Microplasticity in Vanadium single crystals

MICROPLASTICITY

IN VANADIUM SINGLE CRYSTALS*+ C. R. CROWE

Engineering Materials Group. University of Maryland. College Park. LID. U.S.A. and Naval Surface Weapons Center. White Oak Laborator). Silver Spring. ?vlD. U.S..\. and R. J. ARSENALLT Engineering Materials Group. Umversit> of Maryland. College Park. &ID. U.S..\

.\bstract-An investigation of the activation parameters for plastic deformation in the mrcrostrain region has been performed. Vanadium single crqstuls uith ,,-t’Jt,j JXIJI orrentations were tested m compression bv strain rate cycling at vartous intervals over the strain range of 1 x lO-‘-2 x IO-’ at a strain sensitivity of 5 x lo-‘. Tests were conducted between 125 and 300 K on a series of crystals containing interstitial solute concentrations in the range 156 at. ppm to 1649 at. ppm o\;)gen plus nitrogen content. The results indicate that in the microstrain region more than one dislocation process is occurrmg The results are consistent with the theory that edge and nonscrew drslocations are the mobile species in the microstrain region at low temperatures. r\s deformation proceeds. the mobile densities of the edge and nonscrew seements decrease and the transition to macroflou IS associated vvith the onset of screw dislocation motion. The data Indicates that in the microstrain region edge and nonscrcvv dislocation mobilit! is strongI> atfected b> solute interactions. In the macrostrain regions. however, Hou rate is apparentI> controlled b> screvv dislocation-lattice interxtions. R&m&-On a Ptudie Ies parametres d’activation de la dPformation plastique dans Ie domaines de In microdeformation. On a deforms en compression des monocristaus de vanadium &orientation (491) avec des cycles de vitesse de deformation dans divers intervalles compris entre 1 x lo-’ a 2 x lo-‘. avec une precision de 5 x LO-‘ sur les deformations. Les essais ont et2 effect&s cntre 125 et 3OOK sur une serie de monocristaux contenant des concentrations de solute d’insertion (oxqgine - azote) comprises entre 456 et l6J9 ppm. Les resultats montrent que dans Is domaine de la microdeformation. plusieurs mecanismes de dislocations jouent un role; ils sont en accord avec la theorie admettant que les dislocattons mobiles a basse temperature dans le domaine de la microdeformation sont des dislocations coins et dcs dislocations non vis. Au fur et a mesure de la deformation, la densite de segments coins et non vis mobiles diminue et Is passage a la macrodeformation est associe au debut du mouvcment des dislocations Vi%

Zusammenfassung-Die Aktivierungsparameter der plastischen Verformung im Mrkrodehnbereich wurden an Vanadium-Einkristallen untersucht. Verwendet wurden .\19l ,>-orientierte Kristalle. die im Druckversuch mit Dshngeschwindigkeitsspriingen verschiedener CriiBe im Abgleitintcrvall van 1 x 10e5 bis 2 x 10e3 bei einer MeBempfindlichkeit von 5 x LO-- verformt wurden. Die Versuche a-urden an einer Reihe von Kristallen. die 456 Atom-ppm bis 1649 ,Atom-ppm interstitiell gel&ten Sauerstoff plus Stickstoff enthielten, zwischen 125 und 300 K durchgefuhrt. Die Ergebnisse wcisen darauf hin, daB im Mikrodehnbereich mehrere Versetzungsprozesse ablaufen. Die Ergebnisse stimmen mit der Theorie iiberein, daB bei tiefen Temperaturen im Mikrodehnbereich Stufen- und Nichtschraubenversetzungen beweglich sind. Slit fortschreitcnder J’erformung sinkt die Dichte von beweglichen Stufen- und Nichtschraubenversrtzungssegmcnten. Der Ubcrgang zum makroskopischen FlieBen ist mit dem Einsetzen der Bewegung von Schraubenversetzungen verbunden.

l3-I’RODCffIOS

of this fact, some attention has been directed toward studying b.c.c. plastic deformation in the microstrain region. Early observations of microplasticity were obtained using a load-unload technique. These investigations. reviewed in detail elsewhere [Z]. showed that significant amounts of plastic deformation could occur at small stresses and low temperatures in b.c.c. metals. The results were originally interpreted [3] as strong evidence that dispersed interstitial atoms controlled the macroscopic deformation rate. This conclusion was reached by reasoning that if the lattice

It is now generally recognized that interstitial solutes affect the temperature dependence of microflow stresses more than macroflow stresses [I]. Because

* Derived from work submitted in partial fulfillment of the requirements for Ph.D. degree at the University of Maryland. t This research was supported in part by the U.S.E.R.D.A. under Contract No. AT (JO-l)-3612. 91

provided an intrinsic barrier to disiocation motion, then plastic deformation could not occur at smail stressesand low temperatures where thermal activation could not assist the dislocations in surmounting an intrinsic type barrier. It has subsequently been shown, however. that significant amounts of plastic strain occur at low stresses and temperatures in metals exhibiting a large Pcierls stress [4]. Two general approaches have been taken to interpret the microstrain results. The first approach assumes that a single mechanism operates throughout the stress-strain regime [5J. According to this model. the rapid increase in stress in the microstrain region is a consequence of the fact that the plastic strain rate is a smali fraction of the total strain rate in the microstrain region. This is because of the low initial mobile dislocation density and low initial dislocation velocity. The model predicts a low temperature dependence of microflow stresses. with the temperature dependence increasing with increasing plastic strain. It should be pointed out that the term microffow stress refers to the value of the flow stress associated with plastic defo~ation in the microstrain region and should not be confused with the term microyield stress as used by some authors in connection with yield criteria. The second approach taken to interpret microstrain phenomena is one in which there are different mechanisms operating over different strain regimes. These theories [6-101 assume that (111) screw dislocations are essentially sessile below macroflow stress levels. Yielding is related to the force necessary to move the screw dislocations and microflow is attributed to the motion of edge and other non-screw dislocation components. It therefore follows that the activation volume and activation free energy determined in the microstrain region should be very different from those determined in the macroflow region. There have been a few measurements of activation parameters in the microstrain region [l I-161 and these generally show that the activation volume is much higher at small strains. IMost observations show a relativeIy smooth increase in the activation volume with decreasing strain. There is additional support for the two mechanism approach. For instance, work on iron [i7] shows that the tem~rature dependence for constant edge disIocation velocity corresponds to a micro rather than macro yield stress. Also, transmission electron microscopy studies on b.c.c. metals deformed at low temperatures support this interpretation since a preponderance of screw dislocations is observed in the substructure [ 18-2 I]. Because of the many controversial opinions concerning rate controlling mechanisms for plastic deformation in the b.c.c. metals. this work focuses attention on the deformation behavior in the microstrain region. Vanadium was chosen as the b.c.c. metal for the study because of its large solubility for interstitial

oxygen and nitrogen atoms and bemuse previous work by Arsenault and Pink [32] sugges:ed that there leas a change in mte controlling mechanism for macroflow from a lattice mechanism to a dispersed interstitial mechanism at about 20&3)0 wt. ppm interstitial concentration. Later, however. Huang and Arsenault [21] studied the dislocation structures developed during deformation in vanadium containing 15 wt. ppm and loo0 wt. ppm oxygen and they arrived at somewhat different conclusions. The significant finding in this work ivas that samples deformed at large effective stresses show a predominance of screw dislocations in the substructure irresFtive of the oxygen content. These findings were taken as indicating that oxygen atoms do not act directly as rate controlling barriers to dislocation motion. even at the high oxygen concentration of 1OOOwt.ppm. A major objective of the current stud! is to examine by thermal activation analysis whether a single dislocation mechanism controls the rat: of deformation at all strains and concentrations or ivhcther different dislocation processes control th: flow rate in the microstrain region for different con~~ntr~t~ons of interstitial solutes. To accomplish this. methods tvere developed to accurately measure the asriration parameters in the microstrain region and these parameters have been measured on a series of vanadium single crystals with varyin, 0 interstitial contents. The parameters Lvere measured over the strain range from about 10-5-10-2. a range sufficientI> isid,- to characterize dislocation motion in the microstrain region as well as the transition from micro to macro How behavior.

The specimens used in this study ~vere obtained from zone refined single crFsta1 vanadium rods produced at the University of Maryland Ccjtal Growth Facility from dendritic crystalline powder supplied by the Bureau of Mines, Boulder City, hy. The powder was compacted in a 0.75 in. dia. die at a pressure of 24,ooOpsi, melted in an arc melter under high purity helium, and then cold swaged in several passes into a 0.270 in, dia. rod. The swaged rod was loaded into the zone refiner with a single crystal see and zone refined to produce high purity single ccs*Ul rods. The techniques used to grow the zone refined rods derive from those described by Beale and Arsenault [23]. All zone refined rods had axial orientations Gvithin 5’ of the (491). Specimens were prepared from the zone refined rods by centerless grinding to a dia. of &IS9 in. in increments of O.ooO5in. Ground rods u’ere cut into lengths appros. 15 mm long in a low sFd Buehler thin sectioning cut-off wheel. The resulting cylinders were chemically polished in a 1: I: 1 HM&-I-IF-H20 solution to remove approx. O.O@in. from the dlameter and were than mounted into a lapping jig and

Table I. Chrmlcal

composition

/

239 236 ‘0 N.O.

I

66

,1

310

/

-0.5

!

10 /

.001160

63

I

340

j

-0.5

!

129

.001649

Wt ppm

N110’6

* N = i3.19

Wt ppm 0 + 3.64

I

= Not detected

lapped on standard m~t~~llographic equipment until the hces of the cl-linders \vere parallel to within 1 min of arc as measured on an optical comparator. Most of the specimens shelved no measurable (i.e. <: 30 xc of arc) departure from parallelism after this procedure. The c! linders were then annealed at high vacuum to rsmo\e any residual hydrogen and doped with varying amounts of osyo,cn. The finished samples were then kept in a vacuum desiccator until tested. Chemical anai>sis of the rod material was performed b) Lcd0u.u and Company. Teaneck. New Jerse>. on compression specimens after they had been tested. The results are given in Table 1. In this table. the rods are iisted in order of increasing oxygen ~1~1s nitrogen content. This is because of the similar effects of os>gen and nitrogen on the flow stress [24] and the fact that control \vas not obtained over the nitropsn content.

The specimens were tested by strain rate c@ing in compression using a 10,ooOkg floor model Instron testing machine at various temperatures between 13 and 19s K. Temperature control was maintained to within i 0. i 5 K. The specimens were compressed het\vren two hardened steel pistons which slid accuratei! in a close-fitting outer guide cylinder as shoun

in Fig. 1. Accurate positioning oi the specimen along the axis of the pistons uas achieved using an alignment disc and two O-rings. Load was transmitted to the pistons ria a loading train u-hich mounted hdou the moving crosshead of the Instron. Th,- loading train uas attached to a stationark Instrom F31 tensile load cell bq means of a pushrod uhich kept the load cell remote from the test asssmblq. The load train incorporated two hardened steel ball bearings. a Brine11 plate. and a universal joint to achieve axial loading free from bending moments. Displacement seas measured using two Dabtronics DS-X0 linear variable differential transformers (LVDf’s) attached to the compression pistons by means of rigid horizontal bars. High ssnsitikity londextension curves Lvere plotted on thz Instron recorder using custom electronics to convert the recorder to an u-j’ plotter with an effectively infinite s-axis. For about one half of the tests. the extension axis signal was taken from the LVDT’s. processed. and fed to the s-nsis of the recorder to a sensitivity of J x lo-- in. The J-asis signal was taken from the Instron load cell using standard Instron circuitry. .A timing mark was imposed on the x-axis using an electronic clock and the pip marker feature of the Instron. A schematic of the jis and measuring system is shown in Fig, 2. The crosshead speed was controlled for all tests by an external constant speed motor mounted to the front of the Instron pushbutton selector and attached through gearing to the Selsqn unit. Strain rate cycling kvas performed using nominal 5:l chances in crosshead speed. The base low strain rate was _ -t x 10mh over the specimen gage. SW-’ Load extension curves were reduced to true stresstrue strain curves by calculating the stress. G, directiy from the load. F. and separating the total strain. +. into elastic and plastic parts. E, and cP according to the relation: E,, =

WIBL

CILIYOER

COYPRESSIOW

PISTOlI

FJ

-E,

=

A/J

lo -

F

.‘lp!z

(1)

for small strains. In these rdations. E is the apparent elastic modulus. AI, is the total specimen length change, and lo and .4,, are the initial specimen length and cross-sectional area. respectively. It is important to obtain an accurate value for the apparent elastic modulus, E. since this paramstsr contains elastic strains from the stressing jis as well as indentation strains associated with punching of the specimen into the pistons 191. The true instantaneous plastic strain rate. $ was determined simultaneously using the superimposed independent timing mark on the force axis of the load+longation record. The quantity eras calculated using Bernstein’s relation (3). (3)

Fiy. I. .A schematic of thz compression jig.

where dG;dcT is ths slope of the stress strain curve.

93

CROwE

.ASD

ARSENAULT:

MICROPLASTICITY

nrrTROWICS

IN VANADIUM

SINGLE CRYST.4LS

for the activation enthalpy where r is the resolved ( Ill > (701) shear stress. The quantities needed to calculate the activation parameters were obtained from either the Calcomp plot or the Instron plot of true stress-true strain. Extrapolations connecting the high strain rate segments and the low strain rate segments of the curves were made and Aa values were taken as the vertical distance between the actual curve and the appropriate extmpoIation. The values of the true plastic strain rates just prior to each cyde were plotted as a function of strain and curves were drawn connecting the high rate points and low rate points. The strain rates were then taken at constant strains to calculate the activation areas according to equation (3).

as.200tvays

Fig. 2. A schematic of the jig and measuring system.

by a computer which provided a Calcomp plot of stress versus plastic microstrain as well as a table of strain rates just prior to each strain rate cycle. For the second half of the tests, an analog computing device was inserted between the transducer amplifier-indicators and the preamplifier-chopped. This de\ics was designed to perform in s&r data reduction according to equations (1 and 2). The use of this device decreased the overall strain sensitivity by a factor of two but was invaluable in solving procedural difficulties. Activation parameters were calcufated in the usual way using the relations The calculations

were accomplished

A* = @T/b) [Zln +pi&]T

(3)

for the activation area and AH = -bTA* I

I

(ST,‘ST),~ I

(4)

Figures 3 and 4 show examples of asial stress-microstrain curves for (491) single crystal va~dium specimens at various temperatures for the high and low interstitial contents. The curves for Rod 238 in Fig. 3 are for samples which had been prestrained from 0.5 to 0.7% at the test temperature. whereas the curves for Rods 160 in Fig. 4 were obtained on samples without prestrain. Prestraining was performed on the high oxygen Rod 238 samples because these specimens strained less than 2 x 10-j when tested in the annealed condition before a rounded macroscopic yield drop occurred. Twinning occurred in a11 tests attempted below 125K. Many workers have reported that the transition from slip to twinning in b.c.c. metals takes place at higher temperatures as interstitial solutes are removed, particularly in compression tests [26]. It is common practice to suppress twinning by prestraining at higher temperatures and by testing in tension. I

I

ROD 238 PRESTRAtNfD AT TRE TEST

Stress-microstmin behncior

30 -

0.5% TEMP.

I

I

I

ROD 160

125'k

113’k

125’k

Oo

1

I

25 AXIAL PLASTIC STRAIN,X lo4

Fig. 3. A.x,ia!_stress-microstrain curves for the high ___ st&il Rod L3Y at various test temperatures.

AXIAL PLASTIC STRAlN.Xi04

inter-

4.

Axial stress-microstrain curves for the low interstitiat Rod 160 at various test temperatures.

CRONE

-\SD

.ARSEN.ACLT:

MICROPLASTICITY

These methods were not used in the present investigation btezause prestraining alters the substructure of the crystals and therefore masks many of the effects under study. Comparison of the stress-microstrain curves of Figs. 3 and 3 shows that microflow stresses of vanadium crystals are considerably lowered with decreasing interstitial content. Another important feature is that the shape of the curves is altered by both temperature and purity. At low interstitial contents there is generally a nearly linear ~-6~ relationship in the microstrain regime and in some instances, the linear region is followed by a region where d’a;‘deb > 0. This concavity of the a,+ relationship becomes more pronounced as the temperature is lowered. The transition to macroscopic yielding becomes less well defined with increasing purity at al1 temperatures. for the transition takes on a quasi-parabolic shape. At highest oxygen content (Rod 235) a distinct transition from microstrain to macrostrain behavior occurs even though the specimens had been prestrained at the test temperature to ensure an adequate supply of mobile dislocations. All of the features described above have been observed in other microstrain studies in those instances where the material was of sufficient purity. The only unique observation is the extent of the S shaped stress-microstrain region. S shaped curves were observed by Chambers ef n[. [27]. but the strain regime over which d’cr;‘de$ > 0 occurred at lower strains and temperatures and was much narrower in extent.

1% V.4NADIU~f

SINGLE CRYST.ALS ROO 148 PLASTICSTRAINRATE

35 -

a lW5 9 .. E E

39

SEC.'

0 3.2<10.6

10r

TEMPERATURE.

K

Fig. j(b).

T~nlper~lrl~re~~pe~~~~en~e of‘ I~isrQ~~~~stresses

The temperature dependencies of the microfow stresses are shown in Figs. j(a-d). These curves are plots of resolved shear stress vs temperature at various constant plastic strain rate levels. The shear stresses have been resolved on the (1 1I> (i-01) slip system using the Schmid factor for each rod orientation. ROO 160

PlASllCSTRAINRATZ

35 -

9

TEMPERATURE. “K Fig. j(c). mom PUSllC STRAIN RATE

35 -

0 Ml05

.

SEC-'

0 3.2=+

30 " .

b 1.10-6 * 3.2110.7

0 1.10-* SEC.' = 3.2w~

c

,"

a Ho-6

30*

ii

+ 3.mo.7

25‘

5 g z CL

zo-

TEMPERATURL'K

Fig. 5(d). Fig. 5. The temperature dependence of the microdow stressat various constant plastic strain rates: (a) low interstitial Rod 160, (b) low intermediate interstitial Rod I-IS, (c) high intermediate interstitial Rod 39. and id1 high interstitial Rod 235.

930

CROK’E ASD ARSENXCLT: ~ICRO~L~STIC~

IN VANADIUM

SI?GLE CRYSTALS

An important observation is that the low strain rate curve begins to rise at a lovver strain than does the high strain rate curve in all samples tested. At the point labelled A in Fig. 6. the low rate approaches the high rate. This causes a rapid drop in the experimental activation area. This pinch-off effect can be understood by examining equation (2) and noting that the stress-strain curves for the high and low rates diverge over a limited strain region. In this region (dg/dC)hi,b p (dG;‘&)r,. This causes the low plastic strain rate to approach the high plastic strain rate even though there is a factor of 5 or 10 difference in the crosshead speed. True plastic strain rate versus plastic strain curves very similar to those of Fig. 6 have been reported by Parikh [lS] for microplastic deformation of Ta and Ta-W alloys. The strctin dependence

Fig. 6. A typical true plastic strain rate vs true plastic strain curve.

One of the more salient features of these curves is the decreasing tem~rature dependence of the flow stress as the strain rate decreases. It is atso apparent that as the interstitial content increases, the temperature dependence of the stress increases more rapidly with plastic strain rate. The effect becomes more pronounced for interstitial concentrations greater than 1160 at ppm 0 + N. Drpettdetm

of pbstic strait1 rate on plastic strain

The true plastic strain rate as a function of plastic strain at 298 and 125 K for Rod 148 is shown in Fig. 6. This behavior is typical of al1 rods tested. As can be seen, the plastic strain rate in the microstrain region is more than an order of magnitude less than the strain rate associated with the crosshead speed. In most cases. the strain rate remains nearly constant up to strains of _ 8 x lo-‘. at which point a sharp rise occurs. The strain rate continues to increase until it nears its limiting value where it again becomes independent of strain. As the temperature is lowered, the transition to the limiting strain rate shifts slightly to higher strains. This reflects the more rounded stress-strain curves at the lower temperatures. If plastic strain rate were plotted vs total strain, then the plastic strain would be zero (unresolvable with present apparatus) until a plasric strain of c 1 x lo--’ is reached. The transition from unresolvable to a plastic strain rate of 5 x lo- ‘-IO- 6 set- ’ was not observed. The true plastic strain rate vs plastic strain curves for Rod 238, the high oxygen material prestrained at the test temperature, showed a more rapid transition to crosshead controlled flow. This reflects the fact that very little microstrain occurred during the defo~ation of this material.

of the apparent actinltion

area

The apparent activation area as a function of plastic strain at various temperatures is shown in Figs. 7(a-d). In general. the curves are broken into two plateau regions roughiy corresponding to the separation of micro- from macro-strain. The value of the activation area in the ~crostrain region is high and relatively constant with increasing strain until the transition zone is reached. At this point the activation area decreases sharply to very low values. These low values are a direct result of the divergence of the high strain rate and low strain rate flow curves in this region and the constraint of equation (2) on the plastic strain rate. The divergence causes the Aln 4, term in equation (3) to decrease while A,r is increasing. This produces the very low values. Although this feature has not been explicitly reported before. it appears to be a feature of the data reported by Meakin [L?] in his study of microstraining of molybdenum. Meakin’s curve, reported for room temperature data only, shows similar behavior except that the transition occurs at slightly higher strains and the value of the activation area in the macrostrain region is an order of magnitude smaller than the room temperature vanadium area. Another interesting feature in Fig. ‘7(a-d) is the small hump occurring just prior to establishing the macrostrain value of the activation area. This hump is probabfy associated with disfocation generation. As the temperature decreases, the magnitude of the activation area decreases in both plateau regions. However, the temperature affects the macroflow value somewhat more than the microflow value. Examination

of data for a single tnechanistn

The most direct indication of whether one or more

rate-controlling mechanisms is operative is to determine the activation free energy or activation area as a function of effective stress. If the results fit single smooth curves with shapes consistent with expectations derived from the rate theory, then there is a strong indication that a single rate-controlling

1000c

E L

,

This assumes that the actisation free energ-. AG AH and AH = PHI:,). It then follows that equation (5) can be written

Rue 14R

2i

2x10-$

,1’

I”

10-i

mechanism is operative. It is therefore necessary to have a detailed knowledge of the local value of thr StKesS.Tr. to test the result against specific dislocation mod& This is so because T, is the stress component under which local dislocation motion occurs and therefore. the natural variable appenrinp in the \vork terms of the theorb. L’nfortunately. there is no _eenerul method to separate short and long range components of stress in the microstrain region. There is an indirect method. however. which can be used to indicate whether or not a singie mech~~nism is operative. The basis of this method. according to Conrad rt a/. [3]. is to examine the temperature dependence of the apparent activation snthalpy to ascertain tvhcther the measured x\iues fall Lvithin a band. tht lvidth of which is determined b> the maximum difference in plastic strain mte. Curnahan et al. [ 1I] use this procedure and consider the rate equation in the following form:

iI’

/ ”

10.'

10-1

,

10-Z For a single mechanism. AHo is independent of strain rate. so measured values of AH vs T must lie bctueen the maximum enthalpl;. AHo. and AH, - kT Aln :.P. provided :. does not change. Results from this analysis are sholvn in Fig. @a-d). Except for Rod 325, the curves do not fit within the band indicated b> the solid lines in the figures. This indicates that more than one mechanism is rate controlling in Rods 160. 148 and 239. Since the data For Rod 739 do fall gvithin the band. the results are consistent with a single rate-controlling mechanism in this alloy. If the low strain rate, low temperature data for Rod 239 is neglected. the results arc rhe same as those of Rod 2X. In fact. all the data are consistent with two rate-controlling mechanisms sine they fall within two bands. It should be pointed out. however. that thz bands are quite wide because of the large strain rate range investigated and because :,, is not constant over the entire range of the tests. These facts limit the degree of confidence of the preceding anall;sis.

DISCUSSION

.Apparen[activation area vs plastic strain at various test temperatures [al for Rod 160. (b) for Rod 1% (cl for Fit,=. 7s.

Rod 239. md i id) for Rod 32% L

In b.c.c. metals. the density of obstacles is not increased by deformation and therefore, the number of possible rate controlling mechanisms is limited. While several possible thermally activated dislocation mechanisms have been proposed to explain the obssrved behavior. there are presently two predominant kkwpoints. The first of these maintains that the low temperature strength is caused by a dispersion

932

CROWE ASD ARSENAL-LT:

MICROPLASTICITY

of interstitial solute atoms in solid solution. The strengthening mechanism derives from the elastic interaction of moving dislocations with the strain fields of the dispersed barriers [2937]. The second viewpoint maintains that the low temperature strength is an intrinsic property of the b.c.c. lattice [3&40]. The dislocation mechanism which controls the deformation is either the interaction of moving didocations with the Peierls potential via double kink formation or the recombination of mildly dissociated screw dislocations. under the action of an applied stress. The hypothesis that microstrain is linked to the motion of edge and nonscrew dislocations has been discussed by several authors [1.7-IO]. In order to explain how large microstrains occur in metals with large Peierls stresses, Arsenauit (411 considers double kink formation as the rate controlling process. One of the unique features of the double kink model is that it predicts a spectrum of activation energies for dislocation motion. This is because the energy of formation of the double kink is strongly dependent upon the value of the Peierls stress which in turn is a strong function of dislocation character. Arsenault estimates that the Peierls stress for a screw dislocation on a (110) slip plane is as much as IO3 larger than for an edge dislocation. The activation energy of formation of a double kink varies as the square root of TAO. so, there may be a factor of up to 30 difference in the activation energies of formation of double kinks for the two types of dislocation. From this analysis, Arsenault concluded that the events which describe the movement of dislocations in the mi~rostrain region could be as described below. First, the motion of geometric kinks occurs, then double kink formation on edge components takes place. Edge components are able to move fairly large distances leaving behind trails of relatively immobile screw didocations. The supply of edge components becomes exhausted, resulting in an increased stress required for further straining. This effect has been termed “exhaustion hardening” by Solomon and McMahon [S] who use a similar model to explain microstrain phenomena in iron. At the end of the microstrain region and towards the beginning of macroflow, the formation of double kinks on screw components takes place and macroflow is controlfed by this process, Seegar and Sestak [lo], using similar ideas, predict in detail stressmicrostrain relationships in the microstrain region. Their predictions are based on the extended core model for screw dislocations in which the motion of (111) screw dislocations requires a local change from a sessile to giissile configuration. Seeger and Sestak describe how a dislocation segment of arbitrary orientation moves as the applied stress is gradually increased. The sequence of events is shown in Fig. 9 and starts with the movement of nonscrew dislocations and the fo~ation of immobile geometric kinks on screw dislocation segments. As the applied stress is further increased. the kinks move

IN VANADIUM SINGLE CRYSTALS

TEMPERATURE, '1

Fig. S(a).

TEMPERATURE. 'K

Fig. 8(b).

.

ROD23s

. PlASflC STRAINRATE +

0lXlfl.S red 5 3; > e i 5 1 E Y

1.f

a 3.2x 10'~ .lXW8 c 3.2x10.7

1.0-

E g Y

s :: e

03 -

2

0

SO

100

150

Fig. S(c).

200

230

300

CROWE

1

.A\D

.ARSEN.\CLT:

UICROPL.ASTICiTY

IN Vr\SXDIUM

SIXGLE CR’tST,\LS

313

I

tain an inflection point at the lower temperatures. The inflection point is associated with the erhaustion of t 0 1 x lV5 r4c.l pre-existing geometric kinks in a manner similar to that described b> Xlcfeld et (I/. [Lfl]. Seeger and Ssstak further predict that solute atoms affect rnicrotIo\b only above _ 50 K. This is because of the small activation energq associated with lateral kink motion and double kink nucleation on edge and nonscrew dislocations. Abobe _ 50 K these processes are especttd to br: completely thermall! activated. UnfortunateIt,. twinning in the specimens studied in this investigation at test temperatures belox 125 K prevented checking the latter predictions. To relate the present iyork to the ideas described abobe. it is instructive to consider some theoretical estimates of the activation parameters associated lvith the relevant thermally activated elemental processes TEMPERATURE “K and to compare them ivith measured quantities. It Fig. 8id1. is also instructive to consider the amount of strain Fig. 5. The apparent activation rnthalpy vs temperature which can be expected from each process. at various constant plastic strain rates for (a) Rod 160. The first elemental prcocrss is associated with lateral (bl Rod 143. k) Rod 39. and id) Rod 235. The straight lines define a strain rate band consistent uith ;I single diskink motion. Ssglectinp kink-kink interrtctions, the location mechanism. kink barrier has been calculated b) Schottk! [13] as ROD

na

PLASTIC STRAIWRATE

I

I

I

along the screw dislocations and the nonscrew segments bow out, presumnblq by a double kink mechanism. The critical point is that kink motion along the screw segments may have a somewhat larger activation energy than does double kink nucleation on the non-screw segments. Further increases in stress eventually- enable the nucleation of double kinks on screw dislocations and macroscopic Ro% begins. Using this sequence of events. Seeger and Sestak conclude that stress-micros&rain curves should con-

Lvhere ik is the stress required to cause the kink to cross the barrier and \cp is the ividth of the kink. The value of the energy barrier is given as AG” = r&b35.

From equations (7 and S) rvith s,,;t 1 10’. h.~, = I:IO. and ii = 5.2 x 10” dyn:cm’. ~2'= O.?M kp, mm' and AGk = 7 x IO-’ sV. The corresponding activation area is .-L*= lob’. Clearly. this process is completely thermally activated over the temperature range investigated. If. as suggested by Ssrgsr and Sestak [IO]. the kinks are abrupt. b wk - 1 and AG, then equals 7 x IO-’ eV: still too small to be considered as rate controlling. For AGk to equal as much as 0.5 eV. h!rvk = 700. which is indeed abrupt. The question arises. however. as to whether all the microstrain can be achieved by motion of pre-existing kinks without the necessit! of nucleating new kinks. Consider the strain resulting from a densit!- pk of kinks moving a distance i.+ The strnin $ is E; 2: &).L&.

-L

Fig. Y. Schematic of the sequence of conjurations descrkng dislocation motion in the microstrain region (adapted from reference II 1.

($1

191

.4ssuming Lk is lo- ’ cm. tvhich is about 1’10 the average distance befiveen dislocation tangles. a plastic strain of 1 x IO-” gives pk = -I x lo-. which is reasonable. For microstrains of Y x lo-‘. however. pt must equal 3 x 10’. which is rather high since the total line length per cubic centimeter in as-grown and annealed crystals is estimated as c 3 x 10’ cm- ‘. Furthermore. a stress-strain curve for a material where only kink motion is occurring should be hi& non-linear because of the depletion of the number of kinks with increasing strain. According to Aiefeid

93

CROWE ASD ARSENAL’LT:

~~ICROPL.~STICI~

rr crl.C-Q]. there should be a region where the stressstrain curve is convex. This condition is observed in this study. but it occurs at strains too large to be associated with this process. Afefeld predicts strains of approx. IO-’ for geometric kink motion. Thus, we conclude that pre-existing geometric kink motion is not important in the microstrain curves measured in this study. The second process to be considered is the movement of edge and non-screw dislocations. The concept of double kink formation on edge dislocations in the b.c.c. lattice requires further consideration because these dislocations do not lie along a close packed direction. According to the theory of the Peierls stress. the lattice provides an appreciable barrier to dislocation motion only if the dislocation line lies parallel to a short lattice vector. Therefore, the resistance to edge motion is expected to be small. There is a mixed dislocation. however, which is predominately edge and which lies in a ( 1I 1) close packed direction. This dislocation is 71” off the screw orientation and the Peierls stress is approximately a factor of three smaller than that of the screw dislocation. If the movement of these dislocations is associated with the anisotropic expansion of dislocation loops in which screw segments are sessile, there can be no genera1 disioc~ltion ml~lt~p[ication until the screw segments become mobile and thus the stress-microstrain behavior is clearly a form of exhaustion hardening. The rate controlling mechanism for the motion of the edge and nonscrew segments could be either double kink nucieation or solute interactions or a combination of these. A good approximation For double kink nucleation processes are the relations.

IN VANAD1t.X SINGLE CRYSTALS

of composition. Christian uses FIeischer‘s theory and the computer calculations of Kochs[45.?6] and Foreman and ?&kin [47]. to write the temperature dependence of the effective flow stress, ;r as r, = (0.8 Fd’b”) [l-(r,:r,,“‘]?(zc”‘),

(12)

where: T is the absolute temperature, c is the atomic conce~t~tion of interstitial atoms, F, and T, are constants. The effective flow stress, :‘r is the local value of the stress acting on the dislocation and not the applied stress. To compare the experiments with the theoretical relations, it is assumed that T, 2 T - t (298 I() at the strain rate of interest. The activation area. A*. is given as A* X -b’ (zc)- Ii2 [(Q/r,)’ ‘-I).

(13)

where ~~ is the effective flow stress at OK. Furthermore, r. = (2~)“’ Fe/b’ and AGO = F. b where F,, is the maximum force exerted on the dislocation at 0 K. If the dislocation is assumed to be edge, the theory predicts F, = F~, b’j2.9.

04)

Using ell zz 0.3 and F, = 3.72 10-j dyn, gives AGO = 0.611 eV. This value is also a reasonable estimate. The values for TV for each of the test crystaIs are therefore expected to be 14 kg’mm’ for Rod 160, 19 kg/mm’ For Rod I@,22 kg/mm’ for Rod 239, and 26 kg/mm’ for Rod 238. These are very reasonable estimates for T, at OK for microflow at h, = 3.2 x IO-’ set-‘. This is good evidence that the mobile species in the microstrain region are edge and nonscrew dislocations. It should be pointed out that it is difficult to estimate a value for A* in the microstrain region for a dispersed barrier mode1 because in the microstrain and region T, is always small up to the anelastic limit. .a* Ic j,rl ‘(tp - T,)- ’ ’ (111 According to equation (13), A* is expected to be large for small rr. Equation (13) predicts that .A*--+ x as due to FriedeI [4&j. Mere To = irh’;‘2 is the line ten?,--*O, but this cannot occur in any real situation. sion and rp is the value of the Peieris stress for the Figures lO(a and b) show plots of T; vs c*!' For particular species of dislocation of interest. Assuming strain rates of 3.2 x lo-’ set- ‘ and 1 x IO-’ set-‘, 3oT;, = jr;’ = ~"p= 50 kg/mm’, where the sub or respectively, at constant temperature. In these plots, superscripts e. 71. and s refer to edge. the 71’ mixed, and screw distodation respectively. AG:’ = 0.81 I eV, it is assumed as a first approximation that t, c t; = AGD: = 0.363. and AG:’ = 0.145 eV at zero effective r - T (298 K) at the strain rate of interest. Taking F, = pbL/8 and estimating To = 35OK at i, = 1 x stress. The corresponding activation areas are 10-j see- 1 From Figs. S(a-d), the gradients of fa (T) ‘4: = lob’. il?, = 3b’. and A: = 5%“. Although the values of the activation energy are reasonable. the against cl ’ should be 122, 66, 32, and 4 at temperatures of 125, 173, 220, and 298 K. respectively, if equavalues of the activation area are considerably smaller tion(12)isvaIid.At(, = 3.2 x lo-‘set-‘. To 2 250K than those measured in the microstrain region. The values. however. are in good agreement with the and the gradients become 64.21, 3, and 0 at the same temperatures. These gradients are shown dotted in measured parameters in the macrostrain region. Figs. lO(a and b). As can be seen, at ep = 1 x lo-’ If the rate controlling mechanism for the motion set- ’ there is no correlation. At concentrations above of the edge and nonscrew segments is primarily 868 at ppm, r> is approximately independent of conrelated to solute interactions, there should be some centration. At 3.2 x lo-’ set- I, however. the correlacorrelation with the theory of dispersed barrier hardening. According to Christian [32]. a sensitive test tion is quite good for concentrations below 1160 at ppm, but at the high concentration, rk increases with of dispersed barrier theories is to examine the temcl,2 much more rapidiy than predicted. perature dependence of the flow stress as a function

CROWE A% .ARSENACLT:

MICROPL.KIICITY

IN V.ANADIL \I SISGLE

935

CR\IST.\LS

mars in the microstrain region than in the macrostruin region. strongly suppesting that the dominant dislocation species is ditfsrent in the two regions. The observations that :;, and .-I” are nearly indspendent of concentration at i, = I x IOY’s~c-’ in Figs. 10(b) and 1l(b) arc consistent nith the lattice mechanism controlling the deformation rat2 in the macrostrain region. Figure 12 shows the HOW jtress
cation mobilit?

30 -

ep

= 3.2

-----“E5

25-

L” L ,Y

20-

0 5

x 1o.‘s,c.’ Predicted

by fltirchar’s

madal

15-

I

Soe 0

_____-e---2; 10

[ATOMIC

20

30

CONCENTRATION

40

50

x 10’

O+Nl%

::Fi -------

Predicted

by fltischer’s

model

I

0

(ATOMIC

CONCENTRATION

O+Nl’

x IO’

Fig. 10. Approximate effective stress versus the square root of concentration for constant plastic strain rates of (a) 3.2 x lo-’ set- ’ and (b) 1 x 10-j XC-‘.

Figures 1l(a and b) show the activation area plotted against c’j” at (_ = 2.2 x lo-- set- ‘, respectively. According to equa;ion (13X these plots should be straight lines with slopes as indicated. Again there is no correlation. At the low strain rate the curves show a complex behavior. whereas. at the high strain rate the activation area is nearly independent of concentration. The data are somewhat consistent with the dispersed interstitial model at concentrations below 1160 at ppm in the microstrain region. The data are inconsistent with the dispersed interstitial models in the macrostrain region and are also inconsistent bvith a single mechanism theory. This is in agreement with the previous analysis of the temperature dependence of AH. It is also apparent that interstitials affect dislo-

25

“20

[ATOMIC

35

40

45

O-N;-ii

-.

150

“0

30

CONCENTRATION

t

---

PlLDlCTLC 8”

‘. i

(ATOMIC

CONCENTRATION

O-N+

Fig. 11. Apparent activation area 0s a function of the Inverse square root of the concentration at 2 pk1StiC strain rates of (a) 3.2 x IO-’ and lb) 1 x 1V’ jtC_ ‘.

936

CROWE

ASD

ARSENAL’LT:

MICROPLASTICITY

IN VANADIUM

SINGLE CRYST?rLS

tions in the microstrain region. These same samples in the initial unprestrained condition showed very little strain prior to the occurrence of a rounded yield drop again indicating that few mobile segments existed in the structure. During the expansion of the loop. the screw density should increase as the nonscrew density decreases and there should therefore be a limit to the total strain which can occur without dislocation multipli~t~on. If there are initially .I’ edge segments per unit volume of mean length .T. this maximum microstrain, E,,,~~.is %&lx1 !l’b! b.

I *o

,

I

50

100

I

IS0

I

I

,

200

250

300

TEMPERATURE.'K

Fig. I?. The temperature dependence of the Row stress for various interstitial concentrations at a constant plastic strain rate of I x lo-’ set-‘.

stresses are only slightly dependent on solute content up to concentrations of 1160 at ppm and then there is an apparent transition to a strongly temperature dependent flow stress at the highest solute content. This behavior is not consistent with the lattice models. leading to the conclusion that this mechanism is not rate controlling in the microstrain region. It should be recalled. however, that the high concentration Rod 235 samples were prestrained at the test temperature. The behavior of this material in the microstrain region could be related to the fact that these samples probably contain very few edge and nonscrew dislocations in the structure. If the solute affects are primarily associated with edge and nonscrew dislocation motion and only indirectly associated with screw motion, then this increase in strength could be caused by lack of mobile disloca-

Tf~PERATURf,'K

Fig 13. The temperature dependence of the flow stress for

various interstitial concentrations at a constant ptastic strain rate of 3.2 x IO-‘see-‘.

(1%

where the slip distance. il. is equal to or less than the dimensions of the crystal. With .VS = 3 x 10” cm?. and ,l = IO- * cm, emax= 7.9 x lo-‘, which is in excellent agreement with the location of the transition in the A* vs E, curves of Figs. 7la-d). The corresponding screw density produced as a result of this microstrain is

With .U= lo-‘cm, ps = 6 x 108cm-‘. which is a reasonable number that compares with the electron microscopy results of ps r: I.5 x 108cm-’ obtained by Solomon and McMahon [Y] in iron after a l’!,O strain at 77 K and ps 2 1 x lO”cm-? obtained by Lawley and Gnigher on molybdenum (SO] after a 5 x IO-’ strain at 77K. It should be pointed out. however, that the values chosen for the above calculations require .‘v’= 3 x 10gcm-3 which is a high vatue. Christian [5 l] performs a similar calculation and concludes that some sources most likely operate prior to macroflow. The above calculations indicate that a convex stress-microstrain curve may result from the exhaustion of edge and nonscrew segments. The location of the upsweep would be expected to occur in the strain range lo-’ 5 Ed s lo-‘. This is observed. In contrast, the range c, $ 10-j is expected from the Seeger-Sestak [lo] model where the emphasis is placed on the low mobility of kinks in screw dislocations. The behavior observed during this investigation is therefore consistent with the multiple mechanism theory of m~crostrain in which edge and nonscrew dislocations are more mobile than screw dislocations. The predominant rate process for the edge and nonscrew motion is consistent with the thermally activated jumping of dispersed interstitial solute atoms. Processes of double-kink nucleation on edge and nonscrew dislocations are completely thermally activated in the temperature range investigated. Lateral kink motion is apparently not important as a ratecontroliing mechanism. Macroftow is controlled by screw d&location interaction with the lattice. The results are cc&sistent with double-kjnk nucleation on screw disiocations pinned to finite lengths by interstitial soiute atoms as described by the model of Ono

CROWE

GD

ARSENACLT:

MICROPL.ASTICIT~

and Sommer [-IU]. This is also consistent with the transmission electron microscopy results of Huang and Arxnauit [21] and at variance with the results of Arsenault and Pink [?I. The only observations not consistent with the above picture are the results on Rod 160 in the macrostrain region. These results are consistent with other experimental $vork [Z. 531. but they are not consistent with the On~~mmer model. One possible explanation for this could be that the presence of a smaI1 amount of interstitials increase the lattice resistance to dislocate motion by increasing the Psi& stress. Such an effect aould be related to electronic effects associatsd uith dissolving small quantities of interstitials into solid solution. SLlCL\lARY ASD

COSCLUSIOX3

The principal results of this investigation and the conclusions which are drawn from them are as follor~s: 1. Methods for performing dynamic microstrain tests in compression in the microstrain region at temperatures down to 77 K have been developed. The activation parameters for plastic How in the microstrain region have been evaluated on a series of vanadium single crystals containing interstitial contents ranging from -IS6 to 1649 at ppm 0 -i- N at various temperatures between 125 and 298 K over the strain range 10-‘-I? x IO-‘. ’ Bctcnusc: the true plastic strain rate in the microc. strain region is a function of strain, a Row criteria hassd on a fixed offset strain is inadequate in relating measured Aow stresses to theories of thermaliy activated Row. Flow criteria based on constant plastic strain rates ivere used in a parametric analysis of the observed behavior. Flow criteria based on constant plastic strain rates are more closely related to the dynamics of individual dislocations and therefore thermodynamically more appropriate in relating theory rvith experiment. 2. Activation parameter measurements indicate that a single dislocation mechanism does not operate continuously as a function of strain over the entire micro to m&o strain region. except possibly at very high interstitial contents. Activation enthalpy values do not fall within a single mechanism band and activation area as a function of strain exhibit discontinuities. Both of these observations are inconsistent with a single mechanism theory. 1. Flow stress as a function of interstitial concentration at all temperatures in the microstrain region are consistent with the idea that edge and nonscrew dislocations are the mobile species in the microstrain region and the dynamics of the dislocations are controlled bq solute interactions. 5. Flow stress as a function of interstitial concentration at all temperatures in the macrostrain region are consistent Ivith the idea that screw dislocation motion predominates. the dynamics being controlled

IN VhNDIULI

91’

SINGLE CRyST.ALS

b) double kink nucleation of scre\v se_gmsnts whose ends are pinned by dispersed interstitials according to the model of Ono and Sommer. .-I~~rir~o~\~irtlyr,rlr,irs-Theauthors u ould lik: appreciation to ths 53~31 Surface Weapons G&&l support under Independent R&arch to ths Uniwrsit) of Mnqland Crystal Growth suppl-;ing the sir& crystal vanadium rods.

to express Csntsr for Funds and Facilit! for

REFEREXES 1. C. J. McMahon. .411r..Sl
Rrs. 2. -15 f 1968). 3. N. Brobvn and R. A. Ekvall. .-!cr(zMrr. In. I IOi i 1961). 4. R. J. Arsenault. .A&. .ULUC~.RCS. 2. ?I II 96Sl. 5. D. F. Stein. .UL.. .I~(Icu. Rrs. 2. I-11 f lY681. 6. B. Escaig. J. Plr~s. 27. C-3. 205 (1966). 7. B. Escaig. J. P/I,~s. 28. 171 (19671. 5. H. D. Solomon and C. J. MMahon. in 11.orXHarrit*t~C7y. p. 309. Gordon Lp Breach. Nsw York I 1965). 9. R. .I. Xrssnauit. C. R. Crow and R. D. Carnahan. 3rd Int. Conf. Rrinststoffe in \Visscnschit und Techmk. Dresden (1970).

1. D. Meakin. CM J. Ph~.s. -15. II21 ilY6-I. H. L. PrzkPl and H. Conrad. in Diskmrim Dyrrrmics. p. J3l. McGrakv-Hill. yew York I 19651. P. Groh and R. Contc. .4criz .Mcr. 19. 895 I 1971). P. D. Parikh. Ph.D. Thesis. Drew1 Unixxsitl (19711. T. Vrecland and A. P. L. Turner. S~rirw .\ltit. 3. 193 I 1969). A. P. L. Turner. Ph.D. Thesis. Calif. 11:x of Tech. I 1969). G. Ta) lor and J. ‘A’. Christian. PM. .U+;;. 15. XY> 11967). H. D. Solomon. Ph.D. Thesis. Univ. of Pmns>l\anirt (1968). R. A. Fonall and C. D. Stntham. .Icrcr .Uit. 18. 111’ ( 1970). y. Huang and R. J. .Arsenault. Jfuwr. St-i. Enyny. 11. III (19733. R. J. Arsenault and E. Pink. .Uar
1967. ‘8. H. Conrad. L. Hays. G. Schoek and H. ivirdsrsich. .4cru .Ilrr. 9. 367 (1961). p. X3. Thz 29. F. R. Nabarro. Rrpwt O/I Sweryri1 oiSoliA. Physical Sot.. London (194s). 30. A. W. Cochardt. G. Schoek and H. kVcid:rsich. .Acril .\lrt. 3. 533 (1955). 31. R. L. Flrischer. J. nppl. Phw. 33. ZSN (19621. 32. J. X. Christian. in .?he I&mction Brn\<
938

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Ah-D

.4RSENACLT:

~fICROPLASTIC~

J. Darn and A. K. Mukherjee. Trms. .-lI.kfE 245. 1193 (1969). R. J. Arsenault. .-lcm .\frt. 1-L.831 (1966). G. Alefeld. R. Chambers and T. E. Fide. f’h_~ Rer. l-40, 1771 (1965). G. Schottky. Phy. Srtmrs Safitli 5. 697 (1964. J. Friedel. Dislocariow p. 65. Addison-Wesley. Reading. hf.4 (1964). _ U. F. Kocks. Phil .ifoo. 13. 541 i 1968). L’. F. Kosks. .4cm. .U:r. 14. 629 (196$). A. J. E. Foreman and M. H. Makin. PM. .Vag. 14. 911 (1966).

I?j VANADIUM

SI?;GLE CRYSTALS

48. K. Ono and A. W. Sommrr. Mrr. Trcms. 1. 877 (1970). 49. A. S. Kch and Y. yakada. Cnn. J. Plrys. 45. 1101 (1967). 50. .A. Lawle), and H. L. Galgher. PM. .UN~. 10. 15 (1964. 51. J. W. ChrIstian. in Pm. 31tl [UC. Co@ on r/w Srrrrqth of‘&lrtds trnd Moms. p. 31. AS&l. Metals Park. OH (19701. 52. T. E. Mitchell. R. J. Fields and R. L. Smialek. J. Less Corwnor~.Ifrrtrls 20. 167 (19701. j3. J. Bressers. M. Heerschap and P. DeXIeester. J. Less Cof?lffloff .\frrds 21. 32 1 c19701.