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The effect of temperature and composition on the deformation of single crystals of iron
THE EFFECT OF TEMPERATURE AND COMPOSITION ON THE DEFORMATION OF SINGLE CRYSTALS OF IRON* H. W. PAXTONf and A. T. CHURCHMANI: Ail investigation has been made of the types of stress-strain curve which it is possible to produce in single crystals of iron in the range of temperature between - 180°C and 213”C, for two different carbon contents. It is found that all the effects which can be produced in polycrystalline iron, i.e. cleavage fracture, mechanical twinning, simple and repeated yielding, and smooth stress-strain curves, can also be observed in single crystals containing 0.003 per cent carbon at approximately the same temperature. Crystals containing about 0.0005 per cent carbun also show all the effects except repeated yielding. The main difference between the single crystals of the two compositions is in the rate and magnitude of strain ageing effects. The tem~ratLlre dependence of the initial yield stress is discussed for crystals containing 0.003 per cent carbon. L’EFFET
DE LA TEMPBRATURE DE
ET DE LA COMPOSITIOS MONOCRIST,4UX DE FER
SUR
L.4 Dl?FORRlATIOS
Une investigation a 6th faite du genre de courbe tension-d6formation qu’il est possible de tracer pour des monocristaux de fer dans l’intervalle de tempCratures de - 180°C B 213”C, pour deus teneurs en carbone diff6rentes. 11 a 6th constat que tous les effets qui peul-ent Ctre produits dans du fer po~~crysta~Iin, c-8-d. rupture par clivage, maclage mPcanique, ~coulell~e~~t simple et r6p&, ainsi que des courbes tension-d&formation uniformes, peuvent aussi &tre trouves dans des monocristaux contenant 0.003 pour cent de carbone, Q Ia m&me temp&ature approximativement. Des cristaus contenant environ 0.0005 pour cent de carbone montrent au& tous ces effets, B l’exception de I’dcoulement r&p&C. La diffCrence principale entre les monocristaux des deux compositions consiste en la grandeur et la vitesse des effets de vieillissement de dt!formation (strain ageing). La dCpendance de la tension initiale d’Ccoulement, de la temperature, est discutee pour le cas des cristaux contenant 0.003 pour cent de carbone. DER
EFFEKT
VON TEMPERATUR VERFORMUNG VOX
UND ZUSA~~~IENSETZU~G EISENEIXKRISTALLEiS
AUF
DIE
Die verschiedenen Typen der Spannungs-Verzerrungskurve, die man von Eiseneinkristall,zn mit und +213’C erhalten kann, werden zwei verschiedenen Kohlenstoffgehalten zwischen -180°C untersucht. Es zeigte sich, dass alle im polykristallinen Eisen auftretenden Erscheinungen, wie Spaltbarkeit, mechanische Zwillingsbildung, einfaches und wiederholtes Fliessen uud glatte Verzerrungs-S~l~nungskurven, such an Einknstalien nit 0.003 prozent Kohlensto~ bei umgef&hr gleicher Temperatur beobachtet werden k&men. Einkristalle mit 0.0005 prozent Kohlenstofi zeigen gleichfalls die oben erwghnten Effekte mit Ausnahme des wiederholten Fliessens. Der wesentlichste Unterschied zwischen den Einkristailen verschiedenen KohIenstoffgehaIts ist die Geschwindigkeit und Griisse der spannungsbedingten Alterung. Die TemperaturabhPngigkeit der urspriinglichen Fliess-spannung wird fiir Kristalle mit 0.003 prozent C diskutiert.
Material and Apparatus
Introduction The efTect of temperature on the deformation of polycrystalline iron containing carbon and nitrogen is interesting and complicated. At low temperatures (e.g. - 18O’C) deformation twinning and brittle fracture occur, At higher temperatures, up to about lOO”C, the yield phenomenon is observed, the yield point itself showing a strong temperature dependence; at temperatures in the range lOO-300°C the yield phenomenon changes into that of blue brittleness, or repeated yielding. The purpose of the present investigation has been to explore the corresponding behaviour of single crystals of iron, since it is now known that these crystals, if they contain a little carbon or nitrogen, show yield phenomena [l; 21. *Received February 9, 1953. ~Departmerit of ~~etallurg~, England. $Now at A. E.I. Research Berks., England. ACTAA ILIETALLURGICA,
University Laboratories,
VOL.
1, SEPT.
of Birtningham, Aldermaston, 1953
The material used for most of the work was Armco iron with an original anaIysis C 0.0450,;
Si O.Ol’,&
Mn nil
s 0.005%
o.o&
N 0.005?*
although a small number of confirmatory tests were also done with two different mild steels. All the material was received as hard-drawn wire of diameter 2 mm., and grown into single crystals of length 5 cm. and upwards. These were made by first decarburising the wire in wet hydrogen (bubbly rapidly through water at room temperature giving about 3 per cent water vapour by volume) for 18 hours at 72O”C, then straining 24 to 33 per cent at room temperature, and finally annealing at 880°C for about four days in a slow stream of wet hydrogen. The crystals were then subjected to one of two different treatments. In the first, about 0.003 per cent carbon was introduced into them b,y a treatment
ACT.1
474
NETALLL-RGICA,
at 700°C for 15 minutes in dry hydrogen, which had been bubbled through n-heptane at room temperature, followed by homogenizing them for 5 days at 67O”C, furnace cooling to precipitate excess carbide in particles of reasonably large size and to minimize quench-ageing. Crystals given this treatment will be termed “carburised.” In the second treatment, “as grown” crystals were further decarburised at 720°C for periods up to 240 hours in hydrogen saturated with water vapour at room temperature. The flow rate was about 0.5 cu. ft. per hour. These crystals will be termed “decarburised,” although strain ageing experiments described below suggested that very small amounts of carbon or nitrogen were still present. All the crystals were strained in a hard-beam testing machine of the Polanyi type. For convenience of gripping, the specimens were soft soldered axially into cylindrical mild steel endpieces attached to the straining shackles by flexible Bowden cable (Figure 1). The cables on each grip were of the same length,
I
spccmen
I
Soldor
stoci endpecc
Boudcn cabb
\-OL.
1,
1953
often occurred on a (0011 plane after a few per cent extension by twinning. At -7O”C, well-marked upper ?-ielcl points followed by lower yield point extensions up to 3 per
Ml soatq
FIGURE 1. Diagram of grips used for tensile experiments on single crystals of iron.
but of opposite twist to prevent torsion of the specimen. The normal plastic strain rate in specimens 5 cm. long was 2 X 1OV per minute. Temperatures above room temperature were obtained by immersing the specimen in a bath of liquid paraffin during the experiment. Below room temperature ice and salt, dry ice and alcohol, and liquid air, were used in constant temperature baths.
FIGURE 2. Carburised specimen strained showing large load drops caused by mechanical
at -185°C twinning.
cent were observed (Figure 3). As the temperature of test increased, the magnitude of the stress drop at the yield and the lower yield point extension, during the first experiment on each annealed crystal, fell
Carburised Crystals Several different types of stress-strain curve were obtained on carburised crystals pulled at temperatures in the range - 185°C to 230°C. The effects observed, which are shown in Figures 2 to 8, are qualitatively the same as those in polycrystalline iron and occur roughly at the same temperatures. The behaviour between -185°C and 20°C has already been described by Churchman and Cottrell [a]. _4t -185”C, mechanical twins formed in “bursts” [3] very reminiscent of the martensitic transformation in high nickel steels. A large load drop was observed at each burst (Figure 2), the slope of which is a characteristic of the testing machine. The crystallography of this twinning has been described elsewhere [a]. Cleavage fracture
FIGURE 3. Carburised specimen strained (a) first experiment; (b) immediate re-load.
at
-70°C:
P;\S’~ON
.\SD
CH7-RCHIIXN:
DEFORRI;\TlOS
steadil). until the temperature range of 50-70°C was reached. Here the character of the curves changed again. The phenomenon of “blue-brittleness” or repeated I-ielding was observed above 60°C. The average magnitude of the drops in load increased with temperature up to about 13O”C, and above this temperature decreased again until at about 200°C and above, the stress-strain curves were entirely smooth (Figures 5, 6, 7, 8).
OF
IRON
CRYSTALS
stress. Andrade [3] has recentl!. sho\vn that the yield stress u of single crystals of gol(1, silver, cadmium, zinc and bismuth, over quite wide ranges of temperature, is given by a relation of the form suggested by Orowan [6] u = co - AT+ where uo and A are constants. The value of the critical shear stress in aluminium is markedly dependent on purity. The lowest
a
/ L
0
6
6
“E :
-2 ‘4 1”
475
213Oc
4
r”
I%
4
2
2
0
0
2b
5
(
3b
8
FIGURE 4. Carburised specimen strained at 19°C: (a) first experiment; (b) immediate re-load; (c) aged 80 minutes at 6OiF;ilk iFmediate re-load. Carburised specimen strained at 61.5”C: (a) first expe’riment, two hours after reaching 61.5”C; (b) aged 1 hour at 61.5”C; (c) aged 40 hours at 61.5”C.
FIGURE 7. Carburised specimen strained at 193°C: (a) first experiment; (b) aged 2 hours at 193°C; (c) aged 16% hours at 193°C; (d) aged 4% hours at 193°C. FIGURE 8. Carburised specimen strained at 213°C: (a) first experiment; (b) aged 1 hour at 213°C; (c) aged 1 hour at 213°C.
The upper yield stress measured in the first experiment on each of the carburised crystals is plotted a.gainst temperature in Figure 9. The two main features of these results are the very steep temperature dependence of yield stress and the two distinct branches of the curve formed at temperatures above and below about 80°C.
reported values, and thus presumably those for the highest purity of material, are the ones of Rosi and Mathewson [7] on 99.996+ per cent aluminium. They found that the temperature dependence is sufficiently steep to be represented by an equation u = A exp (Q;IRT) where A is a constant Cottrell and Bilby
and Q is an activation energy. [8] have proposed an equation
I ”
2oo
FIGURE 6. Carburised specimen strained at 133°C: (e) first experiment; (b) aged 2 hours at 133°C; (c) aged 18 hours at 133°C; (d) aged 2 hours at 133°C; (e) aged 40 hours at 133°C.
FIGCRE 9. Initial yield stress experiment for carburised crystals.
It is interesting to consider the mathematical form of this curve. Several equations have been proposed for the temperature dependence of yield
for materials in which the dislocations are anchored by atmospheres of solute atoms. They suggest that at a constant testing rate, yielding should occur
T'C versus
temperature
of
ACTX
476
METALLURGICX,
when the quantity I/‘;lkT reaches a characteristic fixed value. L’ (which is a known function of U/UO) is an activation energy for the formation of a stable loop of dislocation, and uo is a constant corresponding to the yield stress at 0°K. The equation U/kT = constant was fitted to the results of McAdam and Mebs [9] for polycrystalline iron, and gave lJ/kT = 47 and uo = 125 Kg/mm2. The results for the single crystals can be fitted better by the Cottrell-Bilby formula than one of the Orowan or Rosi-Mathewson type, between -185°C and 80°C. The value at -185°C is not known absolutely, but since the material forms mechanical twins here at about 28 Kg/mm*, the stress to initiate slip must be larger than this. The values of the constants, for best fit between theoretical and experimental curves, are u. = 117 Kg/mm2 U/kT = 90 Thus uo is approximately equal to that for polycrystalline iron, but I;/kT is appreciably larger. These results are summarized in Figure 10. The Orowan curve is fitted so that u remains positive in
A Cottrell-BItby B. Orcwan
%mpcraturr
VOL.
1,
1953
specimen causes the initial \vield point to be raised above its normal value.
Decarburised
Crystals
These crystals, which have been subjected to anneals up to 240 hours in wet hydrogen at 72O”C, showed much less pronounced yield phenomena, too small to be detected by routine testing procedures. However, a small upper yield point could be produced by straining and ageing (in situ, and without ever fully unloading the specimen, so that the axiality was undisturbed). The rate of strain ageing was also slowed down very markedly relative to that of carburised crystals. A load drop such as could be produced by ageing for about 1 hour at room temperature in carburised crystals was only produced in decarburised crystals after some 10 to 20 hours at 100°C. The increase in upper yield stress over the final previous applied stress, even after ageing for these long periods, was also much less than that usual for the crystals containing about 0.003 per cent carbon (see Figures 4(c), 12(d)). The types of stress-strain curve which were obtained with the decarburised crystals are as follow: At -185”C, it was possible with fully annealed specimens to produce mechanical twinning just as with carburised crystals, a result different from that obtained earlier [2]. At -7O”C, a small upper yield point was obtained in the first experiment on an annealed crystal. The lower yield stress was comparable with that for a crystal containing 0.003 per cent carbon but the lower yield extension was much less-about 0.4 per cent as against 3 per cent (Figure 11). At room temperature, small load drops were produced after straining 1 per cent and ageing for
“K
FIGURE IO. Comparison of experimental carburised crystals with theoretical curves Cottrell-Bilby and Orowan hypotheses.
results (0) (full lines)
on for
the range considered, and is equal to the twinning stress at -180°C. A further analogy with polycrystals is seen in the rise in initial yield stress which occurs at about 80°C. This temperature coincides closely with that at which repeated yielding begins, i.e. ageing is sufficiently rapid to occur significantly during the time of the experiment. It seems likely that the two phenomena are closely connected, particularly since Holden and Kunz [lo] and Paxton [II] have shown that ageing during the initial stressing of a
FIGCRE 11. Decarburised specimen strained at -73°C: (a) first experiment; (b) immediate re-load; (c) aged 22 hours at 87°C.
18 hours jrl silzt at 110°C (Figure 12). .After straining approximately 3 per cent, it was no longer possible to produce a yield point even after 24 hours ageing at 110°C.
stated limit of accuracy was 0.0002 to 0.0003 per cent, and these results must be considereci as upper limits for the carbon content. It seems very likely that the results on all the decarburised crystals can be reasonably explained on the grounds that insufficient carbon is present to saturate the dislocations. The theoretical amount needed to provide one carbon atom per atom plane intersected by the dislocation (assuming a density of lo8 lines/cm’) is lo+ wt. per cent. The work of Harper [Ia] indicates that in material which has
Decarburised specimen strained at 18°C: FIGURE 12. (a) first experiment; (b) aged 1% hours at 110°C; (c) aged 1 hour at 110°C; (d) aged 18 hours at 110°C; (e) aged 1 hour at 110°C; (j) aged 134 hours at 110°C; (g) aged 24 hours at 110°C; (h) aged 18 hours at 110°C.
*%t lWC, very small initial yield points were observed after strain ageing, increasing to a maximum after about 100 minutes ageing at this temperature. Repeated yielding was not observed (Figure 13).
6
,
1% ,
2
abed
e
f
0
Decarburised FIGURE 13. (a) first experiment; (6) aged $1 minutes at 143°C; (d) aged 47 minutes at l43T; cf) aged
specimen strained at 143T: 100 minutes at 143°C; (c) aged 17% hours at 143*C; (e) aged 17 minutes at 143°C.
At 193”C, yield phenomena were almost nonexistent. A very slight lower yield extension with small strain age-hardening occurred in one crystal after straining 0.25 per cent and ageing 17 hours at 193°C. The rate of work hardening in this crystal was considerably less than in a carburised crystal at this same temperature. A chemical analysis of crystals given a decarburising treatment was kindly arranged by Dr. N. P. Allen of the National Physical Laboratory. Three crystals given 18 hours treatment at 720°C in wet hydrogen contained 0.0006 per cent, 0.0003 per cent and 0.0005 per cent C whilst a crystal decarburised for 240 hours contained 0.0004 per cent C. The
FIGURE11. &carburised specimen strained at IW’C: (n) tirst experiment; (6) aged 17 hours at 193°C; (c) aged iJ4 hours at 193°C; (d) aged 1% hours at 103°C.
been strained a few per cent, the dislocation density is about 10” lines/cm2. Hence, a minimum of about 1O-3 wt. per cent is necessary to saturate all the dislocations in this case. This amount is certainly not present in the decarburised crystals, and so the dislocation atmospheres are not complete. Yield effects are thus reduced, in much the same way as has been noted recently by Wain [13] using zinc containing 0.0022 per cent nitrogen. This is illustrated by comparison of Figure 12(d) and 12(h). A yield point is observed after about 1 per cent strain prior to ageing, but not after about 3 per cent. The number of dislocations has increased so that insu~cient solute atoms are present to saturate the whole length of the dislocation lines. The results of Harper [12] suggest that the density of dislocations p is roughly related to the plastic strain E by the formula p = 2.5 X 101” X E en? Hence for p = 2.5 X to provide ted by the
1 per cent plastic strain, E = 10-s and lOlo lines/cm2. The wt. per cent carbon one carbon atom per atom plane intersecdislocation is 2.5 x 1o1Ox IO_& ---S--
assuming IO+ wt. per cent C for lo8 lines/cm” [8], i.e. 0.00025 per cent. A similar calculation for 3 per cent plastic strain
478
ACT&%
NETALLURGICA,
indicates that 0.00075 per cent is necessary for saturation of the dislocations. The analysis of the crystals gave,a value of about 0.0005 per cent for the carbon content. Thus, although the calculation is approximate, it does indicate that the carbon content is in the right range for yielding to disappear with increasing strain. Repeated yielding does not occur in decarburised crystal since the ageing time is not of the same order as the duration of the experiment.
Repeated Yielding Consideration of the mechanism of repeated yielding is complicated by the fact that it may occur in different forms depending on the metal, and whether this is in single crystal or polycrystalline form, and on the nature of the testing machine. The phenomenon of jerky creep was observed in metal single crystals by Becker and Orowan [14] using commercial-purity zinc. Repeated yielding has been observed by Dumbleton [15] in zinc single crystals, and by Ardley and Cottrell [16] in single crystals of 01- and P-brass. The basic feature of the dislocation theory of the effect is that the speed of diffusion of impurity atoms is sufficiently large to anchor the dislocations very- quickly once these become held up anywhere in the crystal, but insufficiently large to diffuse so rapidly- that a dislocation never effectively breaks away from an atmosphere. There is thus an optimum temperature, for each given strain rate, at which the load drops are a maximum; in the carburised iron crystals this was about 130°C. The nature of the testing machine is important in determining the form of the phenomenon. In a “soft” machine, or with dead loading, the stress does not relax appreciably during a sudden small extension. Thus one would expect deformation to propagate through the entire length of the specimen. This has been observed by McReynolds [17] in impure polycrystalline aluminium. On the other hand, in a “hard” testing machine a sudden extension can cause a marked stress drop. This may be sufficient to reduce the average speed of the dislocations substantially, and to enable anchoring to occur before the deformation has occurred throughout the entire specimen. Examples of this have been noted in polycrystalline iron by Hall [18] and Paxton [19]. At temperatures in the region lOO-2OO”C,remarkably regular repeated yielding occurs in the first experiment on an annealed specimen. This occurs in the portion of the stressstrain curve corresponding to the lower yield exten-
\‘OL.
1,
1953
sion at room temperature. ;it each fall in stress, the yield front moves a constant distance into t~he undeformed material quite rapidly. Anchoring occurs and the stress begins to rise again immediately. When the yield front has passed completely along the specimen, a rising stress-strain curve ensues which is accompanied by much more irregular jerky flow. It would appear that the detailed mechanism in iron single crystals is different from that in other single crystals or in polycrystalline iron. Metallographic study of the initial yield in carburised iron single crystals indicates that a deformation front passes along the specimen in a manner rather similar to that in polycrystals [19]. The lower yield extension in these single crytals decreases with increasing temperature, and it seems probable that at the temperatures at which repeated yielding occurs, it is of the order of 0.1 per cent, which is of the same magnitude as the extension corresponding to each of the load drops. Thus the regular repeated yielding was not observed, since the majority of the specimen has been traversed by the yield front: the second and subsequent load drops are presumably caused by movement of the band front through work hardened material, and as a result occur at successively higher stresses.
Conclusions In single crystals of iron containing about 0.003 per cent carbon it is possible to produce all the phenomena previously found in polycrystals, i.e. cleavage fracture, mechanical twinning, simple and repeated yielding, and, at sufficiently high temperatures, smooth stress-strain curves. In crystals with much less than 0.003 per cent carbon most of the same phenomena occur, but to a much less marked degree. Repeated yielding does not occur at all, for the time of ageing is increased by a factor of lo3 to 10”.
Acknowledgements The authors wish to express their gratitude to Professor A. H. Cottrell for many helpful discussions and Professor D. Hanson and the University of Birmingham for the provision of facilities and financial support.
References 1. SCHWARTZBART, H. and Low, J. R. Trans. A.I.M.E., 185 (1949) 637. 2. CHURCHMAN, A. T. and COTTRELL, A. H. Nature, 167 (1951) 943. 3. MACHLIS, E. S. and COHEN, M. J. Metals, 3 (1951) ‘746. 4. PAXTON, H. R’. Acta Met., 1 (1953) 141.
F':\XTON
AND
CHURCHXAN:
DEFORRI:1TIOS
5. ~~KDRADe, E. 3;. DA C. Phil. Msg., 43 (1952) 1218. 6. OROWAX, E. Z. Phys., 89 (1934) 605. 7. ROSI, F. D. and hTHEWSON, C. H. Trans. A.I.M.E., 188 (19*50) 1159. 8. COTTRELL, A. H. and BILBY, B. h. Proc. Phys. Sot. (London:, A62 (1949) 49. 9. NICADAM, D. J. and MESS, R. W. Trans. A.S.T.M., 43 (19431 SM. 10. HOLDE?;, A. K. aud Kusz, F. W. J. App. Phys., 23 (1952) X19.
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IROS
CR\-ST.\LS
479
11. Pnsror, H. \V. J. _\pp. Phys., 24 (1953) 10-k. 12. 13. 1-l. 15, 16.
HARPER, S. Phys. Rev., 83 (1!)51) TO!!. \YAIK, H. L. Proc. Phys. Sec. (London), B65 (1952) 886. BECKER, R. and OKOWAK, E. 2. Phys., 72 (1932) 566. DUMBLETOY, hf. J. Ph.D. thesis, Birmingham (1952). ARDLEY, G. W. and COTTRELL, A.%. To be published in Proc. Roy. Sot. 17. MCREYNOLDS, -1. \V. Trans. A.I.N.E., 185 (1949) 32. 18. HALL, E. 0. J. Iron and Steel Inst., 170 (1952) 331. 19. PASTOX, H. iv. Ph.D. thesis, Birlni~~harn <1952).
DE LA TEMPBRATURE DE
ET DE LA COMPOSITIOS MONOCRIST,4UX DE FER
SUR
L.4 Dl?FORRlATIOS
Une investigation a 6th faite du genre de courbe tension-d6formation qu’il est possible de tracer pour des monocristaux de fer dans l’intervalle de tempCratures de - 180°C B 213”C, pour deus teneurs en carbone diff6rentes. 11 a 6th constat que tous les effets qui peul-ent Ctre produits dans du fer po~~crysta~Iin, c-8-d. rupture par clivage, maclage mPcanique, ~coulell~e~~t simple et r6p&, ainsi que des courbes tension-d&formation uniformes, peuvent aussi &tre trouves dans des monocristaux contenant 0.003 pour cent de carbone, Q Ia m&me temp&ature approximativement. Des cristaus contenant environ 0.0005 pour cent de carbone montrent au& tous ces effets, B l’exception de I’dcoulement r&p&C. La diffCrence principale entre les monocristaux des deux compositions consiste en la grandeur et la vitesse des effets de vieillissement de dt!formation (strain ageing). La dCpendance de la tension initiale d’Ccoulement, de la temperature, est discutee pour le cas des cristaux contenant 0.003 pour cent de carbone. DER
EFFEKT
VON TEMPERATUR VERFORMUNG VOX
UND ZUSA~~~IENSETZU~G EISENEIXKRISTALLEiS
AUF
DIE
Die verschiedenen Typen der Spannungs-Verzerrungskurve, die man von Eiseneinkristall,zn mit und +213’C erhalten kann, werden zwei verschiedenen Kohlenstoffgehalten zwischen -180°C untersucht. Es zeigte sich, dass alle im polykristallinen Eisen auftretenden Erscheinungen, wie Spaltbarkeit, mechanische Zwillingsbildung, einfaches und wiederholtes Fliessen uud glatte Verzerrungs-S~l~nungskurven, such an Einknstalien nit 0.003 prozent Kohlensto~ bei umgef&hr gleicher Temperatur beobachtet werden k&men. Einkristalle mit 0.0005 prozent Kohlenstofi zeigen gleichfalls die oben erwghnten Effekte mit Ausnahme des wiederholten Fliessens. Der wesentlichste Unterschied zwischen den Einkristailen verschiedenen KohIenstoffgehaIts ist die Geschwindigkeit und Griisse der spannungsbedingten Alterung. Die TemperaturabhPngigkeit der urspriinglichen Fliess-spannung wird fiir Kristalle mit 0.003 prozent C diskutiert.
Material and Apparatus
Introduction The efTect of temperature on the deformation of polycrystalline iron containing carbon and nitrogen is interesting and complicated. At low temperatures (e.g. - 18O’C) deformation twinning and brittle fracture occur, At higher temperatures, up to about lOO”C, the yield phenomenon is observed, the yield point itself showing a strong temperature dependence; at temperatures in the range lOO-300°C the yield phenomenon changes into that of blue brittleness, or repeated yielding. The purpose of the present investigation has been to explore the corresponding behaviour of single crystals of iron, since it is now known that these crystals, if they contain a little carbon or nitrogen, show yield phenomena [l; 21. *Received February 9, 1953. ~Departmerit of ~~etallurg~, England. $Now at A. E.I. Research Berks., England. ACTAA ILIETALLURGICA,
University Laboratories,
VOL.
1, SEPT.
of Birtningham, Aldermaston, 1953
The material used for most of the work was Armco iron with an original anaIysis C 0.0450,;
Si O.Ol’,&
Mn nil
s 0.005%
o.o&
N 0.005?*
although a small number of confirmatory tests were also done with two different mild steels. All the material was received as hard-drawn wire of diameter 2 mm., and grown into single crystals of length 5 cm. and upwards. These were made by first decarburising the wire in wet hydrogen (bubbly rapidly through water at room temperature giving about 3 per cent water vapour by volume) for 18 hours at 72O”C, then straining 24 to 33 per cent at room temperature, and finally annealing at 880°C for about four days in a slow stream of wet hydrogen. The crystals were then subjected to one of two different treatments. In the first, about 0.003 per cent carbon was introduced into them b,y a treatment
ACT.1
474
NETALLL-RGICA,
at 700°C for 15 minutes in dry hydrogen, which had been bubbled through n-heptane at room temperature, followed by homogenizing them for 5 days at 67O”C, furnace cooling to precipitate excess carbide in particles of reasonably large size and to minimize quench-ageing. Crystals given this treatment will be termed “carburised.” In the second treatment, “as grown” crystals were further decarburised at 720°C for periods up to 240 hours in hydrogen saturated with water vapour at room temperature. The flow rate was about 0.5 cu. ft. per hour. These crystals will be termed “decarburised,” although strain ageing experiments described below suggested that very small amounts of carbon or nitrogen were still present. All the crystals were strained in a hard-beam testing machine of the Polanyi type. For convenience of gripping, the specimens were soft soldered axially into cylindrical mild steel endpieces attached to the straining shackles by flexible Bowden cable (Figure 1). The cables on each grip were of the same length,
I
spccmen
I
Soldor
stoci endpecc
Boudcn cabb
\-OL.
1,
1953
often occurred on a (0011 plane after a few per cent extension by twinning. At -7O”C, well-marked upper ?-ielcl points followed by lower yield point extensions up to 3 per
Ml soatq
FIGURE 1. Diagram of grips used for tensile experiments on single crystals of iron.
but of opposite twist to prevent torsion of the specimen. The normal plastic strain rate in specimens 5 cm. long was 2 X 1OV per minute. Temperatures above room temperature were obtained by immersing the specimen in a bath of liquid paraffin during the experiment. Below room temperature ice and salt, dry ice and alcohol, and liquid air, were used in constant temperature baths.
FIGURE 2. Carburised specimen strained showing large load drops caused by mechanical
at -185°C twinning.
cent were observed (Figure 3). As the temperature of test increased, the magnitude of the stress drop at the yield and the lower yield point extension, during the first experiment on each annealed crystal, fell
Carburised Crystals Several different types of stress-strain curve were obtained on carburised crystals pulled at temperatures in the range - 185°C to 230°C. The effects observed, which are shown in Figures 2 to 8, are qualitatively the same as those in polycrystalline iron and occur roughly at the same temperatures. The behaviour between -185°C and 20°C has already been described by Churchman and Cottrell [a]. _4t -185”C, mechanical twins formed in “bursts” [3] very reminiscent of the martensitic transformation in high nickel steels. A large load drop was observed at each burst (Figure 2), the slope of which is a characteristic of the testing machine. The crystallography of this twinning has been described elsewhere [a]. Cleavage fracture
FIGURE 3. Carburised specimen strained (a) first experiment; (b) immediate re-load.
at
-70°C:
P;\S’~ON
.\SD
CH7-RCHIIXN:
DEFORRI;\TlOS
steadil). until the temperature range of 50-70°C was reached. Here the character of the curves changed again. The phenomenon of “blue-brittleness” or repeated I-ielding was observed above 60°C. The average magnitude of the drops in load increased with temperature up to about 13O”C, and above this temperature decreased again until at about 200°C and above, the stress-strain curves were entirely smooth (Figures 5, 6, 7, 8).
OF
IRON
CRYSTALS
stress. Andrade [3] has recentl!. sho\vn that the yield stress u of single crystals of gol(1, silver, cadmium, zinc and bismuth, over quite wide ranges of temperature, is given by a relation of the form suggested by Orowan [6] u = co - AT+ where uo and A are constants. The value of the critical shear stress in aluminium is markedly dependent on purity. The lowest
a
/ L
0
6
6
“E :
-2 ‘4 1”
475
213Oc
4
r”
I%
4
2
2
0
0
2b
5
(
3b
8
FIGURE 4. Carburised specimen strained at 19°C: (a) first experiment; (b) immediate re-load; (c) aged 80 minutes at 6OiF;ilk iFmediate re-load. Carburised specimen strained at 61.5”C: (a) first expe’riment, two hours after reaching 61.5”C; (b) aged 1 hour at 61.5”C; (c) aged 40 hours at 61.5”C.
FIGURE 7. Carburised specimen strained at 193°C: (a) first experiment; (b) aged 2 hours at 193°C; (c) aged 16% hours at 193°C; (d) aged 4% hours at 193°C. FIGURE 8. Carburised specimen strained at 213°C: (a) first experiment; (b) aged 1 hour at 213°C; (c) aged 1 hour at 213°C.
The upper yield stress measured in the first experiment on each of the carburised crystals is plotted a.gainst temperature in Figure 9. The two main features of these results are the very steep temperature dependence of yield stress and the two distinct branches of the curve formed at temperatures above and below about 80°C.
reported values, and thus presumably those for the highest purity of material, are the ones of Rosi and Mathewson [7] on 99.996+ per cent aluminium. They found that the temperature dependence is sufficiently steep to be represented by an equation u = A exp (Q;IRT) where A is a constant Cottrell and Bilby
and Q is an activation energy. [8] have proposed an equation
I ”
2oo
FIGURE 6. Carburised specimen strained at 133°C: (e) first experiment; (b) aged 2 hours at 133°C; (c) aged 18 hours at 133°C; (d) aged 2 hours at 133°C; (e) aged 40 hours at 133°C.
FIGCRE 9. Initial yield stress experiment for carburised crystals.
It is interesting to consider the mathematical form of this curve. Several equations have been proposed for the temperature dependence of yield
for materials in which the dislocations are anchored by atmospheres of solute atoms. They suggest that at a constant testing rate, yielding should occur
T'C versus
temperature
of
ACTX
476
METALLURGICX,
when the quantity I/‘;lkT reaches a characteristic fixed value. L’ (which is a known function of U/UO) is an activation energy for the formation of a stable loop of dislocation, and uo is a constant corresponding to the yield stress at 0°K. The equation U/kT = constant was fitted to the results of McAdam and Mebs [9] for polycrystalline iron, and gave lJ/kT = 47 and uo = 125 Kg/mm2. The results for the single crystals can be fitted better by the Cottrell-Bilby formula than one of the Orowan or Rosi-Mathewson type, between -185°C and 80°C. The value at -185°C is not known absolutely, but since the material forms mechanical twins here at about 28 Kg/mm*, the stress to initiate slip must be larger than this. The values of the constants, for best fit between theoretical and experimental curves, are u. = 117 Kg/mm2 U/kT = 90 Thus uo is approximately equal to that for polycrystalline iron, but I;/kT is appreciably larger. These results are summarized in Figure 10. The Orowan curve is fitted so that u remains positive in
A Cottrell-BItby B. Orcwan
%mpcraturr
VOL.
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1953
specimen causes the initial \vield point to be raised above its normal value.
Decarburised
Crystals
These crystals, which have been subjected to anneals up to 240 hours in wet hydrogen at 72O”C, showed much less pronounced yield phenomena, too small to be detected by routine testing procedures. However, a small upper yield point could be produced by straining and ageing (in situ, and without ever fully unloading the specimen, so that the axiality was undisturbed). The rate of strain ageing was also slowed down very markedly relative to that of carburised crystals. A load drop such as could be produced by ageing for about 1 hour at room temperature in carburised crystals was only produced in decarburised crystals after some 10 to 20 hours at 100°C. The increase in upper yield stress over the final previous applied stress, even after ageing for these long periods, was also much less than that usual for the crystals containing about 0.003 per cent carbon (see Figures 4(c), 12(d)). The types of stress-strain curve which were obtained with the decarburised crystals are as follow: At -185”C, it was possible with fully annealed specimens to produce mechanical twinning just as with carburised crystals, a result different from that obtained earlier [2]. At -7O”C, a small upper yield point was obtained in the first experiment on an annealed crystal. The lower yield stress was comparable with that for a crystal containing 0.003 per cent carbon but the lower yield extension was much less-about 0.4 per cent as against 3 per cent (Figure 11). At room temperature, small load drops were produced after straining 1 per cent and ageing for
“K
FIGURE IO. Comparison of experimental carburised crystals with theoretical curves Cottrell-Bilby and Orowan hypotheses.
results (0) (full lines)
on for
the range considered, and is equal to the twinning stress at -180°C. A further analogy with polycrystals is seen in the rise in initial yield stress which occurs at about 80°C. This temperature coincides closely with that at which repeated yielding begins, i.e. ageing is sufficiently rapid to occur significantly during the time of the experiment. It seems likely that the two phenomena are closely connected, particularly since Holden and Kunz [lo] and Paxton [II] have shown that ageing during the initial stressing of a
FIGCRE 11. Decarburised specimen strained at -73°C: (a) first experiment; (b) immediate re-load; (c) aged 22 hours at 87°C.
18 hours jrl silzt at 110°C (Figure 12). .After straining approximately 3 per cent, it was no longer possible to produce a yield point even after 24 hours ageing at 110°C.
stated limit of accuracy was 0.0002 to 0.0003 per cent, and these results must be considereci as upper limits for the carbon content. It seems very likely that the results on all the decarburised crystals can be reasonably explained on the grounds that insufficient carbon is present to saturate the dislocations. The theoretical amount needed to provide one carbon atom per atom plane intersected by the dislocation (assuming a density of lo8 lines/cm’) is lo+ wt. per cent. The work of Harper [Ia] indicates that in material which has
Decarburised specimen strained at 18°C: FIGURE 12. (a) first experiment; (b) aged 1% hours at 110°C; (c) aged 1 hour at 110°C; (d) aged 18 hours at 110°C; (e) aged 1 hour at 110°C; (j) aged 134 hours at 110°C; (g) aged 24 hours at 110°C; (h) aged 18 hours at 110°C.
*%t lWC, very small initial yield points were observed after strain ageing, increasing to a maximum after about 100 minutes ageing at this temperature. Repeated yielding was not observed (Figure 13).
6
,
1% ,
2
abed
e
f
0
Decarburised FIGURE 13. (a) first experiment; (6) aged $1 minutes at 143°C; (d) aged 47 minutes at l43T; cf) aged
specimen strained at 143T: 100 minutes at 143°C; (c) aged 17% hours at 143*C; (e) aged 17 minutes at 143°C.
At 193”C, yield phenomena were almost nonexistent. A very slight lower yield extension with small strain age-hardening occurred in one crystal after straining 0.25 per cent and ageing 17 hours at 193°C. The rate of work hardening in this crystal was considerably less than in a carburised crystal at this same temperature. A chemical analysis of crystals given a decarburising treatment was kindly arranged by Dr. N. P. Allen of the National Physical Laboratory. Three crystals given 18 hours treatment at 720°C in wet hydrogen contained 0.0006 per cent, 0.0003 per cent and 0.0005 per cent C whilst a crystal decarburised for 240 hours contained 0.0004 per cent C. The
FIGURE11. &carburised specimen strained at IW’C: (n) tirst experiment; (6) aged 17 hours at 193°C; (c) aged iJ4 hours at 193°C; (d) aged 1% hours at 103°C.
been strained a few per cent, the dislocation density is about 10” lines/cm2. Hence, a minimum of about 1O-3 wt. per cent is necessary to saturate all the dislocations in this case. This amount is certainly not present in the decarburised crystals, and so the dislocation atmospheres are not complete. Yield effects are thus reduced, in much the same way as has been noted recently by Wain [13] using zinc containing 0.0022 per cent nitrogen. This is illustrated by comparison of Figure 12(d) and 12(h). A yield point is observed after about 1 per cent strain prior to ageing, but not after about 3 per cent. The number of dislocations has increased so that insu~cient solute atoms are present to saturate the whole length of the dislocation lines. The results of Harper [12] suggest that the density of dislocations p is roughly related to the plastic strain E by the formula p = 2.5 X 101” X E en? Hence for p = 2.5 X to provide ted by the
1 per cent plastic strain, E = 10-s and lOlo lines/cm2. The wt. per cent carbon one carbon atom per atom plane intersecdislocation is 2.5 x 1o1Ox IO_& ---S--
assuming IO+ wt. per cent C for lo8 lines/cm” [8], i.e. 0.00025 per cent. A similar calculation for 3 per cent plastic strain
478
ACT&%
NETALLURGICA,
indicates that 0.00075 per cent is necessary for saturation of the dislocations. The analysis of the crystals gave,a value of about 0.0005 per cent for the carbon content. Thus, although the calculation is approximate, it does indicate that the carbon content is in the right range for yielding to disappear with increasing strain. Repeated yielding does not occur in decarburised crystal since the ageing time is not of the same order as the duration of the experiment.
Repeated Yielding Consideration of the mechanism of repeated yielding is complicated by the fact that it may occur in different forms depending on the metal, and whether this is in single crystal or polycrystalline form, and on the nature of the testing machine. The phenomenon of jerky creep was observed in metal single crystals by Becker and Orowan [14] using commercial-purity zinc. Repeated yielding has been observed by Dumbleton [15] in zinc single crystals, and by Ardley and Cottrell [16] in single crystals of 01- and P-brass. The basic feature of the dislocation theory of the effect is that the speed of diffusion of impurity atoms is sufficiently large to anchor the dislocations very- quickly once these become held up anywhere in the crystal, but insufficiently large to diffuse so rapidly- that a dislocation never effectively breaks away from an atmosphere. There is thus an optimum temperature, for each given strain rate, at which the load drops are a maximum; in the carburised iron crystals this was about 130°C. The nature of the testing machine is important in determining the form of the phenomenon. In a “soft” machine, or with dead loading, the stress does not relax appreciably during a sudden small extension. Thus one would expect deformation to propagate through the entire length of the specimen. This has been observed by McReynolds [17] in impure polycrystalline aluminium. On the other hand, in a “hard” testing machine a sudden extension can cause a marked stress drop. This may be sufficient to reduce the average speed of the dislocations substantially, and to enable anchoring to occur before the deformation has occurred throughout the entire specimen. Examples of this have been noted in polycrystalline iron by Hall [18] and Paxton [19]. At temperatures in the region lOO-2OO”C,remarkably regular repeated yielding occurs in the first experiment on an annealed specimen. This occurs in the portion of the stressstrain curve corresponding to the lower yield exten-
\‘OL.
1,
1953
sion at room temperature. ;it each fall in stress, the yield front moves a constant distance into t~he undeformed material quite rapidly. Anchoring occurs and the stress begins to rise again immediately. When the yield front has passed completely along the specimen, a rising stress-strain curve ensues which is accompanied by much more irregular jerky flow. It would appear that the detailed mechanism in iron single crystals is different from that in other single crystals or in polycrystalline iron. Metallographic study of the initial yield in carburised iron single crystals indicates that a deformation front passes along the specimen in a manner rather similar to that in polycrystals [19]. The lower yield extension in these single crytals decreases with increasing temperature, and it seems probable that at the temperatures at which repeated yielding occurs, it is of the order of 0.1 per cent, which is of the same magnitude as the extension corresponding to each of the load drops. Thus the regular repeated yielding was not observed, since the majority of the specimen has been traversed by the yield front: the second and subsequent load drops are presumably caused by movement of the band front through work hardened material, and as a result occur at successively higher stresses.
Conclusions In single crystals of iron containing about 0.003 per cent carbon it is possible to produce all the phenomena previously found in polycrystals, i.e. cleavage fracture, mechanical twinning, simple and repeated yielding, and, at sufficiently high temperatures, smooth stress-strain curves. In crystals with much less than 0.003 per cent carbon most of the same phenomena occur, but to a much less marked degree. Repeated yielding does not occur at all, for the time of ageing is increased by a factor of lo3 to 10”.
Acknowledgements The authors wish to express their gratitude to Professor A. H. Cottrell for many helpful discussions and Professor D. Hanson and the University of Birmingham for the provision of facilities and financial support.
References 1. SCHWARTZBART, H. and Low, J. R. Trans. A.I.M.E., 185 (1949) 637. 2. CHURCHMAN, A. T. and COTTRELL, A. H. Nature, 167 (1951) 943. 3. MACHLIS, E. S. and COHEN, M. J. Metals, 3 (1951) ‘746. 4. PAXTON, H. R’. Acta Met., 1 (1953) 141.
F':\XTON
AND
CHURCHXAN:
DEFORRI:1TIOS
5. ~~KDRADe, E. 3;. DA C. Phil. Msg., 43 (1952) 1218. 6. OROWAX, E. Z. Phys., 89 (1934) 605. 7. ROSI, F. D. and hTHEWSON, C. H. Trans. A.I.M.E., 188 (19*50) 1159. 8. COTTRELL, A. H. and BILBY, B. h. Proc. Phys. Sot. (London:, A62 (1949) 49. 9. NICADAM, D. J. and MESS, R. W. Trans. A.S.T.M., 43 (19431 SM. 10. HOLDE?;, A. K. aud Kusz, F. W. J. App. Phys., 23 (1952) X19.
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11. Pnsror, H. \V. J. _\pp. Phys., 24 (1953) 10-k. 12. 13. 1-l. 15, 16.
HARPER, S. Phys. Rev., 83 (1!)51) TO!!. \YAIK, H. L. Proc. Phys. Sec. (London), B65 (1952) 886. BECKER, R. and OKOWAK, E. 2. Phys., 72 (1932) 566. DUMBLETOY, hf. J. Ph.D. thesis, Birmingham (1952). ARDLEY, G. W. and COTTRELL, A.%. To be published in Proc. Roy. Sot. 17. MCREYNOLDS, -1. \V. Trans. A.I.N.E., 185 (1949) 32. 18. HALL, E. 0. J. Iron and Steel Inst., 170 (1952) 331. 19. PASTOX, H. iv. Ph.D. thesis, Birlni~~harn <1952).