The anisotropy of thermal expansion as a cause of deformation in metals and alloys B y W. B oas and R. W. K. H oneycombe Council for Scientific and Industrial Research, Section of Tribophysics, Melbourne, and Rosenhain Memorial Laboratory, University of Melbourne (Communicated by Sir David Rivett, F.R.S.—Received 24 January 1946) [Plates 15-18] Plastic deformation produced by repeated heating and cooling of certain non-cubic metals has been studied over a temperature range from —190 to 250° C. The extent of the deforma- tion which results from the anisotropy of thermal expansion of individual crystals becomes greater as the temperature range is increased. In the case of cadmium, plastic deformation was detected even after 20 cycles over the temperature range 30 to 75° C; in cyclic treatment to higher temperatures the deformation was associated with extensive grain-boundary migra- tion. Cyclic treatment of tin, cadmium and zinc between room temperature and that of liquid air resulted in complex slipping and twinning, but grain-boundary migration was practically absent. Cooling from the liquid state which represents half a thermal cycle sets up stresses in metals possessing anisotropy of thermal expansion, and leads to plastic deformation. This is shown by the detection of slip lines and grain -boundary accentuation in certain cast non- cubic metals. In cadmium, subsequent annealing results in marked grain growth. In order to investigate the interaction between the crystals of the two phases of a duplex alloy during cyclic thermal treatment, experiments were carried out with a series of tin-rich tin-antimony alloys. The majority of the alloys consisted of the tin-rich matrix in which particles of a hard second phase of cubic crystal structure were embedded. It was found that the deformation in the region of the boundaries between crystals of the two phases was considerably smaller than that in the region of the crystal boundaries of the anisotropic matrix. Similar results were obtained with tin-base bearing alloys. 1. I ntroduction In a previous paper (Boas & Honeycombe 1946) it has been shown that certain non- cubic metals are deformed by heating and cooling. Electrolytically polished speci- mens of tin, cadmium and zinc were subjected to thermal cycles between 30 and 150° C, and in each case, signs of plastic deformation were detected after only a small number of cycles. The deformation in cadmium and zinc was clearly visible as slip, while in tin only distortion in the region of the grain boundaries was apparent. This deformation was shown to be due to the anisotropy of thermal expansion which is a characteristic of non-cubic metals. When lead, which is a cubic metal, was subjected to similar treatment, no signs of deformation were detected. This paper describes an extension of the work to cover a wider range of experi- mental conditions and to include other metals and alloys; the effects of temperature, purity and preferred orientation on the deformation have been investigated. The work has led to a general consideration of the phenomenon in the casting and annealing of metals. The behaviour on cyclic thermal treatment of certain duplex alloys forming the basis of tin-base bearing metals has been examined in some detail. The experimental technique employed was in most cases the same as that described previously, namely, the specimens of pure metals were annealed, e'ectrolytically Vol. 188. A. (25 February 1947) [ 427 ] 28 on July 5, 2018 http://rspa.royalsocietypublishing.org/ Downloaded from
Transcript
The anisotropy of therm al expansion as a cause of deformation in metals and alloys
B y W. B oas and R. W. K. H oneycombe
Council for Scientific and Industrial Research, Section of Tribophysics, Melbourne, and Rosenhain Memorial Laboratory, University of Melbourne
(Communicated by Sir David Rivett, F.R.S.— Received 24 January 1946)
[Plates 15-18]
Plastic deformation produced by repeated heating and cooling of certain non-cubic metals has been studied over a temperature range from — 190 to 250° C. The extent of the deformation which results from the anisotropy of thermal expansion of individual crystals becomes greater as the temperature range is increased. In the case of cadmium, plastic deformation was detected even after 20 cycles over the temperature range 30 to 75° C; in cyclic treatment to higher temperatures the deformation was associated with extensive grain-boundary migration. Cyclic treatment of tin, cadmium and zinc between room temperature and that of liquid air resulted in complex slipping and twinning, but grain-boundary migration was practically absent.
Cooling from the liquid state which represents half a thermal cycle sets up stresses in metals possessing anisotropy of thermal expansion, and leads to plastic deformation. This is shown by the detection of slip lines and grain -boundary accentuation in certain cast non- cubic metals. In cadmium, subsequent annealing results in marked grain growth.
In order to investigate the interaction between the crystals of the two phases of a duplex alloy during cyclic thermal treatment, experiments were carried out with a series of tin-rich tin-antimony alloys. The majority of the alloys consisted of the tin-rich matrix in which particles of a hard second phase of cubic crystal structure were embedded. I t was found that the deformation in the region of the boundaries between crystals of the two phases was considerably smaller than that in the region of the crystal boundaries of the anisotropic matrix. Similar results were obtained with tin-base bearing alloys.
1. I ntroduction
In a previous paper (Boas & Honeycombe 1946) it has been shown that certain non- cubic metals are deformed by heating and cooling. Electrolytically polished specimens of tin, cadmium and zinc were subjected to thermal cycles between 30 and 150° C, and in each case, signs of plastic deformation were detected after only a small number of cycles. The deformation in cadmium and zinc was clearly visible as slip, while in tin only distortion in the region of the grain boundaries was apparent. This deformation was shown to be due to the anisotropy of thermal expansion which is a characteristic of non-cubic metals. When lead, which is a cubic metal, was subjected to similar treatment, no signs of deformation were detected.
This paper describes an extension of the work to cover a wider range of experimental conditions and to include other metals and alloys; the effects of temperature, purity and preferred orientation on the deformation have been investigated. The work has led to a general consideration of the phenomenon in the casting and annealing of metals. The behaviour on cyclic thermal treatment of certain duplex alloys forming the basis of tin-base bearing metals has been examined in some detail.
The experimental technique employed was in most cases the same as that described previously, namely, the specimens of pure metals were annealed, e'ectrolytically
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polished, and subjected to cyclic thermal treatment. Microscopic examination could then be carried out satisfactorily without further polishing, for with most of the metals used little tarnishing occurred. Every care was taken to avoid mechanical deformation of the specimens. The electrolytic polishing method was found to be inadequate in dealing with the alloys, and normal metallographic polishing was resorted to, the specimens being annealed after final polishing.
2. D eformation of metals by cyclic thermal treatment
(a) Variation of maximum temperature of the cycleIn the work described in the previous paper, the temperature range for the cyclic
treatment of all the specimens was 30 to 150° C. Slip lines were, however, observed microscopically at temperatures far below the maximum temperature (150° C). Deformation would therefore be expected to occur during cyclic treatment within a smaller temperature range.
To confirm this point, a series of cadmium specimens, which had been annealed for 1 hr. at 200° C and were of similar grain size, was subjected to 20 cycles within various temperature ranges. Figure la , plate 15, shows an area representative of all specimens as polished. The specimens were immersed alternately in hot and cold oil- baths, the duration of a cycle being 7 min. Figure 1 b-f, plate 15, show photomicrographs of typical areas from the specimens after cyclic treatment. For the range 30 to 75° C slip lines were produced after 20 cycles (figure 16, plate 15), but no grainboundary migration was observed in this temperature range even after 50 cycles. With increasing range of temperature, the deformation became much more pronounced, more grains were deformed, and grain-boundary migration became increasingly evident (figures 1 c-e, plate 15). In the range 30 to 250° C after 20 cycles, the small original grains had been replaced by large grains. This process of grain growth resulted from the high maximum temperature of the cyclic treatment, and would have taken place in any case if the specimen had originally been annealed at 250° C instead of 200° C. The deformation was very pronounced, and was confined principally to the large new grains which themselves showed extensive grain-boundary migration. An examination of figure 1/, plate 15, shows the network of grain-boundary impressions produced by this migration; it can be seen that the slip lines cross the old grain boundaries. I t should be emphasized that this specimen had originally a grain size similar to that of the other specimens of the series; some of the original grain-boundary impressions are still visible.
Marked grain growth was also observed during the cyclic treatment of spectroscopically pure tin (99-998 %) between 30 and 150° C (see figure 2a, plate 15). This had not been obtained with the less pure tin (99-85%) used in the earlier experiments.
(6) Cyclic cooling in liquid airThe experiments described previously were carried out between 30° C and higher
temperatures. If the deformation is due to the anisotropy of thermal expansion, then it should also occur when the cycles are carried out between room temperature
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and lower temperatures. An advantage of such a temperature range is that grainboundary migration is practically eliminated and recovery greatly reduced. To investigate this, the cycles were carried out by immersing the specimen, contained in a thin glass tube, in liquid air. To complete the cycle, the tube was removed and the specimen allowed to reach room temperature. The total time of such a cycle was 20 min.
After several such cycles, slip lines and some twinning were detected in zinc, cadmium and tin, but no effects were observed with lead. Some difficulty was encountered because of the tarnishing of the lead specimens, so to overcome this a lead specimen was sealed in a thin-walled glass tube in an atmosphere of dry oxygen- free nitrogen. To make a direct comparison a cadmium specimen was treated in the same manner, and the two specimens were subjected to 16 cycles. Subsequent microscopic examination showed slip lines and twinning in the cadmium, while the lead was free from any signs of deformation. No grain-boundary migration was observed in either case.
A specimen of spectroscopically pure tin (99-998 %) contained in a glass tube and subjected to 10 cycles showed slip lines and some twins. When a specimen of less pure tin (99-85 %) was similarly treated, few slip lines were observed, the main effect being grain-boundary accentuation. As shown in figure 26, plate 15, the slip lines observed in very pure tin after cyclic treatment at low temperatures are straight. This is in contrast to slip lines produced during cyclic treatment at elevated temperatures, which are usually curved and less well defined (see figure 2a, plate 15). Similar curved slip lines have been described by Greenland (1937) in the case of mercury crystals.
I t was also observed that the cyclic treatment at low temperatures produced complex slip indicated by the occurrence of two or more sets of slip lines in the one grain (see figure 26). This phenomenon was observed in zinc, cadmium and tin.
The anisotropy of thermal expansion 429
(c) Specimens with preferred orientation
Deformation produced by cyclic thermal treatment has been shown to be due to the anisotropy of thermal expansion of the crystals comprising the material. If a preferred orientation exists in the metal, i.e. if the same crystallographic axes are parallel in all the crystals, then the thermal expansion parallel to the common boundary of neighbouring crystals will be the same, and no stresses will be set up on heating or cooling.
Many attempts were made to produce specimens with a strongly preferred orientation both by annealing subsequent to severe cold working and by casting. Such specimens should behave in a similar manner to a single crystal, and cyclic thermal treatment should produce no deformation. The results with pure metals (cadmium and zinc) were not conclusive because it was apparently not possible to produce a sufficiently strong preferred orientation. However, cast tin-antimony alloys possessing a marked columnar structure showed very little distortion in the
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region of the grain boundaries even after 100 cycles between 30 and 150° C. This is in contrast to the behaviour of similar alloys consisting of equi-axed grains which, after the same treatment, showed marked deformation. This is shown in figure 3 a and 6, plate 16.
(d) Aluminium and magnesiumLead has a cubic crystal structure with isotropic thermal properties. For this
reason it shows no plastic deformation on heating or cooling. We should, therefore, expect that aluminium which is also cubic would behave similarly. Rolled and annealed aluminium*^99*97 % pure) was electrolytically polished and subsequently annealed for 3 hr. at 250° C. I t was then subjected to 50 cycles between 30 and 200° C, a greater temperature range than that used in most of the previous experiments. Micro-examination after this treatment revealed no signs of plastic deformation or grain-boundary migration.
Magnesium which has a melting-point close to that of aluminium and is not cubic was treated in exactly the same manner. Again, no deformation or grain-boundary migration was detected after 50 cycles. This is due to the fact that, although magnesium possesses a hexagonal crystal structure, its thermal properties are very nearly isotropic, and the stresses set up are presumably too small to produce observable effects.
3. Casting and annealing of metals
(a) Metals as castThe cooling of a metal from the liquid state already represents half a thermal
cycle over a very wide temperature range. Consequently, if the metal possesses a high anisotropy of thermal expansion, then stresses will be set up in the cast metal.
Small ingots of zinc, cadmium, tin and lead were cast into preheated moulds with armour plate-glass bases. In the case of tin and lead it was possible to observe the free surface of the ingot, but with zinc and cadmium observations were more satisfactorily made on the under surface. In either case, no polishing of the resultant smooth surfaces was required in order to examine the ingots microscopically.
In cast cadmium and zinc, slip lines were observed in a number of grains. Typical examples are shown in figure 4 a and 6, plate 16. In all specimens examined, complicated networks of grain boundaries were apparent without etching. Similar networks have been observed in many metals by Vogel (1923). With tin, observation of the mirror-like free surface as the ingot solidified and cooled revealed, even to the naked eye, the gradual accentuation of the grain boundaries which had become very marked by the time room temperature was reached. This effect is similar to that observed previously during the cyclic thermal treatment of annealed tin specimens. In similar experiments with lead, no slip lines were produced, but grain boundaries were visible under the microscope, and a very limited amount of grain-boundary migration was detected.
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(6) Annealing of cast metalsAs the above experimental evidence indicates that stresses are present in some
metals in the as-cast state, experiments were made to determine the effect of these stresses on subsequent annealing. Ingots of tin, cadmium, zinc and lead, 1 § x 3 x J in., were cast in a shallow steel mould, which was, in each case, preheated before casting.
Cadmium and lead ingots cast into moulds preheated to approximately 300° C were macro-etched on the free surfaces and photographed. The ingots were then annealed in an air oven for 24 hr. at 290 to 300° C; they were allowed to cool slowly and were then re-etched. In each experiment, a lead ingot and a cadmium ingot were treated simultaneously to ensure comparable results. Figure 5 and 6, plate 17, are photo- macrographs of ingots prior to annealing, while figure 5 c andd, plate 17, show the same two ingots on re-etching after annealing. I t is apparent that marked grain growth has occurred in the cadmium ingot, while the lead ingot has remained substantially unchanged. This effect was observed in castings over a range of grain sizes (0-5-3 mm.) and occurred both when the specimens were placed directly into the air oven at 290° C and when they were slowly heated up with the oven to the final temperature.
In tin ingots (99-975 % pure), annealed for 24 hr. at 190 to 200° C, grain growth was detected in one case only, and even here it occurred in a limited area of the ingot. This would be expected in view of the relatively small anisotropy of thermal expansion in tin.
Zinc ingots (99-99 %+ pure) of the same size were cast and annealed for 24 hr. at 365° C. No general change in grain size was observed by the macroscopic technique employed, even in the case of an ingot annealed for 96 hr. at 380 to 390° C, although some localized absorption of grains occurred. This result is surprising in view of the great anisotropy of thermal expansion in zinc. Further experiments with specimens of equally pure zinc, but possessing different grain sizes, were carried out and the same results obtained. The absence of grain growth may be a question of purity, but no definite explanation can be offered.
4. D epth and extent of deformation
The metallographic observation of plastic deformation, as indicated by slip lines, twinning and distortion in the vicinity of grain boundaries, is limited to the surface of the metal. Removal of the surface layer by etching or polishing removes also the slip lines; however, X-ray photographs taken after etching will reveal if any deformation is present in the interior of the specimen.
A zinc specimen approximately 0-15 in. thick was subjected to 100 cycles between 30 and 150° C and an X-ray 'back-reflexion photograph was taken; further back reflexion photographs were then made after the removal of 0-005, 0-012 and 0-080 in. from one face of the specimen by etching. In each case, lattice distortions were shown by the blurring of the spots, and no marked difference in the extent of blurring was detected. Thus the deformation occurs throughout the whole specimen and is not restricted to the surface layers.
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432I t might thus be expected that sufficiently prolonged cyclic thermal treatment
would produce a change in the physical properties of the metals. To investigate this, hardness measurements were carried out on specimens of cadmium and zinc after various numbers of cycles. Even after 400 cycles between 30 and 150° C, practically no increase in hardness was detected in either zinc or cadmium. Since it was possible that recovery occurred during the thermal cycles with the elimination of the work hardening, cyclic treatment of zinc was carried out between room temperature and the temperature of liquid air. After 75 such cycles an increase in hardness of only 2 Brinell units was obtained. This increase indicates that, in spite of the marked visual evidence, the plastic deformation is not very severe. This result can be compared with the increase in hardness produced by mechanical working. A specimen of annealed zinc compressed by 9 % showed an increase in hardness of 5 Brinell units.
5. P urity of metals
W. Boas and R. W. K. Honeycombe
I t has already been mentioned that a significant difference has been observed in the behaviour of two grades of tin when subjected to cyclic treatment. First, very few slip lines were observed in specimens of the less pure tin (99-85 %), both when the treatment was carried out in liquid air and at elevated temperatures. The more obvious sign of deformation was distortion occurring in the region of the grain boundaries. When specimens of spectroscopically pure tin (99-998 %) were employed, many slip lines were detected as a result of cyclic treatment in both temperature ranges (figures 2 a and 6, plate 15). Another point of difference between the two materials was the extent of grain-boundary movement at elevated temperatures. In the less pure tin, grain-boundary migration occurred during cyclic treatment between 30 and 150° C. A specimen of spectroscopically pure tin, when subjected to 25 cycles in the same temperature range, showed pronounced grain growth. This occurred early in the cyclic treatment because marked slip lines were evident in the large new grains, and only very slight evidence of slip lines could be detected in the small original grains. The large grains once formed were not stable, but showed grain-boundary migration as the cyclic treatment was continued.
The effect of purity was also marked in the case of zinc. Zinc of 99-95 % purity* showed no grain-boundary migration after cyclic thermal treatment in the range 30 to 150° C, whereas a purer grade of zinc (99-99 % + )* showed grain-boundary
* The results of spectroscopic analyses carried out on specimens prepared from the two grades of zinc were as follows:
migration associated with the usual sighs of deformation. Figure 6 plate 17 shows an area on such a zinc specimen after 50 cycles between 30 and 150° C. Some thickening of the grain boundaries is evident; a t higher magnifications this can be resolved into a series of grain boundaries (figure 66, plate 17).
These results are summarized in table 1.
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T a b l e 1. E f f e c t o f i m p u r i t i e s i n t i n a n d z in c
metal Sn 99-85 %
99-998 %Zn 99-95 %
99-99 % +Sn 99-85 %
99-998 %
temperature range (° C)
30-150
30-15030-150130-150/
-180-30
-180-30
deformation few slip linesaccentuation of grain boundaries many curved slip lines
straight slip lines
few slip linesaccentuation of grain boundariesstraight slip lines multiple slip, some twinning
boundary movement some migration
marked grain growthno migration some migrationnone
none
6. E x p e r i m e n t s w i t h d u p l e x a l l o y s
The deformation described above occurs as a result of interaction between crystals of the one phase. In alloys in which two phases are present, deformation due to the different thermal expansion of the two phases is superimposed on the deformation due to the anisotropy of the primary phase. In order to investigate the relative importance of these two effects some experiments were carried out with tin-antimony alloys. These alloys are of some practical importance as they form the basis of tin-base bearing alloys.
Tin-rich tin-antimony alloys were chosen because large particles of a second phase could be obtained as a suitable distribution in the primary solid solution. This solid solution has the tetragonal structure of tin, while the second phase is the inter- metallic compound SnSb which possesses a cubic crystal structure (Bowen & Morris-Jones 1931). The microstructure of the 5 % antimony alloy consists solely of the solid solution, whereas in the alloys of higher antimony content, cuboids (SnSb) are embedded in the tetragonal matrix (Hanson & Pell-Walpole 1936).
Alloys containing approximately 5,10,15 and 20 % antimony were cast and small specimens were mechanically polished. After final polishing, the specimens were annealed for 1 hr. at 200° C, and were then subjected to cyclic thermal treatment between 30 and 150° C in glass tubes in order to minimize tarnishing. Selected areas were photographed at intervals during the experiment. In all cases the surfaces of the specimens acquired a ‘rumpled’ appearance as a result of distortion in the vicinity of the grain boundaries of the matrix.
That these distortions coincide with the grain boundaries has been shown by macro-etching. The deformation has the appearance of cracks in the alloy. How-
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ever, it has been shown by cross-sectioning that the cracks are usually limited to the surface of the metal, although the deformation extends much farther. With increasing antimony content, this surface rumpling became less pronounced. A few slip lines were detected in the 5 % antimony alloy (figures 7 a and 6, plate 18), but none were observed in the other alloys (figures 7 c andd, plate 18), although the matrix has nearly the same composition in all cases. These observations indicate that the cuboids have a stiffening effect on the matrix, which shows less plastic deformation on cyclic thermal treatment the greater the number of cuboids present. Two factors contribute to this stiffening of the solid solution comprising the m atrix: first, the cuboids are much harder than the matrix, and secondly, their presence in increasing numbers reduces the volume of the anisotropic phase in the alloy. The effect is clearly shown in figures 7 a-d, plate 18. Micro-examination of the cuboids embedded in the grains of the matrix showed slight distortion in the vicinity of some cuboids, but the main deformation was restricted to the region of the grain boundaries of the primary solid solution.
Similar results were obtained with tin-base bearing alloys. The composition typical of those investigated is as follows:
tin 91-9 % copper 4-0 %antimony 4-0% nickel 0-1%
In such alloys the second phase consists of acicular particles of CuSn (Farnham 1934) which possess a hexagonal crystal structure (Westgren & Phragmen 1928). Again on cyclic thermal treatment, deformation occurred as distortions in the regions of the grain boundaries of the matrix. The hard particles contributed little to the total deformation. No such distortions were obtained with lead-base bearing alloys.
7. D iscussion and conclusions
The work described in our previous paper was based on experiments carried out with tin, cadmium, zinc and lead in the temperature range 30 to 150° C. This work has now been extended by varying the temperature range and employing additional metals. The deformation observed in non-cubic metals is due to their anisotropy of thermal expansion, and a theoretical estimation of the stresses shows that their magnitude is directly proportional to the temperature range. The extent of plastic deformation should therefore decrease as the temperature range of the cycle is narrowed. This has now been shown qualitatively to be the case. The high sensitivity of cadmium to deformation on cyclic thermal treatment should be noted, variation of the temperature between 30 and 75° C being sufficient to produce slip lines.
The fact that the slip lines are not due to the relief of internal stresses present in the metal as a result of previous treatment has already been shown. This is further supported by the following two observations. First, during the cyclic treatment of cadmium between 30 and 250° C, and tin between 30 and 150° C, slip lines appear in new crystals formed as a result of marked grain growth early in the cyclic treatment
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(figures 1/ and 2 a, plate 15). Secondly, zinc, cadmium and tin are plastically deformed when subjected to cyclic treatm ent between room temperature and the temperature of liquid air. Under these conditions the relief of pre-existing internal stresses in metals by slip cannot be expected, and consequently the deformation must have another source.
When the experiments were carried out in liquid air, the density of slip lines was similar to tha t obtained during cyclic treatment to elevated temperatures, as far as could be estimated by microscopic examination. The stress is apparently more complicated, as it gives rise to complex slip and some twinning in zinc, cadmium and tin. The temperature range employed (approximately 210° C) was greater than that used in the previous work (120° C); on the other hand, the critical shear stress of these metals a t the temperature of liquid air is at least twice the value at 150° C (Schmid & Boas 1935). Thus a higher stress can be maintained than at more elevated temperatures without being relieved by plastic deformation. I t follows that the change in temperature, and not the direction of this change, is the important factor in the deformation of non-cubic metals as a results of the anisotropy of thermal expansion. The cubic metal lead showed no signs of deformation when given cyclic treatment both to low temperatures and elevated temperatures.
The metals zinc, cadmium, tin, and lead, which were used in the majority of the experiments, possess low melting-points. In the case of cadmium and lead, the comparison of the behaviour on cyclic thermal treatment was particularly appropriate because of the closeness of their melting-points. The work was then extended to aluminium and magnesium. These metals also possess similar melting-points which are, however, considerably higher than those of the other four metals. As would be expected the cubic metal aluminium showed no signs of plastic deformation even after 50 cycles between 30 and 200° C.
After the same treatment no sign of plastic deformation could be observed in magnesium. In the appendix to our previous paper, a calculation was made of a factor indicating the comparative likelihood of slip for the various metals. This factor was 2 for tin, 12 for cadmium and 15 for zinc. A similar calculation for magnesium, in which the maximum coefficient of thermal expansion is only 6 % higher than the minimum, gave a figure of 0*04.
Grain growth has been shown to occur when cast cadmium is annealed (Cook 1923), and the observations on cadmium described above confirm this result. The same effect has been observed during the annealing of cast zinc of high purity (Guillet 1943), although the present authors have been unable to confirm this result. As early as 1923 Desch suggested that this grain growth occurs because of stresses set up as a- result of the anisotropy of thermal expansion during cooling from the liquid state. The view that deformation is a prerequisite for grain growth is implicit in this explanation. Desch mentioned the absence of grain growth during the annealing of a cast cubic metal, namely, gold (Fraenkel 1922), in support of his contention. This has been further substantiated by the present authors’ observations on lead. Recently, Laszlo (1944) has calculated the order of magnitude of such
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stresses; he has suggested that recrystallization occurs during cooling of non-cubic metals and produces a preferred orientation in the material resulting in lower strain energy.
The detection of slip lines on the surface of cast cadmium and zinc which has already been described (figures 4 a and b, plate 16) fully supports the above explanation of grain growth. I t therefore appears impossible to obtain these non-cubic metals in a completely strain-free condition at room temperature. The stresses may be relieved by annealing at sufficiently high temperatures, but new stresses will be produced on cooling again to room temperature, resulting in further plastic deformation. This is in direct contrast to the conventional principle that stresses due to plastic deformation are removed by prolonged treatment at elevated temperatures. Thus in determining a suitable heat treatment to obtain non-cubic metals in a strain-free condition, it is doubtful whether a high-temperature annealing, after which high new stresses are produced on cooling, is preferable to a low-temperature annealing in which the previous stresses are incompletely eliminated, but only slight new stresses are produced. The most satisfactory procedure probably consists of a low-temperature annealing over a long period of time.
Grain-boundary migration in zinc was only detected with metal of very high purity (99-99 % + ) and not in a less pure grade (99-95 %) when specimens were subjected to cyclic thermal treatment between 30 and 150° C. This emphasizes again the familiar effect of insoluble impurities on the grain-boundary movement in metals. The main impurities in the zinc were lead and iron. The solubility of lead in zinc is less than 0-03 % (Peirce 1922), and the solubility of iron in zinc is no more than 0-0028 % (Truesdale, Wilcox & Rodda 1936). Thus in the zinc of 99-95 % purity which did not show grain-boundary migration, a t least some iron will be present as a second phase. On the other hand, grain-boundary migration does occur in the purer zinc where these impurities are held almost entirely in solid solution.
The nature of the deformation produced by cyclic thermal treatment of tin- antimony alloys was similar to that obtained in the case of pure tin, namely, principally distortion at the grain boundaries of the primary solid solution.
Grain-boundary migration, which occurred to a marked degree in pure tin, was absent in the alloys of higher antimony content. However, a limited amount of migration occurred in the 5% antimony alloy. Carpenter & Elam (1920) also observed grain-boundary migration and accentuation in a 1-5 % antimony alloy in experiments of a similar nature designed to investigate the process of grain growth during annealing.
I t would be expected that some interaction should occur between the cuboids and the matrix in the tin-antimony alloys of higher antimony content, for at least in certain directions there must exist a difference in thermal expansion. Some evidence of deformation as a result of this has been observed, but the effect is very much smaller than that occurring at the grain boundaries of the matrix. This small effect can be understood because the value of the coefficient of thermal expansion of the phase SnSb lies between the limits of the coefficients of expansion of the
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tin-rich matrix.* In tin-base bearing alloys only slight interaction has been observed between the matrix and the acicular particles (CuSn) which possess a hexagonal structure. The main deformation again occurs in the matrix. The same observation has been made in the case of lead-base bearing alloys where there was no interaction between the hard particles of cubic crystal structure (CuSn) and the cubic lead-rich matrix. In these alloys, however, no deformation is observed in the matrix because of its isotropic nature.
I t is clear that in the tin-base alloys, the surface cracks occur in the vicinity of the grain boundaries of the tin-rich solid solution, and correspond to the grain-boundary accentuation observed in pure tin. In the case of bearings, these surface irregularities can extend deeply into the bearing alloy lining, and may ultimately reach the steel outer shell. As these distortions occur in the region of the grain boundaries, their distribution will be related to the size and shape of the grains of the tin-rich phase. The extent to which the effect produces defects in tin-base bearings under service conditions will depend primarily on two factors, namely, the operating temperature of the bearing and the number of times it is raised to this temperature. The above experiments have indicated that marked defects occur even after a few cycles in a temperature range over which many bearings operate.
This work has been confined to the effect of cyclic temperature changes on metals and alloys of relatively low melting-point. Of the metals of higher melting-point, few possess a non-cubic crystal structure, and no determinations of the anisotropy of thermal expansion have been made. The only information refers to cobalt, in which case no anisotropy of thermal expansion has been detected (Wassermann I932)-
In many other substances which possess marked anisotropy of thermal expansion, stresses will occur when they are subjected to temperature changes. For example, the existence of such stresses in rocks had already been discussed by Howe (1910). He considered that the weathering of rocks is partially due to stresses produced by temperature variations, and distinguished two possibilities by which minute intergranular thrusting is produced. Stresses are set up as a result of differences in the coefficients of thermal expansion, first of the various constituents of the rock, and secondly within grains of the one constituent as a result of the anisotropy of thermal expansion. Lord Rayleigh (1934) found that after marble had been heated to a temperature of 100° C its rigidity was diminished. This effect became increasingly marked as the temperature was raised further. He interpreted the results as due to the anisotropy of thermal expansion of calcite. As a result of the stresses set up during heating, the structure is dislocated and loosened with increase of volume, the process being irreversible. I t is thus evident that the continual heating and
* A determ ination o f the coefficient for SnSb gave th e value 17 x 10-6 . M axim um and m inim um values for tin are 30-5 and 15-5 x 10~6, and these w ill n o t be m aterially altered b y th e presence o f antim ony in solid solution . Thus the m axim um difference in therm al expansion betw een hard particles and m atrix is sm aller than th a t possible betw een tw o m atrix grains.
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cooling of rocks, with the resultant inhomogeneous expansion and contraction, contribute to the ultimate disintegration which is apparent both in stone buildings and in the landscape.
The work described in this paper was carried out as part of the programme of the Section of Tribophysics of the Council for Scientific and Industrial Research, Australia.
We wish to express our thanks to Dr F. P. Bowden and Dr D. Tabor for their interest and encouragement in the work, and to Dr S. H. Bastow and Professor J. Neill Greenwood for very helpful discussions. We also wish to thank the staff of the Munitions Supply Laboratories, Maribyrnong, for carrying out the spectroscopic analyses. Finally, we are grateful to Professor E. J . Hartung for laboratory facilities in the Chemistry School of the University of Melbourne.
438 W. Boas and R. W. K. Honeycombe
R eferences
Boas, W. & Honeycombe, R. W. K. 1946 Proc. Roy. Soc. A, 186 , 57-71.Bowen, E. G. & Morris-Jones, W. 1931 Phil. Mag. 12, 441-462.Carpenter, H. C. H. & Elam, C. F. 1920 J. Inst. Met. 24, 83-131.Cook, M. 1923 Trans. Faraday Soc. 19, 43-48.Desch, C. H. 1923 Trans. Faraday Soc. (discussion), pp. 48-49.Famham, G. S. 1934 J. Inst. Met. 55, 69-70.Fraenkel, W. 1922 Z. anorg. Chem. 122, 295—298.Greenland, K. M. 1937 Proc. Roy. Soc. A, 163 , 28-34.Guillet, L. (Jr.) 1943 C.R. Acad. Sci., Paris, 216 , 642-644.Hanson, D. & Pell-Walpole, W. T. 1936 J. Inst. Met. 58, 299—308.Howe, J. A. 1910 The geology of building stones, pp. 342-343. London: Arnold.Laszlo, F. 1944 J. Iron Steel Inst, (pre-print).Peirce, W. M. 1922 Trans. Amer. Inst. Min. (Metall.) Engrs, 68, 768-769.Rayleigh, Lord 1934 Proc. Roy. Soc. A, 144, 266-279.Schmid, E. & Boas, W. 1935 Kristallplastizitdt. Berlin: Springer.Truesdale, E. C., Wilcox, R. L. & Rodda, J. L. 1936 Trans. Amer. Inst. Min. (Metall.) Engrs,
122, 192-228.Vogel, R. 1923 Z. anorg. Chem. 126, 1-38.Wassermann, G. 1932 Metallwirtschaft, 11, 61-65.Westgren, A. & Phragmen, G. 1928 Z. anorg. Chem. 175, 80-89.
D escription of P lates 15-18
Plate 15
F igure 1. Typical areas on cadmium specimens after 20 cycles over various temperature ranges, (a) as polished, (b) 30-75° C, (c) 30-100° C, (d) 30-150° C, (e) 30-200° C, (/) 30-250° C. ( x 60.)
F igure 2. Areas on specimens of spectroscopically pure tin. (a) after 25 cycles between 30 and 150° C, showing marked grain growth and curved slip lines ( x 40), (6) after 10 cycles bv direct immersion in liquid air, showing straight slip lines and twinning ( x 80).
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Plate 16F ig u r e 3. The effect of crystal orientation on the deformation produced by cyclic thermal treatment. Typical areas on tin-antimony specimens containing 10 % antimony after 100 cycles between 30 and 150° C. (a) specimen with columnar crystals (preferred orientation) ( x 44), (b) specimen with equi-axed crystals (random orientation) ( x 80).
F igure 4. Plastic deformation in cast metals as shown by slip lines on the smooth under surfaces of ingots, (a) cadmium ( x 160), (6) zinc ( x 40).
Plate 17F igure 5. The annealing of cast metals, (a) cadmium ingot—as cast, (b) lead ingot—as cast, (c) t o e as (a) after annealing, showing marked grain growth, (d) same as (6) after annealing, showing no grain growth. (All macrographs f natural size.)F igure 6. Cyclic thermal treatment of very pure zinc between 30 and 150° C. (a) typical area after 50 cycles showing slip lines and thickening of grain boundaries ( x 80), (6) an area at higher magnification ( x 400). The thickening is resolved into a grain-boundary network.
Plate 18F igure 7. Cyclic thermal treatment of tin-antimony alloys between 30 and 150° C. (a) area on a 5 % antimony alloy after 10 cycles, (b) same area as (a) after 100 cycles, (c) area on a 15 % antimony alloy after 10 cycles, (d) same area as (c) after 100 cycles. ( x 80.)
The anisotropy of thermal expansion 439
The two-dimensional hydrodynamical theory of moving aerofoils. IVBy R o s a M. M o r r i s , Ph.D.
(Communicated by G. Temple, F.R—Received 21 March 1946)
In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject.
The general results thus amended are then applied to a general discussion of the stability problem including the effect o f the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae.
An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.
I n t r o d u c t io n
1. The previous papers of this series (Morris 1937, 1938, 1939; referred to subsequently as I, II and III) have dealt in detail with the two-dimensional potential motion round an infinite cylinder of quite general shape. In I, I derived the kinetic
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