Direct observation of superplastic flow mechanisms in torsion

OOOI-6160/89 $3.00 + 0.00 Copyright Q 1989 Pergamon Press plc

Acra merall. Vol. 37, No. 4, pp. 1121-1134, 1989 Printed in Great Britain. All rights reserved

DIRECT OBSERVATION OF SUPERPLASTIC FLOW MECHANISMS IN TORSION

Department

of Materials

M. J. MAYO? and W. D. NIX Science and Engineering, Stanford University, Stanford, CA 94305, U.S.A.

(Received 23 November 1987; in reoisedform

I6 June 1988)

Abstract-The microstructures of two alloys, Sn-38wt%Pb and Zn-22wt%Al, are observed during superplastic deformation in torsion, with results that differ strikingly from similar observations in tension. In particular, massive, random grain movements, with associated sliding and rotation, are not observed in torsional deformation. Instead grain locations remain relatively fixed while a steady microstructural evolution produces a distinct inverted hourglass grain morphology. In Sn-38%Pb this grain shape change can be explained by the simultaneous action of two deformation mechanisms operating at different flow rates within a single grain. This in turn leads to a core-mantle theory of superplasticity, as opposed to the sliding-with-accommodation theories envisioned by earlier investigators. Rbum&Deux alliages-&tain B 3% en poids de plomb, et zinc i 23% en poids d’aluminium-prksentent des microstructures tout $ fait diffkrentes selon le mode de deformation superplastique (torsion ou traction) auquel ils sont soumis. Plus pr&is&ment, on n’observe pas, en torsion, les mouvements de grainsd&sordonnts et massifs-auxquels sont associes glissement et rotation. Au contraire, les positions des grains demeurent relativement fixes alors qu’un Bvolution microstructurale stationnaire produit une morphologie de grains en verres de montre renversts. Dans l’alliage d’&ain $ 38% en poids de plomb, cette modification de la forme des grains peut 6tre expliqute par l’action simultantke de deux mitcanismes de d&formation qui agissent $ differtrentes vitesses d’Bcoulement $ I’intirieur d’un mime grain. Ceci, par contre, conduit g une thtorie de manteau et de coeur de la superplasticitC, contrairement aux theories de glissement avec accommodation envisagtes par de prC&dents chercheurs. Zusammenfamuog-Die Entwicklung der Mikrostruktur zweier Legierungen, Sn-3 Gew.-% Pb und Zn-22 Gew.-% Al, wird wlhrend der superplastischen Verformung in Torsion verfolgt. Die Ergebnisse unterscheiden sich sehr deutlich von denen bei Zugverformung. Insbesondere werden massive zufgllige Kornbewegungen mit entsprechender Gleitung und Rotation in Torsionsverformung nicht beobachtet. Stattdessen bleiben die Orte der Kijmer relativ fest, die mikrostrukturelle Entwicklung fiihrt zu einer deutlichen, invertierten Uhrglasmorphologie. In der Legierung Sn_38%Pb kann diese Forminderung der Kiimer mit zwei gleichzeitig ablaufenden Verfonnungsmechanismen, die innerhalb eines Kornes mit unterschiedlichen Geschwindigkeiten auftreten, erklart werden. Daraus folgt eine Kern-Mantel-Theorie der Superplastizitlt, die im Gegensatz zu den Theorien friiherer Autoren auf der Basis der Akkomodation durch Gleitung zu sehen ist.

INTRODUCTION

to push surface

Historically, in situ observations of superplastic deformation have been a primary tool in understanding superplasticity (e.g. refs [l-3]). Many of our current theories about superplasticity have been based on these visual studies, in which the shape and motion of individual grains have been observed in superplastic materials as they were being deformed in tension. Unfortunately, the tensile mode is not ideal for understanding superplastic deformation, for in tension, shearing occurs through the specimen thickness as well as along the specimen face. This creates certain problems. For example, the shear processes responsible for through-thickness straining cannot be observed by viewing the face of the specimen, so the relevance of such observations is immediately called into question. Also, as Fig. 1 illustrates, shear on alternate planes in the thickness direction can combine in such a way as tPresent address: Sandia Laboratories, Division 1845, P.O. Box 5800, Albuquerque, NM 87185, U.S.A. AM

11,“1

grains to the extreme surface, where they no longer participate in bulk deformation. Such grains, which we have termed “floating grains,” would tend to retain their original shapes throughout the deformation of the sample, and would be free to drift or rotate along the sample surface in a manner irrelevant to the bulk processes. It is our opinion that perhaps some of the grains observed in earlier in situ tensile studies were indeed “floating grains” and should be considered artifacts of the tensile mode rather than characteristic of the superplastic process. More practical problems also arise in tensile studies. As shear through the thickness occurs, subsurface grains are brought to the surface, with the result that these heavily deformed subsurface grains dominate the sample surface at large strains. The resulting microstructure is so “messy” that it becomes difficult to observe. In the past this problem was treated in one of two ways, neither of which was particularly satisfying. One method was simply to ignore these “messy” grains even though such grains, having existed in the bulk for some time before emerging to the surface, are

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viewed in cross section; the upper and lower edges correspond to the faces of the sample. “Floating grains” can be produced by the combined action of shear on alternate planes.

Fig. I. Sheet tensile specimen

probably characteristic of the bulk processes. Another approach was to restrict the deformation study to small strains, but this raises questions of whether the processes that occur at small strains are the same

processes as those that occur at very large strains, which are the hallmark of superplasticity. It is for these various reasons that the current study was undertaken; here we examine microstructural activity in superplastic materials as they are deformed in torsion. Torsional deformation has the advantage that all deformation which affects the viewing (surface) plane is confined to that plane. With no shear occurring through the specimen thickness (i.e. in the radial direction), no “floating grains” develop, and no grains emerge from the subsurface to obstruct the observations; in short, one should obtain a much clearer view of the microstructure as it undergoes superplastic deformation. This is in fact the case, as can be seen by comparing Fig. 2(a) and (b).

length (see Ref. [4] for complete dimensions), were machined from this material. The specimens’ gage sections were subsequently hand polished using alumina grit down to a 0.05pm finish. Small scratches were then introduced onto the polished sample surface with 0.3 pm alumina grit, and even deeper scribe marks

EXPERIMENTAL Sample preparation Sn-38wt%Pb. The Sn-Pb eutectic alloy was prepared by melting appropriate quantities of 99.9% pure Pb and 99.99% pure Sn in a 250 ml, 5 cm diameter Pyrex container at 600°C for 2 h while stirring occasionally with a ceramic rod. The molten alloy was then directionally cooled, at room temperature, to prevent the formation of internal porosity in the casting. The 5 cm diameter, 2.5-3.5 cm long ingot which resulted was then extruded to 1. I1 cm diameter and plunged into liquid nitrogen immediately after extrusion. This intensive working of the material via extrusion breaks up the original lamellar microstructure into equiaxed grains of Sn- and Pb-rich phases with a mean linear intercept grain size (r) of < 1 pm. These grains were then allowed to grow a more stable size of T= 34 p by annealing the material at -9°C for 8 months. Further storage at -9°C did not result in any further appreciable grain growth over the course of the following year. Specimens of a solid rod geometry, with gage sections of 6.35 mm diameter and 4.76 mm

Fig. 2. Comparison of superplastically deformed microstructures in tension vs torsion. (a) Tensile deformation (true strain = 96%); arrow indicates tensile direction. Large flat grains are the original surface grains, In between these are the “messy” regions composed of heavily deformed grains from the specimen interior. (b) Torsional deformation (true strain = 101%); line indicates specimen axis, arrow the sense of twist. No difficult-to-observe “messy” regions exist here. All grains are original surface grains. Dots show location of ligaments (to be discussed later).

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were made along the gage length in the axial direction with a diamond scribe. Zn-22wt%Al. Material of this composition possessing a superplastic microstructure was provided by Professor T. G. Langdon of the University of California at Los Angeles. Short, thin-walled cylinder specimens (gage section: 15.9 mm mean diameter, 0.8 mm thickness, and 3.1 mm length-see Ref. [4] for complete sample dimensions) were machined from the original thick sheet. Unfortunately, however, the original microstructure was destroyed in this process. A suitable microstructure was then regained through the following heat treatment: solution treat at 389’C for 24 h; quench in ice brine; anneal at room temperature for 24 h, then anneal at 246 C for 41 h. This procedure produced a very homogeneous distribution of the fine (T= 1.3 ,um), equiaxed Al- and Zn-rich grains necessary for superplastic behavior. The gage sections of these specimens were then hand polished to a 0.05 [cm finish using alumina grit. Dejining the hehacioral

regimes

At a given temperature many superplastic materials, including Sn-38%Pb and Zn22%Al, possess three different regimes of behavior, which together span the range of possible strain rates. These three regimes are defined by the relative value of the strain rate sensitivity, m, where m = dlog o/dlog i, or the slope of a plot of log stress vs log strain rate. Although superplastic behavior takes place in only the middle regime, i.e. at moderate strain rates, where m is large, it was of interest to examine each of the three regimes in turn to better understand the gamut of material behavior. Thus it became necessary to know which strain rates were encompassed by each regime for the materials to be studied. .Sn-38wr%Pb. For this alloy, the requisite plot of log stress vs log strain rate was obtained from compression tests of the same Sn38wt%Pb material as that used in the torsion experiments. Details of the compression testing are given in Ref. [4]; the plot itself is shown in Fig. 3, with the three regimes indicated. From this plot the twist rates for torsion experiments were calculated so that the surface strain rate of the specimen being tested would correspond to a strain rate characteristic of one of the three regimes. The relevant conversion is

(1) which expresses the strain rate in the surface plane of the gage section (i.e. at r = r,,) in terms of the sample twist rate 4 and the gage length I. The surface strain rates thus calculated from the imposed twist rates will heretofore be referred to as “nominal” strain rates and will be shown in parentheses. The same convention will be observed for nominal strains, Of greater interest than these, however, are the actual, or effective, strains and strain rates, which take into account the significant propor-

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Regime III

1oal 10-G

10-S Strain

10-4 rate

10-z (I/s)

Fig. 3. Stress-strain rate relationship for Sn-38%Pb obtained from compression test results. The three regimes of material behavior are indicated. A maximum strain rate sensitivity of M = 0.47 occurs at a strain rate of 3.7 x IO- 5 s-‘.

tion of strain taken up by the sample shoulders during deformation. These were back-calculated from the angle of twist experienced by a scribed line on the gage surface as the sample deformed. Specifically

and

(2b) where B,, is the angle of actual section, in degrees, obtained by

twist of the gage

360

O,K = 27crotan(90

- a)

z is the acute angle, in degrees, measured between a scribed line and the axial direction (at 0 strain G(= 0”; as strain increases c( -+ 900), r,, is the radius of the gage section, I is the specimen gage length, and t is the time duration of the torsion test. Finally, the twist rates employed for the Sn-38wt%Pb samples, with their corresponding norminal and effective strain rates (on the sample surface) are as follows: Regime III: high strain rate, low strain rate sensitivity, non-superplastic behavior fi = 7.38 deg/s P”,, = 1 x IO-? s-1 ivff = 8.5 x 10-j ss’ Regime II: moderate strain rate, high strain sensitivity, superplastic behavior d = 0.02 deg/s i”,, = 1.3 x 10 -4s-’ i,,=6.5 x 10m5s-’ Regime I: slow strain rate, low strain tivity, non-superplastic behavior 4 = 3.53 x 10m4deg/s i,,, = 2.36 x 10.~‘s-’ i,,= 1.1 x IO~hS~’

rate

rate sensi-

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Note the effective values of strain rate still fall within the appropriate deformation regimes. Zn-22%Al. For the log stress-log strain rate plot, appropriate data for a Zn-22%Al alloy virtually identical to that used in the current experiments was obtained from the work of Mohammed et al. f.51. Appropriate strain rates/twist rates for Regimes II and I were calculated from equation (1) and chosen as shown below. It was not possible to test Regime III behavior due to equipment limitations. Regime II: 4 = 0.383 deg/s . = I x IO-*s-i Cnom= Gft Regime I: 0 = 3.8 x 10e3 deg/s e,,ln = 1,, =I:1 x 10-4 s-1. Note that because of the sharper shoulders of the Zn-22%Al samples, the effective strain rates are approximately equal to the nominal strain rates. Also, for all samples, the strains and strain rates in torsion are “true” strains, for the sample gage length does not change appreciably during torsion testing.

not only for the superplastic Regime II but also for Regimes I and III for nominal true strains of O-280%. The testing procedure for Zn-22%Al specimens was somewhat different than that of the Sn-38%Pb. Since superplastic conditions for this alloy demand that defo~ation take place at an elevated temperature (2SO°C), the Zn-22%Al tests were not interrupted for viewing at room temperature in order to avoid unneccessary thermal cycling. Instead, once the temperature of the optical furnace equilibrated, the samples were twisted monotonically at one of the strain rates given above until a true strain of either 98.5% (37” of twist) or 251% (96” of twist) was reached. The samples were observed in the SEM both before and after deformation. Due to the lack of interruptions it was not possible to compile strain histories of individual grains equivalent to those generated in the study of Sn-38%Pb.

Torsion testing The torsion apparatus used for these tests is described in detail elsewhere [4,6,7]. Briefly, the specimen is mounted by sliding its grip ends into matching recesses in opposing horizontal shafts, and the specimen is twisted as one of the shafts rotates (the other is stationary). Technically this apparatus’ design allows for free end torsion; that is, the specimen should be able to shrink or expand freely along the axial direction, with consequent elimination of axial stresses. In practice, however, the friction between the specimen and the grips is such that some axial stresses are introduced. On the other hand, these can be considered minimal in comparison to the shear stresses caused by torsion. For elevated temperature tests, a quad elliptical radiant furnace was used in conjunction with a temperature controller. Specimen temperature was measured with a chrome]-alumel thermocouple wedged tightly between the specimen shoulder and the stationary shaft. In the torsion testing of Sn-38%Pb, all straining for a given Sn3&%Pb specimen was carried out at one of the three twist rates listed earlier, at room temperature. Straining was performed in increments of 60” twist (~40% nominal surface strain), with the microstructure being observed in the scanning electron microscope (SEM) between each strain increment. The experience of the current authors and others [3f is that such interrupted testing does not adverseiy affect the microstructural development. By marking the specimen surface with a fleck of silver paint, it was even possible to relocate a specific group of grains and monitor their progress as straining proceeded. Such microstructural strain histories were compiled

Fig. 4. Regime III deformation of Sn-38%Pb in torsion. Lines correspond to the axial direction; arrows indicate the sense of twist. (a) Microstructure at 104% (121%) true strain. (b) The same microstructural regions after 159% (201%) true strain. Note the grains have elongated.

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Fig. 5. Sn-38%Pb microstructure after 10% (20%) true strain in torsion. Grains have tilted out of the surface plane via grain boundary sliding.

RESULTS

Sn-38%Pb

microstructural observations

Regime III deformations. Simple elongation of the grains occurred during straining in this regime as shown in Fig. 4. Regime II ~s~~er~~ust~c) deformation. During the first 30% or so of strain, some displacement of grains occurred in the radial direction (grains tilted out of the surface plane via grain boundary sliding-see Fig. S), but very little sliding and grain motion occurred within the surface plane. Moreover, as deformation continued, evidence of further grain boundary sliding became imperceptible. At no point was large scale translation or rotation of individual grains observed. Instead a universal, systematic grain rotation was noted in which the grains continually modified their alignment in keeping with the ever-changing direction of maximum elongation. In other words, the grains tended to rotate and elongate so as to wrap around the specimen in an ever-tightening helical configuration as straining progressed. Mathematically speaking, if one defines fi as the angle between the circumferential direction and the axis of maximum elongation then /3 = l/2 arctan (2/y), where y is the current shear strain (see Canova et al. [8]). Thus the angle j? is initially 45” at zero strain and decreases to 0” at infinite strain; i.e. the direction of maximum elongation progressively approaches the circumferential direction. The most dramatic observation, however, was that the microstructure evolved quite steadily into a ~n~guration in which grains (pa~icu~arly Sn-rich grains) developed the distinct inverted hourglass shape illustrated in Fig. 6. Of course the extent to which any particular grain was able to adopt this shape was dependent on the starting shape of the grain and the

homogeneity of deformation in the surroundings, with the idealized case of Fig. 6 holding true for the most equiaxed and homogeneous cases, respectively. Microregions where deformation was more stochastic resulted in approximations to the configuration of Fig. 6. Regardiess of whether this inverted hourglass shape was fully achieved, however, the presence of “ligaments” was ubiquitous. “Ligaments” are here defined as the highly deformed, near-boundary regions corresponding to the tails of the inverted hourglass shape of Fig. 6. These should not be confused with the ligaments observed in cavity formation in other alloys (even more so since this alloy does not internally cavitate). Examples of ligaments are shown in Fig. 7, while Fig 8 follows the evolution of a single ligament over four increments of strain. In the same alloy, the evolution of an entire region of microstructure from 66% (121%) to 118% (242%) true strain is shown in Figs 9 and 10, respectively. To aid comparison between these two figures, the location of a few specific grains has been consistently identified as “El’, “F”, etc. in both micrographs. Note that by 118% true strain the grains’ inverted hourglass shape and associated ligaments can be observed quite clearly, with the ligaments possessing a gooey, plastic visuai texture that is quite different from the smoother, more rigid appearance of the grain cores. Regime I deformation. Deformation in regime I was observed to be similar in character to that in regime II; i.e. the grains acquired an inverted hourglass shape during defo~ation, and ligament formation was prominent. In fact, the primary distinction between the observed deformation of grains in regime I vs regime II was that, typically, a greater proportion of a deformed grain’s volume appeared to involve ligament formation in regime I. An example of regime 1

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Undeformed

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Deformed

Fig. 6. Schematic illustration of the grain shape evolution observed in the superplastic torsional deformation of Sn-38%Pb.

Fig. 7. Sn-38wt%Pb superplastically deformed to a true strain of 79% (161%). Note the ligaments at the tops of Sn-rich grains A and B, which connect to the Pb-rich (white) grains above them.

Fig. 8. Example of a ligament forming between two grains as torsional deformation progresses. True strains are as follows: (a) f = 66% (121%), (b) L = 79% (161%), (c) f = 100% (201%), (d) 6 = 118% (242%).

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Fig. 9. Sn 38%Pb deformed in torsion to 66% (121X) true strain. Line corresponds to the axial direction; arrows indicate the sense of twist.

Fig. IO. Same microstru~tural region as in Fig. 9 above, deformed here to 118% (242%) true strain. Many of the grains have adopted an inverted hourglass shape.

deformation in Sn-38%Pb after 161% (242%) strain is shown in the micrograph of Fig. II.

The starting, undeformed alloy is shown in Fig. 12. Regime

microstructure

IIf d~~~rrnuti~)~. Regime

of this

III was not tested limitations. Regime II d@i,rmation. The torsional deformation of Zn--22%Al at a strain rate characteristic of regime

due to equipment

II for this alloy produced results qualitatively similar to the corresponding regime in Sn-3X%Pb. The significant difference is that in Sn-38%Pb, when the inverted hourglass shape developed. it is wholly comprised of a single grain (usually Sn-rich), whereas in Zn--22%A! the inverted hourglass shape is a composite structure, with the Zn-rich grains forming the highly strained ligaments, and the Al-rich grains making up the lesser deforming cores. At extremely high strains, some recrystallization is observed. An

rLUW

Fig. 11. Sn-38%Pb deformed in Regime I to 161% (242%) true strain. The microstructure is characterized by a gooey, organic appearance, which is due to the substantial volume of grain material involved in ligament formation.

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in torsion supports the hypothesis that such rotating grains were indeed just “floating grains” of the type mentions in the introduction. One very unusual aspect of the torsional observations is that grain boundary sliding, which historically has been held as the fundamental mechanism of superplasticity, was observed during only the first 30% or so of straining in tests performed in Regime IX. Moreover, sliding appeared to take place almost exclusively in the radial direction, toward the free surface, where there was an additional degree of spatial freedom. Apparently the additional degree of freedom associated with the free surface is necessary for such sliding, since almost no in-plane sliding was observed along the specimen surface. This is in contrast to tensile deformation, in which in-plane sliding is observed, but in the tensile case, the ever-increasing surface area of the deforming specimen continually

Fig. 12. Microstructure of undeformed Zn-22%Al.

example of regime II deformation in Zn-22%Al is shown in Fig. 13. Regime I deformation. Regime I deformation seems very similar to that in Regime II except that there appears to be an even greater disparity between the rate at which the Zn-rich grains (ligaments) deform as opposed to their Al-rich (core) counterparts. Thus in regime I almost all straining seems to be taken up by the Zn-rich grains while the rest of the microstructure remains relatively quiescent. R~rystalfization in regime I also seems to occur more readily than in regime II, with the result that, at high strains, the microstructure is a confusing mixture of highly strained, elongated Zn grains (ligaments), alongside small, equiaxed newly recrystallized grains of both sorts. An example of this microstructure is shown in Fig. 14.

Fig. 13. Microstructure of Zn-22%Al deformed in Regime II torsion to a true strain of 98.5%. The Zn-rich grains (white) elongate into Iigament-like structures while Al-rich grains (dark) remain relatively undeformed. Examples of this composite inverted hourglass structure are shown in grains A-a and B-b.

DISCUSSION Deformation in Sn-38%Pb

The fact that individual grains do not randomly rotate during deformation in torsion is notable. These rotating grains had been previously observed in tension on a number of occasions, but their absence

Fig. 14. Microstructure of Zn-22%Al deformed in Regime I torsion to a true strain of 251%. Zn-rich grains have deformed much more rapidly than the Al-rich grains, forming very long ligament-like extensions. Dynamic recrystallization occurs concurrently, as evidenced by the pocket of small, equiaxed grains to the left of the arrow. Line indicates specimen axis, arrows in the sense of twist.

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Starting microstructures, showing size oi mantle region (shaded

Regime III

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Regime

Regime II

(

~~

I

tigame” ts

Strained Microstructures Fig. 15. Summa~ of microstructural evolution during superplastic deformation in torsion for Regimes HI,

II and 1. The increased proportion of ligament vs core material as one approaches Regime I can be explained in terms of an initially larger mantle size for these lower-stress regimes.

generates a certain amount of room to accommodate grain boundary sliding-a situation which does not exist in torsion. It is also interesting to note that even in the radial direction, grain boundary sliding was seen to cease in torsion as soon as the grains had tilted sufficiently to become “stuck” on other grains. There seemed to be no accommodation mechanism to allow grain boundary sliding to continue; nevertheless, Regime II deformation beyond this point still exhibited the same high (superplastic) strain rate sensitivities. Combined, these results indicate that grain boundary sliding is not necessary for superplastic deformation and may be, in fact, an artifact of temporally spacious conditions on the sample surface. The presence of ligaments, however, presents an alternative mechanism for superplastic flow. Here, grain rotation remains relatively fixed, but deformation is non-uniform on the scale of the grain size: the material near the grain boundaries (the mantle region) deforms at a faster rate than that in the grain core. This is an interesting observation, since it implies that different deformation mechanisms are operating in the two regions of the grain, promoting straining at two different rates. At one spans the gamut of stress and strain rate, another observation arises: the volume of grain material devoted to ligament formation (i.e. the size of the mantle) appears to increase as one approaches Regime 1. Figure 15 summarizes this situation. The superplastic Regime II appears to be merely a transition between the rigid uniform deformation of Regime III, where no distinct mantle processes are observed, and the more free-flowing grain deformation of Regime I, in which the mantle processes seem to dominate almost the entire grain.

The transition, in Regime II, consists of grain cores emulating Regime III behavior and the grain mantles emulating Regime I behavior. If there are two different mechanisms responsible for the core vs. mantle type behavior, then superplasti~ity must be occurring at that crossover point in stress and strain rate at which both mechanisms are equally operative and viable, i.e. when the mantle size has become significant with respect to the grain size. The inverted hourglass shape would then arise in order to accommodate the two different flow rates in a physically stable manner. At higher and lower stresses, though, the dominance of one mechanism and one flow rate would cause the grains to elongate more uniformly. A core-mantle

mode/

One can present these ideas in the form of the following simplistic model, which accounts for many of the observed geometric changes (at least in the oneand two-dimensional cases). Three assumptions are needed: first, that there exists a mantle region which blankets the entire surface of the grain and in which deformation occurs faster than in the grain interior; second, that this mantle region remains of$xed size throughout deformation; and third, that this size is determined by, and is inversely proportional to, the applied stress. Of course in Regime III the applied stress is so large that the size of the mantle is negligible, as is its cont~bution to the overall deformation of the grain. The grain deforms unifo~ly according to one set of processes, those of the grain core. In Regime II this same model explains ligament formation quite naturally. Material inside the mantle region deforms at a faster rate than that outside the

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Fig. 16. Simulated deformation of an equiaxed grain into the inverted hourglass shape. Arrows indicate the faster-deforming mantle end-regions.

mantle, in the grain core. By this process the mantle region will of course become thinner and longer (ligament-like) while the core region changes little in shape. However, as elongation of the near boundary region proceeds, material originally near the grain boundary is inexorably drawn further away from the boundary. Such material eventually finds itself outside of the fixed-size mantle region and begins to strain at a slower rate. As this process continues, a gradation of strain from core to grain boundary evolves, reflected in a continuous thickness variation of the ligament. Thus the tapering shape of ligaments is explained. Taken from Ref. [4], Fig. 16 is a one-dimensional computer simulation of this process. Strain is allowed to accumulate in the core vs mantle regions at different rates, and over time, the initially equiaxed grain

Fig. 17. Tensile sample deformed to 96% true strain. Dots show location of ligaments on the sample surface. Arrow indicates tensile direction.

develops into the inverted hourglass shape so often observed. It should be noted that contributions from fastdeforming mantle regions along the side boundaries of the grain have not been included in this simulation. In actual deformation, such flow is necessary, for the ligaments which form at the grain ends would eventually draw to a point were it not for the continual flow of material from the side boundaries sustaining and replenishing them. Also the smoothing of the side boundaries which is seen to occur experimentally cannot be reproduced in Fig. 18 without taking into account enhanced Sow at these boundaries. Unfortunateiy, doing so requires dividing the grain shape into two dimensional grid elements for the calculation,

Fig. 18. Evidence of ligaments in the bulk of a torsion sample (see small black arrow). This sample was su~~lastic~ly deformed in torsion to 159% (282%) true strain, polished to show the subsurface microstructure seen here and then strained an additional 5% to bring some of the grains into relief. Line indicates axial direction; arrow shows sense of twist.

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or a finite element approach. This is a much more complex problem which is still being studied. As for the low stress Regime I, the simplistic model predicts deformation similar in character to that of Regime II but more uniform, since now the mantle is quite large, and one mechanism (and hence one strain rate) clearly dominates. One would also expect almost all of the grain volume to possess the characteristic “gooey” look associated with mantle deformation processes. Both of these effects are observed experimentally. Model predictions In addition to correctly predicting the observed grain shape change, this model also predicts several other observed phenomena. For instance, in a superplastically deforming sample, most of the grains were seen to deform according to the descriptions given above for Regime II, but a few of the anomalously small grains (f< 1 pm) seemed to deform as if they were in Regime I. If the mantle size is indeed set by the applied stress, then this effect would be expected: a medium mantle size for most of the grains would be an exceptionally large mantle size for these small grains. They would be practically all mantle, in fact, and would be expected to deform accordingly, in a Regime I-like fashion. This effect can also explain why, in many materials (including Sn-38%Pb), the superplastic regime is shifted to higher stresses and strain rates when the grain size is smaller. Higher stresses, according to the model, would induce a smaller absolute mantle size, but with sufficiently small grains, this mantle size is still a significant fraction of the grain size. An appropriate balance of core and mantle processes necessary for superplasticity would still exist, even at these higher stresses. Possible mechanisms Up to this point it has not been specified what might be the mechanisms responsible for the different deformation behaviors in the core and mantle. A coherent mathematical and physical model is presented in another paper [9]; however, two key features should be mentioned here. One is that the simple elongation of grains observed in Regime III is consistent with slip-controlled creep, the mechanism long thought to be responsible for deformation in this regime, both for Sn-38%Pb and other superplastic alloys. If this is indeed the mechanism for deformation in Regime III, then the model presented in this paper also assumes it is the mechanism controlling the deformation of grain cores in Regime II. For mantle deformation it is likely that some sort of grain boundary enhanced dislocation climb is responsible. This mechanism could explain the preference for ligament formation at the grain boundaries of Sn grains, for data in the available literature show that the grain boundary diffusion coefficient for the Sn grain boundaries is at least twice that for Pb in Pb

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boundaries and many orders of magnitude larger than that for any volume diffusion coefficient for either element [lo-121. Thus a fast, boundary diffusion enhanced deformation mode in the mantles of Sn grains is not unrealistic. Grain boundary enhanced dislocation climb would also yield Regime I strain rate sensitivities much lower than (i.e. more realistic than) those predicted by other boundary diffusion models, such as Coble creep. Deformation in Zn-2%Al From the observations given earlier it appears that superplasticity in Zn-22%Al has several parallels to that in Sn-38%Pb. For instance, in superplastic deformation of both Sn-38%Pb and Zn-22%Al one part of the microstructure strains at a much faster rate than another, and, in each case, the faster deforming region participates more actively in deformation as the stress decreases. In Sn-38%Pb the grain mantles are the faster deforming region, while in Zn-22%A1 it is entire Zn-rich grains which deform more rapidly, with the Al-rich grains acting more or less as grain cores would in Sn-38%Pb. The fact that one observes a continuum of behavior as stress is decreased from Regime II to Regime I in both alloys, and that the nature of that continuum is similar, suggests that Zn-22%Al, like Sn-38%Pb, exhibits superplasticity because of a transition from one kind of deformation behavior (in the Al-rich grain cores) to another (in the Zn-rich grain mantles). There are several differences, however, in the behavior of the two alloys. The faster deforming regions in the two alloys both respond to lowered stresses with increased contributions to the sample strain, but in different ways. With decreasing stress in Sn-38%Pb more of the deformation is taken up by the faster deforming mantle region because of its increasing size; in Zn-22%AI, more of the strain is taken up by the faster deforming Zn phase because its rate of deformation relative to the Al phase increases. A further difference is that the side mantle regions, so important to continued ligament extension in Sn-rich grains, do not have an equivalent in the Zn-22%Al system. The Zn-rich grains tend to act as end mantle regions only and are not provided with continual material flow from adjoining regions of the microstructure. This fact may account for the observation that in the Zn-22%Al system the ligaments seem able to deform only to a certain extent before recrystalhzation occurs. The lack of side mantle regions, or their equivalent, also disallows grain shape evolution along the lines of Fig. 18 at very large strains. In fact, the inverted hourglass shape can be quite distorted in Zn-22%Al at even moderately large strains, consisting of very long, narrow Zn-rich ligaments connecting almost perfectly equiaxed Al-rich grains. Despite these differences, a dual-mechanism model like that presented for Sn-38%Pb could be constructed for Zn-22%Al. The mechanism involved would probably be quite different and definitely involve

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deformation laws specific to grain type (Al vs Zn) as opposed to laws associated with grain boundaries vs grain cores. Raj and Ghosh [13, 141have shown that even a difference in grain size between grains of the same phase is sufficient to generate two modes of deformation in an alloy, and that superplasticity in 7475 Al and Ti-6A14V can be mathematically described as a transition between laws governing the deformation of one vs the other sized-grains. More importantly, they also maintain that their argument can be extended to two phase systems in which the deformation of each phase is governed by a different law, and superplasticity occurs during a transition between the deformation mechanisms governing each phase. Given the observations above, this seems to be a likely explanation for superplasticity in Zn-22%Al. FURTHER EXPERIMENTS Briefly mentioned in this section are experiments performed to (1) demonstrate the existence of ligaments under other stress states and (2) confirm the presence of ligaments in the interiors of deformed specimens. Ligaments in tension There is strong evidence from experiments [4] which show identical strain rate sensitivity behavior in tension, compression, and torsion that the same mechanisms characteristic of superplasticity operate both in tension/compression and in torsion. The question then arises, if grain shape change and ligament formation are characteristic of these processes, why have they not been previously observed in tension. To answer this question, the authors attempted to replicate earlier studies of superplasticity in tension. Tension samples of 0.635 cm gage length were machined from a 2 mm thick plate of superplastic Sn-38wt%Pb. The exact specimen geometry is given in Ref. [4]. The samples’ microstructure consisted of equiaxed grains of 4pm mean linear intercept grain size. These samples were hand polished, using alumina grit, to a 0.05 pm finish and subsequently scribed numerous times along the axial direction with 0.3 pm alumina grit. Two deep scribe marks also delimited the gage length. The as-polished thickness of these specimens was 1.6 mm. These specimens were mounted in shoulder grips and pulled in tension up to 100% true strain at a constant crosshead speed of 8.47 x 10m5cm/s, corresponding to an initial superplastic strain rate of 1.33 x 10m4s-‘. Measurements of the gage length before and after deformation, however, indicated much of the specimen strain had been accommodated in the shoulder region of the specimen. The effective strain rate for these tests was therefore lower, ranging from 2 to 4 x 10m5s-’ (still well within the superplastic range). The surface microstructure was examined before and after deformation, with the following observations noted. First, at large strains the sample surface was

dominated by heavily deformed grains which had arisen from the subsurface during straining. lnterestingly, the visual texture of these grains was highly reminiscent of the gooey, organic look of the ligaments seen in the torsion studies. This observation suggests that these subsurface grains are encased in a soft mantle, or near boundary region, which is deformed extensively-and in different directions, depending on the requirements of local accommodation-as the grains are subjected to shear through the specimen thickness. For grains which are originally on the sample surface, the top surface layer of the grain is not required to deform and was not observed to do so. On the other hand the side boundaries of these grains were constrained to deform and did so such that the inverted hourglass shape observed in torsion was recreated in tension. An example is shown in Fig. 17. Note that ligaments from these grains are largely obscured by the surrounding chaos of “messy” grains, and this may be why they have not been noted by previous investigators. As in torsion, these ligaments have aligned in the direction of maximum elongation, which in tension is the tensile direction. The classic finding of offsets between the scribe marks on adjoining surface grains was also noted. Thus grain boundary sliding, in the traditional sense, did occur, but its contribution could account for only a small fraction of the strain experienced by the specimen as a whole. It seems much more likely that the severe deformation of grain mantles, whether in three dimensions (in the case of subsurface grains in tension) or two dimensions (in the case of inverted hourglass grains, i.e. surface grains in tension and all grains in torsion) accounts for the greatest part of the imposed strain. A careful examination of the literature also hints of the existence of ligaments in other alloys superplastically deformed in tension. For example several investigators [ 1, 15, 161have noted unusual “striations” forming in the boundaries between grains in Mg32%Al and Al-33%Cu, in addition to Sn-38%Pb. This intergranular material possesses the characteristic “gooey” look of ligaments and resembles ligaments in the initial stages of deformation. Extensive ligamenttype deformation can also be seen in the Regime I deformation of a Mg-Zr alloy (Mg ZK60) studied by Backofen et al. [17]. Certainly several fully-formed ligaments can be seen in some of the micrographs in these references, although they are not mentioned as such. Ligaments as a bulk phenomenon Another concern which arises is that in both tension and torsion, the microstructural changes of interest have so far been observed only at the surface. There is the danger, therefore, that these changes may be merely surface phenomena and not indicative of bulk processes. To disprove this contention, two experiments were performed. First, one of the Sn-38%Pb

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torsion samples, superplastically deformed 163% (292%) was polished to reveal the subsurface microstructure. Narrow protrusions from individual grains were observed. Although they lacked the distinct visual texture of ligaments (having been smoothed by the polishing process), these protrusions did possess an aspect ratio and orientation consistent with the ligaments previously observed on the surface of this sample. The authors therefore conclude that such narrow protrusions are indeed evidence of ligaments in the bulk of the sample. An example taken from the polished specimen is shown in Fig. 18. It should be remarked that the ligaments are somewhat harder to observe in the polished sample than one would expect due to the fact that the microstructure is composed primarily of Sn-rich grains, so one often notices only the outline of a cluster of such grains rather than the details of individual grains within the cluster. Yet another experiment to verify the presence of ligaments in a specimen interior was performed on a Sn-38%Pb tensile sample. The sample, of the kind described earlier, was superplastically deformed 400% at a constant crosshead speed of 8.47 x IO-‘cm/s. In accordance with the method of Raman and Reiley [ 181, a small amount of liquid gallium was then placed on a slightly warmed sample, the absorption of which embrittled the grain boundaries sufficiently to allow easy intergranular fracture. Once the sample was broken manually, the fracture surface was examined in the SEM. Care was taken to avoid locations in which the grains appeared very rounded and/or the boundaries possessed a swirling, molten appearance. Both of these are spurious effects due to prolonged or excessive exposure to liquid gallium. For comparison purposes a fracture surface from an undeformed grip section was examined first. As expected this sample showed regular, equiaxed grains with distinct, faceted boundaries. Surprisingly, the grains observed in the

Fig. 19. Gallium-fractured gage section of a Sn-38%Pb tensile sample superplastically deformed 400%. Grains in this heavily deformed region appear remarkably similar to those in the undeformed grip section. There is, however, some evidence of ligaments between pairs of grains (see arrows), although they are much shorter and more random in direction than those observed on the sample surface.

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highly deformed gage section appeared very similar. There is evidence of ligaments (see Fig. 19), but they are neither as dramatic nor as prevalent as one might anticipate. One reason for this may be that in tension, shear occurs in a multitude of directions simultaneously, so that ligament evolution in any one direction is not heavily preferred. Subsequently, the average ligament length is much shorter, and the ligaments are not easily distinguished from the normal irregularities in grain shape.

CONCLUSIONS

1. Torsional observations of superplastic deformation have yielded results significantly different from similar observations in tension, namely a. grain boundary sliding plays a limited role in the superplastic deformation of Sn-38%Pb and Al-22%Zn in torsion, and in addition, b. random rotation of individual grains was not observed and does not seem to be a prerequisite for superplasticity. 2. In torsion superplastically deforming grains take on an inverted hourglass shape composed of a central, relatively undeformed core and highly deformed extensions called ligaments. 3. In Sn-38%Pb individual grains (usually Sn-rich grains) take on the inverted hourglass shape; in Zn-22%Al the shape is a composite structure, with the Zn-rich phase becoming the highly deformed ligaments and the Al-rich phase comprising the lesser-deforming core. 4. Ligaments have been observed in the interiors of tension and torsion specimens and are therefore not merely surface phenomena or artifacts of the torsional stress state. 5. The grain shape change can be explained in terms of a core-mantle model in which the grain mantle deforms at a much faster rate than the grain core. 6. When comparing superplastic (Regime II) torsional deformation to that in Regime I and III. it seems superplastic deformation is part of a continuum, in which grain mantle processes (as evidenced by ligament formation) increasingly dominate deformation behavior as the stress is decreased (i.e. as one approaches Regime I). Thus superplasticity may be occurring at a crossover point in the domination of grain behavior by core vs mantle processes. 7. Ligaments were probably not recognized in tensile deformation studies of superplastic alloys because of one of the following: a. In large strain studies they were ignored in favor of the less messily deformed and easierto-observe surface “floating grains.” b. In small strain studies the ligaments were simply not very developed, and hence, not very visible (although the beginnings of ligament formation may have evidenced themselves as

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the “striations” mentioned occasionally in the Eterature). c. As has been noted even in torsion, grain boundary sliding dominates at small strains, and most investigators focussed their efforts on this phenomenon. Ack~owfedgeme~ts-This work was supported by the MetalIurgy, Polymers, and Ceramics Section of the Division of Materials Research of the National Science Foundation under Grant No. 8709772. One of the authors (M. J. Mayo) also acknowledges earty support by the Exxon Educational Foundation and by the National Science Foundation through the Center for Materials Research at Stanford University. REFERENCES 1. G. Rai and N. Grant, Metalf. Trans. 14A, 1451 (1983). 2. R. Vastava and T. Langdon, Acia meta&. 27,251 (1979). 3. A. Geqkinli, Ph.D. dissertation, Stanford University (1973). 4. M. J. Mayo, Ph.D. dissertation, Stanford University (1988).

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5. F. Mohamed, M. Ahmed and T. Langdon, Metatl. Trans. 8A, 933 (1977). 6. D. Hughes, Ph.D. dissertation, Stanford University (1986). 7. A. Ziaai-Moayyed, Ph.D. dissertation, Stanford University (1981). 8. G. R. Canova, U. F. Kocks and J. J. Jonas, Acta metali. 32, 211 (1984). 9. M. J. Mayo and W. D. Nix, Aeta metafl. 10. D. Bergner and W. Lange, Physica status solidi 18, 67 (1966). 11. H. Mehrer and A. Seeger, Crystal L,artice Defects 3, I (1972). 12. D. Gupta and K. K. Kim, J. appl. Phys. 51,2066 (1980). 13. A. Ghosh and R. Raj, Acta metall. 29, 607 (1981). 14. R. Rai and A. Ghosh. Acta metall. 29. 283 (19811. 1.5.D. Lee, Acta metall. 17, 1057 (1969). ‘ \ ’ 16. S. Zehr and W. Backofen, Trans. Am. Sot. Metals 61, 300 (1968). 17. W. Backofen, G. Mmty and S. Zehr, T.&f.,%-A.I.M.E. 242, 329 (1968). 18. V. Raman and T. Reiley, IBM Yorktown Heights, private communication.