Viscoplasticity of a recrystallized high purity polycrystalline Mo at near room temperatures

ScriptaMurgicn

et A4ru&k, Vol. 33, No. 3, pp. 399-+ cbpJbol”

Peqpmon

1995

0956-716xl95 s9.50 + .aJ

09s716x(95)ooz19-7

VISCOPLASTICITY OF A RECRYSTALLIZED HIGH PURITY POLYCRYSTALLINE MO AT NEAR ROOM TEMPERATURES* 2. M. Sun”?, 2. G. Wang”, B. Weissb, R. Sti&le? and T. KobayashP *Department of Production Systems Engineering, Toyohashi University of Technology, Toyohashi 44 1, Japan bInstitute for Physical Chemistry, University of Vienna, Waehringer Strasse 42, A-1090 Vienna, Austria ton leave from ‘State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Academia Sinica, Shenyang 110015, P.R China (Received March 8,199s)

Jntroduction The high melting point of molybdenum (MO) at 2610°C makee it attractive to be a candidate for high kmpe&xe applications.As a body-centered cubic metal, however, many aspects on the unique deformation behavior of Mb are stillto be understood. The strongdependence of flow stress upon the strain rate and teanperaturehas provoked mauy investigations into the b.c.c. metals such as MO and the like [e.g. l-41. In our recent attempt to study the cyclic deformation behavior of Mo [5], it was found that at a constant stress far below the yield strength of the material the specimen elongated substnatially. This phenomenon has drawn great attention and inkrest fi-om the authors to understand. The objective of the present paper is to report the m ply and to present some preliminary interpretation and speculation on the mechauisms. An elastic-viscoplastic model incorporated with the kink-pair mechanism was proposed for the deformation Process FmerimentaJ

The materkl used in the present study is a high purity molybdenum with main impurities of (in ppm) 190 W, 30 Fe, 20 0 and 15 C. The material was fabricated through a powder metallmtzy route and rolled to a thickness of 2mm. Recrystallization treatment was done at 1200°C for one hour. Fine grain size of about 15 pm was obtained in result, as indicated in the micrograph of the microstructure in Fig. 1. Plate shaped specimens with gauge dimensions of 25mm x 6mm x 2mm were machined with the loading axis on the rolling direction. straingaugesgluedonthegaugesectionsofthespecimens were used to measure the deformation intbrmation. Specialgl~waschosentosustainanelevatedtemperaturcupto130”C.AChamberwasusedtocoverthe l

Experbnd

work was mainly done at the Universityof Viema.

400

VISCOPLASTICTTY OF MO

Figure1. Microstructure of thehighpurityreaydhd

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ploycryxtal Molybdenum

sample area and the upper and lower grips of the fixture of the testing machine. Hot air at controlled temperature was blown into the chamber for heating. A thermal couple was attached to the specimen as close aspossibletothestraingaugetomeasure the actual temperature of the specimen. A temperature up to 120°C with stability of iO..5”C is available with this system. A 10 kN Shimadzu testing machine was used for loading. Jtesults Tensile ProDerties

The tensile properties of the tested material are smmmkzd in Table 1. A strong yielding phenomenon can be seen from the data, where the upper and lower yield stresses are indicated as YS, and YS,, respectively. This is, accon%q to the well defined theories [e.g. 61,due to the pinning and unpinning effect of the interstitial solutes on dislocations. In this study the main effective pinning solutes are C and 0. Oxygen may play only a minor role since in this material produced with a powder metalhrrgy route it could exist mainly in the form of oxide instead of interstitial atoms. It should be pointed out in the data that the UTS indicates the highest stress afler the work hank&g following the lower yield point. It is worth noting that at some high strain rate and lower temperature (e.g. the data at 25°C 2.1 x 10-4S-’in Table 1) the UTS does not exceed the upper yield point. This information could be of great importnce to the engineering applications. With increasing temperature or decreasing the strain rate the yield point reduces and the difference between the upper and lower yield points becomes smaller. TABLE 1 Tensile Propertiesof the Tested High-PurityMO Tempera25OC

80°C

strain fate ($1)

YWW

YUMPa)

Ws(Mpa)

Elong. (%)

2.1 xlOA

483

371

470

21.0

2.1 x10”

384

291

405

2.1 xlod

251

242

411

61.5

2.1 x10”

221

189

384

64.0

-

strain 0.010

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swain fate (s-1)

0.008 0.008

Tile (min.) Figure2. StrainingofaMospedmenuderamstaatstress loading (1SOMPa) at SOY!.

Time Figure 3. Showing strain variation with time of a MO Specimen loaded at 150 MPa Testing bmpe&um and itschangeareindicatedinthefigure.

Strainme under Constant Tensile Load

When a specinten is kept under a constant tensile stress at a certain temperature, it deforms rapidly to a large extent in addition to a part of the instantaneous elastic strain as shown in Fig. 2. The specimen was loaded at 80°C and at a stress of 150 MPa. Also plotted in Fig. 2 is the strain rate of defmtion at 150 MPa. It can be seen that the strain rate decreases rapidly with time till a zero value a&r a time span of about 5 hours. At the registered stress and temperature the specimen deformed a strain up to about 0.8% at saturation. The specimenWflSthUIllOadedtO zmo stress. Following an instantaneous recovery of the elastic part, the strain actually the length of the specimen, did not change with time, which is also shown in Fig.2. This is in fact indicative of that the large strain resulted from stressing for a period of time in our study is not due to viscoelasticity. TemDerature Effect and Stress DeDendence

Following the test represented in Fig. 2, a&r unloading the experiment was interrupted for about 40 horus. That is, the specimen had been lefi on the machine at zero stress and at ambient temperature of about 27 “C. We resumed tbe test atknvards in the same testing condition, reloading the specimen at 8O”C, 150 MPa. As can be seen in Fig3, it takes a short time for the specimen to reach the previous length, indicated by the same saturation strain level. Consequentially we repeated the testing procedure, with unloading and reloading by ~~thetemperature~80”Cto60°Candthento90”C. TheresultsinFig.3 showsthatwhenthetest is switched to either a lower temperature or ahigheronethan the original, the saturation strain of the specimen keeps almost unchanged. This reveals that the saturation strain indicated with the stable level in Figs. 2 and 3, is not, or at least not to a large extent dependent on the testing temperature. At a certain stress amplitude of 150 MPa, three samples were examined at 7O”C, 80°C and 90°C respectively. The time-base strain records are shown in Fig.4. The strain reached the saturation level much faster for the case at higher temperature. For the selected three temperatures the saturation strain ranges from 7.29 x 10e3to 8.04 x lo-‘. It should be noted that the strains at all the three temperatures were still climbing, though very slowly, when the tests were termina ted. It takes a long time to reach saturation, especially for the case of lower temperature. The difference in saturation strain at dif3brenttemperatures could be minimized for a longer term loading, btxomin g consistent with the result shown in Fig.3. The strain response at 80°C to loading at different stresses were measured and the results are represented in Fig.5 Three specimens loaded at 100 MIQ, 150 MPa and 200 MPa, respectively, show a large difkrence in the resultant saturation strains, having values of 1.4x 10e3,7.9x lo-’ and 2.0x 10V2,respectively.

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OF MO

Strain 0.031

0.02

200 MPa

I-

o.oooI 0

’

200

.

a

400 600 Tiie (min.)

.

.

800

I Fi8m-s5. Slraiuvs. time for Mo specbm loadedatvarious rrtresses.Thetesting temperature is SO’C.

Figure 4. Slrain vs. time for MO specimen at various bmpewwsat-stress.

Thermal Activation Estimate

It can be seen in Fig.4 that the initial strain rates at M&rent temperatures differ substantially. This temperature n can be caused by a thermally activated process. For a preliminary estimate we made dependentphm the following tests at 150 MPa. Having been heated to a homogeneous temperature, a specimen was loaded in a few seconds to a stress of 150 h4Pa and was held for about 2 minutes. The strain was recorded with a timebase rewrder. The specimen was ti unloaded and heated to another temperature and the same loading Fig.6 shows an example of such a measurement, where strain was procedureWaSrepeatedatthiS~. plotted as a function of time for the tests at 150 MPa at 5O”C, 6O”C, 70°C and 8O”C, respectively. Good linearity can be seen in the figure, which indicates well-defined strain rates. The strain rates at difkrent temperatures are extracted from the data in Fig.6 and are plotted in Fig.7. A good linear dependence of the strain rate on the reciprccal ofthe absolute temperature cau be seen in Fig.7. Considering this to be a thermally activated process, we may construct an equation for the strain rate, similar to that for creep, as follows:

k - Ao’exp

(1)

-; (

1

StrainRate(s-l) IO=1

0

50

loo Tiie (second)

Figure6.Timhsedrecordof&ainofaMospechenloaded at 1SOMPaat various temperatures.

Figure7.Therdatidpbetweentirateandthe reciprocal of the absolute kmpedue for MO. stlws is 150MPamQiadicatestheactivaiioneneqy.

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403

(a)

04 Figure 8. (a) Schematicrepresentationof an elastb~lastic unloading.

model and (b) it’s strainresponseto a s&tic loading at 01, and to

whereAandnalZmaterialCom&its and Q is the activation energy, k Boltzmann castant and T temperature in Kelvin. The activation energy for the material tested cau be easily extracted to be 0.44 eV. This value is quite consi-t with that measured with cyclic deformation method [5]. Jxwuwlon

The result represented in Fig.3 indicates that the large deformation resulted from loading at constant stress is not recoverable with aging. Considering that we are discussing the deformation of b.c.c. metals containing interstitial impurities below yield stress, the pinning effect of these solutes on the mobile dislocations is naturally an argument. However, if the large strain resulted from the static loading is attributed to the dislocation unpinning effect, the microstructure of the material should be to a large extent recovered by an aging processing. In other words, a&z this interruption of the test for a period of time, another large strain could be obtained upon n&ading. It is therefore reasonable to conclude that the dislocations and atmosphere me&amsm is not applicable to this case. On the other hand, the rough estimate of thermal activation energy of the material (0.44 eV) is of one order smaher than the normal creep activation energy of Mo [7]. This implies the inadequacy of the normal creep mechanism to the obtained results. We are thus urged to seek a model and mechanisms other than the viscoelasticity, dislocation unpinning as well as creep in normal sense, to intepret the experimental phenomena. ~nElasii c-V isc~~laatic Model A model for the elasti~~lastic medium is proposed as shown in Fig.8a.For convenience, we assume the stressappliedtobeaconstanfa,Thismechanicalmodelconsistsofthreeelements.Thefirstoneisanelastic element obeying Hooke’s law o,=Es, The second element is a viscous element following Newton’s law of viscosity [8]

(2)

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VISCOPLASTICITY OF MO

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where q is the coeflicient ofviscosity, and t the time. The third element is a rigid-plastic body, which does not deform at stresses below the yield point; yelding occurs only at stresses satisfying the yielding condition (a=~,). However, we asume the medium shows linear work hardening instead of perfect plasticity during deformation: a,=aO,+Fq

(4)

where a,” indicates the initial yield stress and F the strain hardening modulus. Considering the limited range of straining the linear hardening assumption could be au appropriate appmximation Apparently, E*=E~ and oO= o,+ a,thenwehave a, = q(d~#t)

+ o i + FE,

(5)

From this differential equation the strain can be obtained as

The total strain of the combination of the three elements is

t - el + e2-

;+5E!$yI_~(_~))

-

(7)

The graphic representation of equation 7 can be schematically shown in Fig.8b. This is actually the trend of straining of the material tested at a constant stress in our study. Upon loading an instantaneous response of elastic deformation a& is obtained. Consequentially the material deforms to an exponential law and tends to saturate, as time goes to intlnite, at a value of

When the model is unloaded au instantaneous recovery of the elastic strain o& is seen while no recovery in strain ~?omthe combination of the viscous and rigid-plastic elements is expected. JMicromechanisms

The pmposed elastic-viscoplasticmodel accouuted satisfactorily the deformation behavior of Mo at a constant stress. However, detailed interpretation in a microstructural point of view is still necessary for a convincing picture. In other words, ditferent mechanisms should be sought and be verified for the individual elements in the model indicated in Fig.8a. It is generally accepted that at low and intermediate temperatures the plastic deformation of bee transition metals is controlled by the mobility of screw dislocations [g-12]. In these cry&&, the straight ~11 l> screw dislocations do not possess welldetined single glide plane because of their three-fold symmetry. As a consequence, their mobility is strongly reduced. This may be formally described by a high Peierls stress. During recent years a model for the mobility of nearly straight dislocations due to the foimationofkinkpairsandthedrattdit%ionofkinksalongthedislccationlineshasbeendeveloped[13,14]. The kink pair formation energy in MOwas reported to be 2&=1.22 eV [ 151,which is close to the value obtained in the present study with a mugh estimation. The energy needed for the kink migration along the dislocation line is of one order smaller [ 161. This implies that once the kink pairs are formed under certain

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thermal activation conditions, say, stress and temperature, the gliding of these kinks, actually parts of dislocation lines, will be able to move very easily. This in fact accounts for the viscous element in the model shown in Fig.8. The deformation process can be hence interpreted in the following way. Upon loading at certain temperature to a constant stress, an initial instantaneous elastic response is expected and well understood. At the same time, certain amount of kink pairs are generated and those kinks start migration imme4l&ly,givingrisetoaquick &r-ease in strain With the progress of kink-pairs formation and migration the dislocation as a whole will be eventually moved. Such dislocation movements inevitably cause dislocation interactions, which results in resistance to the dislocation and kink movements. Such micromechanism accounts for the rigid-plasticelement with work hardening. As a result, the de6ormation becomes slower with time and tinally as the resistance to dislocation gliding in the microstructure increases toacertainvaluethe deformation ceased due to the lack of driving force. Concludine Remarks The deformation behavior of a recrystallized high purity MO at constant stresses and at moderately elevated temperatures up to 90°C were studied. A creep-like viscoplasticity was observed at the tested stress levels well below the yield stress. Upon loading to a constant stress level the specimen indicated a rapid initial incmase in straia Then the material deforms to an exponential law and tends to saturate as time goes intlnite. It was found that the testing temperature has a strong &it on the initial strain rate, while little effect on the saturation strain was found. The saturation strain increases with increasing stress. A mechanitsal model was proposed employing an elastic element, a viscous element and a rigid-plastic element. This model accounts well for the experimentally observed deformation behavior in MO. Micromechanically, the kink-pair model was cited for the interpretation. Possibly some other mechanisms could also operate at the same time, includingthe grain boundary sliding in this tine grain sized microstructure. &knowledPements The provision of the tested material MO corn the Metallwerk Plansee GmbH, Austria is grategilly acknowledged. ‘Theauthors would express their thanks to Mr. H Hoedl and Ms. M. Fischer for their assistance in some of the experimental work. Thanks are due to the tlnancial support to the present work from the Austrian National Science Foundation Part of this work was also supported by the Daiko Foundation (Japan) and the Japan Society for the Promotion of Sciences(JSPS). References 1. 2. 3. 4. 5. 6. 7. 8. 9. IO.

G. D’Anua, W. Benoii Mater. Sci Eslgal5, Al64,191(1993). S. Take&i, T. Ha&ho@ K. Mae&, Trans. Japan Imthte of Metals, 23,2,60(1982). K.P.D. Lagedoef; Acia &tall.. 41,7,2143(1993). D. Brumm, I’. Diehl, Phys. Stat, Sol., (a), 124,155(1991). Z. M. Sun, Z. G. Wang, H. Head&B. Weiss, R Sticlder, Mataialwi~ UlldWeXkSto~inpress. A Cottrell,CM&w and Plastic Flow in Cymtah, Claredm Press, Oxford, 139(1963). R Stickler, et_al., unpublishedwork N. -, I. Suliciu, Viacop~, Marthut NijhoEPublisheq HagueEhhhdq 55(1982). P.B. Hirsch, Proc. IdCod. StreqthofMetalsmdAlloys,Trans JapanIns& Metak,Suppl. 9,30(1%8). J.W. Christian, Pmt. 2nd Id. Cod. Streqth ofMetals and Alloys, Vol.1 Amer. Sot. Metals, 31(1970). 11. M. Wener, A Seeger, ISCMA, ~01.1, Oxford, 173 (1988). 12. F. Adcamao, H. Mu&&i, A Seeger, Acta Metall., Vo1.31,9,1353(1983). 13. A Seqer,Tlmrie&Gittpfehlstell& ia S. Flue.gge@d.), Jhcychpedii of physics, vol, VII/l, Springer, Berlin etc., 383 (1955). 14. A Seem, P. Schiller, in W. P. Mason (ed.). Physical Acoustics, Vo.III A Academic Press. New York London., 36111966). . . 15. ItMu&abi,inProc.ICSMA-7,Mout;eaiP~P1~~, lh7(1986j. 16. U. Holzwah, A m, in Sho#b of Metals ad Alloys, Vol. 1, eds. D.G. Bmdon, R Chaim and A Rosen, p.577, Freud Publisb&CcmpanyLtd.,Ldm(1991).