The temperature dependence of the flow-stress of heavily-deformed doped tungsten

427

JOURNAL OF THE LESS-COMMON METALS Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

THE TEMPERATURE HEAVILY-DEFORMED

DEPENDENCE OF THE FLOW-STRESS DOPED TUNGSTEN

OF

0. BOSER The Bayside Research 11360 (U.S.A.)

Center of General Telephone & Electronics

L&oratories

Inc., Bayside, New York

(Received August 14th, 1970, Revised November 19th, 1970)

SUMMARY

The flow stress of cold-worked, doped tungsten has been determined in the temperature range from 770K (liquid nitrogen) to about 8OU’K. The tungsten specimens were fibrous with a (110) texture in the Qri\bing direction. The measured flow stress was attributed to two components. The temperature independent part is due to a long-range dislocation-dislocation interaction and prevails solely at elevated temperatures. The temperature dependent component was analyzed according to a theory ofelastic dipoles interacting in a thermally activated process with dislocations. The Gibbs free activation enthalpy, AGo, and the dipole concentration, C,, derived from that analysis are AG, = 1.59 eV and C, =800 at. p.p.m., respectively. From these results an activation volume was calculated and compared to the one measured by strain rate changes. The agreement is very good, suggesting that an elastic dipoledislocation interaction indeed explains the increase of the flow stress with decreasing temperature. The origin of the elastic dipoles cannot be determined unambiguously from this investigation. The elastic dipoles might, however, be due either to impurity atoms in interstitial solution, such as carbon or nitrogen, or to small agglomerates of these impurities. Both possibilities are within the limits of the concentrations found by chemical analysis.

INTRODUCTION

To make substantial improvements in the fabrication and application of tungsten, its fundamental deformation behavior1-3 has to be understood.’ There is still a question whether or not tungsten is an inherently brittle material. Deformation experiments with high-purity, single crystals4-’ show, however, that plastic flow occurs at all temperatures, even at the temperature of liquid helium’ O.These qualitative results of a decreasing flow stress with decreasing impurity content seem to invalidate the hypothesis that the overcoming of the Peierls potential by the moving dislocation is the rate-controlling factor. This assumption becomes even more questionable in view of a detailed theory 11*12that makes it possible to explain the temperature dependence of the flow stress on the basis of a thermally-activated interactian between J. Less-Common

Metals, 23 (1971) 427-435

0. BOSER

428

the dislocations and the impurities that are in interstitial solution, which can be described by elastic dipoles. The distortions produced by the impurities have been calculated from the analysis of the temperature dependence of the yield stress and are in agreement with those found from internal friction measurements (Snoeck effect) in iron. It has been further demonstrated that the same principles of impurity interaction can be used to explain the temperature dependence of the yield stress of single crystals of various b.c.c. metals147’ 5 including tungsten. In the following it will be shown that these principles can be applied to the case of heavily-deformed, doped tungsten, and that its flow stress at low temperatures is predominantly due to impurities. MATERIAL AND EXPERIMENTAL

PROCEDURES

The tungsten used was obtained from the Sylvania Chemical and Metallurgical Division, Towanda, Pa., in the form of a ribbon which was produced from aluminasilica-doped tungsten wire. The original 0.023 in. diam. wire was flattened to a ribbon 0.010 in. by 0.040 in. at temperatures of about 1000°C. The ribbon shape was selected instead of the usual round, cylindrical wire shape because a ribbon is much easier to hold in clamps for deformation tests without introducing notches. Analysis of the tungsten ribbon by quantitative emission spectroscopy gave the following concentrations of metallic impurities (in weight p.p.m.) : Ca 0.92

cu 0.01

Mg 1.0

Mn 1.0

Si 1.0

Sn 1.0

Al 7.1

Cr 6.1

Fe 7.5

K 66

MO 13

Na 6

Nitrogen c,=5to50

Hydrogen Cu=6

Carbon cc=50

Oxygen Co = 26-27

Ni 16

Oxygen was determined by neutron activation analysis and carbon by inert gas fusion analysis. The nitrogen content, obtained by three different chemical methods, varied widely. Tensile tests were carried out with specimens 2 in. long, cut from the spool and clamped in flat grips, 1.5 in. apart. The distance between the grips was taken as the gauge length when the elongation was calculated. Tests where the specimens broke close to the grips were rejected to avoid any influence of the grip in introducing notches or other stress concentrations. Tensile tests were performed on an Instron testing machine, Model TT-CM-4, which was modified to allow immersion of the specimen in low-temperature baths as well as in a furnace which could be used up to 500°C. For high-temperature experiments, the specimens were protected from oxidation by an argon atmosphere. The basic extension rate was 0.002 in/mm Strain-rate changes were made to 0.005 in./min. The deformation curve was registered on a recorder and the final extension of the specimen was measured by a dial gauge attached to the Instron whose accuracy was f0.005 in. The microstructure was determined by optical and electron microscopic examination of etched ribbon samples. The structure was very much like that obtained J. Less-Common Metals, 23 (1971) 427-435

429

FLOW STRESS OF HEAVILY DEFORMED DOPED TUNGSTEN

for wireP. The ribbon consisted of a large number of fibers whose average width was N 1 w. The fiber length was diftkult to &ermiue, since the fibers were very long compared with their width and no well-defined end could be detected. The individual fibers were lenticular in cross section. The texture of the ribbons was measured and compared with the texture of 0.010 in. and 0.025 in. diam. tungsten wire. The (110) texture of the ribbon in the drawing and rolling direction was verypronouuced’6~‘7. The texture of the ribbon closely resembled that of the O.OlOin. diam. wire. Opinslcy et al.” determined the dislocation density of tungsten wires of various diameters by an X-ray method. The dislocation density, nn, appropriate for the heavily-deformed tungsten ribbon is approximately 10” cm-‘, RESULTS AND DISCUSSION

The deformation curves of the as-received, heavily-deformed tungsten ribbon at various deformation temperatures are compiled in Fig. 1. Certain characteristic ranges can easily be distinguished : (a) at plastic strains of less than 1% the #low stress increases rapidly, (b) the first range is fohowed by a region of constant stress. ELASTIC

1,.

OO

. 2

UNE

.

.

4

Fig 1. Ihfonnation cunea vs. mginming strain.

.

6 STRAIN

. 6

.d

.

. IO

,

I 12

W

of as-rtxeivcd ribbon at various deformation temperatures. Engineering stress

From the deformation curves (Fig. 1) two eharacte&ic stresses have .been determined : the *ld stress, 6,’ takeal qs ,tlw s.tre!ssataM% *tic strain and the ultb ate tens&strtnq& ma, taken a#reetr(rss ofthe @ate-au. T@ temperature&pen&nce of these two stresses is shown in Fig. 2. The rapid increase of the flow stress with decreasing temperature jsclearly evident. At the high-temperature end of the curve both the yield stress and 0 u 1Sbecome fairly temperature insensitive. Thk behaviour J. Less-Common

Meh,

23 (1971) 427-435

430

0. BOSER

i

I

0 -200

-100

0

100

TEMPERATURE

200

300

400

500

CC)

pig. 2. The temperature dependence of the yield stress, cY, (open symbols and the ultimate tensile strength, o,~, (full symbols) of the as-received tungsten ribbon.

can be explained by assuming that the flow stress can be divided into two components’g~Zo. t =zo+r,

(1)

The StreSS, zG, is due to an athermal interaction occurring between the long range stress fields of dislocations*. The stress, z,, is the component associated with a thermally-activated process. The latter component will become zero above a certain temperature, TO,which means that the thermal energy is sufficient for the dislocation to overcome the obstacle. At temperatures below To, some stress, zs, will be necessary, in addition to the thermal energy to surmount the obstacles. For the analysis of the temperature-dependent component, r,, the ultimate tensile strength, crUts,was selected because B,~, is much easier to determine that a,,, and it is at this stress level where the strain-rate changes have been performed. For the evaluation of the temperature-dependent stress, a value of ro has to be selected in eqn. (1). Since the temperature dependence of the flow stress was negligible at about 800°K, the flow stress at this temperature was assumed to be rG. That Z, is zero at this temperature is demonstrated below. As already mentioned, the Snoeck effect2’ in iron was the first experimental evidence of an interaction between a stress field and the distortions surrounding an impurity atom. The measurements showed that atoms in interstitial solution, especially carbon, were responsible for the internal-friction peaks22. Nabarro23, Cochardt et a1.24,and Fleischer 25*26have demonstrated in their calculations that point defects having a tetragonal symmetry interact strongly with the stress field of a dislocation in cubic crystals. This interaction is best described by assuming an elastic dipole at the location of the point defect 27. Frank1’~12 has further developed the theory of inter* The shear stress and the normal stress are designated by r and IJ,respectively. The maximum shear stress is assumed to be ~=+a. Ji Less-Common Metals, 23 (1971) 427-435

FLOW STRESS OF HEAVILY

DEFORMED

431

DOPED TUNGSTEN

action including the theory of thermally-activated processes. The interaction energy, AG,, between an elastic dipole in the (100) direction and a screw dislocation with an (l/2) (111) Burgers vector in a {TOl) slip plane moving in the (121) direction has been calculated using linear elasticity theory” rz. This calculation yields :

The Gibbs free energy, AGo, is an average of the slightly different Gibbs free energies for the different ( 100) dipole directions ; d is the distance of the center of the dipole from the slip planei and, in the case under investigation, d = l/& AP is the dipole strength, p is the shear modulus and b the Burgers vector. For a fairly large distance between dislocation and point defect, eqn.(2) represents the interaction energy very well. In the case when the dislocation comes close to the defect (low temperatures), deviations can be expected because linear elasticity theory is not valid in the core of the dislocation. By introducing the notion that the Gibbs free energy, AGo, is reduced linearly by the applied stress”*2*, i.e., AG=AG,-vr,

(3)

and assuming that the strain rate ci is governed by an Arrhenius equation : ‘j = b, ,-WkT,

(4)

Frank’ ’ derived the following equations for the temperature

dependence of ;. :

T= To--B x (ts)

X(h)= 7,

(5(a))

c

( 1> 3

-

s

To =

Where Cefr is the effective concentration obstacles is’ 3

of obstacles. The atomic concentration,

C,, of

C,=%.rr* The quantity lid can be expressed as: d0

=

n,bv,

(6)

whex vD is the mbye frequency. The proportionality factor, V, in eqn. (3) is &led the activation volume. It is &f&da.3 J. Less-Common

Metals. 23 (1971) 427-435

0. 3OSER

432 r=---.

8AG

(7)

8% Frank solves explicitly for o by introducing the stress dependence of the Gibbs free energy, AGO, calculated from the above theory:

It can be shown that it is possible to measure the activation volume, u, with the help of the changes in flow stress upon strain-rate changes, by combining eqn. (7) and eqn. (4). This leads to:

(9) In order to demonstrate that the theory of the thermally-activated overcoming of point defects by dislocations can explain the steep rise of the flow stress with decreasing temperature, the values of r, determined as described above were plotted according

0

IO

20

30 40 x ( kg/mm21

50

60

70

Fig. 3. The T-x (23 diagram according to eqn. (5(a)) of Frank’s theory for the as-received tungsten ribbon.

to eqn. (S(a)) and (5(b)) in a T-X@,) diagram (Fig. 3). Since a proper choice of the constant, C, in eqn. (5(b)) makes.the experimental points fall on a straight line, the theory is appropriate to explain the temperature dependence of the flow stress. From the intercept with the temperature axis and the slope, the Gibbs free energy, AGo, and the con~tration, C,,r, can be determined from eqns. (5(c)) and (5(d)), respectively J. Less-Common Metals, 23 (1971) 427-435

FLOW STRESS OF

HEAVILYDEEGRMBD DOPEDTUNGSTEN

433

TABLEI SUMMARY

OF THE

1

OKmm2

[

kg

OF THE ANALYSIS

OF THE

FLOW

STRESS

870

T,COKl B-

RESIJLTS

11.6

8*

0.25

AGolevl AA*

C, [at. p.p.m.1 Co [at. p.p.m.1 CN[at. p.p.m.1

P.P.~-1 C, [at. p.p.m.1

CC [at.

nu[cm-‘1

1.59

0.27 800 300 770 1100 10”

(Table I). The value T,, for the temperature where the process is completely thermallyactivated, turns out to be 87O”K, a result that justifies the assumption above of T, = 800°K. From the results in Table I and the flow stress,.r,, an activation volume, v, can be calculated (eqn. (8)) and compared with that measured by strain-rate changes and calculated according to eqn. (9). In. Fig. 4, the two differently derived activation

. .

/ /

800

400 fEMPERATURE,T

600

I

0

CK)

Fig. 4. The temperature dependence of the activation volume, D.Full circles measured from strain rate changes; open circles calculated according to eqn. (8). J. Less-Common Metals, 23 (1971) 427-435

434

0. BOSER

volumes have been plotted us. deformation temperature. The agreement is very good, especially at low temperatures where the flow stress changes are large and therefore can be measured very accurately. The agreement of the experimental results with the predictions of the theory based on the dislocation impurity interaction validates its application to commercial tungsten. Having derived the Gibbs free energy, AGO, and having shown quantitative agreement of the two differently derived activation volumes, the dipole strength, AA*, can be calculated according to eqn. (2) and appears in Table I. The dipole strength, AL*, has about the same magnitude as in other b.c.c. metals’3-‘s. From Snoeck effect’l measurements in iron, tantalum, and niobium it is known that impurities in interstitial solution, such as carbon, oxygen, and nitrogen, are able to produce such elastic dipoles. To evaluate this possibility in the present case, the number of obstacles, C,, determined from the analysis of the temperature dependence of the flow stress, has to be compared with the number of atoms of impurities capable of forming elastic dipoles in interstitial solution determined by chemical analysis, Table I. From this comparison it is possible that either monoatomic nitrogen or carbon acts as obstacles if they were in solid solution. Since the measured solid solution limit for these elements is very low they might not be present as monoatomic atoms but rather as small precipitates. If these precipitates have a nonspherical shape they can also produce a strain field described by an elastic dipole. Possibly all the elements in interstital solution (oxygen, carbon, nitrogen) will form precipitates of this character. F%llowing a suggestion of FrankI who assumed monoatomic circular layers as the shape of the precipitates, one can estimate the number of atoms in the precipitate from the impurity concentration. In the present investigation, this leads to an estimate of 6-18 impurity atoms per precipitate. Therefore, the increase of the flow stress with decreasing temperature can be explained as due to dislocation precipitate interaction or interaction of dislocations with individual atoms if they are in solution. CONCLUSIONS

Heavily-drawn and rolled commercial tungsten has been deformed at various temperatures between 77’K and 800°K. The deformation curve shows two different stages : (a) the stage below 1‘A plastic deformation is characterized by a rapidly increasing load, (b) the subsequent stage is characterized by a constant load. It has been demonstrated that the flow stress can be separated in two components: (a) the temperature independent component, ro, which prevails solely at high temperatures, is caused by a dislocation-dislocation interaction, (b) the temperature dependent component, zS, was analyzed by the theory based on a point defectdislocation interaction in a thermally-activated process. The Gibbs free energy, AG,,, and the dipole strength, AA*,produced by the impurities in interstitial solution, have been determined. The number of obstacles measured with the help of the activation volume is in good agreement with the number of atoms capable of producing elastic dipoles. It was not possible to decide if the impurity atoms interacted individually or as precipitates. The latter seems to be more likely considering the very low solubility limit and the fact that no Snoeck peaks have been observed in tungsten. In any case the results presented demonstrate that the steep increase of the flow stress with decreasing temperature can be attributed to impurities such as carbon, nitrogen and oxygen. J. Less-Common

Metals, 23 (1971) 427-435

PLOW STRl%% OF HEAVILY DEFORMED DOPED TUNGSTEN

435

ACKNOWLEDGMENTS

The author would like to thank Dr. J. Brett for many s~~~t~g discussions, P. Femandez for assistance in the experimental work, H. Woods for the metallography, and R. Weberling and S. Weisberger for the chemical analysis. REFERENCES 1 J. H. BECHT~LDAND P. G. SHEWMON,Trans. Am. SK Meials, 46 (1954) 397. 2 J. H. BECWTOLD, Trans. AIME, 206 (1956) 142. 3 1. W. PUGH, Am. Sot. Testing Mater. Proc., 57 (1957) 9%. 4 H. W. SCHADLER,Trans. AIME, 218 (1960) 649. 5 R. M. ROSE, D. P. FERRISAND J. WULXF, Trans. AIME, 224 (1962) 981. 6 R. C. Koo, Acta h&t., II (1963) 1083. 7 R. H. SCHNITZEL,J. Less-Common Metals, 8 (1965) 81. 8 P. BEARDMO~EAND D. HULL, J. ~ss-Comma~ Metals, 9 (1965) 168. 9 A. S. ARGON ANLIS. R. MALOOF,Acta Met., 14 (1966) 1449. 10 J. C. BILELU), Trans. AZhfE, 242 (1968) 703. 11 W. FRANK, 2. Naturforsch., 22~ (1967) 365. 12 W. FRANK, Z. Naturforsch., 22a (1967) 377. 13 W. FRANK, Phys. Status Solidi, 19 (1967) 239. 14 0. BARER,Symp. on Interaction Between Dislocations and Point Defects, At. Energy Res. Estab. (G.

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