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Thermal activation analysis on the bubble-strengthening mechanism at high temperatures in PM tungsten fine wires
Suipta Metallurgica etMat&lie.
Vol. 33, No. 9, pp.1469-3477.1995 Elsevim Scicncc Ltd
Pergamon 0956-716X(95)00382-7
‘THERMAL ACTIVATION ANALYSIS ON THE BUBBLE-STRENGTHENING MECHANISM AT HIGH TE:MPERATURES IN P/M TUNGSTEN FINE WIRES K. Tanoue and H. Matsuda Department of Materials Science and Engineering Faculty of Engineering, Kyushu Institute of Technology Kitakyushu 804, Japan (Received April 12,199s) (Revised July 6,199s) Introduction
The doping elements such as Al, K and Si in P/M tungsten develop many arrays of small bubbles, the diameter of which ranges from 10 to 150 nm depending on annealing temperatures, along the wire axis during fabrication (1). Most of them exist on grain boundaries and play a role in controlLing the morphology of secondary recrystallized grains (l-3). On the other hand, the bubbles existing inside a grain interact with dislocations and may strengthen the matrix in three ways (4): (i) When bubbles are cut by dislocations, work has to be done because the surface of the bubbles increases. (ii) The equilibrium shape of bubbles is often polyhedral because it must give the lowest value of the total inter-facialfree energy for fixed volume of the bubbles (5). Ifthe total inter-facialenergy is not minimum, the bubbles are non-equilibrium, their shape being irregular (6). The dislocation then moves into the misfit-stress field around the non-equilibrium bubbles. (iii) Dislocations are attracted by both equilibrium and non-equilibrium bubbles because they annihilate a part of the dislocation stress field. The last strengthening mechanism is the so-called modulus-defect interaction and considered as a most effective one in blocking the climb of dislocations at high temperatures (7). In the present work, we considler the effects of bubbles on the flow stress at high temperatures from a point of view of thermal activation process of dislocation motion. ExDerimentsl Procedure
Doped and non-doped tungsten wires 0.13 mm in diameter of commercial grade (above 99.96%) were used for investigations on the bubble-strengthening mechanism. The concentrations of residual doping elements of Al, K and Si were Q).OO1, Ul.007 and 0.001 * 0.0003 in mass %, respectively. All of the heating was done by applying direct current to the wire specimens in a vacuum of 1OdPa. The magnitude of the current density was 120-300 A/mm2much less than l@ A/mm’ at which the electroplastic effect takes part in the deformation (8). In order to get the similar shape of secondary recrystallized grains, doped and non-doped wires were annealed for 300 s at 2373 and 2473 K after heating at the heating rates of 880 and 0.83 K/s, respectively. The gram boundaries were revealed by etching in a solution of 30gKxFe (CN),+2gNaOH+1Wm3&0 and the two-dimensional shape of a grain was measured along the wire axis. Simple tension and creep tests were 1469
P/M TUNGSTEN FlNE WIRES
1470
1
100
1
I
Test temp. /K i
g go’--- 2073 . b_ 60;-‘ 2273 2 g I---‘ v) 40’
1
x lo-as-’
z1.7
Aspect
---- Doped
2473
t3 2oG /--
-
ratio
9.3 9.9
Non-doped
__+4?;% I 0.3
0
Vol. 33, No. 9
I 0.6
I 0.9
I 1.2
1.5
True plastic strain, E ( % ) Figure 1. True stress-true strain curves as a fimction of temperature for doped and non-doped wires temiled at L = 1.7 x 10’ T’.
carried out at 1873-2673 K after the specimens with a gage length of 50 mm were attached to an Instron type tensile testing machine co~ected to a vacuum system and their secondary recrystallization was completed. While the specimens were deformed at the nominal strain rate of 1.7 x 1O6 s-’ in tensile tests, the loads imposed on them were kept constant by an automatic load controller in creep tests. The activation energy was obtained from differential creep tests which were done by changing abruptly temperature and stress at the middle of steady state creep. The constant power supply was specially designed to control the current so that the mmpemmmof the specimens remained constant during tensile deformation. Details of the procedure are described elsewhere (3,9). ExDerimental Results
The transverse and the longitudinal mean grain sizes were arranged to be about 48 and 450 urn for both materials, respectively, giving the aspect ratio of about 9.5. Typical true stress o-true strain E curves are given
LogtdGJ -4
,
.
I
-3t4
-3.36
I
I I
I
I
I
I
Doped tfmtfnp
/
1
-9 -4.4
.
I -4.0
-3.6 Log
I
I
I -3.2
2673
1 -2.8
a/G)
Figure 2. Logan&& plot of the minimum creep rate against the modulus corrected stress for doped wire rapidly heated to 2373 K and wealed for 300 s.
Vol. 33, No. 9
1471
P/MTUNGSTENPINEWlRES
in Fig. 1. The flow stresses of the doped wire are approximately equal to 2-4 times those of the non-doped wire. Here, the small total elongationsin the case of doped wire may not represent the true ones because Joule heating causes a specimen wire to melt down as soon as plastic instability or necking starts. The minimum creep rates Em obtained from creep curves are plotted in Figs. 2 and 3 against stress normahzed by the respective shear ~modulus G (10). The data of doped wire were located in the region of power law creep in the deformation mechanism maps except for those with a slope of one at 2673 K suggesting the occurrence of diftbsional creep (9). The creep rates of non-doped wire are approximately one and half orders of magnitude larger than those of doped wire. The stress exponent n ranges Tom 3 to 5 and 2 to 7 for doped and non-doped wires, respectively. The drastic increases of n at the high stress levels, viz. the breakdown of power law creep, may originate in the enhanced ditlksion due to the excess vacancies produced during the cutting of dislocations (9, 11). Figure 4 shows the Arrhenius plot to get the activation energy for steady state creep. The apparent activation energy Q were calculated to be 130 and 270 kJ/mol for doped and non-doped wires, respectively. Discussion
When a dislocation penetrates a bubble, it is sheared producing a new surface. The area of the bubble-matrix interface produced by slip is approximately 2rib where b is the Burgers vector of moving dislocations and ri is the average radius of the circular section of a bubble on the slip plane which is related to the mean radius r of bubbles by the following equation (12). ri = (2/3)“2r.
(1)
The work done ey the applied shear stress t in moving a dislocation across a unit area of the glide plane is t b and the increa:se in energy of the system due to the cutting of the bubbles is 2nriby where n is the number of bubbles intemiecting unit area of the glide plane and y is the surface energy of tungsten. We can obtain a
I
.
I
’
1
’
I
I
’
. Non-doped tungsten Heating mte 0.83 K/s
Figure3. WC ad
plot ofthe minimum creep rate against the modulus corrected stress for non-doped wire slowly annealed for 300 s.
heated to 2473 K
1472
P/M TUNGSTENFINEWIRES
-2r
.
I
.
,
’
’
’
.
.
.
.
.
1
Vol. 33, No. 9
7
.
.
.J
0 Non-doped wire Log ( (J/G)=-3.7 Doped wire Log ( 0 /G)=-3.6 l
-8’
4
5
Figure 4. Arrheniusplot to get the activation energy for creep at the stressesof log(o/G) = -3.6 and -3.7 in Figs. 2 and 3, respectively.
lower limit to the applied shear stress necessary to move the dislocation by equating these two quantities as (12) ‘E = 2qy
= 2(2/3)1’2nry.
(2)
It is also reporkd that bubbles are mostly localized in the boundaries, giving n, = 1.6 x 10” me2as the number of bubbles per unit area of a grain boundary (1). The maximum value of z was therefore estimated to be t = 1.5 MPa using n, instead of n, r = 25 mn (1) and y = 2.3 J/m’ (13). The value of a (=2r) = 3.0 MPa is too small to explain the difkrence in stress in Fig. 1. A cluster of cavities with a diameter of about 2 pm were observed along a grain boundary in the present doped wire crept at 2073-2473 K, their shape being regular and polyhedral as seen in Fig. 5. This fact implies
Vol. 33, No. 9
P/MTUNGSTENFlNEWRES
0 Non-doped
1473
wire
400
0 0
2000 1000 Temperature , T I K
Figure6. Tempemturedependenceof the activationenergyobtainedCorndiEerentialcreeptests for dopedand nondo@ wires.
that the vacancy flux into the cavities is small and surface diflhsion is rapid enough to maintain the equilibrium shape of the cavities when they grow (6). It is also reported that individual dislocations are pinned by small bubbles with a diameter of about 50 nm existing inside a grain (1). On the other hand, cavities in non-doped wire appear mostly in irregular “crack-like” form at the fracture surfaces indicating the vacancy flux into the cavities is very large and surface difTusion cannot redistribute matter on the void surface to maintain the equilibrium shape (6). Accordingly, the interaction of non-equilibrium bubbles with dislocations through the misfit stress field may be possible in the case of non-doped wire. Since such cavities were, however, scarcely observed in the present non-doped wire, we do not need consider this mechanism to explain the results of Fig. 1. Es single activationprocess is the rate-controlling mechanism for the deformation, the shear strain rate ?; can be expressed by (14) i - p,bsv
l
cxp [-H(T’)/~T]
(3)
where p, is the mobile dislocation density, H the activation enthalpy (energy) of deformation, ‘t*the effective stress, k the Boltzmann constsnf T the temperature and v the frequency of vibration of the dislocation segment involved in the thermal activation and s is the product of the number of places where thermal activation can occur per unit length of dislocation, the area swept out per successful thermal fluctuation and the entropy of activation. When H is primarily a decreasing function of z* and the preexponential term +j0 (=p, bsv) does not change with temperature or stress, one can show that ( 15) H - kT2[(ah$~T),
+ (ah$8r),
(zi/G)
CdGMT)]
(4)
where zi is the internal stress which depends on temperature only through the shear modulus. By using two
deformation partials obtained from di&rential creep tests and r = ti during steady state creep, H was calculated from eq. (4) and plotted against temperature in Fig. 6, The term T,, in Fig. 6 represents the temperature at which the effective stress becomes almost zero and hereby the total activation energy is
1474
Vol. 33, No. 9
P/M TUNGSTEN FINE WIRES
Strrss/MPo 0 A
4.0
CVkJ~mol-’
30 43
I89 190
4.5
5.0
T‘‘/IO_‘K’ Figure 7. Arrhenius plot free from grain boundary cavitation for doped wire taken from Ref. (18).
designated by II,, as H at T, = 950 K (16). It is evident Corn Figs. 4 and 6 that Q,, are nearly equal to H, for each wire. Namely, Q. = 270 kJ/mol of non-doped wire is in excellent agreement with Q = 275 kJ/mol for surface difl’baionof tungsten fine wires where the grain boundary sliding is dominant (17). However, Q, = 130 kJ/mol of doped wire is much less than the activation energies of tungsten by different controlling mechanism such as for surface 270-330 (17), dislocation core 380, grain boundary 390 and lattice diffusion 640 (18) kJ/mol, respectively. The possibility of grain boundary slidingand the effect of the doping material on it during power law creep in doped wire must be considered. The additionof E;;Oand SiO, to tungsten introduces no impurity atoms into solid solution. However, Al added as Al,O, penetrates into solid solution (1). The potassium is the active element of bubble formation and the potassium atom itself can be regarded as being insoluble in the tungsten lattice because it is 60% larger than the tungsten lattice. The combination of SiO, and Al,O, appears to be essential to prevent the total volatilization during the sintering process. This ensures a mechanical incorporation of the mmaining dopant (= 100 ppm), predominantly metallic potassium, into pores of the sinter bar (1). Greenwood (19) speculatedthat the potassium solubility in the grain boundaries is eventually not entirely negligible and potassium bubbles on the grain boundaries may be coarsened by the grain-boundary diffusion of sohtte potassium However, GaAl(20) analyzed that this kind of ripening seems to be negligible. Moreover, the grain boundary sliding was not observed in the present doped wire. These results imply that the grain boundary sliding in the doped wire is effectively impeded by the dopant controlled grain structure such as the large grain size and the interlocking grain boundary morphology (21). We could give a satisfactoryexplanation for the steady-state creep behavior of doped wire in the previous paper (22) with the model (23) of the constrained cavity growth which is based on the deformation of the constraining surroundings, viz. power law creep in the matrix around the cavities which controls the cavity growth. The resultant strain rate k was derived as follows: .
e = BP(T)
(5)
P/MlYNGSTENFWEWlRES
Vol. 33, No. 9
1475
where
B .-
AbD oL
(6)
k
P(T) -
2Lfd
(7)
and x.l+Yp
l [ (1 - f)’
-1
(8) I
n and Q, are the stress exponent and the activation energy, respectively, for creep without voids, (I, the creep G/l 025 (24), A a constant given by the empirical equation of A = constautsatistiedwitho,=a(~lC.,)-’”~ 1/1025*.’ (24), :D, the frequency factor for lattice di.Eusion,B a constant independent of temperature, p a constant (-0.6), P(T) a parameter containing all other factors dependent on temperature such as void spacing 28,void diameter 2R, spacing of void clusters 2L, the grain boundary area traction of voids f [=(r/@)‘]and grain size d. If L, d and X are independent of temperature, eq. (5) is equivalent to the Dam’s equation of C = t ,(o/a,~, where I?,[=BPexp(-Q&T)]=A DGbkt. In order to obtain Q,, the value of ti J’(T) was plotted against the reciprocal of temperature on the logarithmic scale in Fig. 7. The three levels of stress correspond approximately to the moduhrs corrected stresses of log(a/G)=-3.60, -3.44 and -3.36, respectively which are shown in Fig. 2. The value of Q, was about 190 kJ/mol independent of stress. This result means that QCdoes not approach the value of activation energy for lattice diffusion (640 kJ/mol) as the mechanism of dislocations climb even ifthe effect of grain boundary cavitation on creep rates is removed. The Dam’s equation contains
Figure 8. A grain lmdary
sliding across the wire diameter ofoondoped wire crept for 3.6 ka under a stress of 29 MPa at 2273 k
1476
P/M TUNGSTEN FB% WIRES
Vol. 33, No. 9
the temperature dcpendcnce of (G/T) in C0. If Q, is obtained in the general form of C = exp(-Q&T) without the term of (G/T), it decreases t?om 190 to 160 kJ/mol. These values are almost equal to the activation energy HpN(=150-200 kJ/mol) for overcoming the Peierls-Nabarro stress for tungsten (25). On the other hand, the grain boundary sliding plays an important role in non-doped (22) or doped (@ 0.08mm) (17) wires with a grain boundary traversing the wire diameter as in Fig. 8, giving a following empirical equation (17). i = Ca’eq
(-Q&T)
(9)
where n = 2, C = 0.019 Pa%’ and Q, = 275 kJ/mol. The stress dependence of eq. (9) coincides with n = 2 in Fig. 3 and Q, is very nearly equal to Q. = 270 kJ/mol in Fig. 4. This fact receives a support from the previous conclusion that the dislocations are able to climb either in the vicinity of, or in, the grain boundary with an activation energy close to that for surface diffusion in tungsten fine wires (17). By giving the suflixes 1 and 2 for doped and non-doped wires respectively and equating the two of eqs. (5) and (9), the relationship between a, and o2 was found using b = 2.74 x 10” m, G = 118040 MPa at 2273 K, Qc, = 190 kJ/mol, n, = 7 for creep without voids (26), D,, = 42.8 x 10” m%’ (18) 2L = 60 pm, d = 48 l.un, 2e = 5.0 pm, 2R = 2.0 cun, f = 0.18 for doped wire, and Qcz= 270 kJ/mol, n, = 2 and C = 0.02 Pa%’ for non-doped wire, some of which were measured under conditions of T = 2273 K and a = 43 h@a (22). It leads to (ot)‘/(u*)2
= 2.
(10)
The stmsses of eq. (10) provide a reliable estimation of the maximum tensile stress at which the steady state is almost satistied. However, it is clear that the relation of o i/o, = 2-4 in Fig. 1 can not be obtained from eq. (10) unless 0 is less than 1 MPa. Similarly,the activation energy for breakaway of dislocations from bubbles can be estimated to be about 10skJ/mol using the bubble diameter of 2r = 60 nm (l), G = 118040 MPa (10) at 2273 K and the dislocation core cut-off radius of 5b from Fig. 3 in ref. (27). This value is quite large compared with I-I,,(c2OkT) = 340 kJ/mol which is roughly estimated as the activation energy necessary for the thermally activated overcoming of the short range obstacles by dislocations (28). It is therefore concluded that the increase in flow stress of doped wire results from the athermal strengthening due to bubbles which block the climb of dislocations.
(1) The small activation energy for steady state creep in doped wire results from a combination of the effect
of grain boundary cavitation on creep rates and the deformation of the constraining surroundings which is controlled by the Peierls-Nabarro mechanism. (2) The elementary process of steady state creep in non-doped wire is the surface diffusion which rate-controls the grain boundary sliding. (3) The increase in flow stress of doped wire must result from the athermal strengthening which block the climb of dislocations. References 1. 2. 3. 4. 5.
6.
H. Warliiont, G. Necker and H. Schultz, 2. Metallk.. 66,279(1975). S. F. Chen, H. Komeda, K. Fujii, K. Tanoue andH. Matsuda, J. JapanInst. Metals, 53,1198(1989). K. Tanoue, H. Sakurai, K. Fujii aud H. Matsuda, J. Japan Inst. Metals, 57,14(1993). E. Pink aud I. GaAl, The Metallurgy ofDope&Ion-sag Tungsten, p. 209, Elsevier, Loudou(1989). R. S. Nelson, D. J. Mazey end R. S. Barnes, Phil. Mag., 11,91(1965). 0. Horacsek, TheMetallurgy ofDope&iVon-sag Tungsten, p. 251, Else&r, London(1989).
due to bubbles
Vol. 33, No. 9
7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
PA4TUNGSTENFTNJ.ZWIRES
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R W. Weeks, 13.R. Pati, M. F. Ashby and P. Bamand,Aeta Met_,17,1403(1969). A F. Spreoher,S. L. Manuan and H. Conrad, Aeta Met_,34,1145(1986). K. Tauoue, H. Komeda, K. Fujii and H. Ma&u& J. JapanInst. of Met& 54,991(1990). S. W. H. Yih and C. T. Waug, Tungsten, p. 270, Plenum Press, New York(1979). P. E. Armstrong. W. V. Green, 0. D. Sherby and E. G. Zukas, Aeta Met., 21,1319(1973). A Kelly end R. B. Nicholson, Progress inMuteriuls Science, Vol. 10, p. 151, PergamonPress, New York(1963). A Calverley, P’roc. Phys. See., B70,1040(1957). H. Conrad, J. Metals, 16,582(1964). H. Comad and H. Wiedersich, Acta Met., 8,128(1960). H. Coorad and W. Hayes, Trans. ASM, 56,125(1963). D. M. Moon and R Stickler, Phil. Mag., 24,1087(1971). S. L. Robinson and 0. D. Sherby, Acta Met., 17,109(1969). G. W. Greenwood, Phil. Msg., 31,673(1975). I. Ga&l, The.!&tallurgy ofDope&Non-sag Tungsten,p. 141, Elsevier, Laudon(1989). R.RajandM.F.Ashby,Met_Traos.,2,1113(1971). K. Tanoue, Y. Ghtaui and H. Mats&a, Mater. Trans., JIM, 34, 1177(1993). A C. F. Cocks and M. F. Ashby, Progress inMaterials Science, Vol. 27, p. 189, Pergamon Press, New York(1982). J. P. Pokier, Creep of Crystals, p. 84, Cambridge UniversityPress, London(l985). H. Conrad, The Relation Between the Structure andMechanical Properties ofMetals, p. 475, HMSO, London(1963). K. Tauoue and H. Matsuda, F’roc.of 7th JIM Int. Symp., Nagoya, July, p. 271, JIM(1993). R. W. Weeks, S. R Pati, M. F. Ashby and P. Barrand,Acta Met., 17,1403(1969). U. F. Kocks, A S. Argon and M. F. Ashby, Progress inMa?eriuls Science, Vol. 19, p. 110, Pergamon Press, New York(l975).
Vol. 33, No. 9, pp.1469-3477.1995 Elsevim Scicncc Ltd
Pergamon 0956-716X(95)00382-7
‘THERMAL ACTIVATION ANALYSIS ON THE BUBBLE-STRENGTHENING MECHANISM AT HIGH TE:MPERATURES IN P/M TUNGSTEN FINE WIRES K. Tanoue and H. Matsuda Department of Materials Science and Engineering Faculty of Engineering, Kyushu Institute of Technology Kitakyushu 804, Japan (Received April 12,199s) (Revised July 6,199s) Introduction
The doping elements such as Al, K and Si in P/M tungsten develop many arrays of small bubbles, the diameter of which ranges from 10 to 150 nm depending on annealing temperatures, along the wire axis during fabrication (1). Most of them exist on grain boundaries and play a role in controlLing the morphology of secondary recrystallized grains (l-3). On the other hand, the bubbles existing inside a grain interact with dislocations and may strengthen the matrix in three ways (4): (i) When bubbles are cut by dislocations, work has to be done because the surface of the bubbles increases. (ii) The equilibrium shape of bubbles is often polyhedral because it must give the lowest value of the total inter-facialfree energy for fixed volume of the bubbles (5). Ifthe total inter-facialenergy is not minimum, the bubbles are non-equilibrium, their shape being irregular (6). The dislocation then moves into the misfit-stress field around the non-equilibrium bubbles. (iii) Dislocations are attracted by both equilibrium and non-equilibrium bubbles because they annihilate a part of the dislocation stress field. The last strengthening mechanism is the so-called modulus-defect interaction and considered as a most effective one in blocking the climb of dislocations at high temperatures (7). In the present work, we considler the effects of bubbles on the flow stress at high temperatures from a point of view of thermal activation process of dislocation motion. ExDerimentsl Procedure
Doped and non-doped tungsten wires 0.13 mm in diameter of commercial grade (above 99.96%) were used for investigations on the bubble-strengthening mechanism. The concentrations of residual doping elements of Al, K and Si were Q).OO1, Ul.007 and 0.001 * 0.0003 in mass %, respectively. All of the heating was done by applying direct current to the wire specimens in a vacuum of 1OdPa. The magnitude of the current density was 120-300 A/mm2much less than l@ A/mm’ at which the electroplastic effect takes part in the deformation (8). In order to get the similar shape of secondary recrystallized grains, doped and non-doped wires were annealed for 300 s at 2373 and 2473 K after heating at the heating rates of 880 and 0.83 K/s, respectively. The gram boundaries were revealed by etching in a solution of 30gKxFe (CN),+2gNaOH+1Wm3&0 and the two-dimensional shape of a grain was measured along the wire axis. Simple tension and creep tests were 1469
P/M TUNGSTEN FlNE WIRES
1470
1
100
1
I
Test temp. /K i
g go’--- 2073 . b_ 60;-‘ 2273 2 g I---‘ v) 40’
1
x lo-as-’
z1.7
Aspect
---- Doped
2473
t3 2oG /--
-
ratio
9.3 9.9
Non-doped
__+4?;% I 0.3
0
Vol. 33, No. 9
I 0.6
I 0.9
I 1.2
1.5
True plastic strain, E ( % ) Figure 1. True stress-true strain curves as a fimction of temperature for doped and non-doped wires temiled at L = 1.7 x 10’ T’.
carried out at 1873-2673 K after the specimens with a gage length of 50 mm were attached to an Instron type tensile testing machine co~ected to a vacuum system and their secondary recrystallization was completed. While the specimens were deformed at the nominal strain rate of 1.7 x 1O6 s-’ in tensile tests, the loads imposed on them were kept constant by an automatic load controller in creep tests. The activation energy was obtained from differential creep tests which were done by changing abruptly temperature and stress at the middle of steady state creep. The constant power supply was specially designed to control the current so that the mmpemmmof the specimens remained constant during tensile deformation. Details of the procedure are described elsewhere (3,9). ExDerimental Results
The transverse and the longitudinal mean grain sizes were arranged to be about 48 and 450 urn for both materials, respectively, giving the aspect ratio of about 9.5. Typical true stress o-true strain E curves are given
LogtdGJ -4
,
.
I
-3t4
-3.36
I
I I
I
I
I
I
Doped tfmtfnp
/
1
-9 -4.4
.
I -4.0
-3.6 Log
I
I
I -3.2
2673
1 -2.8
a/G)
Figure 2. Logan&& plot of the minimum creep rate against the modulus corrected stress for doped wire rapidly heated to 2373 K and wealed for 300 s.
Vol. 33, No. 9
1471
P/MTUNGSTENPINEWlRES
in Fig. 1. The flow stresses of the doped wire are approximately equal to 2-4 times those of the non-doped wire. Here, the small total elongationsin the case of doped wire may not represent the true ones because Joule heating causes a specimen wire to melt down as soon as plastic instability or necking starts. The minimum creep rates Em obtained from creep curves are plotted in Figs. 2 and 3 against stress normahzed by the respective shear ~modulus G (10). The data of doped wire were located in the region of power law creep in the deformation mechanism maps except for those with a slope of one at 2673 K suggesting the occurrence of diftbsional creep (9). The creep rates of non-doped wire are approximately one and half orders of magnitude larger than those of doped wire. The stress exponent n ranges Tom 3 to 5 and 2 to 7 for doped and non-doped wires, respectively. The drastic increases of n at the high stress levels, viz. the breakdown of power law creep, may originate in the enhanced ditlksion due to the excess vacancies produced during the cutting of dislocations (9, 11). Figure 4 shows the Arrhenius plot to get the activation energy for steady state creep. The apparent activation energy Q were calculated to be 130 and 270 kJ/mol for doped and non-doped wires, respectively. Discussion
When a dislocation penetrates a bubble, it is sheared producing a new surface. The area of the bubble-matrix interface produced by slip is approximately 2rib where b is the Burgers vector of moving dislocations and ri is the average radius of the circular section of a bubble on the slip plane which is related to the mean radius r of bubbles by the following equation (12). ri = (2/3)“2r.
(1)
The work done ey the applied shear stress t in moving a dislocation across a unit area of the glide plane is t b and the increa:se in energy of the system due to the cutting of the bubbles is 2nriby where n is the number of bubbles intemiecting unit area of the glide plane and y is the surface energy of tungsten. We can obtain a
I
.
I
’
1
’
I
I
’
. Non-doped tungsten Heating mte 0.83 K/s
Figure3. WC ad
plot ofthe minimum creep rate against the modulus corrected stress for non-doped wire slowly annealed for 300 s.
heated to 2473 K
1472
P/M TUNGSTENFINEWIRES
-2r
.
I
.
,
’
’
’
.
.
.
.
.
1
Vol. 33, No. 9
7
.
.
.J
0 Non-doped wire Log ( (J/G)=-3.7 Doped wire Log ( 0 /G)=-3.6 l
-8’
4
5
Figure 4. Arrheniusplot to get the activation energy for creep at the stressesof log(o/G) = -3.6 and -3.7 in Figs. 2 and 3, respectively.
lower limit to the applied shear stress necessary to move the dislocation by equating these two quantities as (12) ‘E = 2qy
= 2(2/3)1’2nry.
(2)
It is also reporkd that bubbles are mostly localized in the boundaries, giving n, = 1.6 x 10” me2as the number of bubbles per unit area of a grain boundary (1). The maximum value of z was therefore estimated to be t = 1.5 MPa using n, instead of n, r = 25 mn (1) and y = 2.3 J/m’ (13). The value of a (=2r) = 3.0 MPa is too small to explain the difkrence in stress in Fig. 1. A cluster of cavities with a diameter of about 2 pm were observed along a grain boundary in the present doped wire crept at 2073-2473 K, their shape being regular and polyhedral as seen in Fig. 5. This fact implies
Vol. 33, No. 9
P/MTUNGSTENFlNEWRES
0 Non-doped
1473
wire
400
0 0
2000 1000 Temperature , T I K
Figure6. Tempemturedependenceof the activationenergyobtainedCorndiEerentialcreeptests for dopedand nondo@ wires.
that the vacancy flux into the cavities is small and surface diflhsion is rapid enough to maintain the equilibrium shape of the cavities when they grow (6). It is also reported that individual dislocations are pinned by small bubbles with a diameter of about 50 nm existing inside a grain (1). On the other hand, cavities in non-doped wire appear mostly in irregular “crack-like” form at the fracture surfaces indicating the vacancy flux into the cavities is very large and surface difTusion cannot redistribute matter on the void surface to maintain the equilibrium shape (6). Accordingly, the interaction of non-equilibrium bubbles with dislocations through the misfit stress field may be possible in the case of non-doped wire. Since such cavities were, however, scarcely observed in the present non-doped wire, we do not need consider this mechanism to explain the results of Fig. 1. Es single activationprocess is the rate-controlling mechanism for the deformation, the shear strain rate ?; can be expressed by (14) i - p,bsv
l
cxp [-H(T’)/~T]
(3)
where p, is the mobile dislocation density, H the activation enthalpy (energy) of deformation, ‘t*the effective stress, k the Boltzmann constsnf T the temperature and v the frequency of vibration of the dislocation segment involved in the thermal activation and s is the product of the number of places where thermal activation can occur per unit length of dislocation, the area swept out per successful thermal fluctuation and the entropy of activation. When H is primarily a decreasing function of z* and the preexponential term +j0 (=p, bsv) does not change with temperature or stress, one can show that ( 15) H - kT2[(ah$~T),
+ (ah$8r),
(zi/G)
CdGMT)]
(4)
where zi is the internal stress which depends on temperature only through the shear modulus. By using two
deformation partials obtained from di&rential creep tests and r = ti during steady state creep, H was calculated from eq. (4) and plotted against temperature in Fig. 6, The term T,, in Fig. 6 represents the temperature at which the effective stress becomes almost zero and hereby the total activation energy is
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P/M TUNGSTEN FINE WIRES
Strrss/MPo 0 A
4.0
CVkJ~mol-’
30 43
I89 190
4.5
5.0
T‘‘/IO_‘K’ Figure 7. Arrhenius plot free from grain boundary cavitation for doped wire taken from Ref. (18).
designated by II,, as H at T, = 950 K (16). It is evident Corn Figs. 4 and 6 that Q,, are nearly equal to H, for each wire. Namely, Q. = 270 kJ/mol of non-doped wire is in excellent agreement with Q = 275 kJ/mol for surface difl’baionof tungsten fine wires where the grain boundary sliding is dominant (17). However, Q, = 130 kJ/mol of doped wire is much less than the activation energies of tungsten by different controlling mechanism such as for surface 270-330 (17), dislocation core 380, grain boundary 390 and lattice diffusion 640 (18) kJ/mol, respectively. The possibility of grain boundary slidingand the effect of the doping material on it during power law creep in doped wire must be considered. The additionof E;;Oand SiO, to tungsten introduces no impurity atoms into solid solution. However, Al added as Al,O, penetrates into solid solution (1). The potassium is the active element of bubble formation and the potassium atom itself can be regarded as being insoluble in the tungsten lattice because it is 60% larger than the tungsten lattice. The combination of SiO, and Al,O, appears to be essential to prevent the total volatilization during the sintering process. This ensures a mechanical incorporation of the mmaining dopant (= 100 ppm), predominantly metallic potassium, into pores of the sinter bar (1). Greenwood (19) speculatedthat the potassium solubility in the grain boundaries is eventually not entirely negligible and potassium bubbles on the grain boundaries may be coarsened by the grain-boundary diffusion of sohtte potassium However, GaAl(20) analyzed that this kind of ripening seems to be negligible. Moreover, the grain boundary sliding was not observed in the present doped wire. These results imply that the grain boundary sliding in the doped wire is effectively impeded by the dopant controlled grain structure such as the large grain size and the interlocking grain boundary morphology (21). We could give a satisfactoryexplanation for the steady-state creep behavior of doped wire in the previous paper (22) with the model (23) of the constrained cavity growth which is based on the deformation of the constraining surroundings, viz. power law creep in the matrix around the cavities which controls the cavity growth. The resultant strain rate k was derived as follows: .
e = BP(T)
(5)
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where
B .-
AbD oL
(6)
k
P(T) -
2Lfd
(7)
and x.l+Yp
l [ (1 - f)’
-1
(8) I
n and Q, are the stress exponent and the activation energy, respectively, for creep without voids, (I, the creep G/l 025 (24), A a constant given by the empirical equation of A = constautsatistiedwitho,=a(~lC.,)-’”~ 1/1025*.’ (24), :D, the frequency factor for lattice di.Eusion,B a constant independent of temperature, p a constant (-0.6), P(T) a parameter containing all other factors dependent on temperature such as void spacing 28,void diameter 2R, spacing of void clusters 2L, the grain boundary area traction of voids f [=(r/@)‘]and grain size d. If L, d and X are independent of temperature, eq. (5) is equivalent to the Dam’s equation of C = t ,(o/a,~, where I?,[=BPexp(-Q&T)]=A DGbkt. In order to obtain Q,, the value of ti J’(T) was plotted against the reciprocal of temperature on the logarithmic scale in Fig. 7. The three levels of stress correspond approximately to the moduhrs corrected stresses of log(a/G)=-3.60, -3.44 and -3.36, respectively which are shown in Fig. 2. The value of Q, was about 190 kJ/mol independent of stress. This result means that QCdoes not approach the value of activation energy for lattice diffusion (640 kJ/mol) as the mechanism of dislocations climb even ifthe effect of grain boundary cavitation on creep rates is removed. The Dam’s equation contains
Figure 8. A grain lmdary
sliding across the wire diameter ofoondoped wire crept for 3.6 ka under a stress of 29 MPa at 2273 k
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the temperature dcpendcnce of (G/T) in C0. If Q, is obtained in the general form of C = exp(-Q&T) without the term of (G/T), it decreases t?om 190 to 160 kJ/mol. These values are almost equal to the activation energy HpN(=150-200 kJ/mol) for overcoming the Peierls-Nabarro stress for tungsten (25). On the other hand, the grain boundary sliding plays an important role in non-doped (22) or doped (@ 0.08mm) (17) wires with a grain boundary traversing the wire diameter as in Fig. 8, giving a following empirical equation (17). i = Ca’eq
(-Q&T)
(9)
where n = 2, C = 0.019 Pa%’ and Q, = 275 kJ/mol. The stress dependence of eq. (9) coincides with n = 2 in Fig. 3 and Q, is very nearly equal to Q. = 270 kJ/mol in Fig. 4. This fact receives a support from the previous conclusion that the dislocations are able to climb either in the vicinity of, or in, the grain boundary with an activation energy close to that for surface diffusion in tungsten fine wires (17). By giving the suflixes 1 and 2 for doped and non-doped wires respectively and equating the two of eqs. (5) and (9), the relationship between a, and o2 was found using b = 2.74 x 10” m, G = 118040 MPa at 2273 K, Qc, = 190 kJ/mol, n, = 7 for creep without voids (26), D,, = 42.8 x 10” m%’ (18) 2L = 60 pm, d = 48 l.un, 2e = 5.0 pm, 2R = 2.0 cun, f = 0.18 for doped wire, and Qcz= 270 kJ/mol, n, = 2 and C = 0.02 Pa%’ for non-doped wire, some of which were measured under conditions of T = 2273 K and a = 43 h@a (22). It leads to (ot)‘/(u*)2
= 2.
(10)
The stmsses of eq. (10) provide a reliable estimation of the maximum tensile stress at which the steady state is almost satistied. However, it is clear that the relation of o i/o, = 2-4 in Fig. 1 can not be obtained from eq. (10) unless 0 is less than 1 MPa. Similarly,the activation energy for breakaway of dislocations from bubbles can be estimated to be about 10skJ/mol using the bubble diameter of 2r = 60 nm (l), G = 118040 MPa (10) at 2273 K and the dislocation core cut-off radius of 5b from Fig. 3 in ref. (27). This value is quite large compared with I-I,,(c2OkT) = 340 kJ/mol which is roughly estimated as the activation energy necessary for the thermally activated overcoming of the short range obstacles by dislocations (28). It is therefore concluded that the increase in flow stress of doped wire results from the athermal strengthening due to bubbles which block the climb of dislocations.
(1) The small activation energy for steady state creep in doped wire results from a combination of the effect
of grain boundary cavitation on creep rates and the deformation of the constraining surroundings which is controlled by the Peierls-Nabarro mechanism. (2) The elementary process of steady state creep in non-doped wire is the surface diffusion which rate-controls the grain boundary sliding. (3) The increase in flow stress of doped wire must result from the athermal strengthening which block the climb of dislocations. References 1. 2. 3. 4. 5.
6.
H. Warliiont, G. Necker and H. Schultz, 2. Metallk.. 66,279(1975). S. F. Chen, H. Komeda, K. Fujii, K. Tanoue andH. Matsuda, J. JapanInst. Metals, 53,1198(1989). K. Tanoue, H. Sakurai, K. Fujii aud H. Matsuda, J. Japan Inst. Metals, 57,14(1993). E. Pink aud I. GaAl, The Metallurgy ofDope&Ion-sag Tungsten, p. 209, Elsevier, Loudou(1989). R. S. Nelson, D. J. Mazey end R. S. Barnes, Phil. Mag., 11,91(1965). 0. Horacsek, TheMetallurgy ofDope&iVon-sag Tungsten, p. 251, Else&r, London(1989).
due to bubbles
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7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
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