2023 Volume 64 Issue 7 Pages 1299-1305
In tensile testing, polycrystalline materials generally fail at relatively low total elongations but under some limited conditions it is possible to achieve exceptionally high elongations of up to and exceeding 400%. This superplastic condition is important scientifically but also it has important uses through the industrial development of superplastic forming operations. This overview traces the historical development of this superplastic effect and it provides a summary of the main characteristics of the superplastic flow process. Conventional thermomechanical processing is not able to produce exceptionally small grain sizes within the submicrometer or nanometer range but this limitation was effectively overcome through processing using severe plastic deformation (SPD). The advantages of SPD processing are discussed and examples are presented. Finally it is demonstrated that the experimental data may be easily and effectively displayed through the construction of deformation mechanism maps based on combinations of stress, grain size and temperature.
Examples of superplastic behavior in a Pb–62% Sn alloy at 413 K showing the variations in elongation at different strain rates.18)
All solids have many properties based on the characteristics associated with their response to thermal, mechanical and other external features. The mechanical properties refer to the response of a material under the action of some form of external load and in practice these properties are exceptionally important in defining and developing a material for use in a wide range of practical applications. In principle, the fundamental mechanical properties may be measured relatively easily by using, for example, an indenter to measure the hardness at a specific point on the solid, but in practice it is more useful to test a machined sample of the material by pulling in tension using a constant strain rate, $\dot{\varepsilon }$, and then measuring the flow stress, σ. From this type of testing, it is found that the stress is related to the strain rate through an expression of the form
| \begin{equation} \sigma = B_{1}\dot{\varepsilon}^{m} \end{equation} | (1) |
Generally, when materials are pulled in tension to ultimate failure the samples break at relatively low total elongations and certainly at elongations that are no higher than ∼100%. Nevertheless, around the turn of the last century there were some isolated reports of even larger tensile elongations that were achieved in a limited number of materials. For example, in 1912 Bengough2) reported an elongation of 163% when testing specimens of brass and later in 1927 Jenkins3) obtained tensile elongations of ∼300% in Cd–Zn and Pb–Sn alloys. Nevertheless, these elongations are not sufficient to denote the occurrence of true superplasticity where, according to the modern definition, it is necessary to achieve a tensile elongation of at least 400%.4)
The birth, and therefore the true advent, of superplasticity may be easily traced to a classic report by Pearson, published in England in 1934, showing a remarkable tensile elongation of ∼1950% in a near-eutectic Bi–Sn alloy and a similarly high elongation of ∼1505% in the tensile testing of a Pb–Sn alloy.5) Figure 1 shows the result for the exceptional Bi–Sn alloy where the tensile sample has been coiled to facilitate easy photography.
An exceptional superplastic elongation of ∼1950% in a Bi–Sn alloy.5)
Although a tensile elongation of ∼1950% was, at that time, easily the highest ductility reported in any metal subjected to tensile testing, nevertheless it is surprising to report that the result attracted little or no attention in western scientific circles and it simply remained as a laboratory curiosity. This was because there was no understanding at that time that superplastic elongations attained in tensile testing provided direct evidence that there was a potential for using these materials for industrial superplastic forming operations. A comprehensive description of the evolution of superplasticity from a laboratory curiosity to use in industry was published recently6) and this provides a convenient supplement to the present report.
Although Pearson’s experiments of 1934 were essentially overlooked in the west, similar investigations were conducted in the Soviet Union with the objective of investigating the potential for achieving exceptionally high tensile elongations using a wide range of metallic alloys. Prominent among this work was the extensive research by Bochvar and Sviderskaya.7) Indeed, it was their use of the Russian word sverkhplastichnost′, meaning “ultrahigh plasticity”, that led directly to the introduction of the word “superplasticity” in Chemical Abstracts in 1947 and subsequently to the use of this term as a general expression to describe the occurrence of these exceptionally high elongations.8) It is noteworthy also that the first book on superplasticity was published in Russian in 19699) and subsequently it was published in 1976 as an English translation titled “Superplasticity of Metals and Alloys”.10)
Much of the Russian research finally received publicity in the west when a review article was published in English describing many of the critical experiments conducted in the Soviet Union from 1943 onwards.11) Surprisingly, this review made no mention of the even earlier research published in 1934 by Pearson.5) Nevertheless, the publicity from this article finally stimulated research in western countries including the establishment of an extensive research facility dedicated to superplastic flow and forming at M.I.T.12) This latter facility provided the nucleus for early attempts to evaluate superplasticity as a tool for use in a viable industrial superplastic forming industry. Thereafter, that industry has now matured to the extent that many thousands of tons of sheet metals are currently subjected annually to superplastic forming in the fabrication of curved components for aerospace, automotive, architectural and a range of other applications.13)
In addition to the industrial applications, the science of superplasticity attracted much attention among academics around the world so that superplasticity laboratories were developed on all continents. It is appropriate, therefore, to now examine the fundamental properties associated with the occurrence of these very high elongations during tensile testing.
Very early experiments demonstrated that the occurrence of superplastic elongations requires two fundamental experimental conditions. First, superplasticity occurs, or at least it is most prevalent, when the testing temperature is reasonably high, typically above ∼0.5 Tm where Tm is the absolute melting temperature of the material. In practice, this is consistent with superplasticity occurring as a thermally-activated deformation process. Second, superplasticity requires the testing of materials having very small grain sizes where typically the average grain size is smaller than ∼10 µm. An early comprehensive review provides a detailed summary of the requirements and the general properties associated with superplasticty.1)
An early problem in conducting experiments on superplastic materials was that there was no clear and well-defined relationship between the applied strain rate in the tensile testing and the measured flow stress. Numerous experiments showed that superplasticity occurred over a limited range of intermediate strain rates, typically covering about two orders of magnitude of strain rate where the strain rate sensitivity was close to ∼0.5, and at higher strain rates there was a region where the value of m was reduced. The situation at lower strain rates, below the superplastic region, was more complex since some early experiments showed an increase in m in this region and other experiments reported a decrease in m: this unusual dichotomy is discussed in detail in the earlier report.1)
A careful examination of the various experimental procedures was undertaken and it revealed the explanation for these inconsistences. In many of the experiments all of the datum points were obtained by using a single sample which was pulled at a fixed strain rate to measure the flow stress and then additional flow stresses were measured at other strain rates without changing the sample. This has the disadvantage that grain growth typically occurs in these materials at elevated temperatures so that the grain size is not constant during these tests. Thus, although this procedure has the advantage that it is quick and rapidly gives an experimental result, the occurrence of concomitant grain growth during the tensile testing produces unacceptable data.
This problem was avoided by undertaking a series of careful experiments on the Zn–22% Al eutectoid alloy where each tensile test was conducted by pulling a different sample to failure using a range of strain rates with all tests conducted at the same testing temperature. By undertaking tests at a constant temperature of 473 K and using specimens with an initial grain size of 2.5 µm, the results showed that the double-logarithmic plot of stress against strain rate followed a sigmoidal or S-shaped configuration with the strain rate sensitivities varying between ∼0.2 at the lower strain rates in region I, ∼0.5 at intermediate strain rates in region II where the material was superplastic and ∼0.2 at even higher strain rates in region III.14) Thus, there are three distinct regions of flow associated with superplastic behavior where the superplastic elongations are recorded in region II and lower elongations are recorded in both regions I and III.
A careful early analysis of many reports showed that the elongations to failure increase with increasing values of m and the relevant plot is shown in Fig. 2 where m is plotted against the elongation to failure, ΔL/Lo%, where ΔL is the total increase in length and Lo is the initial gauge length of the sample;15) additional points are also shown in Fig. 2 for tests conducted on the Zn–22% Al eutectoid alloy16) and the Pb–62% Sn eutectic alloy.17) It is readily evident that all datum points in Fig. 2 scatter about the solid line thereby confirming that superplastic flow requires a high value for the strain rate sensitivity.
It is important to note also that materials may exhibit excellent superplastic properties but the ability to achieve this superplastic effect will depend critically on the precise testing conditions. An example is shown in Fig. 3 where the Pb–62%Sn eutectic alloy was tested at 413 K with a grain size of 11.6 µm and, using strain rates from 2.12 × 10−2 to 2.12 × 10−4 s−1, elongations were recorded from 630% to 7550%.18)
Variation in the elongations to failure with strain rate in Pb–62% Sn at 413 K.18)
In practice, experiments in high temperature creep are conducted under conditions where the sample is subjected to a constant stress and measurements are then taken to record the resultant strain rate over the lifetime of the experiment.19,20) Generally, the sample exhibits an initial region of decreasing strain rate in primary creep, there is often a long and reasonably constant rate of creep in the steady-state or secondary stage and then an increase in the creep rate in the tertiary stage up to final failure. For creep tests of this type, the steady-state strain rate, $\dot{\varepsilon }$, is related to the applied stress, σ, through the following expression which is directly analogous to eq. (1):
| \begin{equation} \dot{\varepsilon} = B_{2}\sigma^{n} \end{equation} | (2) |
The form of eq. (2) follows the conventional format for tests conducted under creep conditions and therefore it follows that superplastic materials exhibit a stress exponent of n ≈ 2 in region II with values of n ≈ 5 in regions I and III. It is often convenient, for any selected material and testing conditions, to display all possible creep mechanisms in the form of a deformation mechanism map in which, for a constant grain size, the normalized stress, σ/G, is plotted against the homologous temperature, T/Tm, where G is the value of the shear modulus and T is the absolute temperature.21) However, there is a significant problem with this type of map because it is not easy to perform the construction without performing extensive computation. However, an alternative, and much simpler, approach is possible by plotting the normalized grain size, d/b, against the normalized stress for experimental data collected at a constant temperature, where d is the grain size and b is the magnitude of the Burgers vector.22)
This approach is used in Fig. 4 where the data are plotted for the superplastic Zn–22% Al eutectoid alloy at a testing temperature of 503 K23) showing the areas in grain size-stress space associated with the superplastic region II, the low and high strain rate regions I and III as measured experimentally and the predicted behavior of the conventional creep mechanisms of Nabarro-Herring24,25) and Coble26) diffusion creep where flow occurs by vacancy diffusion either through the crystalline lattice or along the grain boundaries, respectively: it should be noted that the experiments on the Zn–Al eutectoid alloy were conducted under double-shear conditions and therefore the normalized stress axis in Fig. 4 relates to the value of the shear stress, τ.
Deformation mechanism map for Zn–22% Al at 503 K: the dashed line denotes the lower limiting grain size for the formation of subgrains.23)
Generally, for many metals the rate-controlling flow process in high temperature creep is dislocation climb where the dlslocations climb within the grains and subgrains are formed within the grains during the primary stage of creep. A wide range of experimental data show that the average size of these subgrains, λ, varies inversely with the applied stress through a relationship of the form27)
| \begin{equation} \frac{\lambda}{\mathbf{b}} = B_{3}\left(\frac{\tau}{G}\right)^{-1} \end{equation} | (3) |
An important feature of superplastic flow is that the polycrystalline grains remain essentially equiaxed even after exceptionally high strains. This means that the dominant flow process must be grain boundary sliding (GBS) but some strain must also occur intragranularly to prevent the opening of cracks in the materials.29) The first direct demonstration of the occurrence of intragranular slip during superplastic flow was presented for a superplastic copper alloy where matrix dislocations became trapped in coherent twin boundaries within the grains.30) Later experiments provided support for this intragranular accommodation and also showed that it was oscillatory in nature and made no contribution to the overall strain.31) Other supporting evidence for this intragranular accommodation is also now available32,33) including several very recent reports on a superplastic Al–Mg–Li alloy.34–36)
Making use of the evidence available from the earlier experiments revealing the fundamental characteristics of superplasticity, it is possible to develop a model for GBS for the two separate conditions of superplasticity when the grains are very small and for normal creep conditions when the grains are larger.37) The principles of this dual model are shown in Fig. 5 where (a) corresponds to d > λ where the grains are sufficiently large that subgrains are formed as in normal creep conditions and (b) shows d < λ as in superplasticity where there are no subgrains and therefore no obstacles within the grains.
Schematic illustration of the principles of grain boundary sliding in (a) creep where subgrains are present and (b) superplasticity where there are no subgrains.37)
It is now well-established that in high temperature creep the steady-state creep rate for all flow mechanisms may be expressed through a relationship of the form1,20)
| \begin{equation} \dot{\varepsilon} = \frac{ADG\mathbf{b}}{kT}\left(\frac{\mathbf{b}}{d}\right)^{\boldsymbol{p}}\left(\frac{\sigma}{G}\right)^{\boldsymbol{n}} \end{equation} | (4) |
For the mechanisms depicted schematically in Figs. 5(a) and (b) it is possible to develop the rate equations using the same format as in eq. (4). Thus, in Fig. 5(a), which corresponds to region III in superplastic materials, GBS occurs on the boundary to create a stress concentration at the triple point A, slip is generated in the next grain and these dislocations pile up at the first subgrain boundary at B. For these conditions, the creep rate for GBS, $\dot{\varepsilon }_{\text{gbs}}$, corresponds to the rate of sliding and this may be expressed by a relationship of the form37)
| \begin{equation} \dot{\varepsilon}_{\text{gbs}} = \frac{A_{\text{gbs}}D_{\ell}G\mathbf{b}}{kT}\left(\frac{\mathbf{b}}{d}\right)\left(\frac{\sigma}{G}\right)^{3} \end{equation} | (5) |
Conversely, in Fig. 5(b), which corresponds to true superplastic flow, GBS produces a stress concentration at the triple point C and this leads to slip in the next grain so that the dislocations are able to pass unhindered to the opposite grain boundary and then pile-up and climb into the boundary at D. For these conditions, the superplastic strain rate, $\dot{\varepsilon }_{\text{sp}}$, may be expressed by a relationship of the form37)
| \begin{equation} \dot{\varepsilon}_{\text{sp}} = \frac{A_{\text{sp}}D_{\text{gb}}G\mathbf{b}}{kT}\left(\frac{\mathbf{b}}{d}\right)^{\mathbf{2}}\left(\frac{\sigma}{G}\right)^{\mathbf{2}} \end{equation} | (6) |
Equation (6) is important because it provides a direct measure of the strain rate occurring in these superplastic materials. Furthermore, comprehensive analyses now show that this relationship also provides an excellent description of the mechanical behavior of a number of ultrafine-grained materials.38,39)
Traditionally, it was established in many early experiments that superplastic elongations required polycrystalline grain sizes smaller than ∼10 µm. In practice, these very small grains were achieved using various forms of thermomechanical processing but nevertheless it was not feasible to use these procedures to attain grain sizes below ∼2–4 µm. This situation changed with the introduction of processing using severe plastic deformation (SPD).
In processing by SPD a material is subjected to a high strain but using special equipment and experimental techniques so that there is no significant change in the overall dimensions of the workpiece.40,41) There are now several examples of SPD techniques but the two procedures attracting the most attention are equal-channel angular pressing (ECAP) where a sample, in the form of a bar, is pressed through a die constrained within a channel that is bent through a sharp angle42) and high-pressure torsion (HPT) where the sample, usually but not always in the form of a small disk, is subjected to a high applied pressure and concomitant torsional straining.43) Both of these procedures are effective in producing metals having average grain sizes in the submicrometer or even the nanostructured range.44)
The first recognition that SPD processing may produce very small grains that are suitable for achieving superplastic elongations may be traced to the elegant work of Valiev and co-workers at the Institute of Problems of Superplasticity of Metals, a branch of the Academy of Sciences of the USSR, in Ufa, Russia, and specifically to their classic paper which was published in the Russian literature in 1988.45) In this work, HPT processing was applied to an Al–Cu–Zr alloy to produce a grain size of ∼0.3 µm and it was shown that this ultrafine-grained alloy exhibited excellent superplastic properties. This early research attracted much attention and led to the use of SPD processing in many laboratories around the world where attempts were undertaken to fully document the characteristics of the superplastic properties.
There are two intriguing aspects in the use of SPD processing to achieve submicrometer grain sizes and then testing in tension for superplasticity.46) The first is that the three flow regions I, II and III will be displaced to faster strain rates when the grain size is reduced and this suggests the potential for achieving superplastic elongations at rapid strain rates. The second is that larger elongations should be achieved because at faster rates there will be less time available for the development and interlinkage of any internal cavities. The demonstration of superplasticity at a faster strain rate was first presented in 1997 in research conducted on two ultrafine-grained commercial aluminum alloys and an example is shown in Fig. 6 for an Al–Mg–Li–Zr alloy where, testing at a temperature of 623 K, an elongation of 1180% was achieved without failure when pulling at a strain rate of 10−2 s−1.47) This result constitutes an excellent example of high strain rate superplasticity where the testing strain rate must be at least equal to, or faster than, 10−2 s−1.48)
The first demonstration of high rate superplasticity after SPD processing for an Al–Mg–Li–Zr alloy.47)
The ability to achieve these high elongations at very rapid strain rates opens the possibility of using this procedure in order to increase the speed of component production in industrial superplastic forming operations. The feasibility of this approach was first demonstrated by cutting disks from a bar of an Al–Mg–Sc alloy processed by ECAP, setting in a gas pressure biaxial superplastic forming facility and then blowing into a well-rounded dome under a low gas pressure of 1.0 MPa in a total time of only 60 s.49)
It has been suggested that another possible advantage of using SPD processing to produce ultrafine grain sizes is that it may open the possibility of achieving superplastic flow at room temperature. However, it should be noted that room temperature superplasticity is not unusual because a tensile elongation of 2230% was reported in very early experiments on the room temperature tensile testing of the highly-superplastic Pb–Sn eutectic alloy which was not subjected to SPD processing.50) Nevertheless, it is reasonable to anticipate that the production of ultrafine-grained materials through SPD may facilitate the occurrence of superplasticity in the room temperature testing of other alloys that are generally less superplastic. Examples of this effect are demonstrated by the recent reports of room temperature superplasticity in an ultrafine-grained Mg alloy51) and an Al alloy.52)
Very recent experiments have shown also that SPD processing may be used to produce significant superplastic elongations in high-entropy alloys (HEAs). The first report documented a tensile elongation of more than 600% in a CoCrFeNiMn HEA that was processed by HPT to produce a grain size of ∼10 nm and then tested in tension at 973 K using a strain rate of 1.0 × 10−3 s−1.53) Later experiments produced even higher elongations of up to 2000% using an Al9(CoCrFeNiMn)91 (at%) HEA.54) A recent review provides a comprehensive summary of the mechanical properties and the microstructures that were achieved over the last twenty years in the CoCrFeNiMn HEA.55) The development of superplastcity has also been extended recently to include multi-principal element alloys (MPEAs).56,57)
Finally, it is important to note that, although ECAP and HPT represent the major processing procedures used in the production of ultrafine-grained (UFG) microsstructures, other techniques are available and they may also be used to achieve significant superplastic elongations. For example, tube high-pressure shearing (t-HPS) is a processing procedure in which a tubular sample is subjected to shearing under the imposition of a hydrostatic pressure.58,59) In very recent experiments t-HPS was used to produce a UFG structure in a Pb–40% Sn alloy and an elongation of ∼1870% was achieved when testing in tension at a strain rate of 1.0 × 10−3 s−1 at room temperature.60) This exceptional room temperature superplastivcity was due to the presence of equiaxed grains having a size of the order of one micrometer and the concomitant mixing of the Pb and Sn domains in nearly equal proportions. It is important to note also that this tensile elongation of ∼1870% at room temperature is much higher than the earlier reports of room temperature superplastic elongations of 440% in an Mg alloy51) and close to 500% in an Al alloy,52) respectively.
An important advantage of deformation mechanism mapping is that it provides a broad visual overview of the potential flow mechanisms occurring in the selected material. Furthermore, the maps may be constructed in different forms in terms of stress, temperature and grain size.61) Figure 7 shows examples of maps constructed in grain size-stress space using experimental data from the Zn–22% Al eutectoid alloy initially processed by either (a) ECAP and (b) HPT and with all tensile tests conducted at a temperature of 473 K.61) For both ECAP and HPT, all experimental points are located correctly within the superplastic region II and again the dashed lines show the transitions between region II and region III as given by the onset of subgrain formation within the grains. This type of map provides an excellent visual presentation of the anticipated results that may be attained over a range of stresses and grain sizes.
Deformation mechanism maps for Zn–22% Al at 473 K after processing by (a) ECAP and (b) HPT.61)
Another example is shown in Figs. 8 and 9 for an Al–33% Cu eutectic alloy which was initially tested by HPT as shown in Fig. 8.62) The experimental results were then used effectively to construct a deformation mechanism map as given in Fig. 9.62) Again, this map of normalized grain size against normalised stress provides an excellent representation of the experimental data. In practice, this approach is generally useful for the presentation of flow data for many different materials and it provides a valuable opportunity for presenting an overview of the behavior that may be anticipated over a wide range of experimental conditions.63)
Examples of superplasticity in an Al–33% Cu alloy at 723 K.62)
Deformation mechanism map for Al–33% Cu at 723 K.62)
This work was supported by the European Research Council under ERC Grant Agreement No. 267464-SPDMETALS.
