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Grain boundary strengthening in a fine grained aluminium alloy
Scripta Metallurgica et Materialia, Vol. 32, No. 5, pp. 781-786, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. Au rights resewed 0956-716W95 $9.50 + .OO
GRAIN BOUNDARY STRENGTHENING IN A FINE GRAINED ALUMINIUM ALLOY
R. Mahmudi Department of Metallurgy and Materials Engineering Tehran University, P.O. Box 11365463, Tehran, Iran (Received May l&1994) (Revised October 6,1994)
Introduction The dependence of strength on the grain size of metals has received a great deal of attention since the early work of Hall [l] and Petch [2]. The general form of their relationship is given by: u = o. + Kd-n
(1)
where u is the strength, a,, frictional stress, d the grain size, K a constant and n= l/2. Two models have evolved for explaining the dependence of resistance to plastic deformation on grain size and both models could be used to derive the above equation. The first model is based on the concept that grain boundaries act as barriers to dislocation motion [3], while the second one concentrates on the influence of grain size on dislocation density, and hence on the yield or flow stress [4]. The majority of published data in which grain sizes of 20 pm and larger are considered, support the Hall-Petch equation. However, the situation is somewhat different in the case of fine-grained materials. The detailed work of Fujita and Tabata [5] on polycrystalline aluminium in the grain size range of 33 pm to 490 pm, revealed that while the yield stress can always be correlated with the grain size by the Hall-Petch relationship, the flow stress carmot be expressed by a simple linear relationship. But when cell sizes in the range of 2 pm to 5 pm were considered, these flow stresses could be expressed by a linear function of the inverse of the cell size. Kalish et al. [6,7] have studied the development of subgrain structures and she resulting strengthening in three aluminium conductor alloys. They stated that the 0.2% flow strength of these alloys was always inversely dependent on subgrain size, rather than supporting the usual Hall-Petch relationship. A similar d-i dependency of the yield strength has been observed in tests on fine grain eutectic alloys such as AldNi [8,9] and Al-2Fe [lo]. The fact that the grain size dependence of flow stress is different for different materials, suggests that the exponent n in the Hall-Petch relationship can vary between l/2 and 1, depending on what structural parameters such as grains, subgrains or cell sizes are consiIdered. The pre.sent study examines the grain size dependence of yield and flow stress of the near eutectic AA8014 aluminium alloy. This alloy, when appropriately processed, can develop very fine grain sizes (d < 10 pm) with a uniform distribution of fine intermetallic particles [l 11. Exuerimental Procedure The material was AA8014 aluminium alloy containing 1.4% Fe and 0.4% Mn. It was DC cast, hot rolled to 7 mm thickness and then cold rolled to the final thickness of 0.7 mm. Two kinds of 781
182
FINEG~INEDAIALL~Y
Vol.32.No.5
annealing treatment were applied. The first involved slow heating @A) at 30°C per hour up to the annealing temperature and a holding time of 3 hours in order to produce recovered structures. The second kind of annealing, planned to obtain recrystallized structures, involved fast heating (FA) in a salt bath held at the selected annealing temperature for 5 minutes. Different annealing temperatures were used to generate a range of grain sizes from 1 pm to 8 pm. Due to the very fine structure of the material, grain size measurement was carried out on TEM micrographs using the computerized image analyzer, Video Interactive Display System (VIDS). Since the area of interest on the TEM foils was very limited and in some cases the grain structure was nonuniform, it was necessary to have a more representative grain size value. Thus for each condition, different foils were employed and different locations on each foil were pictured and the number of grains on each micrograph was taken as the weighing factor in the calculation of the final grain size. Uniaxial tensile tests were carried out at a constant cross-head speed of 10 mm/min which produced an initial strain rate of 2x10.’ set-‘. Load-extension curves were obtained with the aid of a 25 mm gauge length extensometer from which the flow stress values were calculated at different strain levels. Results and Discussion Yield stress The grain size dependence of yield strength at 0.2% plastic strain is shown in a conventional d-‘/2 plot in Fig. 1. It is clear that the measured proof stress is not linearly related to d-l0 and the strengths achieved in ultrafine-grained materials are greater than would be expected from extrapolating the coarser grain size results. This departure from a linear dependence with grain size has been observed in other fine-grained aluminium alloys previously [9, lo]. It has been stated that this positive deviation from the Hall-Petch relationship could be due to the inhomogeneous yielding associated with the very fme grain sizes.
160,
0.0
I
0.2
0.4
0.6
0.8
1.0
1.2
d-‘/2 , cun-l/2
FIG. 1. Measured and back extrapolated 0.2 % proof stress data plotted against d-I’*.
FIG. 2. TEM picture of the material showing the grain structure and dispersion of second phase particles.
Vol. 32, No. 5
F’lNEGRAIh’EDAlAL.LQY
183
This inhomogeneous yielding complication was avoided by back extrapolation of the flow stress relationship observed in homogeneous straining. The obtained theoretical proof stress values which exclude the yield point, also shown in Fig. 1, are still non-linear in a d-I’*plot. A possible explanation for higher strength at finer grain sizes, being observed even after back extrapolation, is that in ultrafinegrained ahnninium eutectic alloys the finer grain size is produced by pinning the grain boundaries with intermetallic particles, as shown in Fig. 2. The particle size and distribution for two different conditions, having two different grain sizes of 1.1 pm and 5.6 pm, is shown respectively in Figures. 3a and b. It is observed that the finer the grain size the finer the intermetallic particles. Thus the contribution of particles to the strength may be greater at finer grain sizes. As can be seen in Fig. 1, the curve begins to deviate from the coarse grain size data at a grain size of about 2 pm, so that the amount of deviation at a grain size of 1.5 pm is almost 12 MPa. This is well in agreement with the calculation of strengthening from fine particles based on Orowan’s mechanism of dispersion hardening [12]. According to this mechanism an interparticle spacing (h) of 0.65 pm is necessary to produce the 12 MPa gain in the strength (a) calculated from the following relation:
where b is the .Burgers vector (about 0.2 mn) and E is the modulus of elasticity (70,000 MPa). Despite a variation in the distribution of the intermetallic particles, the mean interparticle spacing is found to be between 0.5 and 0.8 pm, as shown in Fig. 2.
(a)
0)
FIG. 3. The particle size and distribution for materials having grain sizes of 1.1 pm (a), and 5.6 pm (b). The deviation from the Hall-Petch relationship suggests that the alternative d-l dependence of proof stress on grain size could be more applicable. From the measured 0.2% proof stress data plotted in Fig. 4, it is (clear that all the yield strength values are well represented by a d-’ grain size dependence. The d-l relationship also confirms that the improvement in yield strength with grain refinement is considerably greater than would be predicted from a d-l’* Hall-Petch relationship established over coarser grain sizes. Another interesting feature of Fig. 4 is the insensitivity of the strength data to the types of heat treatment which have produced the wide range of grain size. It is clear from this figure that all the slowly
784
FINE GRAINED
Al ALLOY
Vol. 32. No. 5
and rapidly heated conditions could be expressed by a single relationship and one cannot differentiate between them on this basis. This implies that the strength data is more grain size dependent than structure dependent. It should be mentioned that the two annealing regimes, SA and FA, both produce structures with some differences in the degree of misorientation, the difference in the grain boundary angles for two extreme cases of grain size could be quite considerable [13]. This may imply that the d-i dependence of the yield stress is maintained even though some high angle boundaries are present in the structure. Flow stress To study the grain size dependence of flow stress, larger strains were considered and stress values at strain levels of 0.03, 0.06 and 0.10 were superimposed on the back-extrapolated proof stress data as shown in the d-l plot of Fig. 5. It is observed that the slope of the Hall-Petch plot, K, at high strain levels is close to that obtained at much lower strains (e=O.O02). Therefore it can be concluded that the grain boundaries have, to some extent, remained effective barriers to dislocation flow even at high strains.
160,
I
180
(
t
30
OL-----J 0.0
0.2
0.4
0.6
0.8
d-‘.
pm-’
1.0
1.2
FIG. 4. Measured 0.2% proof stress data plotted against d-i.
,k 0.0
1
0.2
0.4
0.6
0.8
1.0
1.2
d-‘. v-’ FIG. 5. Tensile flow stress at different strain levels as a function of d-!.
However, there is a tendency for the K value to decrease with strain and since the flow stresses are all in the work hardening region, this could reflect some differences in the work hardening behaviour in the coarse and fine grained materials. Fig. 6 shows the grain size dependence of work hardening rates It is clear that while the for both the coarse (d=5.6 ,um) and fine-grained (d= 1.1 pm) conditions. difference in work hardening rates for these two conditions is small at low strain levels, it becomes larger at higher strains. Therefore, for a given high strain level, the coarser material has a higher rate of work hardening, which is believed to cause the observed slight change in the slope of the Hall-Petch plot as the strain increases. The difference in work hardening behaviour could be attributed to the different rates of dynamic recovery occurring at different grain sizes. This in turn, is reflected in the rate of decrease in work hardening rate with strain, the higher the rate of decrease the higher the rate of dynamic recovery. The origin of this difference in rate of dynamic recovery can be sought in the dislocation structures generated during the straining of the material with different grain sizes. At fine grain sizes the structure is almost clear of dislocations before stretching, as shown in Fig. 2 for the condition having a grain size of 2.2 pm.
785
Vol. 32, No. 5
50
-0.00
0.05
0.10
0.15 0.20 TRUE STRAIN
0.25
0.30
FIG. 6. Work hardening behaviour of two fine and coarse-grained
conditions.
But it is expected that at higher strains dislocations would be concentrated around the grain boundaries with a few dislocations within the grains. This is because these fine grain sizes are of the order of the free slip distance and therefore little dislocation accumulation occurs in the grain interior. However, at coarse grain sizes less dislocation annihilation and rearrangements occur because of a larger free slip distance, and thus the dynamic recovery rate is lower. Conclusions 1.
In the present fine-grained alloy, the fine grain size is produced by pinning of grain boundaries with intermetallic particles.
2.
The measured proof and flow stress data are well represented by a d” relationship rather than supporting the classic Hall-Petch equation. This d-’ dependence was found to be insensitive to the type of structure and thus, the high and low angle boundaries both form effective barriers to dislocation propagation.
3.
In addition to the grain boundary strengthening, there is some contribution from particle hardening to the strength achieved, the effect being more pronounced at very fine grain sizes (d < 2 pm).
4.
The Hall-Petch constant (K), which basically measures the effectiveness of grain boundaries increasing the strength, showed a slight decrease with increasing strain, possibly due to dynamic recovery processes. References
1. 2. 3. 4. 5. 6. 7.
E.O. Hall, Proc. Phys. Sot. London, 643, 747 (195 1). NJ. Petch, J. Iron Steel Inst. London, 174, 25 (1953). J.C.M. :Li and Y.T. Chou, Met. Trans., lA, 1145 (1970). T.L. Johnston and C.E. Feltner, Met. Trans., lA, 1161 (1970). H. Fujita and T. Tabata, Acta Met., 21, 355 (1973). D. Kalish and B.G. LeFevre, Met. Trans., 6A, 1319 (1975). D. Kalis,h, B.G. LeFevre and S.K. Varma, Met. Trans., 8A, 204 (1977).
786
a. 9. 10. 11. 12. 13.
FINE GRAINED Al ALLOY
Vol. 32, No. 5
L.R. Morris, H. Sang and D.M. Moore, Proc. 4th ZCSMA, Nancy, France, p.131 (1976). D.J. Lloyd, Met. Sci., 14, 193 (1980). H. Westengen, Proc. 6th ZCSMA, Melbourne, Australia, p.461, Pergamon Press, Oxford (1983). R. Mahmudi, W.T. Roberts, D.V. Wilson, P. Furrer and P.M.B. Rodriguez, Aluminium, 63, 62 (1987). E. Orowan, discussion in “Symposium on Internal Stresses”, p.451, Institute of Metals London (1947). R. Mahmudi, Aluminium, 70, 590 (1994).
GRAIN BOUNDARY STRENGTHENING IN A FINE GRAINED ALUMINIUM ALLOY
R. Mahmudi Department of Metallurgy and Materials Engineering Tehran University, P.O. Box 11365463, Tehran, Iran (Received May l&1994) (Revised October 6,1994)
Introduction The dependence of strength on the grain size of metals has received a great deal of attention since the early work of Hall [l] and Petch [2]. The general form of their relationship is given by: u = o. + Kd-n
(1)
where u is the strength, a,, frictional stress, d the grain size, K a constant and n= l/2. Two models have evolved for explaining the dependence of resistance to plastic deformation on grain size and both models could be used to derive the above equation. The first model is based on the concept that grain boundaries act as barriers to dislocation motion [3], while the second one concentrates on the influence of grain size on dislocation density, and hence on the yield or flow stress [4]. The majority of published data in which grain sizes of 20 pm and larger are considered, support the Hall-Petch equation. However, the situation is somewhat different in the case of fine-grained materials. The detailed work of Fujita and Tabata [5] on polycrystalline aluminium in the grain size range of 33 pm to 490 pm, revealed that while the yield stress can always be correlated with the grain size by the Hall-Petch relationship, the flow stress carmot be expressed by a simple linear relationship. But when cell sizes in the range of 2 pm to 5 pm were considered, these flow stresses could be expressed by a linear function of the inverse of the cell size. Kalish et al. [6,7] have studied the development of subgrain structures and she resulting strengthening in three aluminium conductor alloys. They stated that the 0.2% flow strength of these alloys was always inversely dependent on subgrain size, rather than supporting the usual Hall-Petch relationship. A similar d-i dependency of the yield strength has been observed in tests on fine grain eutectic alloys such as AldNi [8,9] and Al-2Fe [lo]. The fact that the grain size dependence of flow stress is different for different materials, suggests that the exponent n in the Hall-Petch relationship can vary between l/2 and 1, depending on what structural parameters such as grains, subgrains or cell sizes are consiIdered. The pre.sent study examines the grain size dependence of yield and flow stress of the near eutectic AA8014 aluminium alloy. This alloy, when appropriately processed, can develop very fine grain sizes (d < 10 pm) with a uniform distribution of fine intermetallic particles [l 11. Exuerimental Procedure The material was AA8014 aluminium alloy containing 1.4% Fe and 0.4% Mn. It was DC cast, hot rolled to 7 mm thickness and then cold rolled to the final thickness of 0.7 mm. Two kinds of 781
182
FINEG~INEDAIALL~Y
Vol.32.No.5
annealing treatment were applied. The first involved slow heating @A) at 30°C per hour up to the annealing temperature and a holding time of 3 hours in order to produce recovered structures. The second kind of annealing, planned to obtain recrystallized structures, involved fast heating (FA) in a salt bath held at the selected annealing temperature for 5 minutes. Different annealing temperatures were used to generate a range of grain sizes from 1 pm to 8 pm. Due to the very fine structure of the material, grain size measurement was carried out on TEM micrographs using the computerized image analyzer, Video Interactive Display System (VIDS). Since the area of interest on the TEM foils was very limited and in some cases the grain structure was nonuniform, it was necessary to have a more representative grain size value. Thus for each condition, different foils were employed and different locations on each foil were pictured and the number of grains on each micrograph was taken as the weighing factor in the calculation of the final grain size. Uniaxial tensile tests were carried out at a constant cross-head speed of 10 mm/min which produced an initial strain rate of 2x10.’ set-‘. Load-extension curves were obtained with the aid of a 25 mm gauge length extensometer from which the flow stress values were calculated at different strain levels. Results and Discussion Yield stress The grain size dependence of yield strength at 0.2% plastic strain is shown in a conventional d-‘/2 plot in Fig. 1. It is clear that the measured proof stress is not linearly related to d-l0 and the strengths achieved in ultrafine-grained materials are greater than would be expected from extrapolating the coarser grain size results. This departure from a linear dependence with grain size has been observed in other fine-grained aluminium alloys previously [9, lo]. It has been stated that this positive deviation from the Hall-Petch relationship could be due to the inhomogeneous yielding associated with the very fme grain sizes.
160,
0.0
I
0.2
0.4
0.6
0.8
1.0
1.2
d-‘/2 , cun-l/2
FIG. 1. Measured and back extrapolated 0.2 % proof stress data plotted against d-I’*.
FIG. 2. TEM picture of the material showing the grain structure and dispersion of second phase particles.
Vol. 32, No. 5
F’lNEGRAIh’EDAlAL.LQY
183
This inhomogeneous yielding complication was avoided by back extrapolation of the flow stress relationship observed in homogeneous straining. The obtained theoretical proof stress values which exclude the yield point, also shown in Fig. 1, are still non-linear in a d-I’*plot. A possible explanation for higher strength at finer grain sizes, being observed even after back extrapolation, is that in ultrafinegrained ahnninium eutectic alloys the finer grain size is produced by pinning the grain boundaries with intermetallic particles, as shown in Fig. 2. The particle size and distribution for two different conditions, having two different grain sizes of 1.1 pm and 5.6 pm, is shown respectively in Figures. 3a and b. It is observed that the finer the grain size the finer the intermetallic particles. Thus the contribution of particles to the strength may be greater at finer grain sizes. As can be seen in Fig. 1, the curve begins to deviate from the coarse grain size data at a grain size of about 2 pm, so that the amount of deviation at a grain size of 1.5 pm is almost 12 MPa. This is well in agreement with the calculation of strengthening from fine particles based on Orowan’s mechanism of dispersion hardening [12]. According to this mechanism an interparticle spacing (h) of 0.65 pm is necessary to produce the 12 MPa gain in the strength (a) calculated from the following relation:
where b is the .Burgers vector (about 0.2 mn) and E is the modulus of elasticity (70,000 MPa). Despite a variation in the distribution of the intermetallic particles, the mean interparticle spacing is found to be between 0.5 and 0.8 pm, as shown in Fig. 2.
(a)
0)
FIG. 3. The particle size and distribution for materials having grain sizes of 1.1 pm (a), and 5.6 pm (b). The deviation from the Hall-Petch relationship suggests that the alternative d-l dependence of proof stress on grain size could be more applicable. From the measured 0.2% proof stress data plotted in Fig. 4, it is (clear that all the yield strength values are well represented by a d-’ grain size dependence. The d-l relationship also confirms that the improvement in yield strength with grain refinement is considerably greater than would be predicted from a d-l’* Hall-Petch relationship established over coarser grain sizes. Another interesting feature of Fig. 4 is the insensitivity of the strength data to the types of heat treatment which have produced the wide range of grain size. It is clear from this figure that all the slowly
784
FINE GRAINED
Al ALLOY
Vol. 32. No. 5
and rapidly heated conditions could be expressed by a single relationship and one cannot differentiate between them on this basis. This implies that the strength data is more grain size dependent than structure dependent. It should be mentioned that the two annealing regimes, SA and FA, both produce structures with some differences in the degree of misorientation, the difference in the grain boundary angles for two extreme cases of grain size could be quite considerable [13]. This may imply that the d-i dependence of the yield stress is maintained even though some high angle boundaries are present in the structure. Flow stress To study the grain size dependence of flow stress, larger strains were considered and stress values at strain levels of 0.03, 0.06 and 0.10 were superimposed on the back-extrapolated proof stress data as shown in the d-l plot of Fig. 5. It is observed that the slope of the Hall-Petch plot, K, at high strain levels is close to that obtained at much lower strains (e=O.O02). Therefore it can be concluded that the grain boundaries have, to some extent, remained effective barriers to dislocation flow even at high strains.
160,
I
180
(
t
30
OL-----J 0.0
0.2
0.4
0.6
0.8
d-‘.
pm-’
1.0
1.2
FIG. 4. Measured 0.2% proof stress data plotted against d-i.
,k 0.0
1
0.2
0.4
0.6
0.8
1.0
1.2
d-‘. v-’ FIG. 5. Tensile flow stress at different strain levels as a function of d-!.
However, there is a tendency for the K value to decrease with strain and since the flow stresses are all in the work hardening region, this could reflect some differences in the work hardening behaviour in the coarse and fine grained materials. Fig. 6 shows the grain size dependence of work hardening rates It is clear that while the for both the coarse (d=5.6 ,um) and fine-grained (d= 1.1 pm) conditions. difference in work hardening rates for these two conditions is small at low strain levels, it becomes larger at higher strains. Therefore, for a given high strain level, the coarser material has a higher rate of work hardening, which is believed to cause the observed slight change in the slope of the Hall-Petch plot as the strain increases. The difference in work hardening behaviour could be attributed to the different rates of dynamic recovery occurring at different grain sizes. This in turn, is reflected in the rate of decrease in work hardening rate with strain, the higher the rate of decrease the higher the rate of dynamic recovery. The origin of this difference in rate of dynamic recovery can be sought in the dislocation structures generated during the straining of the material with different grain sizes. At fine grain sizes the structure is almost clear of dislocations before stretching, as shown in Fig. 2 for the condition having a grain size of 2.2 pm.
785
Vol. 32, No. 5
50
-0.00
0.05
0.10
0.15 0.20 TRUE STRAIN
0.25
0.30
FIG. 6. Work hardening behaviour of two fine and coarse-grained
conditions.
But it is expected that at higher strains dislocations would be concentrated around the grain boundaries with a few dislocations within the grains. This is because these fine grain sizes are of the order of the free slip distance and therefore little dislocation accumulation occurs in the grain interior. However, at coarse grain sizes less dislocation annihilation and rearrangements occur because of a larger free slip distance, and thus the dynamic recovery rate is lower. Conclusions 1.
In the present fine-grained alloy, the fine grain size is produced by pinning of grain boundaries with intermetallic particles.
2.
The measured proof and flow stress data are well represented by a d” relationship rather than supporting the classic Hall-Petch equation. This d-’ dependence was found to be insensitive to the type of structure and thus, the high and low angle boundaries both form effective barriers to dislocation propagation.
3.
In addition to the grain boundary strengthening, there is some contribution from particle hardening to the strength achieved, the effect being more pronounced at very fine grain sizes (d < 2 pm).
4.
The Hall-Petch constant (K), which basically measures the effectiveness of grain boundaries increasing the strength, showed a slight decrease with increasing strain, possibly due to dynamic recovery processes. References
1. 2. 3. 4. 5. 6. 7.
E.O. Hall, Proc. Phys. Sot. London, 643, 747 (195 1). NJ. Petch, J. Iron Steel Inst. London, 174, 25 (1953). J.C.M. :Li and Y.T. Chou, Met. Trans., lA, 1145 (1970). T.L. Johnston and C.E. Feltner, Met. Trans., lA, 1161 (1970). H. Fujita and T. Tabata, Acta Met., 21, 355 (1973). D. Kalish and B.G. LeFevre, Met. Trans., 6A, 1319 (1975). D. Kalis,h, B.G. LeFevre and S.K. Varma, Met. Trans., 8A, 204 (1977).
786
a. 9. 10. 11. 12. 13.
FINE GRAINED Al ALLOY
Vol. 32, No. 5
L.R. Morris, H. Sang and D.M. Moore, Proc. 4th ZCSMA, Nancy, France, p.131 (1976). D.J. Lloyd, Met. Sci., 14, 193 (1980). H. Westengen, Proc. 6th ZCSMA, Melbourne, Australia, p.461, Pergamon Press, Oxford (1983). R. Mahmudi, W.T. Roberts, D.V. Wilson, P. Furrer and P.M.B. Rodriguez, Aluminium, 63, 62 (1987). E. Orowan, discussion in “Symposium on Internal Stresses”, p.451, Institute of Metals London (1947). R. Mahmudi, Aluminium, 70, 590 (1994).