MECHANICAL PROPERTIES OF MATERIALS AT LOW TEMPERATURES D. A. WIGLEY Engineering Laboratories, The University, Southampton, UK Received 11 August 1967
I N a review paper of this nature it is impossible to cover adequately all aspects of such a large subject as the mechanical properties of materials at low temperatures, and any choice of topics must inevitably leave some areas completely uncovered and others barely indicated. The selection of topics has been made on personal preference but it is hoped that this paper will convey some idea of the present position in the major branches of this subject. It has been said that in the early days of low temperature physics, the most important person in the laboratory was the glass blower; certainly, to judge from diagrams of Kammerlingh Onnes' original apparatus, he must have been kept very busy. Even today it is probable that there are more glass dewars than metal ones used in the low temperature laboratories of this country. However, glass has its limitations, and as the scope of low temperature physics grew so did the techniques of cryostat construction. Good thermal conductors like copper and brass, and poor thermal conductors such as german silver, inconnel, and 18/8 stainless steel were found to be reliable materials for this purpose. The first fundamental investigation of the strength and plasticity of metals at very low temperatures was the work of Polany, Meissner, and Smidt' in the early 1930s on cadmium and zinc single crystals. At higher temperatures and on a more practical level, rule of thumb criteria for selection of materials enabled the successful construction and operation of large scale liquid air plants without serious trouble from brittle fracture. It was the introduction of all-welded Liberty ships in World War 2 that showed how serious a problem cold brittleness can be, even at temperatures close to ambient. From the large amount of research which followed these failures we now have a much clearer understanding of the nature of the tough-brittle transition in metals and also a new area of research known as fracture toughness. The need for tonnage quantities of liquid hydrogen for rocketry and nuclear uses which arose in the early 1950s triggered off an avalanche of work on mechanical properties at 20°K and below, especially in the USA and USSR. In retrospect, I think it fair to say that some of this data is now of questionable value, but in view of the C R Y O G E N I C S • F E B R U A R Y 1968
urgency of the project any data was considered better than none. In the last 5-10 years, the fundamental aspects of this work have become more prominent and there is now a reasonable framework on which to base the experimental results. As in many fields of research, the f.c.c. metals were tackled first and then the b.c.c. metals; the latter proving somewhat more intractable due to the strong dependence of their properties on very small levels of impurities. * Finally, there is increasing use of plastics and composites for structural and other purposes at low temperatures. The high strength/weight and strength/thermal conductivity ratios of many plastics make them attractive propositions, while in addition to these two factors composites can often offer superior fracture toughness characteristics because of their tendency to fracture progressively. Metals When a metal is stressed, the strain produced is initially elastic and there is a linear relationship between stress and strain, the constant of proportionality being the relevent elastic modulus. When the temperature is lowered, the elastic modulus increases by approximately 0-03 %/°K, which means that its value at 4°K is about 10% higher than that at room temperature.^ The elastic strain developed by a metal within its elastic limit ranges from about 10"^% for some soft single crystals to about 5 % for some whiskers. Further increases in stress result in plastic deformation and modern theories of solids explain these deformation processes in terms of the motion and interactions of dislocations. As these processes are temperature dependent we might therefore expect a decrease in temperature to change the yield and deformation properties of metals. Face centred cubic metals Figure 1 shows-the behaviour of single crystals of copper and nickel oriented for single slip—i.e. oriented in such a way that, out of all the possible operative slip systems, only one, initially, will have the resolved shear stress greater than the critical value required for slip. Consider
(4) The onset of stage 2 is raised to higher stresses, and (5) The strain hardening rate in stage 3 is increased.
These last two factors follow from the fact that cross slip in f e e . metals is a thermally activated process and therefore occurs more readily at higher temperatures. The curves for copper^ differ slightly from those for nickel in that there is almost no easy glide region and also that at 4-2°K stage 2 lasts all the way to fracture indicating that there are no recovery mechanisms operating. Similar three stage strain hardening can, under favourable circumstances, be observed for single crystals of f c.c, h.c.p., and b.c.c. metals. In polycrystalline metals there is no easy glide region and multiple slip is observed immediately after yielding because of the constraints imposed on any one grain by its neighbours. Figure 2 shows the behaviour of annealed polycrystalline aluminium (99-996 %AI).5 These are simple engineering stress-strain curves for tensile tests at 300, 78, and 4°K; the following points may be noted:
Figure 1. Shear stress-shear strain curves for nickel and copper single crystals
first the results for nickel.^ Stage 1 is the easy glide region where there is just one slip system operative and the strain hardening rate (slope of curve) is low. Stage 2 starts when the material has work hardened sufficiently for the critical resolved shear stress to be exceeded on another slip system. The strain hardening rate now increases considerably because interactions occur between dislocations gliding on different slip systems. These interactions produce sessile or immobile dislocations and the passage of subsequent dislocations down these glide plaines is made more difficult. Finally in stage 3 the strain rate decreases because recovery mechanisms such as cross slip allow some dislocations to overcome these barriers to their motion. The effect of temperature on these stages for nickel can be summarized thus; as the temperature is decreased, (1) The yield stress rises slightly (2) Stage 1 is increased in extent but the strain hardening rate is not affected (3) The strain hardening rate of stage 2 is unchanged
• \ 78°K
(1) The elongation at fracture rises from —22% at 300°Kto~75%at4°K (2) The capability of the material to strain harden increases considerably as the temperature is lowered. Thus, whereas at 300°K the ultimate tensile stress (-^10 kg/mm^) is ~ ' 2 5 % greater than its yield stress, at 4°K the UTS of ~ 3 0 kg/mm^ is ~300 % of the yield stress '^lO kg/mm^, and (3) The high value of UTS reached at 4°K approaches the values achieved by high strength aluminium alloys and thus pure metals have a much greater capacity for strain hardening than alloys. The original 4°K curve showed a number of serrations, or load drops, which were probably caused in this case by localized temperature increases in the specimen due to its low specific heat. In copper, however, similar load drops have been found to be a result of mechanical twinning,* an idea which was initially received with hostility because of the previous absence of twinning in f e e . metals. Two points may be noted in summary of the main features of the effect of temperature on the mechanical properties of f e e . metals as shown in Figure 3.'' First, where the yield stress and tensile stress (UTS) are plotted as a function of temperature for the annealed metal the curves can be seen to diverge greatly as the temperature is decreased. This accounts for the extreme reliability of f e e . metals at low temperatures; they are able to accommodate a large amount of plastic deformation before fracture which, when it occurs, is always ductile in pure f e e metals. The other point to be noted is the vast difference in yield stresses of the annealed and cold worked metal. If however, one wished to take full advantage of this increase in yield stress, the exact degree of cold work must be known. This question of the necessity to know accurately the prehistory of a sample is of the greatest importance and this topic will be reconsidered later.
Body centred cubic metals
The b.c.c. lattice structure is often associated with brittle behaviour at low temperatures but there is in fact no such simple relationship between crystal structure and brittle fracture. Potassium and y? brass remain ductile at
Figure 2. Stress-strain curves for polycrystalline aluminium at various temperatures
C R Y O G E N I C S • F E B R U A R Y 1968
~ 5 0 kg/mm^. More recent results' on very pure metal lowered this value to •~2 kg/mm^. The general effects of a decrease in temperature on the mechanical properties of zone refined molybdenum single crystals are shown in Figure 4."> The points to notice are:
(1) The large increase in yield stress and flow stress with decrease in temperature (2) The strain hardening rate is relatively temperature insensitive down to '~77°K, but it increases between 77 and 4°K, and (3) There is a reasonable amount of ductility even at 4°K. The load drops at this temperature are due to the formation of mechanical twins. The occurrence of twinning at 4°K is in fact so common as to be the limiting factor in the amount of plastic deformation observable. Its onset may often be delayed by small amounts of prestraining at room temperature.
:£ 40 Annealed
In Figure 5 a similar series of stress-strain curves'' are shown for polycrystalline Armco iron and as before the yield stress increases strongly as the temperature is lowered. This large increase in the yield stress of b.c.c. metals at low temperatures is thought to be due to the existence of strong Peierls-Nabarro forces in these metals. At temperatures below about 200°K iron does not show any strain hardening at all; yield is followed
Tensile Yield I
_L I 100 200 Temperature < "K
/4-2°K Figure 3. Temperature dependence of tiie yield and tensile strength of OHFC copper
4°K; lithium and sodium, although complicated by the occurence of martensitic phase transformations at 110 and 51°K, still remain ductile at liquid helium temperatures. In the case of iron and the refractory metals molybdenum, tungsten, tantalum, and niobium the picture is less clear. The details of the yield and flow phenomena, the factors affecting the transition between ductile and brittle fracture, and the role of twinning in these processes have been studied in great detail over the last 5-10 years. The field is still in a considerable state of flux and it is quite possible that some of the points raised are out of date. Much of the change has arisen because in the last few years it has become possible to grow very much purer single crystals of the refractory metals. It has been found that much of their brittle nature is due to the effect of interstitial impurities—especially carbon, nitrogen, oxygen, and hydrogen. Tungsten, which is usually considered as a brittle metal, has recently been shown* to be ductile at 20°K if sufficiently pure and free from surface cracks. Similarly the high yield strength obtained with the lower purity metals appear, in the light of recent results on high purity metal, to have been due to impurity pinning. To give a specific example: 5-10 years ago the yield stress of niobium at room temperature was typically C R Y O G E N I C S • F E B R U A R Y 196B
Figure 4. Stress-strain curves for molybdenum single crystals at various temperatures
Figure 7. Tensile elongation of cold rolled SAE 1010 and Izod impact energy for normalized SAE 1030 plain carbon steels
Brittle fracture is thus a common occurrence in b.c.c. metals, especially in the presence of interstitial impurities; it is never observed in pure f e e . metals although it can occur in certain f.c.c. alloys. The hexagonal close packed metals occupy an intermediate position; zinc undergoes a transition to brittle behaviour in tension, zirconium and pure titanium remain ductile.
Figure 5. Stress-strain curves for polycrystalline Armco iron at various temperatures
Figure 6. Ductility and impact energy as a function of temperature for a material which undergoes a ductilebrittle transition
immediately by local necking of the specimen. Consequently the ductility decreases as the temperature is lowered, a direct contrast to the behaviour of the f e e . metals where ductility usually increases at low temperatures. Some workers have reported observing a few per cent ductility in iron at 4°K, but more often negligible ductility is found, although fracture often occurs by a ductile mechanism. There is a further point on which there is, as yet, no definite agreement, and that is the role of twinning in brittle fracture. Both phenomena occur frequently in b.c.c. metals at low temperatures. There is a strong school of thought which says that twinning nucleates brittle fracture, whereas others hold that twins are nucleated by the stress waves set up by fracture.
Ferrous alloys From a practical point of view the most important class of materials which show a ductile-brittle transition are steels, and it seems appropriate to consider their behaviour in some detail. If the elongation measured at fracture in a standard tensile test is plotted as a function of temperature for a material which undergoes a tough/brittle transition, the ductility is found to fall off steeply between temperatures Tz and Ti as shown in Figure 6. If the same material is tested under impact loading conditions,! the ductile/ brittle transition occurs between the higher temperatures T^ and T3. Returning to the curves shown in the figure, one can say that above TA the material is ductile under all normally encountered strain rates, and below T\ it is brittle. Between T2 and T^ the material will be ductile if tested at slow strain rates under 'uniaxial stress conditions, but will be brittle if subjected to triaxial stresses at high loading rates. In Figure 7 these two curves'' are shown for plain carbon steels and it can be seen how pronounced these transitions can become. In this case the impact transition is spread over a larger temperature range than the ductility transition. These steels are ferretic, i.e. they have a b.c.c. crystal structure. In Figure 8 the tensile strength| of a similar plain-carbon steel is shown as a function of t The impact energy of a material is measured by fracturing a notched specimen by a blow from a pendulum hammer, the difference between initial and fmal pendulum heights giving a measure of the energy absorbed in fracture. By the rapid transfer of precooled specimens to the anvil just before impact such tests may be carried out down to liquid nitrogen temperatures with a reasonable degree of reliability. For lower temperatures much more sophisticated apparatus is needed, although attempts have been made at transferring specimens directly from liquid hydrogen to a standard impact testing machine. % Tensile strength, or ultimate tensile strength (UTS), being the maximum stress attained before necking commences. C R Y O G E N I C S • F E B R U A R Y 1968
temperature.'' It can be seen that at ~'70°K these curves run together. Thus as soon as the metal yields it either fails in a completely brittle manner or it necks down rapidly to form a ductile type fracture but after negligible elongation. This latter case illustrates an interesting difference between the metallurgist and the engineer. The former would class this as ductile failure because fracture occurred by a ductile mechanism, the latter would, however, describe the metal as brittle because it showed negligible general deformation before failure. In order to produce reliable steels for very low temperature applications the steel must be retained in the austenitic f.c.c. phase which is normally stable only above 723°C. This stabilization is achieved by alloying with suitable amounts of nickel, chromium, and other elements. Figure 9 shows the temperature dependence of the UTS and yield strength of an 18-20% chromium, 8-10% nickel stainless steel AISI type 304.'' Considering first the annealed material, it can be seen that both the yield and ultimate tensile stresses rise with decrease in temperature, but that the UTS rises more rapidly. This ensures that the metal is able to absorb a large amount of plastic deformation before fracture. The second feature to be noted is the large rise in yield stress of the cold drawn metal compared to the annealed. This increase can obviously be very useful in cases where high stresses have to be supported elastically. The difficulty in benefiting from this effect of cold drawing usually reduces to two factors: (1) being able to find a supplier to produce it in the cold drawn state, and/or (2) knowing the amount of cold work received by the metal and hence its increase in yield stress. In Figure 10 the tensile strength and impact energy of a similar, fully stabilized, austentic stainless steel are shown as a function of temperature.'' Although both of these properties decrease in magnitude at lower temperatures their very high values at 4°K make them ideal for use at these temperatures. If the amounts of chromium
Cold drawn \ ^ ( T o UTS: 210 000 Ib/in2)
^ s ^
200 \ ^* ,^^
(To UTS: 210 000 ib/in2)
Tensile ---Y-'d ,
and nickel are reduced the steel is no longer fully austentic and spontaneous or stress induced martensitic transformations occur on cooling below about 77°K. The presence of martensite increases the yield and tensile strengths but considerably decreases the percentage
, 200 °K
Figure 9. Temperature dependence of the yield and tensile strengtiis of AISI 304 stainless steel
Figure 8. Temperature dependence of the yield and tensile strengths of cold rolled Alsi SAE1020 steel. C R Y O G E N I C S - F E B R U A R Y 1968
100 200 Temperature, "K Figure 10. Tensile elongation and Charpy K Impact energy of AISI 316 stainless steel
elongation and impact strength, thus care must be taken if these semi-stabilized steels are used. Precipitation liardened and other high strength alloys We saw earlier that strain hardening in pure metals occurred because the barriers produced by dislocation interactions impeded the movement of other dislocations. In precipitation hardened metals, dislocation movement is hindered by the precipitates and the sessile dislocation loops which form around them. An important class of
100 Temperature .
Figure 11. Effect of welding on the ultimate tensile strength of a TI-13V-11Cr-3AI alloy 400 • 0 - - Annealed Age hardened 300
0 100 200 Temperature. "K
Figure 12. Tensile strength and notched-unnotched strength ratio of 18Ni-8Co-5Mo maraging steel
these materials are the aluminium alloys which are of particular interest for use in aircraft and rocket structures .where their strength/weight ratio is important. The American Aluminium Association 2 000 series alloys have copper as the main alloy constituent and are heat treated and age hardened to produce a CuAlj intermetallic precipitate. They have high tensile strengths, typically -^80 000 Ib/in^, and are fairly ductile at low temperature.'^ However the aged structure is destroyed during welding, and without post-weld heat treatment, which is not usually possible with large structures, this is a serious limitation to their use. The 5 000 series alloys have magnesium as the major alloying element and strength is developed not by age hardening but by a combination of cold work and solid solution hardening. The tensile strengths achieved by these alloys arp lower than those for the 2 000 series alloys, but tensile elongations are higher. They are not so notch sensitive and welding does not seriously reduce their strength and ductility. The limitations set by the weldability of a material or by the loss of its desirable properties during welding are often the critical factors in deciding whether or not a material is suitable for a particular application. In general all precipitation hardened alloys will suffer from this limitation if post weld heat treatment is not possible. In high strength titanium alloys a similar loss of strength occurs during welding. The alloy shown in Figure 11'^ is stabilized in the b.c.c. y?-phase to give it its high strength, and the loss of strength and ductility after welding is probably due to the growth of very large grains and grain boundary impurity segregation in the weld metal. If however the material does not have to be welded, its high strength makes it an attractive material for use at low temperatures. To conclude this section on high strength materials, the behaviour of a typical maraging steel, shown in Figure 12,'^ is considered. This is a low carbon, high alloy steel which is martensitic and which is age hardened to produce an intermetallic precipitate and give the material its high strength. Its low ductility, about 4% elongation in the hardened condition, restricts its general use but its high yield strength and easy machinability make it an ideal material for specialized components such as the grips of a tensile cryostat. Its main weakness is its relatively low value of notched/ unnotched tensile strength. The phenomenon of notch embrittlement is a serious problem at low temperatures and is one aspect of the field of fracture toughness which is still receiving much attention. In a paper such as this it is only possible to indicate briefly one or two aspects of this problem. Fracture toughness If an ideally sharp symmetrical notch is placed in a tensile specimen and a load is applied, the material in the notched region will be in a state of triaxial tension. Plastic deformation in the notched region will be constrained by the material above and below the notch, and the true tensile stress (tensile load/notched sectional area) will be about three times as high as that for an unnotched specimen. The constraint to plastic deformation introduced by the notch will also encourage the C R Y O G E N I C S • F E B R U A R Y 1968
transition from ductile to brittle fracture in those metals susceptible to such a transition. Figure 13 illustrates the Orowan criterion for brittle fracture. Plastic flow and brittle fracture are assumed to be independent processes each with its own characteristic tensile stresses Y and F, respectively. The flow stress Y increases rapidly with decrease in temperature while the fracture stress F is assumed to be relatively temj^erature insensitive. Then at high temperatures where F > 3 y the material is simply ductile; at low temperatures where 7^ < K it is simply brittle. At intermediate temperatures where Y < F < 3 K the material is notch brittle, i.e. ductile in plain tensile tests but brittle in notch tests with large plastic constraint factors. The sharper the tip of tVie notch the higher will be the stress concentration factor and the more brittle will the material appear. As there is a limit to the sharpness of a notch which can be machined into a specimen, fatigue cracks are often used to reproduce the most embrittling conditions likely to be met in service. Many years ago Griffith" showed that a cleavage crack in a brittle material propagates spontaneously when the elastic strain energy released by the extension of the crack equals the surface energy gained by such an extension. Orowan''' has shown that a similar criterion can exist for non-ideally brittle materials if the energy necessary to produce plastic deformation at the crack tip is added to the true surface energy. As this plastic energy term in metals is often very much larger than the true surface energy the Orowan-Griffith criterion for the fracture stress reduces to
however, there has been a move towards adoption of a notched tensile/unnotched yield strength criterion, the significance of which is illustrated in Figure 14." If the material from which specimen A is made has a value of the notched strength/unnotched yield ratio which is less than unity, then the specimen will fracture at the notch before it yields in the straight portion. The greater the value of this ratio the more plastic deformation that occurs before fracture and the tougher the material. A more realistic example is shown in case B, which represents a smooth tensile specimen with a scratch across its surface. If the depth of the scratch is 10% of the thickness of the sheet then a design criterion of notched yield/unnotched strength ratio exceeding 1-1 would allow some protection against failure in service due to scratching.
Temperature Figure 13. The Orowan criterion for brittle fracture
E is Youngs modulus p is the work of plastic deformation at the crack tip c is the crack length The resistance of a material to the propagation of a crack is known as its fracture toughness; the greater the toughness, the larger the crack that the material can tolerate without fracture when loaded to any given stress. It can be seen that the fracture toughness is basically associated with the amount of plastic work which accompanies crack growth. This work depends on tlie magnitudes of the stresses and strains developed in the material and it is found that those metallurgical factors which increase the yield and tensile stresses also decrease the operative strains. Thus, for example, precipitation hardening treatments which raise the yield stress also decrease the amount of plastic deformation before fracture by the production of internal cavities resulting from interfacial decohesion. Thus, increase in fracture toughness and increase in yield strength are incompatible and, as we saw earlier with the aluminium alloys, one is often forced to choose a lower strength alloy because of its greater fracture toughness. The usual measure of notch toughness of a material is the ratio. Ultimate tensile strength of notched material Ultimate tensile strength of unnotched material If the value of this ratio falls much below ~0-7 the material is considered excessively notch brittle. Recently, C R Y O G E N I C S • F E B R U A R Y 1968
s / Scratch
J \ Notched and smooth tensile specimens in series
/ V Scratched tensile specimen
Figure 14. Significance of fhe notched tensile/unnotched yield strength criterion
Polymers These materials, often known loosely as plastics, are finding an increasing number of usesinHow temperature equipment. Their properties often differ considerably from those of metals and so it is appropriate to consider them from a more fundamental position. Polymers consist of long chains of molecules which are made up of relatively simple molecular units or mers. These chains are often arranged at random and in a tangled fashion throughout the material. If the material is thermo-plastic and there is little or no cross linking between adjacent chains, a considerable amount of yielding can occur by the uncoiling and straightening of these molecular chains until they are oriented parallel to the applied stress. At high enough temperatures, and this often includes room temperature, entire segments of the molecular chain are in thermal motion about their equilibrium positions and this thermal motion makes it very easy for the molecular chains to slide over each other during deformation. As the temperature is lowered this thermal motion decreases, the Van der Waals forces between adjacent chains become stronger and yield by molecular straightening becomes more difficult. This effect is most pronounced in a temperature range of about 10 degK known as the 'glass transition temperature' which is usually between ^ and f of its melting point. Below this temperature the polymers are organic glasses and behave, in practically every respect, like ordinary inorganic glass; for example, they are almost completely brittle and show the same type of relation between crack size and strength as found by Griffith for ordinary glass. This is also the temperature range in which the thermal contraction of the material is largest showing that the increased rigidity is due primarily to an increase in the Van der Waals forces and a consequent decrease in the effective distance between adjacent molecular chains. Certain polymers, in particular those with a very regular arrangement of side groups on their long chain molecules, can show quite a high degree of crystallinity at temperatures above the glass transition. In these crystalline polymers parts of the molecular chains lie in disordered amorphous regions and other parts lie in crystalline regions. Tensile rigidity is provided by the crystalline regions and the ability to undergo appreciable extension is provided by the rubbery amorphous regions together with a process which involves changes in the crystalline ordering. The crystalline regions consist of a regular parallel arrangement of molecular chains which are folded back and forth through the crystal. When a tensile stress is applied these chains unfold progressively and align themselves along the tensile axis. The macroscopic effect of this process is illustrated in Figure 15 which is for polyvinyl chloride at room temperature. The yield drop is due to the instability in deformation produced by the unfolding of these crystalline regions and the production of a neck in the specimen. Enough molecular orientation hardening occurs in the necked region to raise the flow stress above the yield stress of the rest of the specimen and the necked region starts to propagate or 'draw' through the specimen. This process of cold drawing is in many ways analogous to the propagation of Liiders bands through ferrous metals. Once the drawn region has passed completely through 10
the specimen the molecular chains are left aligned roughly along the specimen axis. The strain hardening rate now increases considerably and the degree of molecular orientation increases to quite high values. The resultant structure can, in some respects, be considered as recrystallization parallel to the tensile axis. Fracture when it occurs is often highly fibrous, a further indication of the high degree of molecular orientation. If there is a flaw in the specimen, as at the shoulder of specimen 2 or at the centre of specimen 3, slow crack growth occurs initially to enlarge the flaw to its critical size. Fracture of specimen 3 occurred finally in a brittle manner, while in specimen 2 it transformed to fibrous before the critical crack length was reached. If similar tensile tests are now carried out at 77°K, which is belo\y the glass transition temperature for pvc, brittle fracture occurs with no previous plastic deformation (Figure 16). The point of fracture is determined by the location of the largest crack or notch in the specimen and in the case of these specimens always occurred at the shoulder unless a notch was deliberately placed in the central region. In this brittle condition, polymers have very low impact strengths. Comparison between the fracture stresses indicated in these two figures shows a three-fold increase in the tensile strength at 77°K compared to that at room temperature. Results from other plastics show similar increases at low temperatures of between 1-5 and 8 times that at room temperature. The elastic moduli of polymers also increase considerably as the temperature is decreased, the majority of the increase occuring during the glass transition range. For example, the Youngs modulus of PVC at 77°K was twice that at 290°K while the modulus of PTFE at 20°K is 20 times its room temperature value. As a result of their disordered structure plastics have very low thermal conductivities at low temperatures. This fact taken together with the relatively high strengths they achieve gives many plastics higher values of the ratio yield stress/thermal conductivity than metals. In
PVC AT ROOM TEMPERATURE lo = 25mm < =8rT
100 Strain y
Figure 15. Stress-strain curve for PVC at room temperature CRYOGENICS • FEBRUARY 1968
unless the compressive load can be increased to compensate for the stress relaxation of the PTFE. In order to overcome this difficulty, composites of PTFE and glass fibre have been produced which do not suffer from this drawback of cold flow.i' The glass fibre improves the tensile and compressive properties of the material while the PTFE gives the composite sufficient ductility to accommodate plastically the strains developed in the material.
2 Sfrain ^ %
Figure 16. Stress-strain curve for pvc at 77°K
applications where their low impact strengths are not a serious limitation, plastics can therefore replace metals as load bearing thermal insulators. The main limitations on the use of plastics at very low temperatures is their very small or negligible ductility. At 4°K only Mylar and Teflon (PTFE, polytetrafluoroethylene) show measurable ductility in tensile tests,'^ -^1 % in the case of PTFE, but even this small amount has proved extremely useful for applications such as valve seats and bearings. It is however unfortunate that another low temperature property of polymers limits severly the use of PTFE; that is its very large contraction on cooling. Typical values for the linear thermal contraction between 290 and 4°K for common materials a r e : " stainless steel, 3 x 10~^; nylon, 14 X 10-^ PTFE, 21 X 10-3. It can be seen from these figures that there is a difficult compatibility problem in the use of plastics, especially PTFE, in conjunction with metals as during cooling the plastic will either contract on to or away from the metal. One final difficulty with polymers which are not in their completely brittle state is the phenomenon of stress relaxation. If during the room temperature tensile test on pvc the crosshead had been stopped, the stress would have relaxed to a value 30-40% lower than the value at the instant the test was stopped. This is due to the ability of the long chain molecules to slide over each other and rearrange themselves so as to relieve the internal stresses. In a similar manner, if a cold drawn sample is unloaded and heated slightly a considerable amount of the deformation is recovered by molecular rearrangement. As PTFE is still ductile at 4°K, it too is capable of stress relaxation and this limits its use for sealing purposes C R Y O G E N I C S • F E B R U A R Y 1968
Composites Thus we have reached the final class of materials to be considered in this paper. In the case of the PTFE/glass fibre composite the matrix was ductile, even if only slightly so. In most common composites with glass or fabric reinforcements and epoxy, phenolic, or polyester resin matrices, both components are brittle at low temperatures. However, these composites are able to absorb a considerable amount of energy before fracture in an impact test. It would be interesting to investigate this point. It has been shown that once fracture was nucleated in homogeneous brittle materials it became self sustaining and propagated very rapidly through the whole of the sample. In the case of a composite, a crack nucleated in one fibre spreads rapidly through it and then slows down as it passes through the matrix. A separate crack has then to be nucleated in each successive fibre in order that the fracture can proceed. In this way the total energy absorbed before fracture is more nearly characteristic of the sum of the energies of the compound fibres than the energy of a solid piece of equivalent cross section. Thus although these composites are not ductile, their ability to fracture progressively is for many purposes an adequate substitute for ductility. Tensile strengths of glass fibre reinforced composites typically increase by 50-100% on cooling from room temperature to 4°K. and attain values of the order 75-100 000 Ib/in2.i9 These are by any standard quite high, and when one also realises that these materials have low densities it will be seen that high strength/weight ratios can be achieved. This is one reason why these composites are being evaluated for the construction of rocket fuel tanks and structural members. Glass fibres and resins have inherently low thermal conductivities and when they are fabricated together the resultant composite has an even lower thermal conductivity. Couple this characteristic to the high strength/ weight ratio and it can be seen that very high ratios of strength/thermal conductivity are possible. In Table 1 the TABLE 1 _ », ay Material
Stainless steel, type 35 304 annealed Stainless steel, type 304 cold drawn to 150 210 000lb/in= Titanium alloy, 130 13V-11Cr-3AI 2 PTFE 10 Nylon Epoxy-glass fibre 75 laminate
ReferM \K/Rel ences
45 3 2-8 3-5
2-89 90 0-66 1-9 3-6 11^2 21-4
7,21 7,20 22 22
*o>.is the yield stress at 300°K t K is the average thermal conductivity between 20 and 300°K 11
value of this ratio is shown for a range of constructional materials at 4°K. The units are, unfortunately, a little mixed but for comparative purpja^es they may be neglected. In the final column the value ofdy/K is shown relative to that of annealed stainless steel. Composites are not however the universal panacea for all our cryogenic materials problems as they suffer from a number of drawbacks. Their mechanical properties are highly directional and are much better parallel to the fibre axis then perpendicular to it. Two dimensional reinforcement can be obtained by cross plying the fibres but simultaneous reinforcement in all three directions is not practicable. Joints between two or more composite components or between a composite and a metal are a difficulty, but the problem can be overcome. As the thermal contraction of a composite lies between the low value of the glass fibre and the high value of the resin, matching of the contraction of the composite to that of a metal is not such a serious problem as it was with polymers. When an epoxy-glass cloth composite is tested in tension at '~20°K two distinct moduli are found.^^ The initial modulus of 3-5 x 10* Ib/in^ which is characteristic of the whole composite and a lower secondary modulus of 1-6 X 10* Ib/in^. The transition stress, or proportionality limit is the stress at which microcracking occurs at the resin-fibre interface and the epoxy can be seen to craze and flake off" test specimens at this point. Porosity troubles are thus to be expected if such a composite is stressed above the transition stress but they are sometimes experienced with unstressed composites. A thin layer of electrodeposited nickel has proved quite successful in reducing this porosity, but attempts at bonding nylon films on to the surface seem to have met with limited success due to the differential contraction between film and composite." Throughout this paper the emphasis has been on the results obtained from simple tensile, compressive, and impact tests. Clearly there are occasions when other tests are necessary in order to determine the suitability of a material for a particular application. Knowledge of flexural strength and modulus are often needed and where cyclic loading occurs the fatigue life must be known. Such additional data may tip the balance more strongly in favour of one material than another. For example, from static tests, epoxy resins appear most promising for use as matrices in composites for use at cryogenic temperatures closely followed by the polyesters and phenolics. However, when the tests are extended to include fatigue life, the epoxies and phenolics continue to show excellent mechanical properties while the polyesters fail much sooner." In conclusion, two points may be stressed. The first concerns the availability of data on the mechanical properties of materials at low temperatures. Here our American colleagues are fortunate in that a considerable amount of data exists on materials which conforms to ASTM or other recognized standards. Some of these may be obtained in this country but one is often faced with the problem of having to use materials for which no data exists. It is possible to be guided by data obtained for a material of similar specification but the necessity of adding healthy safety factors inevitably leads to inefficient designs. In the absence of a national facility for testing materials at cryogenic temperatures, the only other 12
possibility is for each potential user to carry out his own tests. Second, as we have seen, there are many factors which can affect the performance of a component stressed at cryogenic temperatures; its mechanical and thermal history, the presence of small flaws, cracks, or stress raisers, the closeness to which an alloy adheres to its specification, etc. Thus, in order that the cryogenic engineer may be able to decide the best material for a particular application he must be able to make his choice in the light of a sound knowledge of these factors and also a clear understanding of the advantages and disadvantages of the many different materials now available to him. This work is a review paper which was presented originally to a joint meeting of the Low Temperature and Materials and Testing groups of the Institute of Physics and the Physical Society on 15 March 1967. REFERENCES 1. PoLANYi, M., MEISSNER, W . , and SCHMID, E . Z . / . Phys. 66,
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