A micro-indentation study of superplasticity in Pb, Sn, and Sn-38 wt% Pb

Acta metall. Vol. 36, No. 8, pp. 2183-2192, 1988 Printed in Great Britain. All rights reserved

0001-6160/88 $3.00+ 0.00 Copyright © 1988 Pergamon Press plc

A MICRO-INDENTATION STUDY OF SUPERPLASTICITY IN Pb, Sn, AND Sn-38 wt% Pb M. J. M A Y O and W. D. NIX Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, U.S.A. (Received 7 December 1987)

Abstract--In this study a method is developed for accurately determining strain rate sensitivities on a submicron scale using an indentation technique. The technique has been developed for use with the Nanoindenter and is applied to pure Pb, pure Sn, and Sn-38 wt% Pb to elucidate the mechanisms responsible for Sn-38% Pb's superplastic behavior. In particular, it has been possible to vary the grain size with respect to the indentation size and thereby obtain strain rate sensitivity values for the interiors of individual grains (behavior of the lattice only) as well as for multiple grains (lattice + grain boundary, i.e. polycrystailine behavior). The results establish the role of grain boundaries in promoting high rate sensitivity and superplasticity. However, the results also indicate that the increase of rate sensitivity in the presence of boundaries is not due to grain boundary sliding. Grain boundary sliding has been consistently observed during the testing of superplastic Sn-38 wt% Pb, but only in the initial stages of deformation. A core-mantle model of supcrplastic deformation is suggested instead to account for the role of grain boundaries in enhancing strain rate sensitivity. Rtstmat--Nous proposons dam cet article une mtthode pour dtterminer avec pr&-ision les sensibilitts la vitesse de dtformation, ~i une 6chelle inftrieure au #m, ~'l'aide d'une technique d'indentation. Nous avons dtvelopp6 cette technique pour qu'elle soit utilisable avec le Nano-indenteur, et nous rayons appliqute an plomb pur, ~ l'ttain pur, et ~il'alllage d'6tain/t 38% en poids de plomb, dans le but d'61ucider les mteanismes responsables de la superplastieit6 de Sn-38%Pb. Nous avons pu eta particulier faire varier la taille des grains en fonetion de la dimension de l'indentation, et obtenir ainsi des valeurs de la sensibilit6 ~i la vitesse de dtformation pour l'inttrieur des grains individuels (comportement de rtseau seul) ainsi que pour des groupes de grains (compartement de rtseau seul) ainsi que pour des groupes de grains comportement de rtseau+joint de grains, c'est-,'i.dire comportement polycristallin). Les rtsultats montrent que les joints de grains favorisent une forte sensibilit6 ~i la vitesse ainsi que la superplasticitt. Cependant, ils indiquent anssi qae l'accroissement de la sensibilit6 a la vitesse en prtsence des joints n'est pas dfa au glissement intergranulaire. Nous avons effectivement observ,~ du glissement intergranulaire au cours de la dfformation de l'6tain ~ 38% en poids de plomb, mais uniquement pendant les premiers stades de cette dtformation. Nous suggtrons un modtle de dtformation superplastique avec un coeur entour6 d'un manteau pour rendre eompte du r61e des joints de grains duns l'aagrnentation de la sensibilit6 ~i la vitesse de d6formation. Zmammenfassung--Eine Methode wird entwickelt, mit der auf der Grundiage von Stempeleindriicken die Dehnungsratenempfindllchkeit im Submikron MaBstab gemessen werden kann. Diese Methode wird anf reines Blei, reines Zinn and Sn-38 Gew.-% Pb angewendet, am den fi3r das superplastische Verhalten des Sn-38% Pb verantwortlicben Mechanismus aufzukl~ren. Insbesondere war es m6glich, die Korngrtfie im Vergieich zur Stempelgrtl3e zu varfieren und damit die Dehnungsratenempfindllchkeit im Inneren einzelner K6mer (Verhalten des Kristallgitters) und fiir viele K6rner (polykristallines Verhalten) zu messen. Diese Ergebnisse liefern den Einflufl der Komgrenzen bei der hohen Dehnungsratenempfindlichkeit und bei der Superplastizitat. Allerdings zeigen die Ergeboisse auch, dab der Anstieg der Dehnungsratenempfindlichkeit bei Anwesenheit der Korngrenzen nicht auf Korngrenzgleitung zuriickgeht. Korngrenzgieitung wurde wahrend der Versuche am superplastischen Sn-38% Pb durchgehend beobachtet, jedoch nur zu Anfang der Vefformung. Ein Kern-Mantelmodell der superplastischen Verforrnung wird damit nahegelegt, urn die Rolle der Korngrenzen bei der Verst/irkung der Dehnungsratenempfindiichkeit zu erklaren.

INTRODUCTION Superplastic alloys, with their astounding ductility at intermediate homologous temperatures and sound mechanical properties at lower temperatures, have fascinated engineers for almost five decades with their promise of providing a low-cost, low-force method of forming complex parts. Most of these alloys manifest so-called "structural superplasticity", in which microstructure plays an important role. Existing superplastic alloys of this type span a wide range of chemical

compositions (for examples, see the Appendix of Ref. [1]), hut virtually all are composed of small, equiaxed grains. Why this specialized microstucture is essential is not yet clear, although the presence of such large numbers of grain boundaries has led m a n y to assume that the mechanism for superplasticity is somehow grain b o u n d a r y controlled. Grain b o u n d a r y sliding in particular is often cited as the cause of the high strain rate sensitivity and hence superplastic behavior of these alloys. Unfortunately, until now there has been no direct

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M A Y O and NIX: A M I C R O - I N D E N T A T I O N STUDY O F SUPERPLASTICITY

method to determine the contribution of different features of this specialized microstructure to the anomalously high strain rate sensitivities of superplastic alloys. The traditional approach has been to perform macroscopic experiments and, from these, attempt to deduce the effects of such microscopic features as grain boundaries, second phases, etc. A more direct approach would be to use a very fine mechanical probe to obtain strain rate sensitivity data in situ from the feature of interest, and compare it to similar data for that of other microstructural features and finally to that of the alloy as a whole. With the advent of the Nanoindenter this possibility has become a reality. The Nanoindenter is capable of providing reproducible data for indentations as small as 20 nm in depth and has the potential to measure mechanical responses on the scale of even the finest superplastic microstructures. Depth, load, and time data are simultaneously recorded as indentation proceeds, allowing one to calculate secondary variables, such as stress and strain rate, for any point during the test. Finally, the entire apparatus is computer controlled, which allows for a variety of custom-programmed tests. With these capabilities it should be possible to measure strain rate sensitivity values in an indentation mode, in a manner analogous to creep testing in tension; thus the first goal of this investigation was to tievelop such a method. The second goal was to take advantage of the small-scale abilities of the Nanoindenter in applying this method to microstructural features--in this case, grain interiors vs grain boundaries--within a superplastic alloy. The alloy chosen was Sn-38 wt% Pb, which is conveniently superplastic at room temperature. It is also comprised of equiaxed grains of essentially pure Pb and pure Sn. The method, therefore, was to make small indentations inside large, single grains of pure Pb and pure Sn and compare the strain rate sensitivities of these lattice-only experiments to equivalent data from the Sn-38% Pb alloy, which should exhibit lattice + g r a i n boundary, or polycrystalline, behavior. Then by comparing the strain rate sensitivities of the same material in the presence vs in the absence of grain boundaries, one could determine whether and to what extent grain boundaries actually do influence the high strain rate sensitivities and hence high ductilities manifested by superplastic alloys. T H E CONSTANT RATE O F LOADING TEST: AN OVERVIEW

a constant rate throughout the course of a single indentation. This rate is then varied from indentation to indentation. The material responds to each applied loading rate with a different deformation rate, which in practice is measured in terms of the indenter descent rate. As a matter of convenience we describe a typical C R L test response as possessing an initial stage, in which the descent rate decreases fairly rapidly, followed by a large depth stage, in which the descent rate is more nearly constant. A more complete discussion on the nature of the C R L test response is given in Ref. [2]. A typical C R L test response is shown in Fig. I. Over the course of several indentations, each made under a different loading rate, the difference between the response of a strain rate insensitive and a strain rate sensitive material becomes apparent. First consider a strain rate insensitive material. If the loading rate is increased by a factor of two between indentations, the resulting descent rate increases by exactly a factor of two. This is not true for strain rate sensitive materials. F o r these materials the deformation rate does not increase in proportion to the increase in applied loading rate. Thus when the loading rate is inci'eased by a factor of two from one indentation to the fiext, the descent rate during the second indentation will be greater than that of the first indentation, but not by a factor of two. Furthermore, this effect becomes more severe as the loading rate is increased yet further. These differences between the response of a rate-insensitive vs rate-sensitive material to the C R L test are illustrated in Fig. 2. Although it is helpful to possess a qualitative understanding of the distinction between strain rate sensitive and strain rate insensitive behavior in CRL tests, a rigorous analysis requires a more quantitative approach. To measure the magnitude of strain rate sensitivity in an indentation test requires one to define 1200

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In the course of this investigation, several methods for obtaining strain rate sensitivity data from indentation tests were attempted. The method that is described herein is that which was ultimately developed as the easiest and most reproducible means to obtain such data: we call this test the constant rate of loading test, or C R L test. As the name implies, the C R L test consists of applying load to the indenter at

Fig. I. In the C R L test an indentation is formed in response

to load being applied to the indenter at a constant rate. Shown here is the typical manner in which the indenter depth increases with time. The data are characterized as having an initial stage, in which the indenter descent rate decreases rapidly, followed by a large depth regime, in which the descent rate is more nearly constant. These particular data are the result of an indentation made in the center of a large Pb grain.

MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY

2185

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Fig. 2. Material response to a CRL test. (a) Load is applied at several different rates to the same material. Each applied loading rate corresponds to a tingle indentation. (b) If the material is strain rate insensitive, the indenter's descent rate will be directly proportional to the loading rate applied to it. (c) If the material is strain rate sensitive, the indenter's descent rate will not increase in proportion to the applied loading rate. an indentation stress and an indentation strain rate. As a first approximation, we define the indentation stress as the pressure underneath the indenter, i.e. stress = load/projected area under the indenter, or o = L/A. The projected area under the indenter is in turn a function of the shape of the indenter, so for a perfectly shaped indenter we have ¢ = L/Kh 2, where K is a constant determined by the shape of the indenter, and h is the current depth of the indenter in the material. In a similar manner we define an indentation strain rate to be the descent rate of the indenter divided by its current depth: i = (l/h)(dh/ dt). With stress-strain rate data such as this, it becomes possible to determine the strain rate sensitivity in much the same manner as that traditionally used in creep test analysis. One first chooses a single depth at which the data from different indentations are to be compared. To minimize the effects of rapidly changing data during the initial stage of indentation, the chosen depth should fall within the large depth regime for all indentations under consideration. Each indentation--that is, each applied loading rate--is characterized by one stress-strain rate pair, taken at the selected depth. These data pairs are than graphed on a log-log plot of stress vs strain rate. Finally, the strain rate sensitivity, m, is simply the slope of that plot: m = d log ¢ / d log i. It should be emphasized that, of course, the indentation stresses and strain rates defined above are not equivalent to uniaxial flow stresses or uniaxial steady state strain rates. The indentation values are, however, proportional to the uniaxial quantities (as a guide, uniaxiai flow stresses tend to be 10-20% of the indentation stresses). If they were not, one would not

consistently obtain the same values for strain rate sensitivity from the polycrystalline CRL tests as one does in uniaxial experiments on the same material. Considering the complexity of the stress and strain distribution underneath a typical pyramidal indenter, this method, and particularly the approximations used for o and ~, may seem exceedingly simplistic. However, this procedure does yield excellent results, as is demonstrated by experiments on pure Pb, pure Sn, and Sn-38 wt% Pb (discussed below) and Pb-20 wt% In [2].

EXPERIMENTAL PROCEDURE

The Nanoindenter The Nanoindenter used in these experiments was obtained from Nano Instruments Inc. and is described in detail elsewhere [3]. Nevertheless it should be mentioned that, in the Nanoindenter, load is delivered in the form of discrete electrical pulses through an electromagnetic coil, so that a change in loading rate is essentially a change in the time between pulses. Loading is therefore not a continuous process; however the load increments for tests described here are so small (each pulse = 0.25 g N of load) that the approximation of continuous loading is quite reasonable. It should also be mentioned that for these experiments a diamond indenter tip of 3-sided pyramid geometry was used. This pyramid is a shallow one, with the angle between the pyramid's vertical axis and the bisector of one of its sides being 65 °. For this geometry the constant K mentioned earner (K = A/h 2) is 24.55. This gives the indenter the

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MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY

same area to height ratio as the more traditional Vickers pyramid.

Sample preparation Several different samples were used in these experiments; they are described individually below. Pure Sn (small grain size). A small piece (approx. 50mm 3) of 99.99% pure Sn was forged by hand for about 15rain. During this process the sample was repeatedly dipped in liquid nitrogen to maintain a cold working temperature. Once cold worked, the sample was placed in a hand press and flattened against a polished sapphire disc to achieve a smooth flat surface for indentation tests. This surface was further polished to a 0.05/tm finish using alumina grit, and the sample was stored in a freezer at - 9 ° C for 6 days before testing. The resulting 26 x 15 x 0.436mm sample possessed a bimodal grain size distribution. The larger grains had a mean linear intercept grain size, [ of about 125 #m; 1" of the smaller grains was 4/zm. The indentation tests were carded out in a region composed of the smaller grains. Pure Sn (large grain size). A small piece (approx. 100 mm 3) of 99.99% pure Sn was forged by hand, at room temperature, for about 15 min. The sample was then flattened in a hand press (see above) and polished to a 0.05/~m finish using alumina grit. Recrystallization and grain growth occurred during the subsequent annealing at 200°C for 3.5 h. The final grain size of this sample was ]'= 0.4 mm; however, most of the indentation data presented in this paper derives from tests conducted on a single grain, with a length of 1 mm and width of 0.6 mm. The dimensions of the sample itself were 6.5 mm (radius) by 0.787 mm (thickness). Pure Pb (large grain size). A small piece (approx. 70mm 3) of 99.9% pure Pb was formed into an indentation sample in the same manner as that described above for the large-grained pure Sn. The resulting sample dimensions were similar (6.5mm radius, 0.521 mm thickness), but the grain size for the Pb sample was much smaller:/'= 27/~m. As a result, indentation tests were distributed among several grains.

Superplastic Sn-38 wt% Pb (medium grain size). This is the same sample as the small-grained Sn-38wt% Pb sample described above, except an additional 34 days at - 9 ° C had allowed the grain size of the sample to increase t o / ' = 3.5/~m.

Prestrained samples of superplastic Sn-38 wt % Pb. These sheet tensile samples were fabricated in the manner described in Ref. [4]. The sample geometry is shown again in Fig. 3. These samples possessed a homogeneous distribution of equiaxed Sn-rich and Pb-rich grains; the mean linear intercept grain size was measured before straining to be 3.5/zm. Sample surfaces were polished to a 0.05/~m finish using alumina grit before straining, and again after straining but before indentation. The samples were mounted in shoulder grips and strained in an Instron Model TT-C electromechanical testing machine at a constant crosshead speed of 4.23 x 10 -4 cm/s. Since the gage section for these samples was 6.35 mm, this corresponds to an initial strain rate of 6.66 x 10 -4 s -~. Using this procedure, one sample was prestrained each of the following amounts: 0, 400 and 800%.

Testing procedure Since no indenter tip can be ground perfectly, the value given earlier for the indenter shape constant, K, deviates quite noticeably from its ideal value in the case of a real indenter. In fact K actually varies systematically with distance from the tip of the indenter. For this reason a full indenter shape calibration was carried out before testing. In this calibration the cross sectional area, and hence K, were determined as a function of distance from the indenter tip; for details, see Ref. [3]. This calibration can significantly affect results [3]. After the indenter shape calibration was performed, the samples to be tested were mounted on small aluminum blocks using double-sided cellophane tape. Prior to each test, the approximate height of the sample surface was determined by a test dent. Of course, the exact point of indenter entry into the material varied from indentation to indentation, hut it was easily determined (within a few Angstroms) by

Superplastic S n - 3 8 w t % P b (small grain size). Approximately 400 mm 3 of a Sn-38 wt% Pb casting was hand forged for 15 min, with repeated dipping in liquid nitrogen to maintain a cold working temperature. The sample was then flattened in a hand press against a polished sapphire disc and annealed at room temperature for 1 day. By this process the lameUar eutectic microstructure of this material was first broken down and then subsequently recrystailized to produce a fine, homogeneous microstructure of equiaxed Sn- and Pb-rich grains (/'= 1.3 #m). The sample was polished to a 0.05 #m finish with alumina grit and stored in a freezer at - 9 ° C for 4 days before testing. Sample dimensions were approx 15 mm radius x 0.67 mm thickness.

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MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY the sudden decrease in the recorded indenter velocity under conditions of constant loading rate (/'~ for all indentations during surface searching was 7.15 × 10 -4 mN/s; this corresponds to an approach velocity between 100 and 150A/s). Knowledge of the point at which the surface was contacted (i.e. the point of depth = 0) led to a more exact assessment of the indenter depth as the test proceeded. As soon as surface contact was made, the loading rate was changed to that desired for the indentation experiment being conducted. As mentioned earlier, the constant rate of loading tests performed here require each indentation to be made under a different applied loading rate. These varied from 1.11 × 10SmN/s to 2.04 × 10 -4 mN/s, with the highest loading rate being employed for the first indentation, and the loading rate lowered by a factor of two or so between successive indentations. The indentations themselves were typically made in a 3 x 4 matrix pattern. The spacing between adjacent indentations was about 10 times the maximum width of the indentations to ensure that the deformed region surrounding one indentation did not interfere with the formation of the next indentation. Since the final depth of most indentations was about 1/~m (width ~ 6/zm), these were spaced 60 F m apart. In a few cases indentations were allowed to proceed to a depth of 3/~m (width ~ 19/~m); these indentations were spaced 200 g m apart. After the final depth for each indentation was reached, loading stopped, and the indenter was allowed to sit in the material, under constant load, for 20 s. Some creep inevitably occurred during this time; that is, the indenter would sink further into the material under constant load conditions. Finally, the indenter was raised from the material at an unloading rate of 2.35 x 10 -3 mN/s. Essentially two types of tests were conducted using the above technique. The samples described as having "small" or "medium" grain sizes were chosen so that the CRL test would yield polycrystalline results; that is, the grain size was sufficiently small for a single indentation to cover several grains, and the rate sensitivity measured was the rate sensitivity of the polycrystalline material. The same test performed on materials with "large" grain sizes was designed to yield a different type of d a t a - - t h a t for the lattice only, without grain boundaries, for here the indentation size was much smaller than the grain size, and the indentations were located in the centers of grains. Analysis procedure

For all materials used here it was determined that a depth of 700 nm lay well within the large depth regime for each, and data to be compared was taken about this point. The indenter stress at 700rim (or = L / K d 2) was taken as the average of values at 600 and 800 nm, using the calibrated values for K. Due to the minor point-to-point variations in data, this method was preferable to simply taking the value

2187

of stress at 700 nm per se. The descent rate, dh/dt, was calculated from a linear regression of depth vs time over the same 600-800 nm interval. Finally, the indentation strain rate, ~, was calculated at the slope of a regression in In (depth) vs time over the interval of interest: ~ = (1/h )(dh /dt ) = d(ln h )/dt. In general one would use the values for plastic depth rather than actual depth in calculating the expressions for stress, descent rate, and strain rate. The difference between these two values is the elastic displacement, which is a considerable fraction of the total depth at small values of depth. One can measure the amount of elastic displacement at the final depth by extrapolating the elastic decrease in depth during unloading. This variation of load vs depth during unloading can also be directly equated to the elastic modulus of the material, and, in fact, one can simply use the known modulus directly to predict the extent of the material's elastic displacement at any depth [3]. Both methods give nearly identical results for the materials used here, although direct use of the elastic modulus was sometimes easier, when, at higher loads in these soft materials, creep occurred even on unloading and distorted the linear elastic unloading curve by superimposing additional plastic displacements. As a matter of convenience, then, all plastic depths in this experiment were ultimately calculated either from known moduli or from moduli previously measured in indentation, but under small loads. In point of fact, however, these calculations were not very consequential in light of the large depths and soft materials used in this experiment: the elastic displacements at 700 nm in Pb, Sn, and Sn-38 wt% Pb proved to be only a small portion of the total depth (1-4%). The plastic depth and total depth are thus virtually interchangeable in the analysis of these data. RESULTS AND DISCUSSION Strain rate sensitivity measurements Single grain results. Results of the single grain indentation tests on pure Pb are shown in Fig. 4. They reveal quite a low strain rate sensitivity: m =0.117, or, in terms of the stress exponent, n, n = l/m =8.5. This value is very close to the m = 0.125 (n = 8) value found for large-grained Pb via creep tests [5--7]. For indentations made in the middle of large Sn grains, the strain rate sensitivity was measured to be m = 0.088 (n = 11.4), also a very low value (Fig. 5). This rate sensitivity is, in fact, even lower than the m = 0.125 value measured for coarsegrained Sn [8]. This is not surprising because the strain rate sensitivity in Sn is extremely grain size dependent; thus the difference between testing reasonably large grains (in the case of polycrystalline creep) and infinitely large grains (in the C R L single grain tests) is expected to be noticeable. The results of the tests on large-grained pure Pb and pure Sn demonstrate an important fact. These single grain indentation tests not not equivalent to

2188

MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY l0° Pb

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single crystal tests in tension or creep. Single crystal experiments can give much higher values of strain rate sensitivity (e.g. m =0.83 for Pb [9, 10] and m = 0.21 for Sn [11]), whereas the single grain indentation tests give very low values. The lower values are much more like those produced by tension and creep tests on coarse-grained materials--as they should be, for essentially the grain size approaches infinity in the indentation case. One might also expect single crystals to behave as infinite grains and give the same results, but they do not. The reason for this is that deformation in a single crystal often occurs via slip on a single slip system. (This is documented for the case of pure Pb--see [10].) In contrast, multiple slip occurs in both polycrystalline creep tests and single grain indentation tests. In polycrystalline creep and tensile tests, the orientation differences between the different grains cause different slip systems to operate simultaneously. In the indentation tests several slip systems must operate because the deformation caused by the indenter is not crystallographically specific. For this reason one also finds that the plastic behavior indicated by a single grain indentation test does not change with the crystallographic orientation of the grain. To prove this, we performed CRL tests on a

Sn grain other than the one documented here and achieved identical results. Polycrystalline results. According to conventional creep tests [8, 12], values for the strain rate sensitivity of pure Sn at room temperature are highly grain size dependent. They range from m = 0 . 1 2 5 to m = 0.212 (n = 8 to n = 4.7), with the higher strain rate sensitivities corresponding to smaller grain sizes. The indentation results show a similar trend. As has been previously noted, the single grain tests yielded a very low strain rate sensitivity of 0.088. For the small grained sample, in which a single indentation covered several grains, the rate sensitivity was much higher: m = 0.159, or n = 6.3. Both sets of results are shown in Fig. 5. In further contrast to the low strain rate sensitivities exhibited by single grain experiments, the CRL tests measured quite high rate sensitivities for all the polycrystalline Sn-38 wt% Pb alloys tested. For example, the small-grained Sn-38 wt% Pb alloy was found to have a rate sensitivity of m = 0.469 (n = 2.13). The data are shown in Fig. 6. Since this was a polycrystalline test, with indentations covering many grins, it was not surprising to find the result, n ~ 2. This result is identical to that obtained by other investigators [ 13-18] in macroscopic creep and tensile tests of the same alloy. The sample with a slightly larger grain size of 1"= 3.5 #m showed a slight decrease in this value to m = 0.385 (n = 2.6). These data are shown in Fig. 7. Finally, prestrained samples of the 3.5 # m grain size Sn-38% Pb alloy showed little variation of strain rate sensitivity with prestrain, even up to 800% (see Fig. 8). In polycrystalline Sn and Sn-38 wt% Pb samples it was interesting to observe that although the indentations were all nominally of the same final depth, the actual size of indentations made under fast loading rate conditions was much larger than that of indentations formed under slower loading rate conditions. In fact a continuous gradation in indentation size existed from dent to dent, commensurate with the loading rate applied in each case. This phenomenon was later seen to hold true for all materials exhibiting 100

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MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY

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Strain Rate(l/s) Fig. 7. Enhancement of strain rate sensitivity associated with the increase in grain boundary area per unit volume in Sn-38 wt% Pb. The mean linear intercept grain size of the small and medium-grained alloys are T= 1.3 ~m and /'= 3.5/zm, respectively. high rate sensitivity, and it is due to differences in creep rate during the 20 s hold which follows the loading part of the indentation process. The fact that a material is rate sensitive means that the loading rate influences the load which can be sustained at a given depth, including the nominal "final" depth. (Conversely, in rate insensitive materials, one obtains the same load at the same depth regardless of the loading rate applied.) Thus for rate sensitive materials all indentations proceed to the same nominal final depth, but at that point the load is different for each. It is then this same load under which creep occurs during the 20s hold. For indentations which have been formed under high loading rate conditions, the final load is higher (due to rate sensitivity considerations), subsequent creep occurs faster, and more depth is achieved in the same 20 s hold. In the end, the total depth (final depth + depth achieved during creep) of such an indentation is much larger than that of its lower-loading-rate neighbors. One fascinating and useful by-product of these tests is that they allow for easy visual check of rate sensitivity in a material: the more exaggerated the size variation across a field of indentations, the more rate sensitive the material.

It seems evident from the results described above that grain boundaries do enhance the strain rate sensitivity. Results from the single grain indentation tests prove that without grain boundaries, deformation in both pure Pb and pure Sn shows little strain rate sensitivity. With grain boundaries, pure Sn becomes much more strain rate sensitive (small-grained pure Pb was not tested for experimental reasons). The same is true of the composite material, Sn-38% Pb, which demonstrates much higher strain rate sensitivity than either pure Pb or pure Sn--without boundaries--would seem to warrant. Figure 9 compares the single grain and polycrystalline behaviors. Furthermore, as one introduces more grain boundaries per unit volume, that is, as the grain size of Sn38% Pb is decreased from ]'= 3.5/am to 1 = 1.5/am, this strain rate sensitivity increases. This latter result agrees with findings in tension and creep that the strain rate sensitivity of superplastic Sn-38% Pb tends to increase with decreasing grain size at intermediate to high stress [I 3, 17]. It would be interesting to ascertain whether pure Sn of grain size comparable to that o f the Sn-38% Pb samples would prove to be as strain rate sensitive, but unfortunately, one cannot obtain ahch small grains in pure Sn due to the lack of second phase particles to pin the grain boundaries.

Grain boundary sliding After indentation, the initially smooth, reflecting surface of the small-grained Sn sample and all the Sn-38% Pb samples showed outlines of grains at indentation sites. Upon inspection, it was clear that the delineation of the grain boundaries occurred due to grain boundary sliding (GBS). Grains which had heretofore been flush with the surface had tilted inwards toward the indentation, such that the part of the grain nearest the indentation was now below the surface and the more distant part was tilted upward

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10-2 Sn-38wt%Pb ,~

10-2

n 0% Prestrain

1o.3 I . . . . .

o 400% Preswain + 800%

10-5

Preswain

10-4

- ............... 10.3

10.2

10-]

Strain Rate (Us)

10 .3

Fig. 9. A comparison of CRL test results from single grain experiments in pure Sn and pure Pb with those obtained Strain Rate (Us) from the Sn-Pb polycrystalline aggregate show the polyFig. 8. CRL tests on prestrained samples of Sn-38 wt% Pb crystalline alloy to be much more strain rate sensitive than show little change in strain rate sensitivity with amount of would be expected from the behavior of either of its constituent materials. tensile prestrain. 10-5

10.4

10.3

10.2

lif t

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MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY

out of the surface. This topographic relief created shadows at grain edges that were visible in the light microscope as simple outlines of the grain shape. The sense of tilting of the grains was confirmed via SEM. Examples of GBS during indentation in two samples of Sn-38 wt% Pb with different grain sizes are shown in the micrographs of Figs 10 and 11. In Sn-38 wt% Pb another characteristic feature of the indentation tests is the unique variation of descent rate with depth during the course of a single indentation. For indentations made within a single grain, as in pure Pb above and pure Zn in another experiment [2], the descent rate of the indenter is either relatively constant or decreases in a steady, asymptotic manner as the test progresses. Single grain tests in pure Sn (and to some extent, polycrystalline Sn) behave somewhat differently, with one and often several glitches in descent rate occurring during testing. These are accompanied by dramatic stress variations. It is not yet clear whether sudden twinning, or possibly a phase transformation, is affecting the descent rate in this latter case. However, SD-38 wt% Pb is yet a third case. Figure 12 shows the variation in descent rate that is often seen in indentations in Sn-38% Pb. First a sharp increase, then a sharp decrease, occurs in the descent rate of the indenter near the beginning of each test, always at a depth below 500 #m. This spike we believe to be due to grain boundary sliding. The depth at which this anomalous event occurs seems appropriate for GBS: visible signs of GBS are seen progressively less often as indentation depth decreases below 500/xm, but GBS is always seen in indentations carried out to larger depths. The actual indenter depth at which GBS is triggered depends, of course, not only on the indentation size with respect to the grain size, but also on how close to a boundary the indentation is placed.

Fig. 11. Scanning electron micrograph of grain boundary sliding in a Sn-38 wt% Pb alloy.

If this event is indeed grain boundary sliding, then the implications arc profound. Sliding during indentation would appear to be a cataclysmic event that occurs when the stress and strain fields surrounding the indenter reach a criticalsize sufficientto affectthe grain boundaries. The grains tiltdownwards suddenly; the indenter responds by sinking in suddenly, but-and this is the remarkable part--the sliding appears to stop almost as soon as it has started. The descent rate drops dramatically back to its prc-sliding value. This appears to indicate that the grains slide freely up to a point, then become stuck on each other. W h e n they are no longer frcc to slide, the indcntcr's progress is suddenly slowed as other deformation mechanisms invariably take over. It is essential to realize that the high strain sensitivities characterizing this alloy were calculated from data taken at 700 nm, after the spike in descent rate had occurred in almost all indentations. Thus the measured rate sensitivity is

Sn-38wt%Pb

Grain Boundary Sliding

i

10

0 0

1000

2000

3000

Depth (rim)

Fig. 10. Optical micrograph of grain boundary sliding in a Sn-38 wt% Pb alloy.

Fig. 12. Sudden variation in descent rate of the indenter observed in C R L testsof superplasticSn-38 wt% Pb. This anomaly is attributedto grain boundary sliding.

MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY not a product of GBS but of the mechanism which takes over once GBS has stopped. The real mechanism for superplasticity, the one responsible for the high strain rate sensitivities, does not appear to be grain boundary sliding. From these results it may seem reasonable to assume that, in superplasticity, GBS occurs and is exhausted after a certain amount of strain. Interestingiy, strain does not actually seem to be a factor. If the value of strain rate sensitivity is an indicator of the operative deformation mechanism, then this mechanism is not changing as strain is increased. CRL tests of the prestrained Sn-38% Pb samples showed almost no variation of strain rate sensitivity from 0 to 800% strain. At the same time, however, GBS is observed near the indentations made in all of the prestrained tensile samples. It is hypothesized that the reason grain boundary sliding starts and suddenly stops may instead be linked to the available degrees of spatial freedom. In the indentation case, a degree of freedom exists in the direction out of the surface plane. Surface grains would be free to move in this direction until they invariably became stuck. Then another, slower, mechanism would have to take over--not because the grains have experienced a certain amount of strain, but because they have lost their initial degree of freedom. Observations of superplastic deformation in torsion [4] also support this theory. Out-of-plane sliding is also observed in these experiments, but again, as in indentation, only until the grains become "stuck" on each other. This occurs after about 30% strain, at which point a different mechanism is seen to take over. A possible contradiction may exist in observations of superplastic deformation in tension [19-21], which have demonstrated sliding not only out of the surface plane but within the surface plane, and the in-plane sliding appears to continue for the duration of these tests. It is important to realize, however, that in tension, the surface area of the sample is continually increasing as the sample elongates. Additional space becomes available on a continual basis for surface grains to slide past each other. By contrast, in torsion the surface area of the deforming sample is not continually increasing; this extra degree of freedom does not exist, and, interestingly, in-plane grain boundary sliding is not observed at all [4]. Sliding thus appears to be a function of the degrees of spatial freedom available to the grains. Since subsurface grains in tension and torsion samples obviously have fewer degrees of freedom than the surface grains, it is reasonable to ask whether these interior grains slide in any significant way. It may be that they do not. In torsion tests of bulk samples the authors have observed that the samples' high strain rate sensitivity is not affected when surface GBS is appears to stoty--a fact which may mean that most of the grains in the interior were not ever sliding significantly. Furthermore, the strain rate sensitivities

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measured in torsion have been proven to be identical to the strain rate sensiti~fies obtained in compression tests of the same Sn-38% Pb material [4]. If GBS is not the primary deformation mode for the bulk of the grains in torsion, then it seems likely that GBS is not occurring in the bulk of compression samples either. By inductive reasoning, one suspects the same may be true for tensile samples. An alternative mechanism

If the grains in the interior of a bulk specimen, such as those used in torsion and tension tests, are not sliding, the question remains as to how they are deforming. This is a particularly important question in light of the indentation results which show that GBS itself is probably not a prerequisite for high strain rate sensitivity, and therefore superplasticity. An answer may lie in the results of the torsion experiments referred to earlier [4]. Briefly, the authors observed the surface of a deforming sample and found that after grain boundary sliding was forced to stop, a new mechanism took over. This mechanism seemed to be of a "core and mantle" type, in which the mantle, or near boundary region of the grain was found fo deform much faster than the grain center, or core./By this mechanism, much of the strain experienced by the deforming sample was taken up by a small region of boundary material surrounding each grain. The importance of the boundary region in this type of deformation may explain why high strain rate sensitivity is so inextricably linked to the presence of boundaries, as has been demonstrated by the indentation experiments. CONCLUSIONS I. An easy, accurate method for measuring strain rate sensitivities from indentation tests has been developed. The method, the constant rate of loading (CRL) test, has provided strain rate sensitivity data from within single grains of pure Pb and pure Sn as well as from polycrystalline samples of Sn and Sn-38 wt% Pb. 2. The strain rate sensitivities taken from within the single grains show that the inherent strain rate sensitivity of pure Pb and pure Sn, minus the effect of grain boundaries, is quite low. With the introduction of grain boundaries, as in the case of polycrystalline Sn and the Sn-38 wt% Pb alloy, the tests reveal much higher strain rate sensitivities. The presence of grain boundaries is therefore seen to enhance the enhanced strain rate sensitivity of the material. 3. Strain rate sensitivities obtained from single grain CRL tests is similar to that obtained from creep and tensile tests on large-grained polycrystailine samples of the same material. Polycrystalline CRL data matches that obtained on the same polycrystalline material via the other methods. 4. Grain boundary sliding was observed as a cataclysmic event occurring during only the initial stages

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MAYO and NIX: A MICRO-INDENTATION STUDY OF SUPERPLASTICITY

of indentation in the superplastic S n - 3 8 w t % Pb samples; this indicates boundary sliding may not be the primary mode of superplastic deformation, particularly since superplastically high strain rate sensitivities were observed long after the grain boundary sliding event had ceased. 5. Results of indentation tests on prestrained S n 38 wt% Pb samples indicate the reason GBS stops suddenly in the indentation tests is probably not linked to a critical strain that is being exceeded. Instead, it is suggested that GBS is merely an artifact of surface conditions and, in particular, the extra degrees of spatial freedom available to surface grains. As these degrees of freedom are consumed, GBS is forced to stop. Likewise, it is postulated that interior grains, due to their lack of such spatial freedom, may never experience significant grain boundary sliding. 6. As an alternative to the grain boundary sliding theories used to explain superplasticity, a core-andmantle model is suggested. This type of model would explain the need for grain boundaries to enhance strain rate sensitivity and promote superplasticity without invoking grain boundary sliding. AcknowledgementslThis work was supported by the Metal-

lurgy, 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 early support by the Exxon Educational Foundation and by the National Science Foundation through the Center for Materials Research at Stanford University. REFERENCES

1. J. W. Edington, K. N. Melton and C. P. Cutler, Prog. Mater. Sci. 21, 61 (1976).

2. M. J. Mayo and W. D. Nix, 8th Int. Conf. Strength of Metals and Alloys (ICSMA-8), Tempere, Finland, 22-26 August, 1988. Submitted. 3. M. F. Doerner and W. D. Nix, J. Mater. Res. 1, 601 (1986). 4. M. J. Mayo and W. D. Nix, Acta metall. Submitted. 5. J. H. Nicholls and P. G, McCormick, Metall. Trans. I, 3469 (1970). 6. R. C. Gifkins, J. Inst. Metals 81, 417 (1952). 7. R. C. Gifkins, Trans. Am. lnsts Min. Engrs 215, 1015 (1959). 8. R. E. Frenkel, O. D. Sherby and J. E. Dorn, Acta metall. 3, 470 (1955). 9. J. B. Baker, B. B. Betty and H. F. Moore, Trans. Am. Inst. Min. Engrs 128, 118 (1938). I0. R. C. Gifkins and K. U. Snowden, Trans. Am. Inst. Min. Engrs 239, 910 (1967). 11. T. Hirokawa, K. Yomogita and K. Honda, Proc. Int. Conf. Strength of Metals and Alloys, Tokyo. 4-8 September, 1967, p. 837. The Japan Institute of Metals

(1968). 12. J. E. Breen and J. Weertman, J. Metal 7, 1230 (1955). 13. D. H. Avery and W. A. Backofen, Trans. Am. Soc. Metall. 58, 551 (1965). 14. H. E. Cline and T. H. Alden, Trans. Am. Inst. Mm. Engrs 239, 710 (1967). 15. S. W. Zehr and W. A. Backofen, Trans. Am. Soc. Metall. 61, 300 (1968). 16. B. P. Kashyap and G. S. Murty, J. Mater. Sci. 18, 2063 '(1983). 17. P. J. Martin and W. A. Backofen, Trans. Am. Soc. Metall. 60, 352 (1967). 18, W. B. Morrison, Trans. Am. Inst. Min. Engrs 242, 2221 (1968). 19. A. E. Ge~kinli, Ph.D. dissertation, Stanford University (1973). 20. R. B. Vastava and T. G. Langdon, Acta metall. 27, 251 (1979). 21. G. Rai and N. J. Grant, Metall. Trans. 14A, 1451 (1983).