Superplasticity of Metals Robert Cahn, Paris Laboratoire de Métallurgie Physique, Université Paris-Sud Forming metals that are in a superplastic state offers the promise of obtaining large and regular deformations at reasonable levels of stress. It is a familiar experience that a rod of the stress there rises. In a material which is soda glass, heated in the flame of a Bunsen inherently plastically stable, while deforma burner and pulled by hand, will stretch out tion would tend to become concentrated in into a long, uniform fibre ; the strain can be the local constriction, the local strain rate thousands per cent, without fracture. A would then become much greater than the bar of mild steel, however, when pulled In a strain rate along the rest of the rod. If, tensile machine, will neck down locally and however, m is fairly high, the stress re break after a mean strain of at most some quired to sustain deformation in the con tens per cent. The glass stretches easily striction would rise to a high level and, long and uniformly, the steel with difficulty and before this could happen, the strain would non-uniformly. The glass, but not the steel, become distributed along the unnecked behaves superplastically. Nevertheless, it is (and major) part of the rod. Moreover, if now possible to produce a polycrystalline the strain-hardening exponent, n, is alloy that will mimic hot glass in its substantial, then a rapidly deforming neck mechanical behaviour, which has led to im requires an even higher stress to sustain portant industrial applications in the past continuing deformation than with a non few years. hardening material like glass, for which n = 0. A proper analysis of the triaxial Fig. 1 — The dependence on strain rate, ε, of the flow stress, a, and the exponent, m, for the Mechanics of Plastic Instability stresses in a developing neck is very com eutectic Al-Cu alloy deformed at 520° C, for 3 The key to all superplastic behaviour, in plex and theories abound. One theory con grain sizes. (After Holt D.L. and Backofen glasses and crystalline materials alike, lies cludes that the critical strain, ε', for a neck W.A., Trans. Quart. ASM 59 (1966) 755. in the relationship between plastic strain to develop in a sustained fashion is given rate, ε, and the stress, σ, required to sus by: ε' = 2n/(1-2m) which implies that if m a very low stress, whereas at 20°C (~ 0.36 tain it. The relationships is : σ = Kεm, where reaches 0.5, the material is plastically stable Tm) it is strong and its ductility is small. K and m (≤ 1) are functions of the material (i.e. ε' is infinite) so long as n>0. For the We can now summarise the essential and of the temperature. The exponent m many superplastic alloys now known, m is characteristics of a superplastic alloy: It (which for hot glass is unity) is not normally in the range 0.4—0.7 and n>0. must be (and remain during its deforma constant, but varies with ε, as seen in Fig. tion) very fine-grained ; the index of strain- 1 which shows both the stress and m as Conditions for Superplasticity rate sensitivity, m, must exceed ~0.4, functions of strain rate for an Al-Cu alloy. When a sustained neck develops, frac which in turn is found to Imply strain rates Fig. 1 is, in practice, characteristic of the ture quickly and necessarily follows: for not usually exceeding 10 -2/s ; high values of majority of superplastic alloys. Such plots any ductile material, therefore, the m must be restricted to temperatures well are, by implication, standardised for a fixed avoidance of neck development is a neces above ambient, and at such temperatures strain, ε, as work-hardening will result in sary condition for very large strains to be the flow stress must be very low, whereas the stress required to produce a given attained, although not sufficient in itself. It at ambient temperature, m must be low strain rate, increasing with strain according is also necessary to avoid, in substantial and the flow stress high. to a relationship often adequately describ proportions, the presence of a phase, ed by the equation : σ∞ εn (n < 1). which is much harder than the matrix; if Mechanisms of Superplasticity In most metal forming operations, defor that happens, cavities develop at grain We next turn to the mechanisms which mation is performed under a constant im boundaries and the material breaks at small make superplastic behaviour possible. A posed strain rate. The Implications can be strains, especially at low strains rates, even very large amount of microstructural understood by considering a long rod stret if no neck develops. The close correlation ched at fixed strain rate, ε*. If a small in between m and the strain to fracture in ten stability (incipient neck) develops, the sion, valid for many alloys, is shown in Fig. cross-sectional area is locally reduced and 2. We have not yet considered the in fluence of temperature and grain size. No practically useful superplastic alloy is superplastic at ambient temperature: superplasticity is normally restricted to the temperature range 0.4 Tm-0.7 Tm(Tm = ab solute melting temperature). Fig. 3 shows, for a Zn78 Al22 alloy, the variation of flow stress with temperature for constant ε, for two quite different grain sizes illustrating a fact which has long been familiar to metal lurgists, that fine-grained metals are stronger than coarse when cold, while the Fig. 2 — Strain rate sensitivity, m, vs. elongation reverse is true when hot. When the grain- Fig. 3 — The influence of grain size on the to failure for various metals and two superplastic size of Zn78 Al22 is kept below about 5 µm strength of Zn78Al22 alloy as a function of tem alloys. (After Langdon T.G. Met. Trans. 13A and it is strained at ~ 0.6 T (200°C), it can perature. (After Ball A. and Hutchison M.M. (1982) 698.) be stretched to strains exceeding 500%, at Met. Sci. J. 3 (1969) 1.) 4 stituent processes are diffusional flow (by sheet ; the starting sheet is pressed by gas combined lattice and grain- boundary diffu or fluid pressure, or by isothermal forging, sion), grain-boundary shear and grain into a die, which can be made from inex boundary migration; a measure of grain pensive materials since the pressures invol rotation is also involved. The version of dif ved are modest. This feature is one of the fusional flow in Fig. 4 differs slightly from principal economic advantages of super the older models and gives faster flow. At plastic forming vis-à-vis such processes as high stresses (near the upper limit for high-pressure pressing of non-superplastic superplastic behaviour) dislocation motion steel sheets. Also the accessible strains are intervenes and grains begin to elongate ; at much higher in superplastic forming than in Fig. 4 — Diffusional flow in a grain under ten low temperatures only diffusional flow ope ordinary pressing or deep drawing, so that sion. (After Ashby M.F. and Verrall R. A., 1973.) rates, grains remain equiaxed and also a complex shape can be made in a single rotate bodily (as evidenced by the gradual forming operation with just one die, in research has been done in the past decade disappearance of any initial preferred orien stead of a multiple process with several to address this question, and even though tation of the grains). The balance of pro dies. The technique has proved particularly the relative emphasis to be given to the dif cesses, and thus also the controlling pro useful for complex consumer goods and ferent constituent processes is still subject cess, varies as stress is increased (and as (using titanium alloys) for air frame com to disagreement, a clear picture is begin the temperature changes). ponents. ning to emerge. Practical superplastic alloys have been The following structural observations are Practical Aspects developed only in the past decade ; serious generally valid : For the metallurgist, the principal task is research has been in progress for about (1) Superplastic behaviour requires grains to provide alloys in which the grains not two decades, whereas the first observation which are not only fine, but "equiaxed" (of only are fine to begin with, but resist of the phenomenon dates back to 1920. Of roughly equal diameter in all directions); coarsening at the temperature of optimum the many alloys which have been develo these equiaxed grains remain equiaxed superplasticity. This is done in practice throughout a deformation which may ex ped, only four are in current industrial use ; ceed 1000% (whereas in normal plastic either by designing a duplex microstructure this is no doubt due to the demanding spe deformation, initially equiaxed grains be in which two phases, both equiaxed in cifications required. The greatest possible come progressively elongated, as a single form, are present in roughly equal propor superplastic strain rate is necessary if pro crystal which is plastically stretched). tions, or else by dispersing a small fraction duction times are not to be unreasonably of second phase in very finely distributed long : 10-2/s is probably the lower accep (2) Neighbouring grains are mutually dis form. In the "duplex" case, a majority of table limit (and is still much lower than placed by shear at grain boundaries. the boundaries are interphase ones, which strain rates current in other forming pro (3) Grain boundaries migrate continuously can behave similarly to ordinary mono cesses). during superplastic straining. phase grain boundaries. In the "disperse" A reasonably wide temperature range of (4) Except at the highest stresses (right- case, the fine particles (too small to cause superplastic working is needed, since it is hand side of Fig. 1), only a small proportion serious cavitation and premature fracture) not practicable to hold a large sheet within of the strain is accomplished by dislocation pin migrating boundaries enough to pre narrow temperature limits, and also a wide motion ; the major part of the strain must vent rapid coarsening of the grains, but not range of ε for which m ~ 0.5 is desirable. therefore be due to "diffusional flow". enough to prevent grain-boundary migra To achieve these aims, it helps to have a Diffusional flow is now a well authentica tion altogether — a delicate balancing act. ted mechanism. In Fig. 4 which outlines range of (small) grain sizes, since for each one version of this process for an irregular Such alloys are used industrially to grain-size component there are different ly shaped grain under tension, the arrows manufacture highly complex shapes from optimum values of T and ε. show, schematically, the paths of atomic self-diffusion, biased by the applied stress : vacancies move in counterflow to atoms. Section-K, the intermediate energy nuclear At higher temperatures, diffusion takes physics section Netherlands of the National In place as shown through the lattice, stitute for Nuclear Physics and High-Energy whereas at lower temperatures the grain Physics (NIKHEF), has an opening for a research associate in nuclear theoretical phy boundary is the preferred diffusion path. sics. The rate of this deformation depends on σ2 (so that for constant conditions m should ideally be 0.5), and on 1/d2, where d is the THEORETICAL NUCLEAR PHYSICIST grain diameter. Plainly the strain rate The institute has started operation of its 500 MeV high duty cycle electron achievable depends crucially on the diffu linac which will be used for research in electron scattering and low energy sion rates. pion/muon physics. Much energy has gone into attempting Applicants are expected to have experience in areas of nuclear theory to establish which property is rate which are closely related to the experimental programme. determining in superplastic flow; can The institute works in collaboration with the Foundation for Fundamental didates include volume diffusion, grain Research on Matter (FOM), the Catholic University at Nijmegen (KUN), the boundary diffusion, resistance to grain University of Amsterdam (UvA) and the Free University at Amsterdam boundary shear, or the rate at which local (VU). stress accumulations can be dispersed by The appointment is for a maximum of two years. localised dislocation motion. It is now clear For further information please contact Justus H. Koch that the governing factor is a function of (tel.: (20) - 592 21 71). metal, temperature, grain size and stress. Applications including a career resume and the names of three references One theory which has repeatedly return should be sent to: ed to favour is that advanced by Ashby and NIKHEF, Personeelszaken, P.O. Box 41882, 1009 DB Amsterdam, Verrall in 1973. The essential idea of this is a before 15 February 1983. "grain-switching" mechanism where con
5 The commercial alloys today are: (1) Zn18Al22 (optimum T ~ 250°C), Metallurgy and Superconductivity German F.R.; (2) Al93 5Cu6Zr0.5 (optimum T ~ 460°C), J. Muller and J.L. Jorda, Geneva Britain ; University of Geneva (3) Al90Ca5Zn5 (optimum T ~ 475°C), Canada ; Superconductivity is undoubtedly one of temperature TA, a complicated curve is ob (4) Ti90Al6V4 (optimum T ~ 950°C), USA. the most remarkable phenomena In solid tained as shown in Fig. 1. Tc varies bet The Zn-Al monotectic alloy is an example state physics : an intriguing curiosity at the ween the extremes of 9 K and 21 K and, of a duplex-phase microstructure, whereas time of Kamerlingh Onnes' discovery, the moreover, will not exceed about 15 K the Al-Cu-Zr alloy is a good instance of an superconducting phase transition gradually unless rapidly quenched after the annealing alloy specifically designed for stabilisation acquired fundamental importance as the treatment. by phase dispersion. A number of duplex signature of a possible ground state of con To attain the maximum value, the pre steels have been shown to be superplastic, densed matter. According to present cise homogeneous phase composition is but these have not yet found a use in in knowledge, the occurrence of supercon first obtained by appropriate annealing and dustrial applications. ductivity in electronically conducting sys quenching, and this is followed by a low Anything which hinders dislocation tems is rather the rule than the exception, temperature annealing (branch I b in Fig. creep without disturbing diffusional flow and the number of superconducting ele 1), performed in a region where segrega (e.g. dissolving tungsten in nickel to lower ments, alloys and compounds far out tion is avoided, so ensuring an improve the stacking-fault energy and thereby weighs that of, e.g., magnetically ordered ment in the long range order parameter. hinder dislocation climb, needed if creep is substances. The main reason why Tc is so dependent to continue) will enhance superplastic for- The physics of superconductivity con upon the detailed heat treatment processes mability. Development of an industrially centrates on understanding the subtle elec is that the peritectically formed A 15 com usable family of superplastic steels and tron interactions responsible for the pheno pound has a strongly temperature-depen- superalloys would be a very desirable prize, menon, the pairing in momentum space. dent phase limit at the Ga rich side as can as also would, more generally, the perfec However, this aspect is only part of the be seen in Fig. 2. The stoichiometric con tion of a stably super-finegrained family of story. The remaining, no less important centration of 25% Ga, a prerequisite for a light alloys (d ~ 0.5 µm) which might offer part, is connected with applications and high Tc is confined to a narrow spike near practical superplastic strain rates approa the prospecting of yet unknown alloy sys the eutectic temperature of 1740°C. ching 1/s. For this last objective, rapid tems — physical metallurgy. The more intriguing niobium-germanium solidification processing (splat-quenching, Superconducting materials, especially system is governed by a topologically see also Cotterill, page 8), may prove to be those considered for the production of high similar phase diagram around the super the key. magnetic fields, are characterized by their conducting A15 phase. However, the limit The above account has not touched at all critical surface in a three dimensional sys falls short of the composition Nb3Ge by 2 upon a second form of superplasticity, tem defined by temperature, external ma atomic percent even at the eutectic tempe which is linked with the building up of a gnetic field and transport current density. rature. Moreover, the tendency towards system of microstructural internal stresses The critical temperature and critical fields segregation below TE is so strong that the by thermally cycling an alloy during trans are, for the most part, properties of the strategy "optimum quench plus ordering formation, either through a phase transi composition within a homogeneous phase anneal" does not work at all here. Yet tion or else by exploiting highly anisotropic of the material (the latter may be an suitably prepared, Nb3Ge holds the record thermal expansion in individual grains, as in equilibrium phase or a metastable one) ; the for T.C It is then clear that the constraints of α-uranium. This phenomenon has had ma microstructure has not much influence three-dimensional equilibrium thermodyna jor implications for nuclear power (less, because the superconducting coherence mics have to be overcome right from the now that metallic uranium is being phased length is usually much smaller than dimen beginning of material synthesis. This can out of use). Attempts have been made, un sions such as grain size. On the other hand, be done by growing films by sputtering or successful up to now, to adapt this form of the critical current density Jc(H, T) physical or chemical vapour deposition. superplasticity for industrial use. depends — even crucially — on micro- The success of these techniques relies structural features such as grain size, BIBLIOGRAPHY dislocation networks, precipitates etc. 1. Edington J.W., Melton K.N. and Cutler C.P., There are thus at least two kinds of "Superplasticity", Prog. Mat. Sci. 21 (1976) "metallurgy" which come into play, the 61-170. first dealing with problems of phase stabili 2. Sherby O.D., Caligiuri R.A., Kayali E.S. and ty and the second focussing on defect White R.A., "Fundamentals of Superplasticity", structures. in Advances in Metal Processing, eds. J.J. Burke, et al., (Plenum Press) 1981 ; pp 133-172. 3. "Symposium on the Mechanical, Microstruc Phase Diagrams & Superconductivity tural and Fracture Processes in Superplasticity", Many superconductors — particularly Metallurgical Trans. 13A (1982) 689-744. the most interesting, those with a high 4. Padmanabhan K.A. and Davies G.J., Super critical temperature Tc — show important plasticity (Springer) 1980. variations of their properties with the 5. Ghosh A.K., "Tensile Instability and Necking method of preparation and with heat treat in Materials with Strain Hardening and Strain- ment, and the first step in understanding or Rate Hardening", Acta Metallurgica 25 (1977) predicting such variations is to examine the 1413-1424. details of their alloy phase diagrams. The 6. Ashby M.F. and Verrall R.A., "Diffusion-ac commodated Flow and Superplasticity", Acta niobium-gallium system which exhibits an Metallurgica 21 (1973) 149-163. A 15-type structure when the composition 7. Cheese R. and Cantor B., "Superplasticity in is near Nb3Ga, illustrates such behaviour. If Fig. 1 — The superconducting critical tempera Splat-Quenched Pb-Sn Eutectic", Mat. Sci. and one measures TC for one and the same ture Tc of the niobium-gallium A 15 phase vs. the Eng. 45 (1980) 83-93. specimen as a function of the annealing annealing temperature TA.
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