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Flow localization and neck formation in a superplastic metal
Acta M~rallurgicu Printed in Great
Vol 29. pp. 91 I to 920. 1981. Bntam All rights reserved
Copyright
Oool-6160~81/050911-10502.00~0 8 1981 Pergamon Press Ltd
FLOW LOCALIZATION AND NECK FORMATION SUPERPLASTIC METAL FARGHALLI
and TERENCE
A. MOHAMED
IN A
G. LANGDON
Departments of Materials Science and Mechanical Engineering, University of Southern California. Los Angeles, CA 90007, U.S.A. (Received 16 June 1980; in reoisedform 30 October 1980)
Ahtstxact-Experiments were conducted on the superplastic Zn-22% Al eutectoid alloy to investigate the extent of flow localization and neck formation in the three regions of plastic flow. The results show that the behavior is qualitatively similar in the low stress region I and the high stress region III, but there are very significant differences in the superplastic region II. Deformation is essentially uniform in region II up to at least 5 800% and quasi-uniform thereafter, whereas there are marked deviations from uniform flow in regions I and III at 5 200%. Failure occurs by the formation and catastrophic growth of a sharp neck in regions I and III, whereas necking is diffuse at high elongations in region II. The results are consistent with a genuine decrease in the value of the strain rate sensitivity at low strain rates in region I. R&m&Nous avons ttudie experimentalement la localisation de Kcoulement et la formation de la striction dans la trois domaines d’icoulement plastique dun alliage eutectdide superplastique Zn-220/, Al. Nos rtsultats montrent des comportements qualitativement semblables dans la region I des faibles contra&es et dans la region III des fortes contraintes, mais des differences tris significatives dans le domaine superplastique II. La deformation est easentiellement unifortne dam le domaine II jusqu’a au moins 800% environ et quasi-uniforme ensuite, alors qu’il y a des deviations tres net@ par rapport a un ecoulement uniforme dam les domaines I et II pour 200% environ. La rupture dans les domaines I et III se produit par formation et croissance catastrophique dune striction trb franche, alors que la striction est diffuse dans le domaine II pour Ies grands allongements. Nos msultats sont cohtrents avec veritable diminution de la sensibilitt a la vitesse de deformation pour les faibles vitesses de deformation dans le domaine 1. maaaung-An der superplastischen eutektoiden Legierung Zn-220/, Al wurde das Ausmal3 der Gleitlokalisierung und der EinschniIrungabildung in den drei plaatischen Bereichen untersucht. Die Ergebnisae xeigen, da8 das Verhalten im Bereich I niedriger Spannung und im Bereich III hoher Spannung qualitativ lhnlich ist. Dagegen treten erhebliche Unterschiede im superplastischen Bereich II auf. Die Verformung liiuft im Bereich II bis zu mindestens - 800% stetig, dartiber quasistetig ab. Dagegen treten in Bereich I und III bei _ 200% betrlchtliche Abweichungen vom stetigen FlieBen auf. In Bereich I und III entsteht der Bruch durch Bildung und katastrophales Wachstum einer scharfen Einschniirung; dagegen ist die Einschnilrung im Bereich II bei groDen Verliingerungen diffus. Die Ergebnisse sind vertriiglich mit einem echten Abfall in der Dehngeschwindigkeitsempfindlichkeit bei kleinen Dehngeschwindigkeiten im Bereich I.
1. INTRODUCIION Considerable interest has developed in recent years in the mechanical behavior of materials exhibiting extensive superplasticity. This interest has arisen from a scientific viewpoint and also because of the increasing awareness that superplastic materials may be utilized in numerous simple and inexpensive forming operations. The Zn-22% Al eutectoid alloy is a classic superplastic metal which has been subjected to many experimental investigations. However, despite the large volume of work reported for this material to date, there are some very significant discrepancies in the observed behavior. Most of the investigations on Zn-22% Al, and also on other superplastic materials, have been conducted using testing machines (such as an Instron) which
operate at a constant rate of strain or cross-head displacement. Measurements are then taken of the steady-state stress, u, for various values of the imposed strain rate, g, and the results are logarithmically plotted in the form of Q vs k. All of the results from these experiments are reasonably consistent. The datum points fall into two distinct regions which are characterized by two different values of the strain rate sensitivity, m, where m is defined as d In u m= 6)ding *,r
(1)
where d is the grain size and T is the absolute temperature. In general, m has a very low value at the higher strain rates (typically, m < 0.2) but the value increases at the lower strain rates to. typically, -0.5.
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Some of the data obtained in this way indicate the possibility of a further decrease in m at the very lowest strain rates; but the trend is not clear, and it is difficult to reach any firm conclusions because of the problems of attaining extremely low rates of strain on a constant displacenient machine. A simple method of overcoming this problem is to conduct tests under creep (constant stress) conditions, but the results reported from such experiments reveal important differences. In an early investigation of the creep of Zn-22% Al, Vaidya et al. [l] showed that the value of m increased from -0.27 at high stresses to 5 0.5 at intermediate stresses and to * 1.1 at very low stress levels. These three regions of behavior were designated III, II, and I, respectively, and there was also a corresponding change in the activation energy from a high value in region III to much lower values in regions II and I. In this work, the behavior in the low stress region I was attributed to the advent of Coble diffusion creep [2]. Subsequent creep experiments on Zn-22”/, Al have revealed very significant discrepancies in the behavior in region I. On the one hand, Misro and Mukherjee [3] confirmed the earlier results of Vaidya et al. [l] and obtained m = 1.0 and a low activation energy in region I. More recently, Mukherjee and COworkers [4] again confirmed the value of m but obtained a high activation energy in region I due, it was suggested, to the occurrence of Nabarro-Herring diffusion creep [5,6] at larger grain sixes (typically, d 2 3 m). On the other hand experiments by Mohamed and Langdon [7-j revealed a decrease in m to -0.24 in region I, with a corresponding increase in the activation energy for plastic tiow [8]. Furthermore, a similar transition to m 5 0.33 was later reported for region I by Grivas [9], and Vale et al. [lo] also obtained a decrease in m to -0.32 and a corresponding increase in the activation energy in region I. In addition, calculations have shown that the behavior in region I, in which m z 0.24-0.34. and there is a high activation energy, takes place at strain rates which are faster than those predicted by the best estimates for either Coble or Nabarro-Herring diffusion creep [ll], thereby inferring that region I is a distinct deformation mode lying intermediate in stress between the superplastic region II and the diffusion creep processes. There appear to be two possible explanations for this apparent dichotomy in behavior. First, it was pointed out by Rai and Grant [12] that the values recorded for i in region I may rep resent an underestimate due to the occurrence of grain growth. The influence of concurrent grain growth on superplastic deformation was subsequently analyzed in detail by Suery and Baudelet [133 and applied to results on Zn-22% Al by Arieli and Mukherjee [14]. The conclusion from this analysis was that behaviors of the type reported for region I by Mohamed and Langdon [7,8], Grivas [9], and Vale et al. [lo] arose entirely from grain growth, and the results were there-
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fore essentially spurious. However, this explanation seems unlikely because Vale et al. [lo] specifically noted that grain growth was negligible in their experiments, and it has also been demonstrated that there is an important error in the grain growth analysis [15]. Second, it may be argued that it is a simple procedure to overestimate the values oft in region I if the strain rate is recorded within the primary stage of creep before the occurrence of a true steady-state behavior. Indeed, the possibility of a false ‘region I’ with m z 1.0 was demonstrated in a striking manner by plotting the strain rates obtained in a change in stress experiment after strain intervals of only 5% [lS]. Furthermore, this error would tend to be enhanced if the investigators anticipated Nabarro-Herring or Coble diffusion creep and mistakenly assumed an essentially steady-state behavior from the beginning of the test. It is clear from the preceding summary that, due to the very slow strain rates involved and the very small grain sizes inherent in superplastic Zn-22% Al, it is difficult to unambiguously distinguish between these two possible explanations. Thus, it seems desirable to seek some alternative type of experimental result which may provide additional insight into the mechanical behavior in region I. This requirement, which represents the rationale for the present experiments, is described in the following section. 2. RATIONALE FOR THE PRESENT EXPERIMENTS It was shown in a series of early experiments that the total ductility of Z&2% Al specimens pulled in tension at constant displacement rates increased from ~500% in region I, reached maximum values close to 3W/, in region IL and then decreased again to < soo”/, in region III [16]. These results therefore confirm that region II represents the true superplastic condition, and the trend was later examined in detail using different temperatures and grain sizes [lq. At first sight, since diffusion creep is Newtonian viscous with m = 1, the decrease in ductility in region I appears to provide confirmation of the occurrence of a regime of behavior which is intermediate between the superplastic region and diffusion creep. However, an additional problem in the superplastic Zn-22% Al eutectoid alloy is the occurrence of extensive internal cavitation during ,testing [18-203. Thus, it may be argued that the measured ductility is reduced at low strain rates due to the longer times which are then available, thereby permitting the cavities to reach a critical size at a much lower total strain. It appears that a simple method is available to investigate the true value of the strain rate sensitivity in region I. It is well known that the formation of macroscopic necks within the gauge length depends on the value of m. This may be explained in terms of the relationship [ 17 (2)
MOHAMED,
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--I’d-7161514131211 I ’ kl3l4k+l7
Fig. 1. Schematic illustration of the specimen gauge length, LO. showing the division into 14 segments. each of length lo.
where A is the cross-sectional area of the specimen, t is the time, P is the tensile force, and B is a constant (=a/k”). According to equation (2) the probability of necking decreases in importance as m- 1, and the flow is strictly Newtonian viscous in the limit when m= 1.t Some preliminary tests have shown that specimens of the Zn-22% Al alloy exhibit fairly uniform deformation within the gauge length after testing in region II, whereas in region I there is evidence of visible necking [23]. However, no experiments have been conducted to date, on any superplastic material, to measure directly the flow localization and necking characteristics in the three regions of behavior observed in superplasticity. Accordingly, the present investigation was undertaken to examine, in detail, the propensity for necking in Zn-22% Al in regions I, II and III. As will be demonstrated, there are very significant differences in the necking behavior in regions I and II, and the results provide additional support for the experimental behavior reported in region I by Mohamed and Langdon [7,8], Grivas [9] and Vale et al. [lo].
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Sheets of the Zn-22% Al eutectoid alloy were obtained in a superplastic condition from The New Jersey Zinc Company; a semiquantitative spectrographic analysis revealed the following impurities in ppm: Cr < 10, Cu 20, Fe 70. Mg < 10, Mn < 10 and Si 70. The sheets were 0.254cm in thickness, and tensile specimens were cut, parallel to the rolling direction, with initial gauge lengths of either 2.54 or 1.27 cm. The as-received grain size was about 1 pm, and each specimen was annealed for 1 h at 533 & 1 K to give an average spatial grain diameter, d, of 2.5 + 0.3 pm. Prior to testing, each specimen was carefully scribed with a series of parallel lines, perpendicular to the longitudinal axis, to divide the initial gauge length, Lo, into 14 segments, each of length lo. These segments, numbered 1 to 7 about the mid-point of the specimen. are depicted schematically in Fig. 1. A travelling microscope was used to obtain an exact t Equation (2). based on area change rates, serves to demonstrate a correlation between the measured ductility and the strain rate sensitivity. A similar correlation arises also from the more precise theory of Hart 121-J based on area differences, and from the analysis of Kocks et al. [22] based on rela:ive differences in area.
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measure of the separation between each adjacent line before testing. Each specimen was pulled in tension on an Instron testing machine operating at a constant rate of crosshead displacement: the quoted strain rates therefore refer to the initial rates calculated from the values of Lo. The tests were conducted at a constant temperature of 473 + 1 K by immersing each specimen in a bath of silicone oil which was electrically heated and stirred with bubbling argon. The bath temperature was continuously monitored throughout each test by placing a chromel-alumel thermocouple near to the specimen. The experimental procedure consisted of pulling each specimen at a single rate of cross-head displacement, and terminating the test at selected intervals of strain. The total percentage strain at each termination point was given by ALlLo”/, where AL is the overall increase in the gauge length. Each specimen was taken from the oil bath at these points, washed in acetone to remove the silicone oil, and then the separations between adjacent marker lines were measured carefully using a travelling microscope. The accuracy of these measurements was estimated to be + 1%. From the readings, the percentage strain in each of the individual segments of the gauge length was calculated as Al/l,,%, where AI is the increase in length of each small segment. After taking the measurements, each specimen was returned to the testing machine and pulled to a higher strain. 4. EXPERIMENTAL
3. EXPERIMENTAL MATERIAL PROCEDURE
METAL
RESULTS
It was firmly established in earlier experiments with a grain size of 2.5 pm and a testing temperature of 473 K that the relationship between cr and k is sigmoidal on a logarithmic plot, and the total elongation, AL/L,%, reaches a maximum close to 3ooO% at intermediate strain rates [16]. The earlier results are shown schematically in Fig. 2, and the approximate divisions into regions I, II and III are indicated, In the present work, tests were conducted initially at strain rates of 1.67 x 10s5, 1.33 x lo-‘, and 6.6 x 10-r s-l, respectively: these three strain rates are indicated by points A, B, and C in the logarithmic plot of u vs k, and they correspond to regions I, II, and the advent of region III, respectively. Initial tests were performed using a gauge length of 2.54cm, but the later experiments used the shorter gauge length of 1.27 cm. It is convenient to consider these two sets of results separately. 4.1 Experiments with L, = 2.54 cm Specimens were tested using initial strain rates, to, of 1.33 x lo-’ s- ’ in the superplastic region II and 1.67 x 10v5 s-i in the low stress region I. The results are given in Fig. 3. Figure 3(a) shows the variation in local strain along the gauge length for the specimen tested in region II, plotted in the form of A&% for each of the 14 seg-
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I ’
‘““‘I
I
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Zn-22%Al T=473K
8 z
b IO-
Fig. 2. Tensile fracture strain (upper) end flow stress (lower) versus strain rate for Z&2% Al tested at 473 K with a grain size of 2.5 pm, showing the division into three regions of plastic flow.
merits: the section numbers on the lower axis refer to the segments shown in Fig 1. This plot shows that, within the accuracy of the measuring procedure, the deformation is essentially uniform throughout the gauge length up to strains of at least - 1400/, (solid symbols): at higher strains, up to 47So/ there are small but measurable differences in the values of Al/lo% between adjacent sections (open symbols). As anticipated from the nature of a tensile test, the minimum elongations tend to occur in the sections numbered 7 in Fig. 1, immediately adjacent to the grip ping areas. Figure 3(b) shows the equivalent result for the specimen tested in region I. Again, the strain is essent As indicated in Fig. 3(b), there are also very small increases in Al/l& in sections 4 (right) and 6 (right) between 330% and 370”/,: these increases are just outside of the error bars associated with each individual measurement, and they suggest that final deformation within the necked region extends over a length equal to about one segment (lo) when Lo = 2.54 cm. $ As indicated in Fig. 2, the strain rate of 1.67 x lo-) s-* is at the low end of region II. Since the teat in region II with L,, = 2.64 cm indicated a fairly uniform deformation up to strains of at least -SOOo/, at L, = 1.33 x 10-2s-’ [Fig. 3(a)], a lower strain rate was selected for use.with Lo = 1.27 cm to provide some indication of the total range of strain rates associated with an absence of localized necking
tially uniform up to elongations of at least 76% (solid symbols), but at 175% there is evidence of neck formation at two points in the gauge length [sections 4 (left) and 5 (right)], and at 330”/, the neck at section 5 (right) has developed extensively to give a local strain of Al/l,,% = 12500/,.Thereafter, up to an elongation of at least 370”/, all of the additional strain is localized almost entirely in this segment, with a llnal strain in the region of necking of Al/Is% z 18WAt 4.2 Experiments with L,, = 1.27 cm A problem associated with the longer gauge length of 2.544 was the difficulty of attaining high total strains. However, it was not feasible to perform this type of experiment using specimens with extremely short gauge lengths, because of the experimental limitations inherent in the procedure used to measure the line separations. Accordingly, it was found through trial tests that there was an optimum gauge length in the vicinity of Lo = 1.27 cm. Three specimens were tested with L,, = 1.27 cm at initial strain rates of 6.6 x lo-‘, 1.67 x 10s3, and 1.67 x 10-ss-l, respectively: the first specimen corresponds to the advent of the high stress region III (point C in Fig 2). the second specimen is in the superplastic region 11,s and the third specimen is in the low stress region I (point A in Fig 2). The results from these three specimens are shown in Fig. 4.
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i x
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6
I
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Advent of High Stresskgim
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0 2 Section No.
01”
Fig. 4(a).
‘I-
38 192 300 380 395
AL/L,%
T=473K b=l.27cm to= 6.6 x10-1 s-1
Zn-22%Al
I
50
loo
200(
250( I Al
h-22%
0
AL/L,%
550
I
Fig. 4(b).
v 770 0 II30
A
62 A 118 v 150 o 230 o 360 l
t = 1.67*iO-3 s-l
4p; 1.27cm
T= 473K
I
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Superplostic Region II
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I I Low Stress Region I
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Lo= I.27 cm to
=1.67~10-~s-’
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AL/L,% 0 A T
n
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0 u
I00 200 315
A
480(FioCtUE~)
n
r0
7
1
SectIon No Fig. 4(c). Fig. 4. Variation in local strain along the gauge lengm for specimens tested with an initial gauge length of 1.27 cm in (a) the high stress region III, (b) the superplastic region II, and (c) the low stress region I.
Figure 4(a) gives the measurements obtained on the specimen tested within region III. The deformation is uniform at a total strain of 380/, but neck formation is evident near the center of the gauge length at 192% and the flow becomes increasingly Iocalized in the necked region at higher strains. There is a very well defined neck at 380”/,, and subsequent flow is concentrated at the neck to give final fracture at AL/Lo = 395%. The measured strain in the necked segment is + 1200% at AL/L, = 38Oo/W but increases to an estimated c 1340% at the point of fracture. Figure 4(b) shows the results obtained at the low end of the superplastic region Il. As with the specimen tested at 1.33 x iOe2 s-’ [Fig. 3(a)], the deformation is essentially uniform up to * 150%~and then thtre are slight perturbations in the measured strains
t Compare. for example, the profile of the diffuse neck covering segments l-4 (left) at AL/Lo = 1130% in Fig. 4(b) and the highly localized neck at segment 1 (left) at AL/Lo = 3807, in Fig. 4(a).
from point to point along the gauge length. This test was discontinued at AL/Lo = 1130%, and at this point the individual values of Al/i&, ranged from -GO-750% near the gripping sections to -1450% near the center of the gauge length. However, despite this variation, the deformation is quasi-uniform such that neck formation, if it occurs, is diffuse rather than Iocalizedt. The curve in the upper section of Fig. 2 shows that failure occurs at AL/Lo z 1700% at this strain rate. The final set of results is shown in Fig 4(c) for the specimen tested at &, = 1.67 x 10e5 s-i in the low stress region I. At this lower strain rate, the deformation is uniform up to *MOO/, but a neck then forms near the center of the gauge length and develops very rapidly to give fracture. A comparison of Figs 4(a) and (c) shows that the necking behavior in regions III and I is quantitatively similar, and the overall fracture strain at the selected strain rate in region I is only AL/L, = 480%. However, a significaut difference between regions II1 and I is that the latter region exhibits a much higher strain within the region of
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1600 -
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RegionIt Adventof RegionIU 0
0
(AP/90)mx -(A~/~o)~i~ -_-*-
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Zn 22%Al T=473 K
Region I
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/
[.
d’
-
4 800
600
0
0
200
400
600 Al&
800
IO00
12
%
Fig. 5. A plot of the uniformity of deformation within the gauge length for the three regions of plastic flow.
necking: this is indicated in Fig. 4(c), where AljO 2: 37ooo/, in the necked segment at fracture. 5. IM~SSION The present results provide the first detailed measurements of, flow localization within the tensile gauge lengths of a material which is capable of very high superplastic strains. In general, the results obtained in regions I and III appear to be very similar, but a more detailed analysis is required to check the extent of these similarities. Speci&zally, it is 11cxxoga~yto address two di&ent, but complementary, questions which may be formulated as under: (i) How uniform is deformation within the gauge length in each r&on of plastic flow? (ii) How sharp (or diffuse) are the necks in each region? In addition, it is important to examine the significance of these results with reference to the controversy surrounding region I in the 21~22% Al alloy. These three problems are examined in the following SCCtiOSlS.
5.1 The uniformity of deformation in each region
When a tensile specimen deforms in a strictly uniform manner throughout the gauge section, each segment deforms by the same amount so that Ai/l~% P AL/L.&. This situation is indicated by the soiid line labelled Uniform de$mnation in Fig. 5. The broken lines in Fig. 5 plot the maximum (upper) and minimum (lower) values of Al/l& as a function of U/LO% for the three specimens shown in Fig. 4. It is clear from this plot that the deformation is very uniform in the superplastic region II up to an overall elongation of at least -gOOo/, and it is quasiuniform thereafter. By contrast, the two specimens tested in regions I and III behave very similarly, and in each of these regions there is a sharp breakdown in uniformity of deformation at an elongation of _ 200”/,. 5.2 The degree of sharpness associated with the necks Figure 5 depicts the total strain within the necked region by plotting (Al/l&.., but it fails to provide information on the degree of sharpness (or diffuseness] associated with each neck. The latter objective may be achieved by plotting the ratio n/n, against
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Lokm)
01 0
Zn
Region
I
-2’2% Al T=473 K Region II
1.277
0
2.54
a
A
I
I
I
I
200
400
600
800
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Advent of Region l
I IO00
I
AL/Lo% Fig.
6. A plot of the degree of sharpness associated with necking for the three regions of plastic tlow: fully uniform deformation rquires n/n, = 1, and n/n, - 0 as flow becomes increasingly localized.
AL/Lo%, where n, is the total number of segments in the gauge length (14 in these experiments) and n is the number of individual segments having Al/l0 2 AL/Lo. The significance of this ratio is that fully uniform deformation gives n/n, = 1, and the value of n/n, indicates the degree of sharpness of the neck such that a high value represents a diffuse neck in quasiunifbrm flow and a low value represents a sharp neck in non-uniform flow. Thus, as n/n,+ 0, so flow becomes increasingly localized at the point of necking. The results obtained for the five specimens in Figs 3 and 4 are given in Fig. 6. This plot shows that the same trends are obtained for both values of Lo used in these experiments and, in addition, the datum points are essentially identical in regions I and III. In region II, Fig. 6 shows that n/n, = 1 and the flow is uniform up to an elongation of -2000/,.t At higher strains, there is a fall in n/n, to -0.65 at AL& 5 600%, and then the ratio stabilizes at this value up to at least AL/L, = 1200’/_ By contrast, the flow is uniform in regions I and III in only the very early stages of deformation (AL/L,%5 50”/,), and there is then a very rapid decrease in n/n, to values in the vicinity of -0.2 at elongations of -400%. Thus, there is a marked distinction between the diffuse necking which occurs in region II and the sharp, and catastrophic. necking which occurs in regions I and III. t This result applies to a division of the gauge length into 14 segments, so that n, = 14 as shown in Fig. 1. Strictly, it means that any non-uniformity scale which is
in flow is on a
5.3 Significance of these results with reference to region I As indicated by equation (2), there is a correlation between the strain rate sensitivity, m, and AL/L&. This has been demonstrated for several materials [24] and was subsequently extended to include the Zn-22% Al data shown in Fig. 2 [25]: there is also theoretical support for this type of trend [26,273. However, as noted earlier, the decrease in ductility observed in Zn-22% Al in region 1 cannot be taken, a priori, as unambiguous support for a genuine decrease in m, because of the increased possibility of cavitation failure at these very slow strain rates. The present experiments show two important results. First, failure occurs in r&ion I not through the development of internal cavities but through the formation and subsequent growth of a sharp neck within the gauge length, whereas necking either does not occur or is very diffuse in the superplastic region II. Second, both the lack of uniformity of deformation (Fig. 5) and the formation of sharp necks (Fig. 6) take place almost identically in the high stress region III, which is generally attributed to a normal creep condition with m - 0.2, and in the low stress region I. Based on this evidence, it is concluded that the superplastic Zn-22% Al alloy exhibits .a genuine decrease in the value of the strain rate sensitivity at low strain rates in region I, and it is anticipated that this behavior occurs at stress levels which are intermediate between those in the superplastic region II and the diffusion creep processes at even lower strain rates. Thus, the present results support the trends reported in the earlier experiments of Mohamed and Langdon [7j, Grivas [9], and Vale et al. [lo], but they are
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not consistent with the results of Vaidya et 01. [l] and Mukhetjee and co-workers [3,4].
6. SUMMARY AND CONCLUSIONS 1. Experiments were conducted on the superplastic Zn-22% Al eutectoid alloy to investigate flow localization and neck formation in the three regions of plastic flow. 2. Deformation is essentially uniform in the superplastic region II up to elongations of at least -Solo/, and quasi-uniform thereafter, whereas in regions I and III there are marked deviations from uniform deformation at elongations as low as -200%. 3. Diffuse necking occurs at high elongations in region II, whereas in regions I and III the necking is sharp and catastrophic at low elongations. 4. In both the low stress region I and the high stress region III, failure occurs by the formation and subsequent growth of a sharp neck within the gauge length; by contrast, sharp necks do not develop in the superplastic region II. 5. The results are consistent with a genuine decrease in the value of the strain rate sensitivity, m, at low strain rates in region I: they are not consistent with a transition from superplastic behavior to diffusion creep and Newtonian viscous flow with m = 1. Acknowledgement-The work of one of us (TGL) was sup Ported by the NationaI Science Foundation under Grant No. DMR79-25378.
REFERENCES 1. M. L. Vaidya, K. L. Murty and J. E. Darn, Acta metall. 21, 1615 (1973). 2. R. L. Coble, J. appl. Phys. 34, 1679 (1%3). 3. S. C. Misro and A. K. Mukherjee; Rate Processes in
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Plastic Deformation of Materials, (edited by J. C. M. Li and A. K. Mukherjee), p. 434. Amerjcan Society for Metals, Metals Park, Ohio (1975). 4. A. Arieli, A. K. S. Yu and A. K. Mukherjee, Metall. Trans.A 11, 181 (1980). 5. F. R. N. Nabarro. Report o[a Conference on Strenarh of Solids. p. 75. The Physical-Society, London (1948; ’ 6. C. Herring, J. appl. Phys. 21,437 (1950). 7. F. A. Mohamed and T. G. Langdon, Acta metall. 23, 117 (1975). 8. F. A. Mohamed, S.-A. Shei and T. G. Langdon, Acta metafl. 23. 1443 (1975). 9. D. Grivas, Report No. LBL-7375, Lawrence Berkelev Laboratory, University of California Berkeley (1978).10. S. H. Vale. D. J. Eastnate and P. M. Hazzledine. Scripta metall. 13, 1157 (i979). 11. T. G. Langdon and F. A. Mohamed, Scripta metall. 11, 575 (1977). 12. G. Rai and N. J. Grant, Metal!. Trans. A 6, 385 (1975). 13. M. Suery and B. Baudelet, Rev. Phys. Appl. 13, 53 (1978). 14. A. Arieli and A. K. Mukherjee, Scripta mecall. 13, 331 (1979). 15. D. Grivas, J. W. Morris, Jr. and T. G. Langdon, Scripta mecall. (in press). 16. H. Ishikawa, F. A. Mohamed and T. G. Langdon, Phil. Mag. 32, 1269 (1975). 17. F. A. Mohamed, M. M. I. Ahmed and T. G. Langdon, Metall. Trans. A 8, 933 (1977). 18. H. Ishikawa, D. G. Bhat. F. A. Mohamed and T. G. Lanadon, Metall. Trans. A 8, 523 (1977). 19. D. A. Miller and T. G. Langdon,. Met& 7’bans. A 9 1688 (1978). 20. D. A. Miller and T. G. Langdon, Metall. Trans. A 10, 1869 (1979). 21. E. W. Hart, Acta metall. 15, 351 (1967). 22. U. F. Koeka, J. J. Jonas and H. Mecking, Acta metall. 27, 419 (1979). 23. M. M. I. Ahmed, F. A. Mohamed and T. G. Langdon, J. Mater. Sci. 14; 2913 (1979). 24. D. A. Woodford, Trans. Am. Sot. Metals 62,291 (1969). 25. T. G. Langdon, Scripta metall. 11, 997 (1977). 26. A. K. Ghosh and R. A. Ayrea, Me&all. Trans. A 7, 1589 (1976).
27. J. W. Hutchinson and K. W. NeaIe, Accq metall. U, 839 (1977).
Vol 29. pp. 91 I to 920. 1981. Bntam All rights reserved
Copyright
Oool-6160~81/050911-10502.00~0 8 1981 Pergamon Press Ltd
FLOW LOCALIZATION AND NECK FORMATION SUPERPLASTIC METAL FARGHALLI
and TERENCE
A. MOHAMED
IN A
G. LANGDON
Departments of Materials Science and Mechanical Engineering, University of Southern California. Los Angeles, CA 90007, U.S.A. (Received 16 June 1980; in reoisedform 30 October 1980)
Ahtstxact-Experiments were conducted on the superplastic Zn-22% Al eutectoid alloy to investigate the extent of flow localization and neck formation in the three regions of plastic flow. The results show that the behavior is qualitatively similar in the low stress region I and the high stress region III, but there are very significant differences in the superplastic region II. Deformation is essentially uniform in region II up to at least 5 800% and quasi-uniform thereafter, whereas there are marked deviations from uniform flow in regions I and III at 5 200%. Failure occurs by the formation and catastrophic growth of a sharp neck in regions I and III, whereas necking is diffuse at high elongations in region II. The results are consistent with a genuine decrease in the value of the strain rate sensitivity at low strain rates in region I. R&m&Nous avons ttudie experimentalement la localisation de Kcoulement et la formation de la striction dans la trois domaines d’icoulement plastique dun alliage eutectdide superplastique Zn-220/, Al. Nos rtsultats montrent des comportements qualitativement semblables dans la region I des faibles contra&es et dans la region III des fortes contraintes, mais des differences tris significatives dans le domaine superplastique II. La deformation est easentiellement unifortne dam le domaine II jusqu’a au moins 800% environ et quasi-uniforme ensuite, alors qu’il y a des deviations tres net@ par rapport a un ecoulement uniforme dam les domaines I et II pour 200% environ. La rupture dans les domaines I et III se produit par formation et croissance catastrophique dune striction trb franche, alors que la striction est diffuse dans le domaine II pour Ies grands allongements. Nos msultats sont cohtrents avec veritable diminution de la sensibilitt a la vitesse de deformation pour les faibles vitesses de deformation dans le domaine 1. maaaung-An der superplastischen eutektoiden Legierung Zn-220/, Al wurde das Ausmal3 der Gleitlokalisierung und der EinschniIrungabildung in den drei plaatischen Bereichen untersucht. Die Ergebnisae xeigen, da8 das Verhalten im Bereich I niedriger Spannung und im Bereich III hoher Spannung qualitativ lhnlich ist. Dagegen treten erhebliche Unterschiede im superplastischen Bereich II auf. Die Verformung liiuft im Bereich II bis zu mindestens - 800% stetig, dartiber quasistetig ab. Dagegen treten in Bereich I und III bei _ 200% betrlchtliche Abweichungen vom stetigen FlieBen auf. In Bereich I und III entsteht der Bruch durch Bildung und katastrophales Wachstum einer scharfen Einschniirung; dagegen ist die Einschnilrung im Bereich II bei groDen Verliingerungen diffus. Die Ergebnisse sind vertriiglich mit einem echten Abfall in der Dehngeschwindigkeitsempfindlichkeit bei kleinen Dehngeschwindigkeiten im Bereich I.
1. INTRODUCIION Considerable interest has developed in recent years in the mechanical behavior of materials exhibiting extensive superplasticity. This interest has arisen from a scientific viewpoint and also because of the increasing awareness that superplastic materials may be utilized in numerous simple and inexpensive forming operations. The Zn-22% Al eutectoid alloy is a classic superplastic metal which has been subjected to many experimental investigations. However, despite the large volume of work reported for this material to date, there are some very significant discrepancies in the observed behavior. Most of the investigations on Zn-22% Al, and also on other superplastic materials, have been conducted using testing machines (such as an Instron) which
operate at a constant rate of strain or cross-head displacement. Measurements are then taken of the steady-state stress, u, for various values of the imposed strain rate, g, and the results are logarithmically plotted in the form of Q vs k. All of the results from these experiments are reasonably consistent. The datum points fall into two distinct regions which are characterized by two different values of the strain rate sensitivity, m, where m is defined as d In u m= 6)ding *,r
(1)
where d is the grain size and T is the absolute temperature. In general, m has a very low value at the higher strain rates (typically, m < 0.2) but the value increases at the lower strain rates to. typically, -0.5.
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Some of the data obtained in this way indicate the possibility of a further decrease in m at the very lowest strain rates; but the trend is not clear, and it is difficult to reach any firm conclusions because of the problems of attaining extremely low rates of strain on a constant displacenient machine. A simple method of overcoming this problem is to conduct tests under creep (constant stress) conditions, but the results reported from such experiments reveal important differences. In an early investigation of the creep of Zn-22% Al, Vaidya et al. [l] showed that the value of m increased from -0.27 at high stresses to 5 0.5 at intermediate stresses and to * 1.1 at very low stress levels. These three regions of behavior were designated III, II, and I, respectively, and there was also a corresponding change in the activation energy from a high value in region III to much lower values in regions II and I. In this work, the behavior in the low stress region I was attributed to the advent of Coble diffusion creep [2]. Subsequent creep experiments on Zn-22”/, Al have revealed very significant discrepancies in the behavior in region I. On the one hand, Misro and Mukherjee [3] confirmed the earlier results of Vaidya et al. [l] and obtained m = 1.0 and a low activation energy in region I. More recently, Mukherjee and COworkers [4] again confirmed the value of m but obtained a high activation energy in region I due, it was suggested, to the occurrence of Nabarro-Herring diffusion creep [5,6] at larger grain sixes (typically, d 2 3 m). On the other hand experiments by Mohamed and Langdon [7-j revealed a decrease in m to -0.24 in region I, with a corresponding increase in the activation energy for plastic tiow [8]. Furthermore, a similar transition to m 5 0.33 was later reported for region I by Grivas [9], and Vale et al. [lo] also obtained a decrease in m to -0.32 and a corresponding increase in the activation energy in region I. In addition, calculations have shown that the behavior in region I, in which m z 0.24-0.34. and there is a high activation energy, takes place at strain rates which are faster than those predicted by the best estimates for either Coble or Nabarro-Herring diffusion creep [ll], thereby inferring that region I is a distinct deformation mode lying intermediate in stress between the superplastic region II and the diffusion creep processes. There appear to be two possible explanations for this apparent dichotomy in behavior. First, it was pointed out by Rai and Grant [12] that the values recorded for i in region I may rep resent an underestimate due to the occurrence of grain growth. The influence of concurrent grain growth on superplastic deformation was subsequently analyzed in detail by Suery and Baudelet [133 and applied to results on Zn-22% Al by Arieli and Mukherjee [14]. The conclusion from this analysis was that behaviors of the type reported for region I by Mohamed and Langdon [7,8], Grivas [9], and Vale et al. [lo] arose entirely from grain growth, and the results were there-
IN A SUPERPLASTIC
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fore essentially spurious. However, this explanation seems unlikely because Vale et al. [lo] specifically noted that grain growth was negligible in their experiments, and it has also been demonstrated that there is an important error in the grain growth analysis [15]. Second, it may be argued that it is a simple procedure to overestimate the values oft in region I if the strain rate is recorded within the primary stage of creep before the occurrence of a true steady-state behavior. Indeed, the possibility of a false ‘region I’ with m z 1.0 was demonstrated in a striking manner by plotting the strain rates obtained in a change in stress experiment after strain intervals of only 5% [lS]. Furthermore, this error would tend to be enhanced if the investigators anticipated Nabarro-Herring or Coble diffusion creep and mistakenly assumed an essentially steady-state behavior from the beginning of the test. It is clear from the preceding summary that, due to the very slow strain rates involved and the very small grain sizes inherent in superplastic Zn-22% Al, it is difficult to unambiguously distinguish between these two possible explanations. Thus, it seems desirable to seek some alternative type of experimental result which may provide additional insight into the mechanical behavior in region I. This requirement, which represents the rationale for the present experiments, is described in the following section. 2. RATIONALE FOR THE PRESENT EXPERIMENTS It was shown in a series of early experiments that the total ductility of Z&2% Al specimens pulled in tension at constant displacement rates increased from ~500% in region I, reached maximum values close to 3W/, in region IL and then decreased again to < soo”/, in region III [16]. These results therefore confirm that region II represents the true superplastic condition, and the trend was later examined in detail using different temperatures and grain sizes [lq. At first sight, since diffusion creep is Newtonian viscous with m = 1, the decrease in ductility in region I appears to provide confirmation of the occurrence of a regime of behavior which is intermediate between the superplastic region and diffusion creep. However, an additional problem in the superplastic Zn-22% Al eutectoid alloy is the occurrence of extensive internal cavitation during ,testing [18-203. Thus, it may be argued that the measured ductility is reduced at low strain rates due to the longer times which are then available, thereby permitting the cavities to reach a critical size at a much lower total strain. It appears that a simple method is available to investigate the true value of the strain rate sensitivity in region I. It is well known that the formation of macroscopic necks within the gauge length depends on the value of m. This may be explained in terms of the relationship [ 17 (2)
MOHAMED,
AND
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NECK FORMATION
--I’d-7161514131211 I ’ kl3l4k+l7
Fig. 1. Schematic illustration of the specimen gauge length, LO. showing the division into 14 segments. each of length lo.
where A is the cross-sectional area of the specimen, t is the time, P is the tensile force, and B is a constant (=a/k”). According to equation (2) the probability of necking decreases in importance as m- 1, and the flow is strictly Newtonian viscous in the limit when m= 1.t Some preliminary tests have shown that specimens of the Zn-22% Al alloy exhibit fairly uniform deformation within the gauge length after testing in region II, whereas in region I there is evidence of visible necking [23]. However, no experiments have been conducted to date, on any superplastic material, to measure directly the flow localization and necking characteristics in the three regions of behavior observed in superplasticity. Accordingly, the present investigation was undertaken to examine, in detail, the propensity for necking in Zn-22% Al in regions I, II and III. As will be demonstrated, there are very significant differences in the necking behavior in regions I and II, and the results provide additional support for the experimental behavior reported in region I by Mohamed and Langdon [7,8], Grivas [9] and Vale et al. [lo].
IN A SUPERPLASTIC
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Sheets of the Zn-22% Al eutectoid alloy were obtained in a superplastic condition from The New Jersey Zinc Company; a semiquantitative spectrographic analysis revealed the following impurities in ppm: Cr < 10, Cu 20, Fe 70. Mg < 10, Mn < 10 and Si 70. The sheets were 0.254cm in thickness, and tensile specimens were cut, parallel to the rolling direction, with initial gauge lengths of either 2.54 or 1.27 cm. The as-received grain size was about 1 pm, and each specimen was annealed for 1 h at 533 & 1 K to give an average spatial grain diameter, d, of 2.5 + 0.3 pm. Prior to testing, each specimen was carefully scribed with a series of parallel lines, perpendicular to the longitudinal axis, to divide the initial gauge length, Lo, into 14 segments, each of length lo. These segments, numbered 1 to 7 about the mid-point of the specimen. are depicted schematically in Fig. 1. A travelling microscope was used to obtain an exact t Equation (2). based on area change rates, serves to demonstrate a correlation between the measured ductility and the strain rate sensitivity. A similar correlation arises also from the more precise theory of Hart 121-J based on area differences, and from the analysis of Kocks et al. [22] based on rela:ive differences in area.
913
measure of the separation between each adjacent line before testing. Each specimen was pulled in tension on an Instron testing machine operating at a constant rate of crosshead displacement: the quoted strain rates therefore refer to the initial rates calculated from the values of Lo. The tests were conducted at a constant temperature of 473 + 1 K by immersing each specimen in a bath of silicone oil which was electrically heated and stirred with bubbling argon. The bath temperature was continuously monitored throughout each test by placing a chromel-alumel thermocouple near to the specimen. The experimental procedure consisted of pulling each specimen at a single rate of cross-head displacement, and terminating the test at selected intervals of strain. The total percentage strain at each termination point was given by ALlLo”/, where AL is the overall increase in the gauge length. Each specimen was taken from the oil bath at these points, washed in acetone to remove the silicone oil, and then the separations between adjacent marker lines were measured carefully using a travelling microscope. The accuracy of these measurements was estimated to be + 1%. From the readings, the percentage strain in each of the individual segments of the gauge length was calculated as Al/l,,%, where AI is the increase in length of each small segment. After taking the measurements, each specimen was returned to the testing machine and pulled to a higher strain. 4. EXPERIMENTAL
3. EXPERIMENTAL MATERIAL PROCEDURE
METAL
RESULTS
It was firmly established in earlier experiments with a grain size of 2.5 pm and a testing temperature of 473 K that the relationship between cr and k is sigmoidal on a logarithmic plot, and the total elongation, AL/L,%, reaches a maximum close to 3ooO% at intermediate strain rates [16]. The earlier results are shown schematically in Fig. 2, and the approximate divisions into regions I, II and III are indicated, In the present work, tests were conducted initially at strain rates of 1.67 x 10s5, 1.33 x lo-‘, and 6.6 x 10-r s-l, respectively: these three strain rates are indicated by points A, B, and C in the logarithmic plot of u vs k, and they correspond to regions I, II, and the advent of region III, respectively. Initial tests were performed using a gauge length of 2.54cm, but the later experiments used the shorter gauge length of 1.27 cm. It is convenient to consider these two sets of results separately. 4.1 Experiments with L, = 2.54 cm Specimens were tested using initial strain rates, to, of 1.33 x lo-’ s- ’ in the superplastic region II and 1.67 x 10v5 s-i in the low stress region I. The results are given in Fig. 3. Figure 3(a) shows the variation in local strain along the gauge length for the specimen tested in region II, plotted in the form of A&% for each of the 14 seg-
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I
NECK FORMATION IN A SUPERPLASTIC METAL I
I ’
‘““‘I
I
I
Zn-22%Al T=473K
8 z
b IO-
Fig. 2. Tensile fracture strain (upper) end flow stress (lower) versus strain rate for Z&2% Al tested at 473 K with a grain size of 2.5 pm, showing the division into three regions of plastic flow.
merits: the section numbers on the lower axis refer to the segments shown in Fig 1. This plot shows that, within the accuracy of the measuring procedure, the deformation is essentially uniform throughout the gauge length up to strains of at least - 1400/, (solid symbols): at higher strains, up to 47So/ there are small but measurable differences in the values of Al/lo% between adjacent sections (open symbols). As anticipated from the nature of a tensile test, the minimum elongations tend to occur in the sections numbered 7 in Fig. 1, immediately adjacent to the grip ping areas. Figure 3(b) shows the equivalent result for the specimen tested in region I. Again, the strain is essent As indicated in Fig. 3(b), there are also very small increases in Al/l& in sections 4 (right) and 6 (right) between 330% and 370”/,: these increases are just outside of the error bars associated with each individual measurement, and they suggest that final deformation within the necked region extends over a length equal to about one segment (lo) when Lo = 2.54 cm. $ As indicated in Fig. 2, the strain rate of 1.67 x lo-) s-* is at the low end of region II. Since the teat in region II with L,, = 2.64 cm indicated a fairly uniform deformation up to strains of at least -SOOo/, at L, = 1.33 x 10-2s-’ [Fig. 3(a)], a lower strain rate was selected for use.with Lo = 1.27 cm to provide some indication of the total range of strain rates associated with an absence of localized necking
tially uniform up to elongations of at least 76% (solid symbols), but at 175% there is evidence of neck formation at two points in the gauge length [sections 4 (left) and 5 (right)], and at 330”/, the neck at section 5 (right) has developed extensively to give a local strain of Al/l,,% = 12500/,.Thereafter, up to an elongation of at least 370”/, all of the additional strain is localized almost entirely in this segment, with a llnal strain in the region of necking of Al/Is% z 18WAt 4.2 Experiments with L,, = 1.27 cm A problem associated with the longer gauge length of 2.544 was the difficulty of attaining high total strains. However, it was not feasible to perform this type of experiment using specimens with extremely short gauge lengths, because of the experimental limitations inherent in the procedure used to measure the line separations. Accordingly, it was found through trial tests that there was an optimum gauge length in the vicinity of Lo = 1.27 cm. Three specimens were tested with L,, = 1.27 cm at initial strain rates of 6.6 x lo-‘, 1.67 x 10s3, and 1.67 x 10-ss-l, respectively: the first specimen corresponds to the advent of the high stress region III (point C in Fig 2). the second specimen is in the superplastic region 11,s and the third specimen is in the low stress region I (point A in Fig 2). The results from these three specimens are shown in Fig. 4.
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IN A SUPERPLASTIC METAL
915
i x
.o i;”
6
I
I
0 A v
0
l
I”
4
2
I I I
‘I-
- Fmcture
-
4
8
Advent of High Stresskgim
I
0 2 Section No.
01”
Fig. 4(a).
‘I-
38 192 300 380 395
AL/L,%
T=473K b=l.27cm to= 6.6 x10-1 s-1
Zn-22%Al
I
50
loo
200(
250( I Al
h-22%
0
AL/L,%
550
I
Fig. 4(b).
v 770 0 II30
A
62 A 118 v 150 o 230 o 360 l
t = 1.67*iO-3 s-l
4p; 1.27cm
T= 473K
I
I
I
I
Superplostic Region II
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I
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Zn-22%Ai
T =473K
I I Low Stress Region I
METAL
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-
Lo= I.27 cm to
=1.67~10-~s-’
-Fracture
AL/L,% 0 A T
n
50
0 u
I00 200 315
A
480(FioCtUE~)
n
r0
7
1
SectIon No Fig. 4(c). Fig. 4. Variation in local strain along the gauge lengm for specimens tested with an initial gauge length of 1.27 cm in (a) the high stress region III, (b) the superplastic region II, and (c) the low stress region I.
Figure 4(a) gives the measurements obtained on the specimen tested within region III. The deformation is uniform at a total strain of 380/, but neck formation is evident near the center of the gauge length at 192% and the flow becomes increasingly Iocalized in the necked region at higher strains. There is a very well defined neck at 380”/,, and subsequent flow is concentrated at the neck to give final fracture at AL/Lo = 395%. The measured strain in the necked segment is + 1200% at AL/L, = 38Oo/W but increases to an estimated c 1340% at the point of fracture. Figure 4(b) shows the results obtained at the low end of the superplastic region Il. As with the specimen tested at 1.33 x iOe2 s-’ [Fig. 3(a)], the deformation is essentially uniform up to * 150%~and then thtre are slight perturbations in the measured strains
t Compare. for example, the profile of the diffuse neck covering segments l-4 (left) at AL/Lo = 1130% in Fig. 4(b) and the highly localized neck at segment 1 (left) at AL/Lo = 3807, in Fig. 4(a).
from point to point along the gauge length. This test was discontinued at AL/Lo = 1130%, and at this point the individual values of Al/i&, ranged from -GO-750% near the gripping sections to -1450% near the center of the gauge length. However, despite this variation, the deformation is quasi-uniform such that neck formation, if it occurs, is diffuse rather than Iocalizedt. The curve in the upper section of Fig. 2 shows that failure occurs at AL/Lo z 1700% at this strain rate. The final set of results is shown in Fig 4(c) for the specimen tested at &, = 1.67 x 10e5 s-i in the low stress region I. At this lower strain rate, the deformation is uniform up to *MOO/, but a neck then forms near the center of the gauge length and develops very rapidly to give fracture. A comparison of Figs 4(a) and (c) shows that the necking behavior in regions III and I is quantitatively similar, and the overall fracture strain at the selected strain rate in region I is only AL/L, = 480%. However, a significaut difference between regions II1 and I is that the latter region exhibits a much higher strain within the region of
918
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1600 -
I
A
RegionIt Adventof RegionIU 0
0
(AP/90)mx -(A~/~o)~i~ -_-*-
1400-
I
I
I
Zn 22%Al T=473 K
Region I
IN A SUPERPLASTIC METAL
/
[.
d’
-
4 800
600
0
0
200
400
600 Al&
800
IO00
12
%
Fig. 5. A plot of the uniformity of deformation within the gauge length for the three regions of plastic flow.
necking: this is indicated in Fig. 4(c), where AljO 2: 37ooo/, in the necked segment at fracture. 5. IM~SSION The present results provide the first detailed measurements of, flow localization within the tensile gauge lengths of a material which is capable of very high superplastic strains. In general, the results obtained in regions I and III appear to be very similar, but a more detailed analysis is required to check the extent of these similarities. Speci&zally, it is 11cxxoga~yto address two di&ent, but complementary, questions which may be formulated as under: (i) How uniform is deformation within the gauge length in each r&on of plastic flow? (ii) How sharp (or diffuse) are the necks in each region? In addition, it is important to examine the significance of these results with reference to the controversy surrounding region I in the 21~22% Al alloy. These three problems are examined in the following SCCtiOSlS.
5.1 The uniformity of deformation in each region
When a tensile specimen deforms in a strictly uniform manner throughout the gauge section, each segment deforms by the same amount so that Ai/l~% P AL/L.&. This situation is indicated by the soiid line labelled Uniform de$mnation in Fig. 5. The broken lines in Fig. 5 plot the maximum (upper) and minimum (lower) values of Al/l& as a function of U/LO% for the three specimens shown in Fig. 4. It is clear from this plot that the deformation is very uniform in the superplastic region II up to an overall elongation of at least -gOOo/, and it is quasiuniform thereafter. By contrast, the two specimens tested in regions I and III behave very similarly, and in each of these regions there is a sharp breakdown in uniformity of deformation at an elongation of _ 200”/,. 5.2 The degree of sharpness associated with the necks Figure 5 depicts the total strain within the necked region by plotting (Al/l&.., but it fails to provide information on the degree of sharpness (or diffuseness] associated with each neck. The latter objective may be achieved by plotting the ratio n/n, against
MOHAMED
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NECK FORMATION IN A SUPERPLASTIC METAL I
Lokm)
01 0
Zn
Region
I
-2’2% Al T=473 K Region II
1.277
0
2.54
a
A
I
I
I
I
200
400
600
800
919
I
Advent of Region l
I IO00
I
AL/Lo% Fig.
6. A plot of the degree of sharpness associated with necking for the three regions of plastic tlow: fully uniform deformation rquires n/n, = 1, and n/n, - 0 as flow becomes increasingly localized.
AL/Lo%, where n, is the total number of segments in the gauge length (14 in these experiments) and n is the number of individual segments having Al/l0 2 AL/Lo. The significance of this ratio is that fully uniform deformation gives n/n, = 1, and the value of n/n, indicates the degree of sharpness of the neck such that a high value represents a diffuse neck in quasiunifbrm flow and a low value represents a sharp neck in non-uniform flow. Thus, as n/n,+ 0, so flow becomes increasingly localized at the point of necking. The results obtained for the five specimens in Figs 3 and 4 are given in Fig. 6. This plot shows that the same trends are obtained for both values of Lo used in these experiments and, in addition, the datum points are essentially identical in regions I and III. In region II, Fig. 6 shows that n/n, = 1 and the flow is uniform up to an elongation of -2000/,.t At higher strains, there is a fall in n/n, to -0.65 at AL& 5 600%, and then the ratio stabilizes at this value up to at least AL/L, = 1200’/_ By contrast, the flow is uniform in regions I and III in only the very early stages of deformation (AL/L,%5 50”/,), and there is then a very rapid decrease in n/n, to values in the vicinity of -0.2 at elongations of -400%. Thus, there is a marked distinction between the diffuse necking which occurs in region II and the sharp, and catastrophic. necking which occurs in regions I and III. t This result applies to a division of the gauge length into 14 segments, so that n, = 14 as shown in Fig. 1. Strictly, it means that any non-uniformity scale which is
in flow is on a
5.3 Significance of these results with reference to region I As indicated by equation (2), there is a correlation between the strain rate sensitivity, m, and AL/L&. This has been demonstrated for several materials [24] and was subsequently extended to include the Zn-22% Al data shown in Fig. 2 [25]: there is also theoretical support for this type of trend [26,273. However, as noted earlier, the decrease in ductility observed in Zn-22% Al in region 1 cannot be taken, a priori, as unambiguous support for a genuine decrease in m, because of the increased possibility of cavitation failure at these very slow strain rates. The present experiments show two important results. First, failure occurs in r&ion I not through the development of internal cavities but through the formation and subsequent growth of a sharp neck within the gauge length, whereas necking either does not occur or is very diffuse in the superplastic region II. Second, both the lack of uniformity of deformation (Fig. 5) and the formation of sharp necks (Fig. 6) take place almost identically in the high stress region III, which is generally attributed to a normal creep condition with m - 0.2, and in the low stress region I. Based on this evidence, it is concluded that the superplastic Zn-22% Al alloy exhibits .a genuine decrease in the value of the strain rate sensitivity at low strain rates in region I, and it is anticipated that this behavior occurs at stress levels which are intermediate between those in the superplastic region II and the diffusion creep processes at even lower strain rates. Thus, the present results support the trends reported in the earlier experiments of Mohamed and Langdon [7j, Grivas [9], and Vale et al. [lo], but they are
920
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NECK FORMATION
not consistent with the results of Vaidya et 01. [l] and Mukhetjee and co-workers [3,4].
6. SUMMARY AND CONCLUSIONS 1. Experiments were conducted on the superplastic Zn-22% Al eutectoid alloy to investigate flow localization and neck formation in the three regions of plastic flow. 2. Deformation is essentially uniform in the superplastic region II up to elongations of at least -Solo/, and quasi-uniform thereafter, whereas in regions I and III there are marked deviations from uniform deformation at elongations as low as -200%. 3. Diffuse necking occurs at high elongations in region II, whereas in regions I and III the necking is sharp and catastrophic at low elongations. 4. In both the low stress region I and the high stress region III, failure occurs by the formation and subsequent growth of a sharp neck within the gauge length; by contrast, sharp necks do not develop in the superplastic region II. 5. The results are consistent with a genuine decrease in the value of the strain rate sensitivity, m, at low strain rates in region I: they are not consistent with a transition from superplastic behavior to diffusion creep and Newtonian viscous flow with m = 1. Acknowledgement-The work of one of us (TGL) was sup Ported by the NationaI Science Foundation under Grant No. DMR79-25378.
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