- Email: [email protected]
On the grain boundary particle pinning during recrystallization of AlLi alloys
Scripta METALLURGICA et ~ % T E R I A L I A
Vol. 25, pp. 8 3 S - 8 ~ 0 , 1991 Printed in t h e U . S . A .
Pergamon Press plc All rights reserved
ON THE GRAIN BOUNDARy PARTICLE PINN[NG DURING RECRYSTALLIZATION
OF AI-Li ALLOYS
Marcelo Goncalves Instituto de Pesquisas Tecnologicas do Estado de Sao Paulo - IPT Cidade Universitaria 05508 Sao Paulo, SP Brazil (Received (Revised
December 7, 1990) January 29, 1991) Introduction
The interaction force between particles and moving grain boundaries was first described by Zener (1) and the quantitative treatment given in this early work has been used to this day when calculations involving particle pinning during recrystallization are made (2). Following that proposition, the pinning force results from the saving in grain boundary energy when a moving grain boundary intersects and passes through a particle. It is considered that the maximum saving in energy, with consequent maximum restraining force, is approached when the equatorial plane of intersection is considered. Although previous modifications of this model have been proposed (3), they are almost invariably founded on the same principles described above, in which the boundary cuts through the precipitates. Rios (4) has recently published a paper in which a new model for grain boundary pinning is postulated, and the intention of the present work is to show that for the AI-Li alloys studied such a mechanism is more likely to be operative than Zener's,and a new equation for calculating the pinning force is developed. Results and Discussion The materials used in the experiments were the 8090 and 8091 alloys of composition
shown below:
8090 - 2.42% Li, 1.23% Cu, 0.6% Mg, 0.11% Zr 8091 - 2.52% Li, 1.86% Cu, 0.81% Mg, 0.15% Zr From as-homogenized blanks samples were cut for experimental hot rolling. These were reheated to 535°C and a total reduction of 60% was applied in three passes. Several start rolling temperatures were used within the interval 490-300°C, so that different levels of strain energy could be introduced in the materials. Subsequent solution heat treatments were done at 530°C for times ranging from I/2 to 48 hours. Optical metallography and transmission electron microscopy were carried out using standard techniques (5). The metallographic analysis revealed that the microstructures after solution treatment were different depending on the rolling temperature. This can be seen in figure I, where a long time of 24 hours solution treatment was used so that the contrasting effects on the microstructures can be observed. As seen in this figure, for the same amount of strain and the same solution treatment time and temperature, the structures tend to be more elongated for higher deformation temperatures. As pointed out by Nes et al (3) and Humphreys et al (6), recrystallized elongated structures result when the particles that cause the pinning effect on the moving boundaries are aligned along the rolling direction. Such a distribution of precipitates would therefore be responsible for the anisotropic growth during recrystallization. This fact would account for the laminar nature of the recrystallized structures, as seen for the high deformation temperature samples in this work. However, no directionality of precipitates could be revealed during the metallographic studies carried out - T.E.M. observations are restricted to very small areas, on the one hand, and on the other,optical metallography does not resolve small precipitates that cause pinning. Nevertheless, in AI-Li alloys containing Zr additions, there is the presence of AI3Zr particles, which produce a drag effect on grain boundaries. T.E.M. studies revealed that these precipitates impinge the moving high angle boundaries during recrystallization. In figure 2
835 0036-9748/91 $ 3 . 0 0 + .00 Copyright (c) 1991 P e r g a m o n Press
plc
836
RECRYSTALLIZATION
OF A I - L i
Vol.
25,
No.
4
such an example of an AI3Zr precipitate acting against the movement of a high angle boundary is depicted for a sample of 8091 rolled at the high temperature of 490°C, and solution treated for I hour. The marker shows the unrecrystalllzed grain towards which the high angle boundary is moving. The important feature presented by figure 2 is that the moving boundary does not seem to be cutting through the particle, in fact it is apparent that the boundary is "enveloping" the AI3Zr precipitate, surrounding it almost completely. This micrograph is representative of a very frequent configuration found throughout this work. T.E.M. studies also revealed that the coherency condition of the interface between AI3Zr particles and matrix was lost when a moving grain boundary passed by the AI3Zr precipitates during recrystallizatlon. This fact is illustrated in figure 3 in which the strain field around the AI3Zr particles, as seen in figure 3a, disappears when a recrystallizatlon front passes by, as observed in figure 3b. This means that for the particles under consideration, the "enveloping" effect can be associated with the change from coherent to incoherent of the interface between precipitate and matrix. This effect of coherency loss during recrystalllzation has been mentioned to occur for AI3Zr precipitates in alumlnlum-lithlum alloys (7). The analysis of the restricting and driving forces for recrystallizatlon can help in clarifying the pinning mechanism involved. The theory predicts that the driving force for recrystalllzatlon is given by (8): F R - G b2(01 - ~) (I) where:
DI 02 G b
= = =
dislocation density of the unrecrystallized grains dislocation density of the recrystalllzed grains Shear modulus = 2,6xi0 I0 N/m2 Burger's vector = 2,8xi0 "IO m
The dislocation densities 01 were measured for the different conditions of rolling temperature (9) and, therefore, values of driving force for recrystalllzation could be calculated and the resuits are shown below: Alloy
Rolling Temp.(°C)
8090 8090 8090 8091 8091 8091 8091
480 400 300 490 450 400 350
F R (N/m 2) 1.15xi0 5 4.24x10 5 1.67xi06 1.65xi0 5 2.45xi0 5 5.10x10 5 1.08xi06
The Zener formula given in literature to calculate the pinning force is (8): Fp = 3 f ~s/2r where:
(2)
f - volume fraction of AI3Zr: 0.14% for 8090 and 0.19% for 8091 o s i grain boundary energy - 0.324J/m 2 (10) r ~ AI3Zr particle radius - 33xi0 "9 (8090) and 27xi0 -9 m (8091)
The volume fractions were obtained from the Zr levels of the alloys, and the particles radii were measured (9). By working out equation (2) for both alloys, the following results are yielded: Fp - 2.06xi04 N/m 2, for 8090 and Fp = 3.42xI04 N/m 2, for 8091 if one compares these results with the driving forces shown earlier, it is observed that by using Zener's equation, no pinning effect is present, even for the highest deformation temperatures, when the driving forces are the smallest. The mlcrographs, however, show that there is a pinning effect, which is expected to act when the rolling temperature is higher than 400°C, approximately (see ref.5). Rios proposed that a new model can be operative during grain boundary pinning and a different equation should be used for estimating the critical radius for grain growth (4). it is suggested that for spherical precipitates of radius ~ and volume fraction ~, the value of the critical
Vol.
25,
No.
4
RECRYSTALLIZATION
OF
AI-Li
$37
radius of a growing grain is equal to: Rc = r / 6 f
(3)
The classical theory of grain growth establishes that the driving force for grain growth is given by (i0) 2 0 S /R. At the point when grain growth ceases, then R - RC, and the driving force is counterbalanced by the pinning force, so that the following equation is valid: 2~S/ By combining equations given by:
R c = Fp
(4) and (3) it is possible
(4)
to obtain a new equation for the pinning
force,
Fp ~ [2 o s f / r
(5)
where o~, f and r have the same meaning as in equation (2). By introducing in the new equation, one can calculate the pinning force as:
the respective
values
Fp = 1.65xi05 N/m 2, for 8090 and Fp = 2.74xi05 N/m 2, for 8091 If now these values are compared with the driving force data it can be seen that the condition in which the driving and pinning forces are counterbalancing each other is given when the start rolling temperature is within the interval 400-450oc. This means that when the rolling temperature is higher than 450°C, then Fp >FR and an elongated recrystallized structure is expected after solution treatment. Conversely, if the temperature is lower than 400°C, Fp < FR and the structure should be equiaxed. The above observations are in total agreement with the microstructural features presented by both alloys, which showed that for samples rolled at temperatures lower than 400°C, the recrystallized structures were equiaxed, and that for samples deformed at temperatures higher than -400°C there was an increasing tendency for the formation of laminar recrystallized structures, the higher the rolling temperature. Conclusion The results provided in this work show that for the AI-Li alloys investigated there is a particle pinning effect exerted by AI3Zr particles on grain boundaries during static recrystallization. More importantly, it is shown that the mechanism by which such a pinning effect is exerted upon the high angle boundaries does not follow the classic Zener interaction between boundary and particle, in this approach the boundary by-passes the particle, enveloping it, rather than cutting through it. By interacting with the precipitates in this way, the moving boundary causes the coherency loss between precipitates and matrix, indeed, the derivation of a new equation, obtained from the relationship for critical grain radius during grain growth proposed by Rios (4), proved to be more suitable in evaluating the pinning forces for the alloys studied, and the mechanism supporting these new equations is different from Zener's. The data here provided are indicative that the proposition made by Rios (4), originally applied for grain growth, can be extended to cases when quantification of pinning forces during static recrystallization are required. The resulting pinning force thus calculated is eight times higher than that given by Zener's equation. Acknowledgements The author is grateful to the School of Materials of the University of Sheffield, UK, where work was carried out, especially to Prof. C.M. Sellars for his helpful discussions. The staff of Alcan international
- Banbury Laboratories,
UK, is also gratefully
acknowledged.
this
858
RECRYSTALLIZATION
OF A I - L i
Vol.
Z5, No.
4
References I. 2.
C.S. Smith, Trans. Metall. Soc. A.I.M.E. 175, 15 (1948). E. Hornbogen and U. KSster, in Recrystalllzatlon of Metallic Materials (edited by F.HaessneO, pp.159-193. Riederer-Verlag, Stuttgart (1978). 3. E. Nes, N. Ryum and O. Hunderl, Acta Metall. 33, 11 (1985). 4. P.R. Rios, Acta Metall. 35, 2805 (1987). 5. M. GonGalves and C.M. Sellars, Journal de Physique 48-C3, 171 (1987). 6. F.J. Humphreys and D. Juul Jensen in Proc. Int. Riso Conf., 93 (1986). 7. W.S. Miller, J. White and D.J. Lloyd, Aluminum Alloys - Their Physical and Mechanical Proper ties, (edited by E.A. Starke and T.H. Sanders), vol.3, p.1799 (1986). 8. U. KSster, Metal Science 8, 151 (1974). 9. M. Goncalves, Ph.D. Thesis, University of Sheffield (1989). I0. D.A. Porter and K.E. Easterllng, Phase Transformations in Metals and Alloys, p.139, Van Nostrand Reinhold, UK (1984).
Voi.
25, No.
4
RECRYSTALLIZATION
OF AI-Li
Fig. 1 - Microstructures for alloy 8091 after 24h solution treatment at 530°C. Samples rolled from: (a) 490°C; (b) 400°C; (c) 350°C. Barker's etching. Polarized light.
839
840
RECRYSTALLIZATION
OF AI-Li
Vol.
25, No.
m
Fig. 2 - T.E.M. micrograph of alloy 8091 showing "enveloping" of particle by grain baundary during recrystallization.
(a) Fig. 3
(b)
T.E.M. micrographs of alloy 8091 depicting: (a) coherent nature of AI3Zr precipitates (showing strain field around precipitates); (b) incoherent nature of AI3Zr after recrystallization.
4
Vol. 25, pp. 8 3 S - 8 ~ 0 , 1991 Printed in t h e U . S . A .
Pergamon Press plc All rights reserved
ON THE GRAIN BOUNDARy PARTICLE PINN[NG DURING RECRYSTALLIZATION
OF AI-Li ALLOYS
Marcelo Goncalves Instituto de Pesquisas Tecnologicas do Estado de Sao Paulo - IPT Cidade Universitaria 05508 Sao Paulo, SP Brazil (Received (Revised
December 7, 1990) January 29, 1991) Introduction
The interaction force between particles and moving grain boundaries was first described by Zener (1) and the quantitative treatment given in this early work has been used to this day when calculations involving particle pinning during recrystallization are made (2). Following that proposition, the pinning force results from the saving in grain boundary energy when a moving grain boundary intersects and passes through a particle. It is considered that the maximum saving in energy, with consequent maximum restraining force, is approached when the equatorial plane of intersection is considered. Although previous modifications of this model have been proposed (3), they are almost invariably founded on the same principles described above, in which the boundary cuts through the precipitates. Rios (4) has recently published a paper in which a new model for grain boundary pinning is postulated, and the intention of the present work is to show that for the AI-Li alloys studied such a mechanism is more likely to be operative than Zener's,and a new equation for calculating the pinning force is developed. Results and Discussion The materials used in the experiments were the 8090 and 8091 alloys of composition
shown below:
8090 - 2.42% Li, 1.23% Cu, 0.6% Mg, 0.11% Zr 8091 - 2.52% Li, 1.86% Cu, 0.81% Mg, 0.15% Zr From as-homogenized blanks samples were cut for experimental hot rolling. These were reheated to 535°C and a total reduction of 60% was applied in three passes. Several start rolling temperatures were used within the interval 490-300°C, so that different levels of strain energy could be introduced in the materials. Subsequent solution heat treatments were done at 530°C for times ranging from I/2 to 48 hours. Optical metallography and transmission electron microscopy were carried out using standard techniques (5). The metallographic analysis revealed that the microstructures after solution treatment were different depending on the rolling temperature. This can be seen in figure I, where a long time of 24 hours solution treatment was used so that the contrasting effects on the microstructures can be observed. As seen in this figure, for the same amount of strain and the same solution treatment time and temperature, the structures tend to be more elongated for higher deformation temperatures. As pointed out by Nes et al (3) and Humphreys et al (6), recrystallized elongated structures result when the particles that cause the pinning effect on the moving boundaries are aligned along the rolling direction. Such a distribution of precipitates would therefore be responsible for the anisotropic growth during recrystallization. This fact would account for the laminar nature of the recrystallized structures, as seen for the high deformation temperature samples in this work. However, no directionality of precipitates could be revealed during the metallographic studies carried out - T.E.M. observations are restricted to very small areas, on the one hand, and on the other,optical metallography does not resolve small precipitates that cause pinning. Nevertheless, in AI-Li alloys containing Zr additions, there is the presence of AI3Zr particles, which produce a drag effect on grain boundaries. T.E.M. studies revealed that these precipitates impinge the moving high angle boundaries during recrystallization. In figure 2
835 0036-9748/91 $ 3 . 0 0 + .00 Copyright (c) 1991 P e r g a m o n Press
plc
836
RECRYSTALLIZATION
OF A I - L i
Vol.
25,
No.
4
such an example of an AI3Zr precipitate acting against the movement of a high angle boundary is depicted for a sample of 8091 rolled at the high temperature of 490°C, and solution treated for I hour. The marker shows the unrecrystalllzed grain towards which the high angle boundary is moving. The important feature presented by figure 2 is that the moving boundary does not seem to be cutting through the particle, in fact it is apparent that the boundary is "enveloping" the AI3Zr precipitate, surrounding it almost completely. This micrograph is representative of a very frequent configuration found throughout this work. T.E.M. studies also revealed that the coherency condition of the interface between AI3Zr particles and matrix was lost when a moving grain boundary passed by the AI3Zr precipitates during recrystallizatlon. This fact is illustrated in figure 3 in which the strain field around the AI3Zr particles, as seen in figure 3a, disappears when a recrystallizatlon front passes by, as observed in figure 3b. This means that for the particles under consideration, the "enveloping" effect can be associated with the change from coherent to incoherent of the interface between precipitate and matrix. This effect of coherency loss during recrystalllzation has been mentioned to occur for AI3Zr precipitates in alumlnlum-lithlum alloys (7). The analysis of the restricting and driving forces for recrystallizatlon can help in clarifying the pinning mechanism involved. The theory predicts that the driving force for recrystalllzatlon is given by (8): F R - G b2(01 - ~) (I) where:
DI 02 G b
= = =
dislocation density of the unrecrystallized grains dislocation density of the recrystalllzed grains Shear modulus = 2,6xi0 I0 N/m2 Burger's vector = 2,8xi0 "IO m
The dislocation densities 01 were measured for the different conditions of rolling temperature (9) and, therefore, values of driving force for recrystalllzation could be calculated and the resuits are shown below: Alloy
Rolling Temp.(°C)
8090 8090 8090 8091 8091 8091 8091
480 400 300 490 450 400 350
F R (N/m 2) 1.15xi0 5 4.24x10 5 1.67xi06 1.65xi0 5 2.45xi0 5 5.10x10 5 1.08xi06
The Zener formula given in literature to calculate the pinning force is (8): Fp = 3 f ~s/2r where:
(2)
f - volume fraction of AI3Zr: 0.14% for 8090 and 0.19% for 8091 o s i grain boundary energy - 0.324J/m 2 (10) r ~ AI3Zr particle radius - 33xi0 "9 (8090) and 27xi0 -9 m (8091)
The volume fractions were obtained from the Zr levels of the alloys, and the particles radii were measured (9). By working out equation (2) for both alloys, the following results are yielded: Fp - 2.06xi04 N/m 2, for 8090 and Fp = 3.42xI04 N/m 2, for 8091 if one compares these results with the driving forces shown earlier, it is observed that by using Zener's equation, no pinning effect is present, even for the highest deformation temperatures, when the driving forces are the smallest. The mlcrographs, however, show that there is a pinning effect, which is expected to act when the rolling temperature is higher than 400°C, approximately (see ref.5). Rios proposed that a new model can be operative during grain boundary pinning and a different equation should be used for estimating the critical radius for grain growth (4). it is suggested that for spherical precipitates of radius ~ and volume fraction ~, the value of the critical
Vol.
25,
No.
4
RECRYSTALLIZATION
OF
AI-Li
$37
radius of a growing grain is equal to: Rc = r / 6 f
(3)
The classical theory of grain growth establishes that the driving force for grain growth is given by (i0) 2 0 S /R. At the point when grain growth ceases, then R - RC, and the driving force is counterbalanced by the pinning force, so that the following equation is valid: 2~S/ By combining equations given by:
R c = Fp
(4) and (3) it is possible
(4)
to obtain a new equation for the pinning
force,
Fp ~ [2 o s f / r
(5)
where o~, f and r have the same meaning as in equation (2). By introducing in the new equation, one can calculate the pinning force as:
the respective
values
Fp = 1.65xi05 N/m 2, for 8090 and Fp = 2.74xi05 N/m 2, for 8091 If now these values are compared with the driving force data it can be seen that the condition in which the driving and pinning forces are counterbalancing each other is given when the start rolling temperature is within the interval 400-450oc. This means that when the rolling temperature is higher than 450°C, then Fp >FR and an elongated recrystallized structure is expected after solution treatment. Conversely, if the temperature is lower than 400°C, Fp < FR and the structure should be equiaxed. The above observations are in total agreement with the microstructural features presented by both alloys, which showed that for samples rolled at temperatures lower than 400°C, the recrystallized structures were equiaxed, and that for samples deformed at temperatures higher than -400°C there was an increasing tendency for the formation of laminar recrystallized structures, the higher the rolling temperature. Conclusion The results provided in this work show that for the AI-Li alloys investigated there is a particle pinning effect exerted by AI3Zr particles on grain boundaries during static recrystallization. More importantly, it is shown that the mechanism by which such a pinning effect is exerted upon the high angle boundaries does not follow the classic Zener interaction between boundary and particle, in this approach the boundary by-passes the particle, enveloping it, rather than cutting through it. By interacting with the precipitates in this way, the moving boundary causes the coherency loss between precipitates and matrix, indeed, the derivation of a new equation, obtained from the relationship for critical grain radius during grain growth proposed by Rios (4), proved to be more suitable in evaluating the pinning forces for the alloys studied, and the mechanism supporting these new equations is different from Zener's. The data here provided are indicative that the proposition made by Rios (4), originally applied for grain growth, can be extended to cases when quantification of pinning forces during static recrystallization are required. The resulting pinning force thus calculated is eight times higher than that given by Zener's equation. Acknowledgements The author is grateful to the School of Materials of the University of Sheffield, UK, where work was carried out, especially to Prof. C.M. Sellars for his helpful discussions. The staff of Alcan international
- Banbury Laboratories,
UK, is also gratefully
acknowledged.
this
858
RECRYSTALLIZATION
OF A I - L i
Vol.
Z5, No.
4
References I. 2.
C.S. Smith, Trans. Metall. Soc. A.I.M.E. 175, 15 (1948). E. Hornbogen and U. KSster, in Recrystalllzatlon of Metallic Materials (edited by F.HaessneO, pp.159-193. Riederer-Verlag, Stuttgart (1978). 3. E. Nes, N. Ryum and O. Hunderl, Acta Metall. 33, 11 (1985). 4. P.R. Rios, Acta Metall. 35, 2805 (1987). 5. M. GonGalves and C.M. Sellars, Journal de Physique 48-C3, 171 (1987). 6. F.J. Humphreys and D. Juul Jensen in Proc. Int. Riso Conf., 93 (1986). 7. W.S. Miller, J. White and D.J. Lloyd, Aluminum Alloys - Their Physical and Mechanical Proper ties, (edited by E.A. Starke and T.H. Sanders), vol.3, p.1799 (1986). 8. U. KSster, Metal Science 8, 151 (1974). 9. M. Goncalves, Ph.D. Thesis, University of Sheffield (1989). I0. D.A. Porter and K.E. Easterllng, Phase Transformations in Metals and Alloys, p.139, Van Nostrand Reinhold, UK (1984).
Voi.
25, No.
4
RECRYSTALLIZATION
OF AI-Li
Fig. 1 - Microstructures for alloy 8091 after 24h solution treatment at 530°C. Samples rolled from: (a) 490°C; (b) 400°C; (c) 350°C. Barker's etching. Polarized light.
839
840
RECRYSTALLIZATION
OF AI-Li
Vol.
25, No.
m
Fig. 2 - T.E.M. micrograph of alloy 8091 showing "enveloping" of particle by grain baundary during recrystallization.
(a) Fig. 3
(b)
T.E.M. micrographs of alloy 8091 depicting: (a) coherent nature of AI3Zr precipitates (showing strain field around precipitates); (b) incoherent nature of AI3Zr after recrystallization.
4