indicated that the geometrically-necessary dislocations would swamp the statistically-stored dislocations at the early stages of deformation but that they would become a smaller percentage of the total as the strain was increased. This appears to be consistent with the observed behavior: the linear region must correspond largely to the increase in statistically-stored dislocations, whilst the data point at the beginning of the linear region for polycrystalline copper must be due to a large initial accumulation of geometrically-necessary dislocations. Returning to the initial datum point for polycrystalline copper, it appears that the initial rate of energy storage is less than that at larger strains. This could be due to scatter in the data. However, similar behavior has been observed in polycrystalline nickel [7]. It may be that the lack of dislocation tangles and locks at lower strains allows dislocation annihilation and rearrangement to occur more easily at lower strains. In other words, recovery removes a larger percentage of the energy put into the material as dislocations. It is worth noting that the two data points at the highest strains recorded for polycrystalline copper are the same. Again, this could be due to scatter in the data. However, these two points suggest that the stored energy is approaching the saturation value, Es~t. In fact, the strain (~200%) is similar to that at which Esat was suggested to have been reached in a (111)[110] copper crystal containing -80nm diameter alumina particles [4]. However, it is much less than the 350% strain that was needed to reach saturation in a (112)[111] copper single crystal [3]. The "saturation" values obtained from two different 50~tm grain-sized specimens of polycrystalline copper by Haessner, Hoschek and Tolg [5] were -75 J. mol -I and 47 J. mol "1 whilst that obtained by Lucci et al. [8] was 52.5 J. mo1-1. Thus, the value obtained here (46 J. mo1-1) is similar, if not quite the same, as the lower end of the values obtained previously. The recrystallization temperature is shown as a function of rolling strain in Figure 3. Data for (111)[1 i0] and (112)[111] copper single crystals [3,4] are also shown. At the highest strains examined (200%) Train seems to have been reached for polycrystalline copper, suggesting that the highest value of the stored energy measured above was indeed Esat. The value of Train at 234°C is very close to that obtained by Lucci et al. [8] in polycrystalline copper but is much higher than the values of 125-170oc obtained by Haessner, Hoschek and Tolg [5]. It is somewhat difficult to make any comparisons between the results of different workers since small increases in solute content can decrease the recrystallization kinetics dramatically: values as low as 70°C have been recorded for very high purity poly.crystalline copper [9]. Note that Haessner, Hoschek and Tolg [5] found that Tmin occurred at a similar strata to that recorded here, see Figure 3.
200
ROLLING
STRAIN
IN COPPER
Vol.
28, No.
k
500'
400' Recrystallization Temperature ('12) 300
200
100 0
I
I
100
200
I
300 Strain (%)
I
i
400
500
Figure 3. Recrystallization temperature as a function of percentage strain for rolled poly.cyystalline copper (o). Each po_int is the average of three measurements. Data are also shown for (112)[111] (i) [3,5] and (111)[ 110] copper single crystals (4) [4].
~onclusions Measurements of the stored energy of deformation of polycrystalline copper as a function of strain have been performed. Initially the stored energy increase is nonlinear and slow. Over the strain range ~35 to ~200% the stored energy increases approximately linearly with increasing strain, in agreement with previous observations [3,4]. At ~200% strain the stored energy appears to saturate at a value of 46 J. tool "1, comparable to values obtained by others in polycrystalline copper [3,8]. This value is reached at a temperature which corresponds to a minimum recrystallization temperature of-234°C. Acknowledgments This work was supported by the National Science Foundation through Grant DMR-9022824. References 1. A.L.Titchener and M. B. Bever, Progress in Metal Physics 7, 247 (1958). 2. M. B. Bever and A.L.Titchener, Progress in Materials Science 17, 168 (1973). 3. F. Haessner and G. Hoschek, Scripta Metallurgica 10, 63 (1976). 4. I. Baker and J.W. Martin, Metal Science 17, 469 (1983). 5. F. Haessner, G. Hoschek and G. Tolg, Acta Metallurgica 27, 1539 (1979). 6. M.F. Ashby, Philos. Mag. 21, 399 (1970). 7. L. Liu and I. Baker, to be published. 8. A. Lucci, R. Riontino, M.C. Tabasso, M. Tamanini and G. Venturello, Acta Metallurgica 26, 615 (1978). 9. F. Haessner and W. Hemminger, Z. Metallkunde 69, 553 (1978).
2
Vol. 28, pp. 197-200, 1993 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved
THE DEPENDENCE OF RECRYSTALLIZATION TEMPERATURE AND STORED ENERGY ON ROLLING STRAIN IN POLYCRYSTALLINE COPPER L. Liu and I. Baker Thayer School of Engineering, Dartmouth College, Hanover, NH 03755 (Received
November
17, 1992)
Introduction There have been several measurements of the stored energy of cold work for rolled copper [1-5]. Haessner and Hoschek [3] showed that in a high-purity (112.)[111] copper single crystal the stored energy of cold work, Ecw, increased linearly with increasing strain until a saturation stored energy of cold work, Esat, was reached at a rolling reduction of about 96%. Baker and Martin [4] also showed an approximately linear relationship between Ecw and strain up to strains of about 200% in both an internally-oxidized, high-purity (111)[1 i0] copper single crystal and a similar crystal containing A1203 particles. For the (112.)[111] crystal examined by Haessner and Hoschek [3] the increase in Ecw with increasing strain produced a concomitant decrease in recrystallization temperature, TR. However, once Esat was attained increasing the rolling strain further did not lead to a further reduction in TR [3]. Esat for the (112)[111] copper crystal was 84 J.mo1-1 and the minimum recrystallization temperature, Tmin, reached was 120oc. Measurements of Esat and Train for other orientations of copper single crystals by Haessner, Hoschek and Tolg gave values as low as 29 J.mo1-1 for Esat and as high as 300°C for Tmin for (111)[1 10] and (111)[ 112] crystals respectively [5]. The latter authors showed a rough correlation between Esat and Tmin: as Esat increased Train decreased [5]. However, some orientations clearly did not fit into this scheme: a (110)[1 i0] crystal had both one of the lowest Esat values, at 42 J.molA, and also one of the lowest Train values, at 153oc [5]. This indicates indirectly that the stored energy alone does not determine the recrystallization kinetics. In other words, as is well known, the microstructure developed during rolling is important for the subsequent recrystallization kinetics. The purpose of the present paper is to present measured values of Ecw and TR for polycrystalline copper as a function of rolling strain and to compare the results with those cited above. Exoerimental Blocks, 50mm long by 12mm wide by 7.5mm high, of 99.99% polycrystalline copper were annealed at 550oc for 36 hours under vacuum, after which a heavily-twinned 16.5 ktm grain size was obtained, Figure 1. The annealed blocks were rolled at room temperature with reductions of -0.02 mm per pass. After certain rolling reductions, specimens (three at each strain) for differential scanning calorimetry (6mm square) were cut from the blocks using a slow-speed diamond saw. Subsequently, the specimens were etched in 50% nitric acid in order to remove any surface damage which might have caused preferential recrystallization at the specimen's surface. Specimens were placed in one of the two furnaces of a Perkin Elmer DSC7 controlled by a DEC station 325C. A well-annealed copper block of similar weight was placed in the other furnace. The two furnaces were heated at 40oc min-1 and the difference in power between the two furnaces needed to maintain the beating rate was recorded as a function of temperature. When recrystallization occurred in the rolled specimen, a lower power input was required for the specimen furnace, and a peak occurred on a plot of power input versus temperature. The stored energy of deformation for weight of sample used is then the area under the peak; the recrystallization temperature is taken to be the apex of the peak.
197 0956-716X/93 $6.00 + .00 Copyright (c) 1992 Pergamon Press Ltd.
198
ROLLING STRAIN IN COPPER
Vol.
28,
Figure 1. Optical micrograph of 99.99% polycrystaUinecopper annealed at 550°C for 36 hours. Results and Discussion The stored energy of cold work is presented graphically as a function of percentage rolling in Figure 1. Data for (111)[1 i0] and (112.)[111] copper single crystals [3,4] are included for comparison. 50
i
4O 30
~
10
0
i
0
I
50
i
I
100
i
I
150
i
I
200
i
250
Strain ( % )
Figure 2. Stored Energy as a function of percentage strain for rolled polycrystalline copper (o). Each point is the average of three measurements. Also shown are data for (112)[111] (m) [3,5] and (111)[1 i0] copper single crystals (A) [4].
No.
2
Vol.
28, No.
2
ROLLING STRAIN IN COPPER
199
Owing to the limitation imposed by the highest operating temperature of the DSC, no data were obtained for strains less than 20% since recrystallization occurred above 700oc. Ignoring for the moment the datum at 20% strain, the stored energy is an approximately linear function of strain over the range shown. This is to be expected for a metal which exhibits a parabolic work hardening rate [4]. The plot for the polycrystalline copper over this range is approximately parallel to the plots for the (111)[110] and (112)[111] copper single crystals [3,4], except that it is higher. Thus the approximately linear relationship between stored energy and strain appears to be quite general over this range. The line for polycrystalline copper is, of course, higher than those of the two single crystals. This, again, is to be expected. For single crystal copper the dislocations present, to a first approximation, are statistically-stored dislocations [6]. In polycrystalline copper, in addition to the statistically-stored dislocations, geometrically-necessary dislocations are required to accommodate the strain differences at the grain boundaries [6]. Thus, the stored energy of cold work for polycrystalline copper can be written in terms of the dislocation density as Ecw = Gb2 (p s +P o ), where G is the shear modulus, b is the magnitude of the Burgers' vector of the dislocations, andps andpG are the statistically-stored and geometrically-necessary dislocations respectively. Ashby [6] indicated that the geometrically-necessary dislocations would swamp the statistically-stored dislocations at the early stages of deformation but that they would become a smaller percentage of the total as the strain was increased. This appears to be consistent with the observed behavior: the linear region must correspond largely to the increase in statistically-stored dislocations, whilst the data point at the beginning of the linear region for polycrystalline copper must be due to a large initial accumulation of geometrically-necessary dislocations. Returning to the initial datum point for polycrystalline copper, it appears that the initial rate of energy storage is less than that at larger strains. This could be due to scatter in the data. However, similar behavior has been observed in polycrystalline nickel [7]. It may be that the lack of dislocation tangles and locks at lower strains allows dislocation annihilation and rearrangement to occur more easily at lower strains. In other words, recovery removes a larger percentage of the energy put into the material as dislocations. It is worth noting that the two data points at the highest strains recorded for polycrystalline copper are the same. Again, this could be due to scatter in the data. However, these two points suggest that the stored energy is approaching the saturation value, Es~t. In fact, the strain (~200%) is similar to that at which Esat was suggested to have been reached in a (111)[110] copper crystal containing -80nm diameter alumina particles [4]. However, it is much less than the 350% strain that was needed to reach saturation in a (112)[111] copper single crystal [3]. The "saturation" values obtained from two different 50~tm grain-sized specimens of polycrystalline copper by Haessner, Hoschek and Tolg [5] were -75 J. mol -I and 47 J. mol "1 whilst that obtained by Lucci et al. [8] was 52.5 J. mo1-1. Thus, the value obtained here (46 J. mo1-1) is similar, if not quite the same, as the lower end of the values obtained previously. The recrystallization temperature is shown as a function of rolling strain in Figure 3. Data for (111)[1 i0] and (112)[111] copper single crystals [3,4] are also shown. At the highest strains examined (200%) Train seems to have been reached for polycrystalline copper, suggesting that the highest value of the stored energy measured above was indeed Esat. The value of Train at 234°C is very close to that obtained by Lucci et al. [8] in polycrystalline copper but is much higher than the values of 125-170oc obtained by Haessner, Hoschek and Tolg [5]. It is somewhat difficult to make any comparisons between the results of different workers since small increases in solute content can decrease the recrystallization kinetics dramatically: values as low as 70°C have been recorded for very high purity poly.crystalline copper [9]. Note that Haessner, Hoschek and Tolg [5] found that Tmin occurred at a similar strata to that recorded here, see Figure 3.
200
ROLLING
STRAIN
IN COPPER
Vol.
28, No.
k
500'
400' Recrystallization Temperature ('12) 300
200
100 0
I
I
100
200
I
300 Strain (%)
I
i
400
500
Figure 3. Recrystallization temperature as a function of percentage strain for rolled poly.cyystalline copper (o). Each po_int is the average of three measurements. Data are also shown for (112)[111] (i) [3,5] and (111)[ 110] copper single crystals (4) [4].
~onclusions Measurements of the stored energy of deformation of polycrystalline copper as a function of strain have been performed. Initially the stored energy increase is nonlinear and slow. Over the strain range ~35 to ~200% the stored energy increases approximately linearly with increasing strain, in agreement with previous observations [3,4]. At ~200% strain the stored energy appears to saturate at a value of 46 J. tool "1, comparable to values obtained by others in polycrystalline copper [3,8]. This value is reached at a temperature which corresponds to a minimum recrystallization temperature of-234°C. Acknowledgments This work was supported by the National Science Foundation through Grant DMR-9022824. References 1. A.L.Titchener and M. B. Bever, Progress in Metal Physics 7, 247 (1958). 2. M. B. Bever and A.L.Titchener, Progress in Materials Science 17, 168 (1973). 3. F. Haessner and G. Hoschek, Scripta Metallurgica 10, 63 (1976). 4. I. Baker and J.W. Martin, Metal Science 17, 469 (1983). 5. F. Haessner, G. Hoschek and G. Tolg, Acta Metallurgica 27, 1539 (1979). 6. M.F. Ashby, Philos. Mag. 21, 399 (1970). 7. L. Liu and I. Baker, to be published. 8. A. Lucci, R. Riontino, M.C. Tabasso, M. Tamanini and G. Venturello, Acta Metallurgica 26, 615 (1978). 9. F. Haessner and W. Hemminger, Z. Metallkunde 69, 553 (1978).
2