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Grain elongation and anisotropic grain growth during superplastic deformation in an AlMgMnCu alloy
Actu mufer. Vol. 45. No. 9, pp. 3887-3895,
Pergamon
Published
PII: S1359-6454(97)00032-3
1997 T; 1997 Acta Metallurgica Inc. by Elsevier Science Ltd. All nghts reserved Printed in Great Bmain 1359-6454/97 $17.00 + 0.00
GRAIN ELONGATION AND ANISOTROPIC GRAIN GROWTH DURING SUPERPLASTIC DEFORMATION IN AN Al-Mg-Mn-Cu ALLOY F. LI, D. H. BAE and A. K. GHOSH Department
of
Materials
Science
and Engineering, MI 48109-2136, (Received
The University U.S.A.
14 November
of
Michigan,
Ann
Arbor,
1996)
Abstract-Evolution of grain morphology in a fine grained Al-Mg-Mn-Cu alloy during uniaxial superplastic deformation is studied quantitatively. Grains undergo elongation, as well as dynamic grain growth along all directions, the separation and analysis of which is attempted here. Based on such analysis, the computed true grain growth rate along directions transverse to the tensile axis are found to exceed that parallel to the tensile axis. Possible mechanisms for this new observation are suggested. A unique relationship between grain boundary sliding rate and dynamic grain growth rate is found at different applied strain rates; this indicates that grain boundary sliding and grain boundary migration rates are inherently connected through the same mechanism. 0 1997 Acta MetaNurgica Inc.
1. INTRODUCTION It is well known that concurrent grain growth during superplastic deformation is significantly more rapid than static grain growth [l-6]. This strain-induced grain growth generally leads to strain hardening which, in addition to high strain rate sensitivity, may provide a superplastic alloy an increased resistance to strain localization, and may result in higher ductility [7, 81. It is generally believed that grain boundary migration (GBM), as in concurrent grain growth, is coupled with grain boundary sliding (GBS) [93. Much experimental evidence supports this view [lo-121. During deformation of fine grain, polycrystalline materials, extensive GBS leads to GBM, resulting in strain-induced grain growth for which several mechanisms have been suggested. Clark and Alden [2] and Senkov and Myshlyaev [3] proposed that GBS produces excessive vacancies to accelerate diffusion that and grain growth. Sato et al. [4] suggested coalescence of grains during grain rotation leads to grain growth. Wilkinson and Caceres [5] proposed that GBS creates damaged zones, and that the grain boundary migrates to consume these regions leading to grain growth. A similar proposal from Ghosh and Raj [6] also considered grain corner damage which drives migration into these regions via local curvature. Grain elongation during superplastic flow is generally not emphasized in earlier studies of superplasticity. Consequently, the grain growth models [2-61 mentioned above have only predicted isotropic grain growth. It is possible in some cases, for dynamic grain growth to obscure grain
elongation, and in many cases both dynamic grain refinement and coarsening have been observed [13], thereby confusing significant changes in terms of grain shape and size. It is also necessary to quench specimens immediately after deformation to retain the grain structure existing at the time of deformation. However, there is clear evidence of grain elongation reported in initially statically recrystalslip by lized aluminum alloys [ 14, 151. Intragranular dislocation motion leads to grain elongation along the applied stress axis and results in grain strain. As is typical of dislocation creep, subgrain formation may be expected as a function of imposed stress, temperature and the level of strain, but migration of high angle grain boundaries leading to grain growth may not be expected. Conventional dislocation creep has been recognized to have an important contribution to superplastic strain in addition to GBS [6, 14-161. Systematic investigation of dislocation activities during superplastic deformation in an AlL4.5% Mg alloy has confirmed these suggestions [lo, 171. The term “strain contribution by GBS” has been used loosely throughout this paper to include strain due to GBS, grain rotation and their accommodation processes. Because grain boundary motion is a net result of grain extension and grain boundary migration, it has been difficult in the past to separate the extent of true grain growth tendencies during superplastic deformation. By conducting a series of strain rate change tests after prestraining specimens, stress vs strain rate characteristics have been recorded for a variety of prestained microstructures. Then using appropriate assumptions that grain elongation results only from
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dislocation creep, it has been possible to distinguish grain elongation from true strain-induced grain growth and to investigate its anisotropic behavior. The method used to achieve this also provides a relatively simple yet reasonably quantitative measure of GBS over a wide strain rate range. This new procedure differs from the conventional techniques such as surface observation [18, 191 and so-called “internal marker” experiments [20]. It is believed that this study aids both a better understanding of superplastic deformation mechanisms and the modeling of the flow behavior of superplastic materials. 2. EXPERIMENTAL
METHOD
The material used in this study was a fine grained A14.7% Mg-0.7% Mn0.4% Cu alloy. It was cold rolled to 1.5 mm final thickness. The incipient melting temperature of the alloy was approximately 580°C. The material was solution treated at 500°C for 30 min before any further static anneal treatment and tensile testing. After static annealing at 550°C for 20 min, it had average linear intercept grain sizes of 7.5 pm x 7.5 pm x 4.5 pm in the longitudinal (rolling) (L), transverse (T) and short transverse or thickness (S) directions, respectively. Uniaxial tensile tests were carried out in the temperature range of 450-550°C and a strain rate range of 4 x 10m4SK’ to lo-* s-l to evaluate the superplastic properties of the alloy. The tensile specimens had 12.7 mm gauge length. The flow of material from the grip section into the gauge section of the specimens was significant. To eliminate this effect, all the tests were controlled by a microcomputer, using the recently improved crosshead speed schedule [2l], to obtain a constant applied strain rate throughout the test. The tests were performed by placing the specimen and load train within a clamshell furnace with three heating zones. The temperature gradient along the specimen’s gauge was generally maintained within _+2”C. The material exhibited larger elongation and strain rate sensitivity indices near 550°C and intermediate strain rates between 4 x 10m4s-’ and 4 x 10e3 s-l. These two strain rates and 550°C were therefore selected for deformation experiments to different interrupted strain levels in order to assess grain morphology evaluation. Samples were cut and prepared from regions of tested specimens where cross-sections were measured to determine the actual local strain levels. Separate static annealing tests were carried out to obtain static grain growth data. These specimens were water quenched immediately after the annealing, and in the case of tested tensile specimens, a few seconds after unloading. In order to characterize the material’s flow behavior at different grain morphology, a series of step strain rate tests were conducted at 550°C immediately after different prestrains carried out at 4 x 10e4 s-’ and 4 x lo-’ ss’. The step strain rate
GRAIN
GROWTH
tests covered a wide strain rate range, from 1O-5 SK’ to 2 x 10-i s-l, each strain segment being controlled by the new and improved crosshead speed control schedule [21] to maintain a constant strain rate. In addition, by utilizing a series of start decremental strain rate steps, combined with periodic incremental steps, the entire strain rate range was explored with a total strain less than 0.15 to minimize strain accumulation. This helped produce an isostructural condition, and it was assumed that the grain morphology established after a particular prestrain did not alter significantly during this step strain rate (further verified by grain size measurements). Thus the stress-strain rate behavior obtained by the step strain rate tests indeed represented the grain structure after prestrain. The water quenched samples were aged at 130°C for 24 h or longer, and mechanically polished then etched using Graff-Seargent reagent (15.5 ml HNO,, 0.5 ml HF, 3 g CrzOz and 84 ml water) to reveal grain boundaries. Linear intercept measurements were collected along the L, T and S directions from the micrographs taken from the L-S and T-S planes of the tested specimens. The mean grain diameter was determined by the cube root of the grain size measured along each of the three directions, i.e. d ,,,ean= (4
x d7 x ds)033. 3. EXPERIMENTAL
RESULTS
Figure 1 shows stress-strain curves from constant strain rate tensile tests. The flow stress is found to increase nearly linearly with strain at both strain rates used in this study. The apparent strain hardening rate is higher at the higher strain rate; however, when normalized by stress, it is actually lower for the higher strain rate. This strain hardening behavior is believed to be associated with the concurrent grain growth during the deformation, as previously reported [7, 81. The grain structures of the material before and after the superplastic test are shown in Fig. 2. These samples were water quenched from the test temperature. The initial grains were slightly pancake shaped rather than equiaxed. After being deformed at 4 x lo-’ s-’ and 4 x 10m4s-l, a significant change in 151
(550°C t
1
of 0.0
0.5
1.0
1.5
2.0
Strain Fig. 1. Stress-strain
relationship at 55O”C, 4 x 10m4 SK’and 4 x 10-j s-1.
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GRAIN GROWTH
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Fig. 2. Optical micrographs showing the grain structure of the material before (a) and after testing at 550-C. 4 x 1O-J s-’ and 4 x 10e3 SK’,strained to 1.6 (b) and 1.3 (c), respectively. Significant dynamic grain growth and grain elongation had occurred.
grain morphology occurred. The grains had grown in all directions, and appeared to become more equiaxed when viewed on the T-S plane [Fig. 2(b), (c)l. Although concurrent grain growth tended to be somewhat reduced due to intermixing of grain elongation, significant grain elongation was evident in Fig. 2(b), (c) (L-S plane). Grain size from specimens tested to different strain levels, as measured by the linear intercept along the
L, T and S directions, together with the mean grain diameter, are plotted against time in Fig. 3. Tensile specimens were initially held at the test temperature for about 1000 s to achieve thermal equilibrium before the tests were started. By using time as a common reference, the grain size after separate static annealing is also shown in this figure for comparison. More importantly, by doing so true dynamic grain growth and grain elongation may be separated as will
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ANISOTROPIC
be shown in the following section. An empirical linear relationship was used to fit each set of experimental data reasonably well. This is in agreement with the data reported by Caceres and Wilkinson [22] in which a copper alloy was investigated and a variety of other alloys were reviewed [5]. The linear relationship has the following general form: d=d,+ft
(I)
where d and t are grain size and time, respectively, and do and f are constants obtained by curve fitting.
Fittedto:d=d,+ft
IO4
Time (s) Fittedto:dL=d,L+ft
statically
annealed 4
GRAIN
GROWTH
Table 1. Constants
for dynamic grain growth equation [equation (l)] do (urn)
Laoallcd (s-l) 4 x IO-’
I’ (rtmis)
-2.32
4 x IO-4
9.88
5.49
The values of do and f for fitting the relationship between the mean grain size and time at the applied strain rates are listed in Table 1. These values will be used in the following sections. It is clear from Figs 2 and 3 that the concurrent dynamic grain growth was far greater than the static grain growth along all three orthogonal directions in this alloy. In fact the static grain growth appeared to be negligible after annealing for about 1000 s at 550°C indicating a reasonable degree of grain boundary pinning effect in the present alloy. It is also clear that the concurrent dynamic grain growth was dependent on the applied strain rate. At the faster strain rate the grain growth was more rapid than that at the slower strain rate. With the equations fitted to the grain size data, the change of grain aspect ratio with strain was calculated and the result is shown in Fig. 4. Being consistent with the results shown in Fig. 2, the grains had an initially elongated structure before the deformation, with an average aspect ratio of about 1.75 for both dL/ds and dT/ds [Fig. 2(a)]. The grains on the T-S plane tended to become more equiaxed (aspect ratio = 1) during deformation, while the grains became continuously more elongated along the L direction when viewed on the L-S plane. Stress vs strain rate plots generated from step strain rate tests after different prestrains at 4 x lo-’ s-l and 4 x 1O-4 s-l, 550°C (each prestrain corresponded to a concurrent mean grain size), are shown in Fig. 5 by the solid lines. All curves exhibited sigmoidal shape in the strain rate range tested. The stresses increased with increasing prestrains or mean grain sizes in the strain rate range tested. The dashed construction lines shown in the figure which have
40 Based
Time
x IO-’
1.94 x 10-3
on Macroscopic
Strain
‘T
‘1
(s)
Fig. 3. Measured mean concurrent grain size (a) and grain size along L (b), T (c) and S (d) directions as a function of time. A linear relationship fitted each set of the experimental data reasonably well. Note that the time axis is in logarithmic scale.
01 lo3
lo4
Time (s) Fig. 4. Change of grain aspect ratios with strain The grains elongated continuously in the L direction, but became more equiaxed when viewed from T-S plane.
LI
et al.:
ANISOTROPIC
GRAIN GROWTH
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4x10-45.1
,I))) I
._
10
0
f 10;o.5’
1
2
1
1 ’I’ .,..‘ ,l I,/
I
10 -4
I T = 55O”C, E= 4x10” s-1
I .,,..,
1o-3
.,
IO +
,,,
IO"
loo
3
Strain
Fig. 5. Stress vs strain rate at 55O’C obtained from step strain rate tests carried out after different prestrains. The prestrains and expected values of mean grain size from the grain growth data are indicated with the curves. (a) At a prestrain rate of 4 x IO-? SK’; (b) at a prestrain rate of E-1.3,d=13.7pm
been used to separate the different mechanistic contributions to strain rate will be discussed in the following section. 4. DATA ANALYSIS
t 10;o_5'
I
~~
.,/
10 -3
10 -4
AND DISCUSSION
Strain
As mentioned earlier in the Introduction, intragranular dislocation creep would lead to grain elongation. If the deformation was solely by dislocation creep, the average grain diameter in the L direction would match the total strain of the specimen gauge and could be calculated by: dL = do exp(t)
tl”l,l = E&s!+ EGBS.
1o'2
10 .'
s-l loo
Rate (s-l)
Fig. 6. Measured grain diameter in the L direction vs time. The dashed curves show the hypothetical upper bounds of grain elongation
range, the material creep:
based
on equation
(1).
obeys a power law of dislocation
(2)
where dL is the grain diameter along the L direction, Ct, is the initial grain diameter along the same direction and c is the strain measured from the specimen gauge. Figure 6 shows the plot of the experimentally determined dr. against time, the dashed curves were those predicted by equation (2). Clearly the concurrent increase in grain size in the L direction (grain elongation plus grain growth) during the deformation was significantly less than that predicted on the basis of macroscopic specimen strain, thereby suggesting that a part of the deformation resulted from GBS. Since GBS and intragranular dislocation creep can occur concurrently and independently, the total superplastic strain rate is the sum of the strain rate due to dislocation creep and that due to GBS [14, 16,23, 241:
1= 4x1 Oa .T..c. .55O”C, . .,
I ,.,.,,
I,!
&, = Aa”
(4)
where A is a temperature-dependent structural constant, rr is the applied stress and n’ is the stress exponent. This is represented by a straight line in the log o vs log k plot of Fig. 7. The sigmoidal shape of the experimentally determined curve (solid curve) is due to a significant contribution of GBS in the intermediate strain rate range based on equation (3). The level of flow stress determined from the experimental data for an applied strain rate, iiippllcd,
I
powar law
;.
(3)
Since grain elongation is related to &, in order to distinguish grain elongation from grain growth, kdlsl and & may be quantitatively separated by the principle shown in Fig. 7. For a superplastic material, its flow behavior typically exhibits a sigmoidal curve when the stress is plotted against strain rate on a logarithmic scale. This is schematically shown by the solid curve in Fig. 7. In the high strain rate
I
I
I
+ %pplied
I.
Log
(Strain Rate)
Fig. 7. Schematic illustration showing how dislocation creep rate and GBS rate may be separated quantitatively from experimentally determined total applied strain rate. Experimental data are collected after prestraining the material to different levels followed by a step strain rate test.
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GRAIN GROWTH
1o-2 T=550"C
I 10.0
12.5
15.0
1.0
dbm)
Strain
Fig. 8. Dislocation creep rate calculated using the method shown in Fig. 7, plotted as a function of mean grain size which increases during test at the two applied strain rates shown on the plot.
when projected horizontally, intersects with the line for dislocation creep at point I, which divides the applied strain rate into two parts: & and &, where tapphed= &, + &. If a series of experimental curves is obtained after different levels of prestrain, a relationship between & and concurrent grain size can be established for each prestrain level corresponding to a different mean grain size as determined by Fig. 3. The results are shown by dashed lines in Fig. 5 for the two different strain rates used. Differing from this graphical construction, an alternative method could be used to separate tdlsl from tappIled and to establish the relationship between idlrl and concurrent grain size. This method involves using a constitutive equation proposed by Ghosh [16] and fitting it to the experimental data points. The details can be found in another report [25]. The relationship between tdlsl and concurrent grain size is plotted in Fig. 8. The data points appeared to fit a logarithmic relationship fairly well; it has the following form: &,,, = a + b x log(d)
(5)
where a and b are constants and A is the concurrent grain size which is a function of time as shown in Fig. 3 and represented by equation (1). As the mean grain size increased, the rates of dislocation creep increased towards the applied strain rates which were shown by the dashed lines. The trend indicated that dislocation creep would be more predominant with increasing grain size. This is in general agreement with experimental observations. The constants a and b obtained by curve fitting for two different applied strain rates are listed in Table 2. Since the relationship between the mean concurrent grain size and time was already known [Fig. 3 Table 2. Constants
used in equation mites
(4) at
different
applied
4 x IO-'
-2.19
x IO-'
3.65 x lo-'
4 x 10-J
-2.13
x IO-"
3.06 x 1Om4
strain
Fig. 9. Calculated
rates of grain elongation in the L direction and rates of contraction in the T and S directions in terms of their absolute values, plotted against strain for the two applied strain rates.
and equation (l)], the dislocation creep rate could be easily computed as a function of time at a given applied strain rate. To simplify the analysis, it is assumed that the dislocation creep was isotropic, so that dislocation creep resulted in grain strain by grain elongation in the L direction, and grain contraction in the T and S directions respectively: &I (L, = -2&l
(T,= -2&l
(S,.
(6)
The subscripts L, T and S denote three directions as described. The elongation and contraction rates were related to the concurrent grain size and dislocation creep rate in that specific direction: &L, = dl. x t&l (l-1
(7)
&T) = dr x t&l ,T)= - 0.5& x &l(L)
(8)
&,sw
(9)
&cs, = ds x &a, CSI= - 0.54
x
Here the subscript ge denotes grain elongation in different directions. Note that &r) and &) have negative values, reflecting grain contraction. Each term on the right-hand side of equations (7))(9) was known as a function of time or strain. This allowed grain elongation and contraction to be calculated assuming isotropy; their absolute values were plotted against strain and shown in Fig. 9. The rate of grain elongation/contraction generally increased with strain at both of the applied strain rates. These rates were higher at the higher applied strain rate. The behavior revealed is understood because increasing grain size and/or increasing applied strain rate would increase & and hence the rate of grain elongation/ contraction. Because Lige(L)was positive while &r) and were negative, considerable grain shape an&@I isotropy developed, more rapidly at the higher strain rates. For the Al-Mg alloy used in this study, the grain aspect ratio, dL/ds, excluding grain growth, reached values of approximately 3.6 at 4 x 10-j SK’, and 2.5 at 4 x 10d4 ss’, from an initial value of about 1.6.
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GRAIN
GROWTH
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The true grain growth rate is simply the difference between concurrent grain growth rate and the rates determined by equations (7)-(9):
1) original structure
The calculated results are shown in Fig. 10. At the beginning of deformation, the true grain growth was nearly isotropic, but subsequently the tensile direction (L) showed considerable anisotropy, the grain growth rates in this direction continuously decreased with increasing strain within the specimen. However, in both the T and the S direction, grain growth rates increased slightly. As grain boundary radii, on average, increase during grain growth, the true grain growth rate along all grain dimensions is expected to decrease if the normal grain growth process were to prevail. The increasing values of &CT1 and dgEcsl, however, suggest that dynamic grain growth may not be an extension of the normal grain growth process. Furthermore, if sliding on the side surfaces of grains is reduced as a result of grain elongation, lateral grain growth may be expected to become less. One possible mechanism for higher growth rates along the transverse direction is the grain coalescence mechanism [2,26], i.e. grain rotation produced by GBS can cause lattice matching of adjoining grains leading to their coalescence, particularly on side surfaces of grains having a greater available surface area [Fig. 1 l(a)]. Alternatively, if dislocation climb in the vicinity of grain boundaries drives atom plating on these boundaries, the lateral boundaries are likely to exchange matter and migrate more rapidly than those normal to the tensile axis [16], as illustrated in Fig. 1 l(b). This mechanism is also discussed elsewhere [25]. It is generally agreed that GBM and GBS are coupled processes [9-121. As deformation proceeds, the grains became more elongated along the tensile direction, which could have an impact on the extent of GBS. For example, uniaxial tests conducted on specimens having an elongated initial
I”
‘Gq,,.,1
4x1 o-3 s-1 T s S
1o‘3
104’ 0.0
0.5
1.0
1.5
2.0
Strain
Fig. 10. Calculated true grain growth rate as a function of strain in three dimensions.
3) after coalescence
2) rotation of one grain
4) after boundary adjustment a
b Fig. 11.Two possible mechanisms of dynamic grain growth: (a) grain coalescence model [2, 261; (b) atom plating model on sliding grain boundaries [16].
grain structure has indicated that the flow stress is higher (or the creep rate is lower) in the direction of the longer grain dimension [27,28]. This experimental evidence has led to the suggestion that GBS is more difficult along the direction of elongated grains. It is expected that GBS would generally be enhanced when a large fraction of grain boundaries are at 45” to the tensile axis (maximum shear stress direction); thus grain extension and growth, in general, would reduce the extent of GBS. A decrease in GBS may result in a decrease in GBM; this may be the reason why the grain growth decelerated in the L direction, while it showed slight acceleration in the T and S directions as the grains tended towards a more equiaxed shape. It is interesting to note that when the true grain growth rate normalized by the total concurrent grain growth rate was plotted against the grain boundary sliding rate normalized by the applied strain rate, the data obtained at different applied strain rates fell together in each direction (Fig. 12). Several features revealed in this plot are to be noted. (1) All three curves tend to converge to &/dtotal = 1 at the slower
LI et al.:
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ANISOTROPIC
strain rate with the ratio of &s/&l,cd approaching unity. This implies that at very low strain rates or at the beginning of deformation, the strain would be mainly contributed by deformation of grain boundary regions and grain strain due to intragranular dislocation creep would be negligible. When this occurs, there would be no grain stretching, and & = &,,,. (2) At higher strain rates or after a substantial amount of superplastic strain, the data in the L direction quickly fall to &/&ial -+ 0, while the data in the T and S directions suggest that &/&,,, (T or S) + very high values as the value of &s/&lrd approaches 60%. In fact, the drop in & is more rapid than that in &. This implies that below &S/&,lled x0.6, there would be negligible grain growth in the L direction, while in the T and S directions both the grain contraction rate and the grain growth rate are numerically equal ((it,,,, x 0). It is not clear why & in the L direction drops so rapidly when tCiss is substantial. This may be related to the absolute size of d,, which, when it becomes very large, does not reflect any observable effects of atom transport (or growth). It is not entirely clear as to how Ligg/&,al would change in the T and S directions as &S/&al falls below 60%. One possibility would be that this ratio would rise to a very high positive value (because &,*, = 0) as & drops. Eventually &,,a, may become somewhat negative after significant grain growth, i.e. the grain contraction rate exceeds grain growth rates in the T and S directions. At this point, &/&,, could become highly negative and then slowly approach zero as & decreases. This part of the curve would be outside the graph shown in Fig. 12 if it could have been detected at faster applied strain rates than those used in the present study. Most interestingly, the data obtained at different applied strain rates fall into a unique curve in each direction (Fig. 12). This indicates that, regardless of the applied strain rate, there is an inherent relationship between the strain-induced grain growth (i.e. GBM) and GBS.
a ii 5
-h ,8
J=---??
1.0
?? ??
0.5 -
0 = 0
L
T s L T s
4x10-3g_’
4x10-4s-1
0.0 0.0
I
0.2
0.4
0.6
0.8
I 1.0
+#b&applled
Fig. 12. Relationship between true grain growth rate normalized by the total concurrent grain growth rate and the CBS rate normalized by the applied strain rate. The data obtained at different applied strain rates fell to a single curve in each direction.
GRAIN
GROWTH
Figure 12 indicates that in the optimum superplastic strain rate range in this fine grained Al-Mg alloy, the contribution to the total strain rate from GBS was higher than 80% at the beginning of the deformation and decreased to about 60% when the specimens fractured. There has been much attempt in the literature to measure the contribution of GBS to the total strain during superplastic deformation. Most of these were based on surface measurements [18, 191, and it has been fairly consistently concluded that this contribution is between 50% and 70%. A more convincing measurement involving an “internal to detect grain boundary offset has marker” suggested that the average contribution is about 63% [20]. All these measurements were performed after deforming the specimens to small strains (typically 30-50%). The present finding, using a completely different technique, is in general agreement with these previously reported values. Grain elongation during the deformation in the optimum superplastic range strongly suggests that the intragranular dislocation creep is indeed an important straining process during superplastic flow. Evidence in a recent transmission electron microscopic study using a similar alloy also supports this view [14, 171. This is not in agreement with the conclusions made in Refs [29, 301, in which GBS is suggested to be the only straining mechanism in the optimum superplastic range. While the error bars associated with the empirical fittings of the experimental data may be arguable, the general trend of the anisotropic behavior of grain growth and GBS should be of general interest for further research. 5. CONCLUSIONS The evolution of grain morphology and the corresponding changes in mechanical responses for a fine grained Al-Mg-Mn-Cu alloy during uniaxial superplastic deformation has been studied quantitatively. Assuming the overall grain size change is the sum of grain elongation due to intragranular dislocation creep and grain growth due to GBS, an approach has been developed to determine the true dynamic grain growth component by analyzing data from constant strain rate and strain rate change tests. Specific conclusions are listed below. (1) The rate of GBS decreased with increasing superplastic deformation as a result of overall grain growth and grain elongation. (2) The grain stretching rate increased with strain in all dimensions. While the true grain growth rate increased with strain in the T and S directions, it showed a decrease in the L direction. The true grain growth can be larger in the T and S directions than that in L direction. (3) The normalized grain growth rate, &/&,,,,, is uniquely related to the normalized GBS rate, &ss/&,pp,l~dr for different &,iled, thus demonstrating that GBS and GBM are inherently connected
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through the same mechanism, possibly by a grain coalescence model or by atom plating due to extensive dislocation climb in the vicinity of grain boundaries. Acknowledgements-The authors would like to acknowledge financial support from the GM Research and Development Center/NASA during the course of this work. REFERENCES 1. Edington, J. W., Melton, K. N. and Cutler, C. P., Prog. Mater. Sci., 1976, 21, 66. 2. Clark, M. A. and Alden, T. H., Acca metall., 1973, 21, 1195. 3. Senkov, N. 0. and Myshlyaev, M. M., Acca mecall., 1986, 32, 97. 4. Sato, E., Kuribayyashi, K. and Horiuchi, R., J. Jap. Inst. Met., 1991, 55, 839. 5. Wilkinson, D. S., and Caceres, C. H.. Acta metall., 1984, 34, 1335. A. K. and Raj, R., Proc. Int. Conf’. 6. Ghosh, Superpluscicity, ed. B. Baudelet and M. Surey. CNRS, 15. Ouai Anaole France. 75700. Paris. 1985. P. 11.1. 7. Ghosh, A. K., Acca metall., 1977, 25, 1413. . 8. Ghosh, A. K. and Hamilton, H., Metall. Trans., 1979, IOA, 699. 9. Ashby, M. F., Surf. Sci., 1972, 31, 498. 10. Mclean, D., J. In.it. Metals., 1952-3, 81, 293. 11. Rist. P. D.. The deformation of metals by GBS at elevated temperatures. M.Sc. thesis, The University of Birmingham, U.K., 1977. 12. Walter, J. L. and Cline. H. E., Trans. Am. Inst. Min. Engrs, 1968, 242, 1823.
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13. Ghosh, A. K. and Raj. R., Acca metall., 1986, 34, 447. 14. Li, F., Mechanism of superplasticity in an A1-4.5% Mg alloy. Ph.D. thesis, The University of Birmingham, U.K., 1994. IS. Vetrano, J. S., Lavender, C. A., Hamilton, C. H., Smith, M. T. and Bruemmer, S. M., Scripta metall. mater.. 1994, 30, 565. 16. Ghosh, A. K., Materials Science Forum. Transtec Publication, 170-172. 1994, p. 39. 17. Li, F., Roberts, W. T. and Bate, P. S.. Actu muter., 1996, 44, 217. 18. Lin, R., Chokshi. A. H. and Langdon, T. G., J. Mater. Sci., 1988, 23, 2712. 19. Valiev, R. Z. and Kaibyshev, 0. A., Acta metal/., 1983, 31, 2121. 20. Matsuki, K.. Morita, H., Yamada, M. and Murakami, Y., Metal Sci., 1977, 11, 156. P. and Ghosh, A. K., Metall. Mat. Trans., 21. Friedman, 1996, 27A, 3030. 22. Caceres, C. H. and Wilkinson, D. S., Acta metal/., 1984, 32, 415. T. G., Phi/. Msg., 1970, 22, 689. 23. Langdon, 1973, 21, 24. Ashby, M. F. and Verrall, R. A., Actametall., 149. 25. Li, F. and Ghosh, A. K., Material Science Forum. Transtec Publication, 217-222, 1996, p. 535. 26. Li, J. C.. J. appl. PhJs., 1962. 33, 2958. J., J. Inst. Metals. 1985, 27. Sherby, O.D. and Wadsworth, 925. K., Abstracts of 117th Meeting of‘ JIM, 28. Maruyama, 1995, p. 157. T. G., Acta metall. mater, 29. Valiev, R. and Langdon, 1993, 41, 949. 30. Langdon, T. G., Acta metall. mater., 1994, 42, 2437.
Pergamon
Published
PII: S1359-6454(97)00032-3
1997 T; 1997 Acta Metallurgica Inc. by Elsevier Science Ltd. All nghts reserved Printed in Great Bmain 1359-6454/97 $17.00 + 0.00
GRAIN ELONGATION AND ANISOTROPIC GRAIN GROWTH DURING SUPERPLASTIC DEFORMATION IN AN Al-Mg-Mn-Cu ALLOY F. LI, D. H. BAE and A. K. GHOSH Department
of
Materials
Science
and Engineering, MI 48109-2136, (Received
The University U.S.A.
14 November
of
Michigan,
Ann
Arbor,
1996)
Abstract-Evolution of grain morphology in a fine grained Al-Mg-Mn-Cu alloy during uniaxial superplastic deformation is studied quantitatively. Grains undergo elongation, as well as dynamic grain growth along all directions, the separation and analysis of which is attempted here. Based on such analysis, the computed true grain growth rate along directions transverse to the tensile axis are found to exceed that parallel to the tensile axis. Possible mechanisms for this new observation are suggested. A unique relationship between grain boundary sliding rate and dynamic grain growth rate is found at different applied strain rates; this indicates that grain boundary sliding and grain boundary migration rates are inherently connected through the same mechanism. 0 1997 Acta MetaNurgica Inc.
1. INTRODUCTION It is well known that concurrent grain growth during superplastic deformation is significantly more rapid than static grain growth [l-6]. This strain-induced grain growth generally leads to strain hardening which, in addition to high strain rate sensitivity, may provide a superplastic alloy an increased resistance to strain localization, and may result in higher ductility [7, 81. It is generally believed that grain boundary migration (GBM), as in concurrent grain growth, is coupled with grain boundary sliding (GBS) [93. Much experimental evidence supports this view [lo-121. During deformation of fine grain, polycrystalline materials, extensive GBS leads to GBM, resulting in strain-induced grain growth for which several mechanisms have been suggested. Clark and Alden [2] and Senkov and Myshlyaev [3] proposed that GBS produces excessive vacancies to accelerate diffusion that and grain growth. Sato et al. [4] suggested coalescence of grains during grain rotation leads to grain growth. Wilkinson and Caceres [5] proposed that GBS creates damaged zones, and that the grain boundary migrates to consume these regions leading to grain growth. A similar proposal from Ghosh and Raj [6] also considered grain corner damage which drives migration into these regions via local curvature. Grain elongation during superplastic flow is generally not emphasized in earlier studies of superplasticity. Consequently, the grain growth models [2-61 mentioned above have only predicted isotropic grain growth. It is possible in some cases, for dynamic grain growth to obscure grain
elongation, and in many cases both dynamic grain refinement and coarsening have been observed [13], thereby confusing significant changes in terms of grain shape and size. It is also necessary to quench specimens immediately after deformation to retain the grain structure existing at the time of deformation. However, there is clear evidence of grain elongation reported in initially statically recrystalslip by lized aluminum alloys [ 14, 151. Intragranular dislocation motion leads to grain elongation along the applied stress axis and results in grain strain. As is typical of dislocation creep, subgrain formation may be expected as a function of imposed stress, temperature and the level of strain, but migration of high angle grain boundaries leading to grain growth may not be expected. Conventional dislocation creep has been recognized to have an important contribution to superplastic strain in addition to GBS [6, 14-161. Systematic investigation of dislocation activities during superplastic deformation in an AlL4.5% Mg alloy has confirmed these suggestions [lo, 171. The term “strain contribution by GBS” has been used loosely throughout this paper to include strain due to GBS, grain rotation and their accommodation processes. Because grain boundary motion is a net result of grain extension and grain boundary migration, it has been difficult in the past to separate the extent of true grain growth tendencies during superplastic deformation. By conducting a series of strain rate change tests after prestraining specimens, stress vs strain rate characteristics have been recorded for a variety of prestained microstructures. Then using appropriate assumptions that grain elongation results only from
3887
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dislocation creep, it has been possible to distinguish grain elongation from true strain-induced grain growth and to investigate its anisotropic behavior. The method used to achieve this also provides a relatively simple yet reasonably quantitative measure of GBS over a wide strain rate range. This new procedure differs from the conventional techniques such as surface observation [18, 191 and so-called “internal marker” experiments [20]. It is believed that this study aids both a better understanding of superplastic deformation mechanisms and the modeling of the flow behavior of superplastic materials. 2. EXPERIMENTAL
METHOD
The material used in this study was a fine grained A14.7% Mg-0.7% Mn0.4% Cu alloy. It was cold rolled to 1.5 mm final thickness. The incipient melting temperature of the alloy was approximately 580°C. The material was solution treated at 500°C for 30 min before any further static anneal treatment and tensile testing. After static annealing at 550°C for 20 min, it had average linear intercept grain sizes of 7.5 pm x 7.5 pm x 4.5 pm in the longitudinal (rolling) (L), transverse (T) and short transverse or thickness (S) directions, respectively. Uniaxial tensile tests were carried out in the temperature range of 450-550°C and a strain rate range of 4 x 10m4SK’ to lo-* s-l to evaluate the superplastic properties of the alloy. The tensile specimens had 12.7 mm gauge length. The flow of material from the grip section into the gauge section of the specimens was significant. To eliminate this effect, all the tests were controlled by a microcomputer, using the recently improved crosshead speed schedule [2l], to obtain a constant applied strain rate throughout the test. The tests were performed by placing the specimen and load train within a clamshell furnace with three heating zones. The temperature gradient along the specimen’s gauge was generally maintained within _+2”C. The material exhibited larger elongation and strain rate sensitivity indices near 550°C and intermediate strain rates between 4 x 10m4s-’ and 4 x 10e3 s-l. These two strain rates and 550°C were therefore selected for deformation experiments to different interrupted strain levels in order to assess grain morphology evaluation. Samples were cut and prepared from regions of tested specimens where cross-sections were measured to determine the actual local strain levels. Separate static annealing tests were carried out to obtain static grain growth data. These specimens were water quenched immediately after the annealing, and in the case of tested tensile specimens, a few seconds after unloading. In order to characterize the material’s flow behavior at different grain morphology, a series of step strain rate tests were conducted at 550°C immediately after different prestrains carried out at 4 x 10e4 s-’ and 4 x lo-’ ss’. The step strain rate
GRAIN
GROWTH
tests covered a wide strain rate range, from 1O-5 SK’ to 2 x 10-i s-l, each strain segment being controlled by the new and improved crosshead speed control schedule [21] to maintain a constant strain rate. In addition, by utilizing a series of start decremental strain rate steps, combined with periodic incremental steps, the entire strain rate range was explored with a total strain less than 0.15 to minimize strain accumulation. This helped produce an isostructural condition, and it was assumed that the grain morphology established after a particular prestrain did not alter significantly during this step strain rate (further verified by grain size measurements). Thus the stress-strain rate behavior obtained by the step strain rate tests indeed represented the grain structure after prestrain. The water quenched samples were aged at 130°C for 24 h or longer, and mechanically polished then etched using Graff-Seargent reagent (15.5 ml HNO,, 0.5 ml HF, 3 g CrzOz and 84 ml water) to reveal grain boundaries. Linear intercept measurements were collected along the L, T and S directions from the micrographs taken from the L-S and T-S planes of the tested specimens. The mean grain diameter was determined by the cube root of the grain size measured along each of the three directions, i.e. d ,,,ean= (4
x d7 x ds)033. 3. EXPERIMENTAL
RESULTS
Figure 1 shows stress-strain curves from constant strain rate tensile tests. The flow stress is found to increase nearly linearly with strain at both strain rates used in this study. The apparent strain hardening rate is higher at the higher strain rate; however, when normalized by stress, it is actually lower for the higher strain rate. This strain hardening behavior is believed to be associated with the concurrent grain growth during the deformation, as previously reported [7, 81. The grain structures of the material before and after the superplastic test are shown in Fig. 2. These samples were water quenched from the test temperature. The initial grains were slightly pancake shaped rather than equiaxed. After being deformed at 4 x lo-’ s-’ and 4 x 10m4s-l, a significant change in 151
(550°C t
1
of 0.0
0.5
1.0
1.5
2.0
Strain Fig. 1. Stress-strain
relationship at 55O”C, 4 x 10m4 SK’and 4 x 10-j s-1.
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ANISOTROPIC
GRAIN GROWTH
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Fig. 2. Optical micrographs showing the grain structure of the material before (a) and after testing at 550-C. 4 x 1O-J s-’ and 4 x 10e3 SK’,strained to 1.6 (b) and 1.3 (c), respectively. Significant dynamic grain growth and grain elongation had occurred.
grain morphology occurred. The grains had grown in all directions, and appeared to become more equiaxed when viewed on the T-S plane [Fig. 2(b), (c)l. Although concurrent grain growth tended to be somewhat reduced due to intermixing of grain elongation, significant grain elongation was evident in Fig. 2(b), (c) (L-S plane). Grain size from specimens tested to different strain levels, as measured by the linear intercept along the
L, T and S directions, together with the mean grain diameter, are plotted against time in Fig. 3. Tensile specimens were initially held at the test temperature for about 1000 s to achieve thermal equilibrium before the tests were started. By using time as a common reference, the grain size after separate static annealing is also shown in this figure for comparison. More importantly, by doing so true dynamic grain growth and grain elongation may be separated as will
LI et al.:
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be shown in the following section. An empirical linear relationship was used to fit each set of experimental data reasonably well. This is in agreement with the data reported by Caceres and Wilkinson [22] in which a copper alloy was investigated and a variety of other alloys were reviewed [5]. The linear relationship has the following general form: d=d,+ft
(I)
where d and t are grain size and time, respectively, and do and f are constants obtained by curve fitting.
Fittedto:d=d,+ft
IO4
Time (s) Fittedto:dL=d,L+ft
statically
annealed 4
GRAIN
GROWTH
Table 1. Constants
for dynamic grain growth equation [equation (l)] do (urn)
Laoallcd (s-l) 4 x IO-’
I’ (rtmis)
-2.32
4 x IO-4
9.88
5.49
The values of do and f for fitting the relationship between the mean grain size and time at the applied strain rates are listed in Table 1. These values will be used in the following sections. It is clear from Figs 2 and 3 that the concurrent dynamic grain growth was far greater than the static grain growth along all three orthogonal directions in this alloy. In fact the static grain growth appeared to be negligible after annealing for about 1000 s at 550°C indicating a reasonable degree of grain boundary pinning effect in the present alloy. It is also clear that the concurrent dynamic grain growth was dependent on the applied strain rate. At the faster strain rate the grain growth was more rapid than that at the slower strain rate. With the equations fitted to the grain size data, the change of grain aspect ratio with strain was calculated and the result is shown in Fig. 4. Being consistent with the results shown in Fig. 2, the grains had an initially elongated structure before the deformation, with an average aspect ratio of about 1.75 for both dL/ds and dT/ds [Fig. 2(a)]. The grains on the T-S plane tended to become more equiaxed (aspect ratio = 1) during deformation, while the grains became continuously more elongated along the L direction when viewed on the L-S plane. Stress vs strain rate plots generated from step strain rate tests after different prestrains at 4 x lo-’ s-l and 4 x 1O-4 s-l, 550°C (each prestrain corresponded to a concurrent mean grain size), are shown in Fig. 5 by the solid lines. All curves exhibited sigmoidal shape in the strain rate range tested. The stresses increased with increasing prestrains or mean grain sizes in the strain rate range tested. The dashed construction lines shown in the figure which have
40 Based
Time
x IO-’
1.94 x 10-3
on Macroscopic
Strain
‘T
‘1
(s)
Fig. 3. Measured mean concurrent grain size (a) and grain size along L (b), T (c) and S (d) directions as a function of time. A linear relationship fitted each set of the experimental data reasonably well. Note that the time axis is in logarithmic scale.
01 lo3
lo4
Time (s) Fig. 4. Change of grain aspect ratios with strain The grains elongated continuously in the L direction, but became more equiaxed when viewed from T-S plane.
LI
et al.:
ANISOTROPIC
GRAIN GROWTH
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4x10-45.1
,I))) I
._
10
0
f 10;o.5’
1
2
1
1 ’I’ .,..‘ ,l I,/
I
10 -4
I T = 55O”C, E= 4x10” s-1
I .,,..,
1o-3
.,
IO +
,,,
IO"
loo
3
Strain
Fig. 5. Stress vs strain rate at 55O’C obtained from step strain rate tests carried out after different prestrains. The prestrains and expected values of mean grain size from the grain growth data are indicated with the curves. (a) At a prestrain rate of 4 x IO-? SK’; (b) at a prestrain rate of E-1.3,d=13.7pm
been used to separate the different mechanistic contributions to strain rate will be discussed in the following section. 4. DATA ANALYSIS
t 10;o_5'
I
~~
.,/
10 -3
10 -4
AND DISCUSSION
Strain
As mentioned earlier in the Introduction, intragranular dislocation creep would lead to grain elongation. If the deformation was solely by dislocation creep, the average grain diameter in the L direction would match the total strain of the specimen gauge and could be calculated by: dL = do exp(t)
tl”l,l = E&s!+ EGBS.
1o'2
10 .'
s-l loo
Rate (s-l)
Fig. 6. Measured grain diameter in the L direction vs time. The dashed curves show the hypothetical upper bounds of grain elongation
range, the material creep:
based
on equation
(1).
obeys a power law of dislocation
(2)
where dL is the grain diameter along the L direction, Ct, is the initial grain diameter along the same direction and c is the strain measured from the specimen gauge. Figure 6 shows the plot of the experimentally determined dr. against time, the dashed curves were those predicted by equation (2). Clearly the concurrent increase in grain size in the L direction (grain elongation plus grain growth) during the deformation was significantly less than that predicted on the basis of macroscopic specimen strain, thereby suggesting that a part of the deformation resulted from GBS. Since GBS and intragranular dislocation creep can occur concurrently and independently, the total superplastic strain rate is the sum of the strain rate due to dislocation creep and that due to GBS [14, 16,23, 241:
1= 4x1 Oa .T..c. .55O”C, . .,
I ,.,.,,
I,!
&, = Aa”
(4)
where A is a temperature-dependent structural constant, rr is the applied stress and n’ is the stress exponent. This is represented by a straight line in the log o vs log k plot of Fig. 7. The sigmoidal shape of the experimentally determined curve (solid curve) is due to a significant contribution of GBS in the intermediate strain rate range based on equation (3). The level of flow stress determined from the experimental data for an applied strain rate, iiippllcd,
I
powar law
;.
(3)
Since grain elongation is related to &, in order to distinguish grain elongation from grain growth, kdlsl and & may be quantitatively separated by the principle shown in Fig. 7. For a superplastic material, its flow behavior typically exhibits a sigmoidal curve when the stress is plotted against strain rate on a logarithmic scale. This is schematically shown by the solid curve in Fig. 7. In the high strain rate
I
I
I
+ %pplied
I.
Log
(Strain Rate)
Fig. 7. Schematic illustration showing how dislocation creep rate and GBS rate may be separated quantitatively from experimentally determined total applied strain rate. Experimental data are collected after prestraining the material to different levels followed by a step strain rate test.
LI et al.:
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ANISOTROPIC
GRAIN GROWTH
1o-2 T=550"C
I 10.0
12.5
15.0
1.0
dbm)
Strain
Fig. 8. Dislocation creep rate calculated using the method shown in Fig. 7, plotted as a function of mean grain size which increases during test at the two applied strain rates shown on the plot.
when projected horizontally, intersects with the line for dislocation creep at point I, which divides the applied strain rate into two parts: & and &, where tapphed= &, + &. If a series of experimental curves is obtained after different levels of prestrain, a relationship between & and concurrent grain size can be established for each prestrain level corresponding to a different mean grain size as determined by Fig. 3. The results are shown by dashed lines in Fig. 5 for the two different strain rates used. Differing from this graphical construction, an alternative method could be used to separate tdlsl from tappIled and to establish the relationship between idlrl and concurrent grain size. This method involves using a constitutive equation proposed by Ghosh [16] and fitting it to the experimental data points. The details can be found in another report [25]. The relationship between tdlsl and concurrent grain size is plotted in Fig. 8. The data points appeared to fit a logarithmic relationship fairly well; it has the following form: &,,, = a + b x log(d)
(5)
where a and b are constants and A is the concurrent grain size which is a function of time as shown in Fig. 3 and represented by equation (1). As the mean grain size increased, the rates of dislocation creep increased towards the applied strain rates which were shown by the dashed lines. The trend indicated that dislocation creep would be more predominant with increasing grain size. This is in general agreement with experimental observations. The constants a and b obtained by curve fitting for two different applied strain rates are listed in Table 2. Since the relationship between the mean concurrent grain size and time was already known [Fig. 3 Table 2. Constants
used in equation mites
(4) at
different
applied
4 x IO-'
-2.19
x IO-'
3.65 x lo-'
4 x 10-J
-2.13
x IO-"
3.06 x 1Om4
strain
Fig. 9. Calculated
rates of grain elongation in the L direction and rates of contraction in the T and S directions in terms of their absolute values, plotted against strain for the two applied strain rates.
and equation (l)], the dislocation creep rate could be easily computed as a function of time at a given applied strain rate. To simplify the analysis, it is assumed that the dislocation creep was isotropic, so that dislocation creep resulted in grain strain by grain elongation in the L direction, and grain contraction in the T and S directions respectively: &I (L, = -2&l
(T,= -2&l
(S,.
(6)
The subscripts L, T and S denote three directions as described. The elongation and contraction rates were related to the concurrent grain size and dislocation creep rate in that specific direction: &L, = dl. x t&l (l-1
(7)
&T) = dr x t&l ,T)= - 0.5& x &l(L)
(8)
&,sw
(9)
&cs, = ds x &a, CSI= - 0.54
x
Here the subscript ge denotes grain elongation in different directions. Note that &r) and &) have negative values, reflecting grain contraction. Each term on the right-hand side of equations (7))(9) was known as a function of time or strain. This allowed grain elongation and contraction to be calculated assuming isotropy; their absolute values were plotted against strain and shown in Fig. 9. The rate of grain elongation/contraction generally increased with strain at both of the applied strain rates. These rates were higher at the higher applied strain rate. The behavior revealed is understood because increasing grain size and/or increasing applied strain rate would increase & and hence the rate of grain elongation/ contraction. Because Lige(L)was positive while &r) and were negative, considerable grain shape an&@I isotropy developed, more rapidly at the higher strain rates. For the Al-Mg alloy used in this study, the grain aspect ratio, dL/ds, excluding grain growth, reached values of approximately 3.6 at 4 x 10-j SK’, and 2.5 at 4 x 10d4 ss’, from an initial value of about 1.6.
LI et al.:
ANISOTROPIC
GRAIN
GROWTH
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The true grain growth rate is simply the difference between concurrent grain growth rate and the rates determined by equations (7)-(9):
1) original structure
The calculated results are shown in Fig. 10. At the beginning of deformation, the true grain growth was nearly isotropic, but subsequently the tensile direction (L) showed considerable anisotropy, the grain growth rates in this direction continuously decreased with increasing strain within the specimen. However, in both the T and the S direction, grain growth rates increased slightly. As grain boundary radii, on average, increase during grain growth, the true grain growth rate along all grain dimensions is expected to decrease if the normal grain growth process were to prevail. The increasing values of &CT1 and dgEcsl, however, suggest that dynamic grain growth may not be an extension of the normal grain growth process. Furthermore, if sliding on the side surfaces of grains is reduced as a result of grain elongation, lateral grain growth may be expected to become less. One possible mechanism for higher growth rates along the transverse direction is the grain coalescence mechanism [2,26], i.e. grain rotation produced by GBS can cause lattice matching of adjoining grains leading to their coalescence, particularly on side surfaces of grains having a greater available surface area [Fig. 1 l(a)]. Alternatively, if dislocation climb in the vicinity of grain boundaries drives atom plating on these boundaries, the lateral boundaries are likely to exchange matter and migrate more rapidly than those normal to the tensile axis [16], as illustrated in Fig. 1 l(b). This mechanism is also discussed elsewhere [25]. It is generally agreed that GBM and GBS are coupled processes [9-121. As deformation proceeds, the grains became more elongated along the tensile direction, which could have an impact on the extent of GBS. For example, uniaxial tests conducted on specimens having an elongated initial
I”
‘Gq,,.,1
4x1 o-3 s-1 T s S
1o‘3
104’ 0.0
0.5
1.0
1.5
2.0
Strain
Fig. 10. Calculated true grain growth rate as a function of strain in three dimensions.
3) after coalescence
2) rotation of one grain
4) after boundary adjustment a
b Fig. 11.Two possible mechanisms of dynamic grain growth: (a) grain coalescence model [2, 261; (b) atom plating model on sliding grain boundaries [16].
grain structure has indicated that the flow stress is higher (or the creep rate is lower) in the direction of the longer grain dimension [27,28]. This experimental evidence has led to the suggestion that GBS is more difficult along the direction of elongated grains. It is expected that GBS would generally be enhanced when a large fraction of grain boundaries are at 45” to the tensile axis (maximum shear stress direction); thus grain extension and growth, in general, would reduce the extent of GBS. A decrease in GBS may result in a decrease in GBM; this may be the reason why the grain growth decelerated in the L direction, while it showed slight acceleration in the T and S directions as the grains tended towards a more equiaxed shape. It is interesting to note that when the true grain growth rate normalized by the total concurrent grain growth rate was plotted against the grain boundary sliding rate normalized by the applied strain rate, the data obtained at different applied strain rates fell together in each direction (Fig. 12). Several features revealed in this plot are to be noted. (1) All three curves tend to converge to &/dtotal = 1 at the slower
LI et al.:
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ANISOTROPIC
strain rate with the ratio of &s/&l,cd approaching unity. This implies that at very low strain rates or at the beginning of deformation, the strain would be mainly contributed by deformation of grain boundary regions and grain strain due to intragranular dislocation creep would be negligible. When this occurs, there would be no grain stretching, and & = &,,,. (2) At higher strain rates or after a substantial amount of superplastic strain, the data in the L direction quickly fall to &/&ial -+ 0, while the data in the T and S directions suggest that &/&,,, (T or S) + very high values as the value of &s/&lrd approaches 60%. In fact, the drop in & is more rapid than that in &. This implies that below &S/&,lled x0.6, there would be negligible grain growth in the L direction, while in the T and S directions both the grain contraction rate and the grain growth rate are numerically equal ((it,,,, x 0). It is not clear why & in the L direction drops so rapidly when tCiss is substantial. This may be related to the absolute size of d,, which, when it becomes very large, does not reflect any observable effects of atom transport (or growth). It is not entirely clear as to how Ligg/&,al would change in the T and S directions as &S/&al falls below 60%. One possibility would be that this ratio would rise to a very high positive value (because &,*, = 0) as & drops. Eventually &,,a, may become somewhat negative after significant grain growth, i.e. the grain contraction rate exceeds grain growth rates in the T and S directions. At this point, &/&,, could become highly negative and then slowly approach zero as & decreases. This part of the curve would be outside the graph shown in Fig. 12 if it could have been detected at faster applied strain rates than those used in the present study. Most interestingly, the data obtained at different applied strain rates fall into a unique curve in each direction (Fig. 12). This indicates that, regardless of the applied strain rate, there is an inherent relationship between the strain-induced grain growth (i.e. GBM) and GBS.
a ii 5
-h ,8
J=---??
1.0
?? ??
0.5 -
0 = 0
L
T s L T s
4x10-3g_’
4x10-4s-1
0.0 0.0
I
0.2
0.4
0.6
0.8
I 1.0
+#b&applled
Fig. 12. Relationship between true grain growth rate normalized by the total concurrent grain growth rate and the CBS rate normalized by the applied strain rate. The data obtained at different applied strain rates fell to a single curve in each direction.
GRAIN
GROWTH
Figure 12 indicates that in the optimum superplastic strain rate range in this fine grained Al-Mg alloy, the contribution to the total strain rate from GBS was higher than 80% at the beginning of the deformation and decreased to about 60% when the specimens fractured. There has been much attempt in the literature to measure the contribution of GBS to the total strain during superplastic deformation. Most of these were based on surface measurements [18, 191, and it has been fairly consistently concluded that this contribution is between 50% and 70%. A more convincing measurement involving an “internal to detect grain boundary offset has marker” suggested that the average contribution is about 63% [20]. All these measurements were performed after deforming the specimens to small strains (typically 30-50%). The present finding, using a completely different technique, is in general agreement with these previously reported values. Grain elongation during the deformation in the optimum superplastic range strongly suggests that the intragranular dislocation creep is indeed an important straining process during superplastic flow. Evidence in a recent transmission electron microscopic study using a similar alloy also supports this view [14, 171. This is not in agreement with the conclusions made in Refs [29, 301, in which GBS is suggested to be the only straining mechanism in the optimum superplastic range. While the error bars associated with the empirical fittings of the experimental data may be arguable, the general trend of the anisotropic behavior of grain growth and GBS should be of general interest for further research. 5. CONCLUSIONS The evolution of grain morphology and the corresponding changes in mechanical responses for a fine grained Al-Mg-Mn-Cu alloy during uniaxial superplastic deformation has been studied quantitatively. Assuming the overall grain size change is the sum of grain elongation due to intragranular dislocation creep and grain growth due to GBS, an approach has been developed to determine the true dynamic grain growth component by analyzing data from constant strain rate and strain rate change tests. Specific conclusions are listed below. (1) The rate of GBS decreased with increasing superplastic deformation as a result of overall grain growth and grain elongation. (2) The grain stretching rate increased with strain in all dimensions. While the true grain growth rate increased with strain in the T and S directions, it showed a decrease in the L direction. The true grain growth can be larger in the T and S directions than that in L direction. (3) The normalized grain growth rate, &/&,,,,, is uniquely related to the normalized GBS rate, &ss/&,pp,l~dr for different &,iled, thus demonstrating that GBS and GBM are inherently connected
LI et al.:
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