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The strain-ageing and quench-ageing of tantalum
JOURNAL
THE
OF THE LESS-COMMOS
STRAIN-AGEING
METALS
AND QUENCH-AGEING
OF TANTALUM
SUMMARY
The quench-ageing and strain-ageing of tantalum containing oxygen, nitrogen and carbon as the major impurities have been studied and compared over a range of ageing temperature from 100’ to ZOO’C. Measurement of the Petch parameters r~i and K, at room temperature as a function of ageing time was used to follow the progress of ageing. It is shown that the change in the discontinuous yield with ageing is dependent on the migration of oxygen alone of the elements present. No precipitation occurs during strain-ageing, nor is the rate of strain-ageing affected by extreme changes in the cooling rate from the annealing temperature prior to straining. The rate of quench-ageing is slower than that of strain-ageing at the same temperature but the maximum value of k, developed by quench-ageing is larger than that produced 1~1~ strain-ageing.
INTROI)UCTIOiX
Strain-ageing and quench-ageing are phenomena produced by the association of interstitial solute atoms with dislocations. Most of the experimental work and nearly all of the theoretical discussions have related to effects produced by carbon or nitrogen in n-iron. In some respects, dilute interstitial alloys of tantalum are more is not polymorphic suitable experimental materials because, unlike iron, tantalum nor is it brittle at low temperatures, while it has a large solubility for interstitial solutes. The few papers on strain-ageing in tantalum that have appeared192 refer to special aspects of the problem. Some work on vanadium that may have some relevance to discussions of the phenomena in tantalum has been published recentlys. In the present study the progress of ageing after either quenching from a temperature above which the discontinuous yield disappears or prestraining an annealed specimen to a strain larger than the Liiders strain was followed by measuring the changes in the Petch parameters k, and oi, the lower yield stress being oy = gi $- k,d-h when
zd is the average
* Now at Central Electricity Gloucestershire, England.
(1)
grain
diameter.
Generating
The straightforward, Board,
Berkeley
Nuclear
but tedious, Laboratories,
way of Berkeley,
26
C. L. FORMBY, W. S. OWEN
determining k, and oi from experimental data is to plot oz/as a function of d-t. It is essential that the annealing treatments used to establish a range of grain size do not cause achange in oi. Inimpure tantalumoaissensitive tochangesinannealing temperatureand so this condition cannot be satisfied4. The value of k, can be obtained for each individual specimen directly from eqn. (I) if (sV and d are known and ut can be obtained by some method other than a Petch plot. It has been suggested4v5 that oi can be taken as the point of intersection of the extrapolated strain-hardening curve (CI in Fig. I) and
i; STRAIN
STRAIN
Fig. I. Schematic
stress-strain
curves illustrating the extrapolation
the elastic line (AD). The extrapolation equation of the form
is carried
method of obtaining G(,
out by fitting
(r = Ken
the curve CI to an (2)
CTis the flow stress, e the total strain, and K and n are constants. ously satisfy eqn. (2) and the elastic equation o = EE
cri must simultane(3)
E is Young’s modulus. The extrapolation method can be criticised because the deduced stress-strain curve contains a marked and discontinuous change in slope on increasing the strain .s from the elastic to the plastic condition, whereas the experimental curves for real specimens in which kl/ = o show a more gradual transition from elastic to plastic strain (as, for example, AHBC in Fig. I). This indicates that eqn. (2) is not applicable at very small strains. Nevertheless, work on iron6 and silicon-iron?, in which the grain size can be changed without inducing significant changes in the substructure and in oi, has shown clearly that the value of oi obtained by the Petch and the extrapolation methods is very nearly the same and that both measured parameters J. Less-Common Metals.
g (1965)
25-34
STRAIS-AGEINGAND
27
OUE~CH-AGEINGOFTANTALl;hl
change in the same way with changes in the thermal further opportunities
to test the significance
and mechanical
of oi obtained
variables.
by extrapolation
Two
occurred
during the course of the present work. The quench-ageing experiments were carried out by quenching specimens from a temperature (~ooo”K) above that at which the interstitial atoms evaporate off the dislocations so that, on testing at 20°C (293”K), there is no discontinuous yield and the stress-strain curve is similar to AHRC in Fig. I. On ageing the specimens the discontinuous yield reappears and 0~ had to btx found by the extrapolation method. Evidently, oi was unaffected by the ageing treatment because the value of (T( obtained agreed very well with the stress corresponding to the point H on the stress-strain curare of the quenched specimen. The strain-ageing experiments
were carried out by straining
an annealed
specimen
to a point C (Fig. I)
on the strain-hardening curve, removing the load, ageing and reloading when a new yield stress occurred at the stress corresponding to FK. Thr stress oj, equivalent to cri for the quenched specimens, Whenever the strain-hardening
was obtained by extrapolation of GK using cqn. (2). curve was unaffected by the ageing treatment, so
that GK coincided with JL, and this was the general case with the tantalum allo! investigated, it was found that oj coincided with the stress CT~at which the specimen was unloaded before ageing. There is no agreement about the physical significance of k,V or of UCbut it is clear that ky is a measure of the discontinuous yield effect. Moreover, it increases as the density of the Cottrell atmosphere increases, thus indicating that it can be used as a measure of the stress required to unpin a locked dislocation. The parameter B{ is less easily identified. It is usually considered to bc a “friction stress”, but it appears to be the stress required to move the dislocations at some critical, but at present unknown,
average velocity.
to the motion
It is affected
bv any factor which increases
the resistance
of a free dislocation.
EXPERIhIENTAL
The tantalum
used in the present
experiments
was obtained
meter wire which had been made from an ingot by a sequence
as 0.030 in. dia-
of cold-working
and
annealing treatments, the surface layer being removed by a chemical treatment before annealing. The final cold reduction was 80 per cent and the material was received in this cold-worked condition. The major impurities were oxygen 48 p.p.m., nitrogen 10-20 p.p.m., and carbon 67 p.p.m. Specimens 12 in. long were polished chemically before annealing by self-resistance heating in an all-glass, preheated vacuum chamber in which, after the initial outgassing of the specimen, a vacuum of about 10-6 mm Hg was maintained. After 6 min at c~oo”C the temperature was dccreased at 100°C min-1 but at lower temperatures the cooling rate was reduced to 25°C min-1. After annealing the average grain diameter measured by a lineal intercept method, using the SMITH-GUTTMAK formula”, was 14.5 mm- :. The wire within 2: in. of the connecting blocks was rejected and it was found that over the remaining 7 in. the properties were uniform. The apparatus has been described in detail elsewheres. The tensile tests were carried out at room temperature in a hard-beam Polanyi machine, the specimen being strained at a uniform rate of 0.025 min-1. The load was measured through a Longham-Thompson dynamometer and the load-elongation curve was recorded on a potentiometric recorder.
28
C.
L.
FORMBY,
W. S. OWEN
In the strain-ageing series of experiments as-annealed specimens, or in a few experiments quenched specimens, either I cm or I in. long were prestrained 3 per cent at room temperature. The specimen was unloaded and the ageing-bath, consisting of silicone oil controlled to within 1°C of the nominal temperature, was placed around the specimen without removing it from the tensile machine. The temperature of the bath fell somewhat when the cold chucks and frame entered the oil, but the temperature quickly returned to the preset temperature and the ageing time was measured from the time the specimen reached the ageing temperature. In some tests ageing times of less than 30 min were used and then it was necessary to remove the specimen and chucks from the machine to reduce the time for the specimen to reach the ageing temperature to a negligible proportion of the total ageing time. After ageing, the specimen, still in the test rig, was quenched to room temperature and testing was continued. To minimise the diffusion of interstitials during the quench from 727°C (~ooo”K)- the first step of the quench-ageing sequence-it was found that very rapid cooling was necessary. An effective quench was obtained by heating the specimen by self-resistance in a vacuum and introducing saturated brine cooled to - IO’C into the chamber*. The quenched specimens were stored in liquid nitrogen until aged and tested. The arrangement and density of dislocations was determined by examination of thin foils in a high-resolution electron microscope. To produce the foils the chemically polished as-received wire was annealed and then rolled to 0.002 in. thickness (a reduction of about 80% as in the final stage of preparation of the wire), chemically polished and annealed. It was then strained and aged and, finally, thinned by a standard chemical method. In most specimens the dislocation density was high and so the density was measured by a procedure used by HIRSCH~~. The distribution is assumed to be random. Randomly orientated lines are drawn on the electron photomicrographs and the number of intersections with dislocation lines made per unit length of random line is measured. Then the dislocation density el is
The major experimental difficulty is the measurement of the thickness In the present experiments a statistical method11 was used.
of the foil, d.
RESULTS
The lower yield stress of the annealed strip specimens, used for the electron microscope observations, was 40-45 kg mm-2 compared with an average of 40.2 kg mm-2 for wire specimens with the same heat treatment. In the annealed condition the dislocations were randomly distributed and the density varied from 2.7 to 4.8 x 1010 cm-z, the average being 3.7 x 1010 cm-2. The density values are in good agreement with those reported in a more extensive systematic studyr2. On ageing specimens after straining 3 per cent at room temperature the changes could be followed experimentally only if the ageing temperature was between 100’ and 200% Above 200% the process occurred too quickly and below 100°C the ageing took an impracticably long time. Accordingly, the temperatures chosen were IOO’, 130°, J. Less-Common
Metals,
g (1965) 25-34
STRAlN-AGEIiXG AND QUENCH-AGEING OF TANTALUM
29
160’ and 2oo’C. The stress uj (Fig. I) was found by extrapolation of stress-strain curves for specimens aged for the longest time at each temperature. Some slight increase of of was found between unaged (when ~‘j = af, the stress at which the specimen is unloaded) and fully aged specimens. The increases were 3 per cent at 13o”C, I per cent at 160°C and zero at 2oo’C .The last specimen was aged for IO times longer than the time for maximum yield drop. These changes are within the limits of experimental accuracy and it is unlikely that they represent a real effect. For specimens aged for shorter times, so that the yield discontinuity was small, the continuity of the prestrain work-hardening curve, (IC, Fig. I) with the work-hardening curve of the aged material (KC) could be seen clearly. Thus, it is concluded that the strain ageing of this material causes no detectable change in the work-hardening characteristics and that cj can be assumed to be coincident with uf. Accordingly, k, was calculated by subtracting of from CT,and dividing by rE_A.
Fig. 2. (a) The variation of k, with ageing time at 2oo’C. O, annealed 9oo”C. prestrained 3 yO at 2oOC; q , annealed goo”C, quenched from 727X, prestrained 3”a at zo”C. (b) The variation of k,, with ageing time at 160°C. Specimens annealed 900°C and prestrained 3:/o at 20%. (c) The variation of k, with ageing time at 13oOC. Specimens annealed 900°C and prestrained 3% at 20%. (d) The variation of k, with ageing time at roo”C. Specimens annealed goo”C and prestrained 3% at zo”C. J. Less-Common Metals, 9 (1965)
25-34
30
C. L. FORMBY, W. S. OWEN
The variation of ky with ageing time at four temperatures is shown in Fig. 2. At all four temperatures the curves have the same form and reach the same maximum value, indicating that the same process occurs at each temperature. The time to reach a specified fraction of the ageing is markedly temperature dependent. The strainageing behaviour of freshly quenched specimens was also examined. Specimens which had been annealed at 900°C were quenched from 727”c, prestrained 3 per cent at room temperature and aged at 200°C. The change of kg with ageing time is shown in Fig. z(a). Clearly, prior quenching has no measurable effect on the strain ageing. By quenching from 727°C (~ooo”K) the discontinuous yield was eliminated and the value of kg was effectively zero. The return of the discontinuous yield on ageing was followed by measurement of the rate of increase of k,. Ageing was carried out at 200’ and 160°C because at these temperatures full quench-ageing occurs in a convenient time. The results are shown in Fig. 3. At both temperatures the curves have
Fig. 3. (a) The variation of k, with ageing time for specimens annealed goo”C, quenched from 727°C and aged at 2oo’C. (b) The variation of k, with ageing time for specimens annealed goc”C, quenched from 727°C and aged at 160°C.
the same shape, k, increasing progressively to a maximum. ~~ithin the experimental error the maximum value of k, is the same at both ageing temperatures and it is within the scatter band of experimental values of ky for specimens cooled slowly from the annealing temperature. There was no systematic change of 06 during quench-ageing. DISCUSSION
Both in the strain-ageing and the quench-ageing experiments it was found that the friction stress, aj or ~6 (Fig. I), was the same in the specimens with unpinned dislocations as in the aged specimens. Thus, within the range of dislocation densities and interstitial solute examined, ageing has no effect on the work-hardening characteristics of impure tantalum. J. Less-Commolz Metals, 9 (1965) 25-34
STRAIN-AGEINGAND
31
QUENCH-AGEINGOFTANTALUM
In general,
the parameter
tions in the same manner
K, is affected
as the effectiveness
by material
and experimental
condi-
of pinning as expressed by the stress to
separate a dislocation from its atmosphere. In terms of the dynamic theory of the discontinuous yieldlap15 the average unpinning stress, and the discontinuous yield effect, increase as the density of mobile dislocations, cerr, decreases. Thus, eerr must decrease as ageing progresses and this has been observed directly by etch pit experiments on silicon iron by STEIN AND LowIG. To explain this, a spectrum of unpinning stresses within any crystal
must be assumed.
The unpinning
stress is unlikely
to be
the same for edge and screw components of a dislocation line. When competition is important the amount of impurity segregated to unit. length of dislocation depends upon the local distribution of the dislocations and is only constant for a completely uniform distribution. The applied stress tending to unlock a dislocation depends upon the orientation of the slip plane with respect to the tensile axis and upon any stress concentrating factors or long-range stresses in the material. For all these reasons it is unlikely that the unpinning stress will have a single value in a real crystal and it is necessary to consider effects averaged over a volume large compared with that occupied by a dislocation of unit length and its associated atmosphere. Considering a polycrystalline K,
specimen
= fl
(W)
(5)
W’ is the fraction of the total interstitial content which has segregated to dislocations and fr is a function independent of the ageing temperature but which depends upon the material action
and which is different
of the elastic
stitial acquires
strain
for quench-ageing
fields of the dislocation
and strain-ageing. and interstitial
By the inter-
atom the inter-
a drift velocity
V is the interaction energy, D the diffusivity, k Boltzmann’s constant absolute temperature. From eqn. (6), and ignoring diffusional flow
and T the
From eqns. (5) and (7)
Dt _ = T and specifying
fs(kg) the temperature
t f3 (k,) -=-------_ T
Do exp
Q is the activation
variation
of the diffusivity,
(c! 1 RT
energy for diffusion,
R is the gas constant
and DO is a constant.
Then, fixing k,, log (t/T) should be a linear function of I/T of slope 0.4343 Q/R. The time t is the time to reach the fixed value of ky. The strain-ageing data are plotted in this manner in Fig. 4, the time t used being that to reach 0.38 of the maximum value of kg. The fraction 0.38 was chosen so that the time measurement was in the region of steeply increasing kg and in a part of the graph with a high density of experimental J. Less-Common Metals, g (1965) 25-34
32
C. L. FORMBY, W. S. OWEN
Fig. 4. The variation of t/T with I/T for constant kl for specimens annealed at goo”C, prestrained 3% at zo°C and aged at different temperatures in the range 100' to zoo’C. The carbon and nitrogen lines make arbitrary intercepts.
points so that the accuracy of the measurement of time was a maximum. At this position the ageing is still at an early stage and drift flow, in accordance with eqn. (6), is likely to be dominant. However, even if there is some contribution from a diffusional flux it will not have a significant effect because the change of t with T is very much greater than the change of T itself. For example, t changes by a factor of about IOOO when T is changed by a factor of 1.2. Thus, Dt which controls the diffusional effect changes by nearly the same factor as Dt/T which determines the drift due to elastic interaction (eqn. (7)). The plot of log (t/T) against I/T (Fig. 4) is a straight line. This adds further support to the view that the same process occurs at each temperature in the range 1oo~-2oo~C. Also, it shows that the process is singly activated and that the same diffusing element is responsible for the locking of the dislocations at all temperatures within the range. The gradient of a line through the experimental points is indistinguishable from one drawn assuming the activation energy to be that for the diffusion of oxygen in tantalum (25.4 kcal mole-l)l7. The activation energy for the diffusion of carbon (38.7 kcal mole-r) or nitrogen (37.7 kcal moleer) is considerably higher and lines plotted on Fig. 4 using these values have slopes which differ from that of the line through the experimental points by much more than the experimental error. Thus, the pinning of dislocations during the strain-ageing of tantalum is due to the segregation of oxygen atoms to the dislocations. This conclusion has been reached also, independently, by HENDRIKS~ studying tantalum with a different impurity content and using a different technique. Only two ageing temperatures were used in the quench-ageing experiments and so only two points were obtained on a plot similar to that in Fig. 4. However, the slope of the line joining the two points showed unambiguously that in quench-ageing also the only element producing pinning of the dislocations is oxygen. During the strain-ageing of iron-carbon or iron-nitrogen KY reaches a maximum J.
LeSS-COmmOtt
Metals, g (1965)
25-34
STRAIN-AGEINGAND
QUENCH-AGEINGOFTASTALUM
33
long before the removal of interstitial solute from the matrix is complete but on further ageing oj increase+. The change in oj is attributed to the formation of precipitate particles, although discrete particles have not been distinguished by electron microscopy until still later in the ageing process. The solubility of oxygen in tantalum (about 2 at. 1: at the relevant temperatures) is much greater than that of carbon in iron. The oxygen content of the specimens in the present series was 0.054 at. y/o, and so no precipitation occurred in the matrix, but this does not exclude the possibility of precipitation occurring on the dislocations. However, specimens aged at 160°C for several times the time required to reach the maximum value of k, were examined in the electron microscope and no evidence of precipitates was found. Further, there was no measurable change of oj during strain ageing. Also, work in which oxygen was introduced until precipitation occurred 19has shown that the precipitate is in the form of oxide platelets in the matrix, with no apparent preference for dislocation sites. Thus, it can be concluded that precipitation did not occur during the strain-ageing experiments. In steel strain-ageing is retarded by prior quench-ageing because precipitation of carbide or nitride, and consequently removal of carbon or nitrogen from the matrix, occurs during quench-ageing20. Ageing occurring during slow cooling from the annealing temperature is sufficient to produce the effect. However, as shown by the data plotted in Fig. z(a), for tantalum-oxygen the rate of strain-ageing is unaffected by a large change in the cooling rate from the annealing temperature. The value of ui and the maximum value of KU are also unchanged, showing that no precipitation occurs during slow cooling from the annealing temperature. .4 striking feature of the experimental results is the clear evidence that at the same temperature quench-ageing is a slower process than strain-ageing and that by quench-ageing amuch higher maximum value of KYis obtained. The value attained by quench-ageing is equal to the value of k, in slowly cooled specimens but is 2.6 times larger than the value developed by strain-ageing. A similar effect has been observed in iron-carbon alloysi*. Since, as has been shown earlier, in the strain-ageing and quench-ageing of tantalum the effective migrating atom is oxygen alone, the distribution of dislocations is random and no precipitation occurs, the sole difference in the two cases is the dislocation density. Thus, the high value of k, obtained by annealing or by quench-ageing is attributed to the relatively low dislocation density. This may be because the average distance from the tip of a slip band to the nearest dislocation source is larger in the specimen with a low dislocation density, as suggested by WILSON ASD I
In tantalum containing 48 p.p.m. of oxygen, 10-20 p.p.m. of nitrogen and 67 p.p.m. of carbon and aged at temperatures between 100' and 200%: (I) The work-hardening characteristics are not changed significantly by ageing. (2) Dislocation pinning is due to oxygen alone. (3) No precipitation occurs during strain-ageing.
34
C. L. FORMBY,
W. S. OWEN
(4) The rate of strain-ageing is not affected by the rate of cooling from the annealing temperature prior to prestraining, indicating that quench-ageing has no effect on strain-ageing. (5) The value of the parameter IQ, in fully quench-aged specimens is the same as in annealed specimens but is much larger than the maximum value which can be developed by strain-ageing. The difference is a direct result of a difference in dislocation density. ACKNOWLEDGEMENTS
The work was supported financially and the experimental material was supplied by the United States Air Force under Manlabs Subcontract AF33(616) 6838 and Contract AF61(o3z)-689, Materials Laboratory, W.A.D.C., Wright-Patterson Air Force Base, Ohio. This assistance is gratefully acknowledged. REFERENCES I A. R. ROSENFIELD AND W. S. OWEN, Trans. AIME, 2 P. L. HENDRIKS, personal communication.
zz7 (1963) 603.
3 J. W. EDINGTON, T. C. LINDLEY AND R. E. SMALLMAN, Acta. Met., 12 (1964) 10~5. A. GILBERT, D. HULL, W. S. OWEN AND C. M. REID, J. Less-Common Metals, 4 (1962) 399. A. H. COTTRELL, Trans. AIME, 212 (1958) 192. I. MOGFORD AND D. HULL, J. Iron SteelInst., zor (1963) 55. W. JOLLEY AND D. HULL, personal communication. 8 C. L. FORMBY, Ph.D. Thesis, Univ. Liverpool, 1964. 9 C. S. SMITH AND L. GUTTMAN, J. Metals, 5 (1953) 81. IO P. B. HIRSCH, J. Inst. Metals, 87 (1959) 406. II C. L. FORMBY, Measurement of the thickeners of thin foils, to be published. 12 I. D. MCIVOR, D. HULL AND W. S. OWEN, The Relation between the Structure and Mechanical Properties of Metals, (Natl. Phys. Lab. Symp. No. IS), H.M. Stationery Office, London, 1963.
4 5 6 7
P. 595. 13 W. G. JOHNSTON AND J. J. GILMAN, J. AppZ. Phys., 30 (1959) 129. 14 G. T. HAHN, Acta. Met., IO (1962) 727. 15 A. H. COTTRELL, The Relation between the Structure and Mechanical Properties of Metals, (Natl. Phys. Lab. Symp. No. 15). H.M. Stationery Office, London, 1963, p. 455. 16 D. F. STEIN AND J. R. Low, General Electric Res. Lab., Rept. No. 6r-RL-z816M, 1961; see also: Trans. AIME, 221 (1961) 744. 17 R. W. POWERS AND M. V. DOYLE; J. Appl. Phys., 30 (1959) 514. 18 D. V. WILSON AND B. RUSSELL, Acta. Met., 8 (1960) 36 and 468. 19 D. A. VAUGHAN, 0. M. STEWART AND C. M. SCHWARTZ, Trans. AIME, 221 (1961) 937. 20 A. H. COTTRELL AND G. M. LEAK, J. Iron Steel Inst., 172 (1952) 301.
J. Less-Common Metals, 9 (1965) 25-34
THE
OF THE LESS-COMMOS
STRAIN-AGEING
METALS
AND QUENCH-AGEING
OF TANTALUM
SUMMARY
The quench-ageing and strain-ageing of tantalum containing oxygen, nitrogen and carbon as the major impurities have been studied and compared over a range of ageing temperature from 100’ to ZOO’C. Measurement of the Petch parameters r~i and K, at room temperature as a function of ageing time was used to follow the progress of ageing. It is shown that the change in the discontinuous yield with ageing is dependent on the migration of oxygen alone of the elements present. No precipitation occurs during strain-ageing, nor is the rate of strain-ageing affected by extreme changes in the cooling rate from the annealing temperature prior to straining. The rate of quench-ageing is slower than that of strain-ageing at the same temperature but the maximum value of k, developed by quench-ageing is larger than that produced 1~1~ strain-ageing.
INTROI)UCTIOiX
Strain-ageing and quench-ageing are phenomena produced by the association of interstitial solute atoms with dislocations. Most of the experimental work and nearly all of the theoretical discussions have related to effects produced by carbon or nitrogen in n-iron. In some respects, dilute interstitial alloys of tantalum are more is not polymorphic suitable experimental materials because, unlike iron, tantalum nor is it brittle at low temperatures, while it has a large solubility for interstitial solutes. The few papers on strain-ageing in tantalum that have appeared192 refer to special aspects of the problem. Some work on vanadium that may have some relevance to discussions of the phenomena in tantalum has been published recentlys. In the present study the progress of ageing after either quenching from a temperature above which the discontinuous yield disappears or prestraining an annealed specimen to a strain larger than the Liiders strain was followed by measuring the changes in the Petch parameters k, and oi, the lower yield stress being oy = gi $- k,d-h when
zd is the average
* Now at Central Electricity Gloucestershire, England.
(1)
grain
diameter.
Generating
The straightforward, Board,
Berkeley
Nuclear
but tedious, Laboratories,
way of Berkeley,
26
C. L. FORMBY, W. S. OWEN
determining k, and oi from experimental data is to plot oz/as a function of d-t. It is essential that the annealing treatments used to establish a range of grain size do not cause achange in oi. Inimpure tantalumoaissensitive tochangesinannealing temperatureand so this condition cannot be satisfied4. The value of k, can be obtained for each individual specimen directly from eqn. (I) if (sV and d are known and ut can be obtained by some method other than a Petch plot. It has been suggested4v5 that oi can be taken as the point of intersection of the extrapolated strain-hardening curve (CI in Fig. I) and
i; STRAIN
STRAIN
Fig. I. Schematic
stress-strain
curves illustrating the extrapolation
the elastic line (AD). The extrapolation equation of the form
is carried
method of obtaining G(,
out by fitting
(r = Ken
the curve CI to an (2)
CTis the flow stress, e the total strain, and K and n are constants. ously satisfy eqn. (2) and the elastic equation o = EE
cri must simultane(3)
E is Young’s modulus. The extrapolation method can be criticised because the deduced stress-strain curve contains a marked and discontinuous change in slope on increasing the strain .s from the elastic to the plastic condition, whereas the experimental curves for real specimens in which kl/ = o show a more gradual transition from elastic to plastic strain (as, for example, AHBC in Fig. I). This indicates that eqn. (2) is not applicable at very small strains. Nevertheless, work on iron6 and silicon-iron?, in which the grain size can be changed without inducing significant changes in the substructure and in oi, has shown clearly that the value of oi obtained by the Petch and the extrapolation methods is very nearly the same and that both measured parameters J. Less-Common Metals.
g (1965)
25-34
STRAIS-AGEINGAND
27
OUE~CH-AGEINGOFTANTALl;hl
change in the same way with changes in the thermal further opportunities
to test the significance
and mechanical
of oi obtained
variables.
by extrapolation
Two
occurred
during the course of the present work. The quench-ageing experiments were carried out by quenching specimens from a temperature (~ooo”K) above that at which the interstitial atoms evaporate off the dislocations so that, on testing at 20°C (293”K), there is no discontinuous yield and the stress-strain curve is similar to AHRC in Fig. I. On ageing the specimens the discontinuous yield reappears and 0~ had to btx found by the extrapolation method. Evidently, oi was unaffected by the ageing treatment because the value of (T( obtained agreed very well with the stress corresponding to the point H on the stress-strain curare of the quenched specimen. The strain-ageing experiments
were carried out by straining
an annealed
specimen
to a point C (Fig. I)
on the strain-hardening curve, removing the load, ageing and reloading when a new yield stress occurred at the stress corresponding to FK. Thr stress oj, equivalent to cri for the quenched specimens, Whenever the strain-hardening
was obtained by extrapolation of GK using cqn. (2). curve was unaffected by the ageing treatment, so
that GK coincided with JL, and this was the general case with the tantalum allo! investigated, it was found that oj coincided with the stress CT~at which the specimen was unloaded before ageing. There is no agreement about the physical significance of k,V or of UCbut it is clear that ky is a measure of the discontinuous yield effect. Moreover, it increases as the density of the Cottrell atmosphere increases, thus indicating that it can be used as a measure of the stress required to unpin a locked dislocation. The parameter B{ is less easily identified. It is usually considered to bc a “friction stress”, but it appears to be the stress required to move the dislocations at some critical, but at present unknown,
average velocity.
to the motion
It is affected
bv any factor which increases
the resistance
of a free dislocation.
EXPERIhIENTAL
The tantalum
used in the present
experiments
was obtained
meter wire which had been made from an ingot by a sequence
as 0.030 in. dia-
of cold-working
and
annealing treatments, the surface layer being removed by a chemical treatment before annealing. The final cold reduction was 80 per cent and the material was received in this cold-worked condition. The major impurities were oxygen 48 p.p.m., nitrogen 10-20 p.p.m., and carbon 67 p.p.m. Specimens 12 in. long were polished chemically before annealing by self-resistance heating in an all-glass, preheated vacuum chamber in which, after the initial outgassing of the specimen, a vacuum of about 10-6 mm Hg was maintained. After 6 min at c~oo”C the temperature was dccreased at 100°C min-1 but at lower temperatures the cooling rate was reduced to 25°C min-1. After annealing the average grain diameter measured by a lineal intercept method, using the SMITH-GUTTMAK formula”, was 14.5 mm- :. The wire within 2: in. of the connecting blocks was rejected and it was found that over the remaining 7 in. the properties were uniform. The apparatus has been described in detail elsewheres. The tensile tests were carried out at room temperature in a hard-beam Polanyi machine, the specimen being strained at a uniform rate of 0.025 min-1. The load was measured through a Longham-Thompson dynamometer and the load-elongation curve was recorded on a potentiometric recorder.
28
C.
L.
FORMBY,
W. S. OWEN
In the strain-ageing series of experiments as-annealed specimens, or in a few experiments quenched specimens, either I cm or I in. long were prestrained 3 per cent at room temperature. The specimen was unloaded and the ageing-bath, consisting of silicone oil controlled to within 1°C of the nominal temperature, was placed around the specimen without removing it from the tensile machine. The temperature of the bath fell somewhat when the cold chucks and frame entered the oil, but the temperature quickly returned to the preset temperature and the ageing time was measured from the time the specimen reached the ageing temperature. In some tests ageing times of less than 30 min were used and then it was necessary to remove the specimen and chucks from the machine to reduce the time for the specimen to reach the ageing temperature to a negligible proportion of the total ageing time. After ageing, the specimen, still in the test rig, was quenched to room temperature and testing was continued. To minimise the diffusion of interstitials during the quench from 727°C (~ooo”K)- the first step of the quench-ageing sequence-it was found that very rapid cooling was necessary. An effective quench was obtained by heating the specimen by self-resistance in a vacuum and introducing saturated brine cooled to - IO’C into the chamber*. The quenched specimens were stored in liquid nitrogen until aged and tested. The arrangement and density of dislocations was determined by examination of thin foils in a high-resolution electron microscope. To produce the foils the chemically polished as-received wire was annealed and then rolled to 0.002 in. thickness (a reduction of about 80% as in the final stage of preparation of the wire), chemically polished and annealed. It was then strained and aged and, finally, thinned by a standard chemical method. In most specimens the dislocation density was high and so the density was measured by a procedure used by HIRSCH~~. The distribution is assumed to be random. Randomly orientated lines are drawn on the electron photomicrographs and the number of intersections with dislocation lines made per unit length of random line is measured. Then the dislocation density el is
The major experimental difficulty is the measurement of the thickness In the present experiments a statistical method11 was used.
of the foil, d.
RESULTS
The lower yield stress of the annealed strip specimens, used for the electron microscope observations, was 40-45 kg mm-2 compared with an average of 40.2 kg mm-2 for wire specimens with the same heat treatment. In the annealed condition the dislocations were randomly distributed and the density varied from 2.7 to 4.8 x 1010 cm-z, the average being 3.7 x 1010 cm-2. The density values are in good agreement with those reported in a more extensive systematic studyr2. On ageing specimens after straining 3 per cent at room temperature the changes could be followed experimentally only if the ageing temperature was between 100’ and 200% Above 200% the process occurred too quickly and below 100°C the ageing took an impracticably long time. Accordingly, the temperatures chosen were IOO’, 130°, J. Less-Common
Metals,
g (1965) 25-34
STRAlN-AGEIiXG AND QUENCH-AGEING OF TANTALUM
29
160’ and 2oo’C. The stress uj (Fig. I) was found by extrapolation of stress-strain curves for specimens aged for the longest time at each temperature. Some slight increase of of was found between unaged (when ~‘j = af, the stress at which the specimen is unloaded) and fully aged specimens. The increases were 3 per cent at 13o”C, I per cent at 160°C and zero at 2oo’C .The last specimen was aged for IO times longer than the time for maximum yield drop. These changes are within the limits of experimental accuracy and it is unlikely that they represent a real effect. For specimens aged for shorter times, so that the yield discontinuity was small, the continuity of the prestrain work-hardening curve, (IC, Fig. I) with the work-hardening curve of the aged material (KC) could be seen clearly. Thus, it is concluded that the strain ageing of this material causes no detectable change in the work-hardening characteristics and that cj can be assumed to be coincident with uf. Accordingly, k, was calculated by subtracting of from CT,and dividing by rE_A.
Fig. 2. (a) The variation of k, with ageing time at 2oo’C. O, annealed 9oo”C. prestrained 3 yO at 2oOC; q , annealed goo”C, quenched from 727X, prestrained 3”a at zo”C. (b) The variation of k,, with ageing time at 160°C. Specimens annealed 900°C and prestrained 3:/o at 20%. (c) The variation of k, with ageing time at 13oOC. Specimens annealed 900°C and prestrained 3% at 20%. (d) The variation of k, with ageing time at roo”C. Specimens annealed goo”C and prestrained 3% at zo”C. J. Less-Common Metals, 9 (1965)
25-34
30
C. L. FORMBY, W. S. OWEN
The variation of ky with ageing time at four temperatures is shown in Fig. 2. At all four temperatures the curves have the same form and reach the same maximum value, indicating that the same process occurs at each temperature. The time to reach a specified fraction of the ageing is markedly temperature dependent. The strainageing behaviour of freshly quenched specimens was also examined. Specimens which had been annealed at 900°C were quenched from 727”c, prestrained 3 per cent at room temperature and aged at 200°C. The change of kg with ageing time is shown in Fig. z(a). Clearly, prior quenching has no measurable effect on the strain ageing. By quenching from 727°C (~ooo”K) the discontinuous yield was eliminated and the value of kg was effectively zero. The return of the discontinuous yield on ageing was followed by measurement of the rate of increase of k,. Ageing was carried out at 200’ and 160°C because at these temperatures full quench-ageing occurs in a convenient time. The results are shown in Fig. 3. At both temperatures the curves have
Fig. 3. (a) The variation of k, with ageing time for specimens annealed goo”C, quenched from 727°C and aged at 2oo’C. (b) The variation of k, with ageing time for specimens annealed goc”C, quenched from 727°C and aged at 160°C.
the same shape, k, increasing progressively to a maximum. ~~ithin the experimental error the maximum value of k, is the same at both ageing temperatures and it is within the scatter band of experimental values of ky for specimens cooled slowly from the annealing temperature. There was no systematic change of 06 during quench-ageing. DISCUSSION
Both in the strain-ageing and the quench-ageing experiments it was found that the friction stress, aj or ~6 (Fig. I), was the same in the specimens with unpinned dislocations as in the aged specimens. Thus, within the range of dislocation densities and interstitial solute examined, ageing has no effect on the work-hardening characteristics of impure tantalum. J. Less-Commolz Metals, 9 (1965) 25-34
STRAIN-AGEINGAND
31
QUENCH-AGEINGOFTANTALUM
In general,
the parameter
tions in the same manner
K, is affected
as the effectiveness
by material
and experimental
condi-
of pinning as expressed by the stress to
separate a dislocation from its atmosphere. In terms of the dynamic theory of the discontinuous yieldlap15 the average unpinning stress, and the discontinuous yield effect, increase as the density of mobile dislocations, cerr, decreases. Thus, eerr must decrease as ageing progresses and this has been observed directly by etch pit experiments on silicon iron by STEIN AND LowIG. To explain this, a spectrum of unpinning stresses within any crystal
must be assumed.
The unpinning
stress is unlikely
to be
the same for edge and screw components of a dislocation line. When competition is important the amount of impurity segregated to unit. length of dislocation depends upon the local distribution of the dislocations and is only constant for a completely uniform distribution. The applied stress tending to unlock a dislocation depends upon the orientation of the slip plane with respect to the tensile axis and upon any stress concentrating factors or long-range stresses in the material. For all these reasons it is unlikely that the unpinning stress will have a single value in a real crystal and it is necessary to consider effects averaged over a volume large compared with that occupied by a dislocation of unit length and its associated atmosphere. Considering a polycrystalline K,
specimen
= fl
(W)
(5)
W’ is the fraction of the total interstitial content which has segregated to dislocations and fr is a function independent of the ageing temperature but which depends upon the material action
and which is different
of the elastic
stitial acquires
strain
for quench-ageing
fields of the dislocation
and strain-ageing. and interstitial
By the inter-
atom the inter-
a drift velocity
V is the interaction energy, D the diffusivity, k Boltzmann’s constant absolute temperature. From eqn. (6), and ignoring diffusional flow
and T the
From eqns. (5) and (7)
Dt _ = T and specifying
fs(kg) the temperature
t f3 (k,) -=-------_ T
Do exp
Q is the activation
variation
of the diffusivity,
(c! 1 RT
energy for diffusion,
R is the gas constant
and DO is a constant.
Then, fixing k,, log (t/T) should be a linear function of I/T of slope 0.4343 Q/R. The time t is the time to reach the fixed value of ky. The strain-ageing data are plotted in this manner in Fig. 4, the time t used being that to reach 0.38 of the maximum value of kg. The fraction 0.38 was chosen so that the time measurement was in the region of steeply increasing kg and in a part of the graph with a high density of experimental J. Less-Common Metals, g (1965) 25-34
32
C. L. FORMBY, W. S. OWEN
Fig. 4. The variation of t/T with I/T for constant kl for specimens annealed at goo”C, prestrained 3% at zo°C and aged at different temperatures in the range 100' to zoo’C. The carbon and nitrogen lines make arbitrary intercepts.
points so that the accuracy of the measurement of time was a maximum. At this position the ageing is still at an early stage and drift flow, in accordance with eqn. (6), is likely to be dominant. However, even if there is some contribution from a diffusional flux it will not have a significant effect because the change of t with T is very much greater than the change of T itself. For example, t changes by a factor of about IOOO when T is changed by a factor of 1.2. Thus, Dt which controls the diffusional effect changes by nearly the same factor as Dt/T which determines the drift due to elastic interaction (eqn. (7)). The plot of log (t/T) against I/T (Fig. 4) is a straight line. This adds further support to the view that the same process occurs at each temperature in the range 1oo~-2oo~C. Also, it shows that the process is singly activated and that the same diffusing element is responsible for the locking of the dislocations at all temperatures within the range. The gradient of a line through the experimental points is indistinguishable from one drawn assuming the activation energy to be that for the diffusion of oxygen in tantalum (25.4 kcal mole-l)l7. The activation energy for the diffusion of carbon (38.7 kcal mole-r) or nitrogen (37.7 kcal moleer) is considerably higher and lines plotted on Fig. 4 using these values have slopes which differ from that of the line through the experimental points by much more than the experimental error. Thus, the pinning of dislocations during the strain-ageing of tantalum is due to the segregation of oxygen atoms to the dislocations. This conclusion has been reached also, independently, by HENDRIKS~ studying tantalum with a different impurity content and using a different technique. Only two ageing temperatures were used in the quench-ageing experiments and so only two points were obtained on a plot similar to that in Fig. 4. However, the slope of the line joining the two points showed unambiguously that in quench-ageing also the only element producing pinning of the dislocations is oxygen. During the strain-ageing of iron-carbon or iron-nitrogen KY reaches a maximum J.
LeSS-COmmOtt
Metals, g (1965)
25-34
STRAIN-AGEINGAND
QUENCH-AGEINGOFTASTALUM
33
long before the removal of interstitial solute from the matrix is complete but on further ageing oj increase+. The change in oj is attributed to the formation of precipitate particles, although discrete particles have not been distinguished by electron microscopy until still later in the ageing process. The solubility of oxygen in tantalum (about 2 at. 1: at the relevant temperatures) is much greater than that of carbon in iron. The oxygen content of the specimens in the present series was 0.054 at. y/o, and so no precipitation occurred in the matrix, but this does not exclude the possibility of precipitation occurring on the dislocations. However, specimens aged at 160°C for several times the time required to reach the maximum value of k, were examined in the electron microscope and no evidence of precipitates was found. Further, there was no measurable change of oj during strain ageing. Also, work in which oxygen was introduced until precipitation occurred 19has shown that the precipitate is in the form of oxide platelets in the matrix, with no apparent preference for dislocation sites. Thus, it can be concluded that precipitation did not occur during the strain-ageing experiments. In steel strain-ageing is retarded by prior quench-ageing because precipitation of carbide or nitride, and consequently removal of carbon or nitrogen from the matrix, occurs during quench-ageing20. Ageing occurring during slow cooling from the annealing temperature is sufficient to produce the effect. However, as shown by the data plotted in Fig. z(a), for tantalum-oxygen the rate of strain-ageing is unaffected by a large change in the cooling rate from the annealing temperature. The value of ui and the maximum value of KU are also unchanged, showing that no precipitation occurs during slow cooling from the annealing temperature. .4 striking feature of the experimental results is the clear evidence that at the same temperature quench-ageing is a slower process than strain-ageing and that by quench-ageing amuch higher maximum value of KYis obtained. The value attained by quench-ageing is equal to the value of k, in slowly cooled specimens but is 2.6 times larger than the value developed by strain-ageing. A similar effect has been observed in iron-carbon alloysi*. Since, as has been shown earlier, in the strain-ageing and quench-ageing of tantalum the effective migrating atom is oxygen alone, the distribution of dislocations is random and no precipitation occurs, the sole difference in the two cases is the dislocation density. Thus, the high value of k, obtained by annealing or by quench-ageing is attributed to the relatively low dislocation density. This may be because the average distance from the tip of a slip band to the nearest dislocation source is larger in the specimen with a low dislocation density, as suggested by WILSON ASD I
In tantalum containing 48 p.p.m. of oxygen, 10-20 p.p.m. of nitrogen and 67 p.p.m. of carbon and aged at temperatures between 100' and 200%: (I) The work-hardening characteristics are not changed significantly by ageing. (2) Dislocation pinning is due to oxygen alone. (3) No precipitation occurs during strain-ageing.
34
C. L. FORMBY,
W. S. OWEN
(4) The rate of strain-ageing is not affected by the rate of cooling from the annealing temperature prior to prestraining, indicating that quench-ageing has no effect on strain-ageing. (5) The value of the parameter IQ, in fully quench-aged specimens is the same as in annealed specimens but is much larger than the maximum value which can be developed by strain-ageing. The difference is a direct result of a difference in dislocation density. ACKNOWLEDGEMENTS
The work was supported financially and the experimental material was supplied by the United States Air Force under Manlabs Subcontract AF33(616) 6838 and Contract AF61(o3z)-689, Materials Laboratory, W.A.D.C., Wright-Patterson Air Force Base, Ohio. This assistance is gratefully acknowledged. REFERENCES I A. R. ROSENFIELD AND W. S. OWEN, Trans. AIME, 2 P. L. HENDRIKS, personal communication.
zz7 (1963) 603.
3 J. W. EDINGTON, T. C. LINDLEY AND R. E. SMALLMAN, Acta. Met., 12 (1964) 10~5. A. GILBERT, D. HULL, W. S. OWEN AND C. M. REID, J. Less-Common Metals, 4 (1962) 399. A. H. COTTRELL, Trans. AIME, 212 (1958) 192. I. MOGFORD AND D. HULL, J. Iron SteelInst., zor (1963) 55. W. JOLLEY AND D. HULL, personal communication. 8 C. L. FORMBY, Ph.D. Thesis, Univ. Liverpool, 1964. 9 C. S. SMITH AND L. GUTTMAN, J. Metals, 5 (1953) 81. IO P. B. HIRSCH, J. Inst. Metals, 87 (1959) 406. II C. L. FORMBY, Measurement of the thickeners of thin foils, to be published. 12 I. D. MCIVOR, D. HULL AND W. S. OWEN, The Relation between the Structure and Mechanical Properties of Metals, (Natl. Phys. Lab. Symp. No. IS), H.M. Stationery Office, London, 1963.
4 5 6 7
P. 595. 13 W. G. JOHNSTON AND J. J. GILMAN, J. AppZ. Phys., 30 (1959) 129. 14 G. T. HAHN, Acta. Met., IO (1962) 727. 15 A. H. COTTRELL, The Relation between the Structure and Mechanical Properties of Metals, (Natl. Phys. Lab. Symp. No. 15). H.M. Stationery Office, London, 1963, p. 455. 16 D. F. STEIN AND J. R. Low, General Electric Res. Lab., Rept. No. 6r-RL-z816M, 1961; see also: Trans. AIME, 221 (1961) 744. 17 R. W. POWERS AND M. V. DOYLE; J. Appl. Phys., 30 (1959) 514. 18 D. V. WILSON AND B. RUSSELL, Acta. Met., 8 (1960) 36 and 468. 19 D. A. VAUGHAN, 0. M. STEWART AND C. M. SCHWARTZ, Trans. AIME, 221 (1961) 937. 20 A. H. COTTRELL AND G. M. LEAK, J. Iron Steel Inst., 172 (1952) 301.
J. Less-Common Metals, 9 (1965) 25-34