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Basal slip in zirconium
BASAL
SLIP
IN ZIRCONIUM*
A. AKHTARt Single crystals of Zr heve been deformed in tension between 295-l 113°K with a range of orientetions. First order prismatic slip continues to be the easiest slip mode, although the rel8tive ease of besel slip incresses with temperature. Extensive b8s81 slip is observed above 850°K in orient&ions unf8voumble for prismatic slip, whereas twinning precedes slip et lower temperatures. Non-basel slip vectors 8nd slip planes other then {OOOZ} 8nd (1010) were not detected et any tempereture within the renge of orientetions investigated. The critical resolved shear stress for basal slip ~8s found to be temper&me and stmin rete dependent. An equ8tion of state of the form: p = BP exp (-Q/kT) with 8 stress exponent equal to 3.48 snd 8n ectivetion energy of 1.48 eV ~8s obeyed. It is proposed that the mechanism of besctl slip involves recombination of extended dislocetions lying on the prism plenes followed by cross slip. On the basis of this model 8 partid dislocetion spacing of 1lb on the { 1010) planes is obt&ned, which is in good sgreement with 8n earlier estimate of the stecking fault energy from the mechanics of prismetic slip. GLISSEMENT
DANS
LE
PLAN
DE
BASE
DANS
LE
ZIRCONIUM
Des monocristeux de zirconium de differentes orientations ont et& deform& en tmction entre 295 et 1113°K. Le glissement prismetique de premier ordre continue 8 6tre le mode de glissement le plus facile, bien que 18 fecilite reletive du glissement de bese sugmente 8vec la temp6rature. Un glissement importsnt dans le plen de bese est observe eu-dessus de 860°K d8ns lea orient&ions defevorables pour le glissement prismatique, elors que le m&clage p&o&de le glissement aux temperatures plus basses. Des vecteurs de glissement non basal et des plens de glissement autres que {0002} et { 1010) n’ont 66 observes 8 eucune des temper8tures pour les orientetions 6tudi6es. L’auteur 8 trouve que l8 cission critique pour le glissement d8ns le plan de bese depend de la temp&&ure et de 18 vitesse de deformation. Le phenombne obeit 8. une equation d’etat de la forme: 3 = BP exp (-Q/kT) d8ns laquelle l’expossnt de 18 contrainte est de 3,48 et l’energie d’aativation de 1,48 eV. L’euteur propose que le m&nisme du glissement dens le plen de bese comprend 18 reoombineison des dislocations dissooibs se trouvent sur les plans prismatiques, suivie d’un glissement d&i& D’apms ce modele, on obtient tm especement des dislocations ptvtielles de 115 sur les plans {lOTO}, ceci Btant en bon 8ocord 8vec un calcul enterieur de l’energie de faute d’empilement 8 pertir de la m&mique du glissement prismatique. BASISGLEITUNG
IN
ZIRKON
Zr-Einkrist8lle verschiedener Orientierungen wurden zwischen 295 und 1113°K im Zugversuch verformt. Obwohl die Basisgleitung mit zunehmender Temperatur immer leichter erfolgt, bleibt die erste oder prismatisahe Gleitung der leichteste Gleitmechanismus. Ausgedehnte Basisgleitung wird oberhelb 850°K in Krist8llen beobechtet, deren Orientienmg fur prismatische Gleitung ungimstig ist; d8gegen erfolgt bei tieferen Temperaturen erst Zwillingsbildung und d8nn Gleitung. Bei den untarsuchten Orientierungen und Temperaturen wurden nur Besisgleitvektoren und {0002}- und {lOTO}Gleitebenen beobachtet. Die kritische Schubspennung ftir Bssisgleitung ist temperatur- und gesch. windigkeitsabhiingig. Folgende Gleichung gilt: p = BrRexp
(-Q/kT)
D8bei ist der Spannungsexponent 3,48 und die Aktivierungsenergie 1,48 eV. Es wird vorgeschlagen, daB bei der B&sisgleitung die euf Prismenebenen aufgesp8ltenen Versetzungen zun&ohst eingesohntirt werden und denn quergleiten. Auf der Grundlage dieses Modells wird eine Versetzungseufspaltung von 1lb euf den { lOTO}-Ebenen ebgeleitet. Diese Aufspaltung ist in guter Obereinstimmung mit einer frtiheren Abschiitzung der St8pelfehlerenergie 8us der Mechanik der prismatischen Gleitung.
INTRODUCTION
The low temperature dislocation mechanism,(i) work hardeningf2) and interstitial solution hardening’3-5) of Zr in prismatic slip have been examined in some detail in the past. Such information, however, is lacking for basal slip of Zr, although rather limited evidence to suggest dislocation motion on the basal planes have been published.‘2*6*) The low temperature CRSS for basal slip of Ti on the other hand has been studied in some detail and a rate controlling mechanism has been proposed.@)
Slip in hexagonal close packed metals primarily occurs in the direction of greatest atomic-density, revealing that the Burgers vector of the active slip dislocations is of the type a/3 [1120], while the two most commonly observed slip planes are the basal (0002) and the 1st order prism (lOiO} planes. Prismatic slip is readily observed in Zr and Ti, both having an axial
ratio
of nearly
1.58.
* Received Meroh 14, 1972; revised M8y 8, 1972. t Department of Metallurgy, The University of British Columbie, V8iWOUver 8, C8n8d8. ACTA 1
METALLURGICA,
VOL.
21, JANUARY
1973
1
The
object
deform
single
of
the
crystals
present
investigation
of Zr in tension
over
was
to
a range
ACTA
2
METALLURGICA,
of strain rates, temperatures and orientations and to examine unusual slip systems. Optical examination of surface deformation markings, lattice rotation and electron microscopy of thin foils have been used as additional aids to interpretation. EXPERIMENTAL
METHODS
Crystal bar zirconium has been used in the present study. Single crystals were grown from the melt using an electron beam %oating zone technique and cooled through the a 2 /l transformation (1135°K) in a controlled fashion to yield up to 20 cm lengths of a - Zr crystals.(s) An attempt was made to obtain the .desired orientations through seeding. However little success was achieved due to the recrystallization of the seed in the process of a + p transformation. As an alternative, therefore, a large number of crystals was grown at random without seeding and the desired orientations were selected from these 4.5 mm rods. The as grown crystals were annealed at 1093’K under a dynamic vacuum of less than 2 x 10m6mm of Hg for 5 days. Tensile specimens having a gauge length of 2.54 cm and circular cross section were obtained using a spark erosion lathe. Electra polishing was carried out at -50°C under a potential difference of 20 V in a 5% perchloric acid +95% methanol solution to remove the spark damaged layer. In order to assess the difference in interstitial content of one batch of crystals from another, two tensile specimens suitably oriented for prismatic slip were chosen from each batch and tested at 78OK. The CRSS measured was 2.6 f 0.2 kg/mm2 in each case, suggesting that the interstitial content was reproducible from one batch to another. From the earlier published datac2) this CRSS of 2.6 f 0.2 kg/mm2 at 78’K is equivalent to approximately 120 ppm interstitial oxygen in zirconium. Tensile tests were carried out on a floor model Instron. A dynamic vacuum of less than lo4 mm of Hg was maintained during all test,s conducted above room temperature. Resistance heating was used to attain temperatures up to 1113°K and controlled to within k2”. The maximum duration of any test including the time required to attain the desired temperature was less than 6 hr. In order to determine whether the interstitial content was affected in this process, one crystal oriented for prismatic slip was subjected to 84O’C at lo4 mm of Hg for 6 hr in the testing apparatus, cooled and subsequently tested at 78°K. The CRSS still remained below 2.8 kg/mm2, thereby suggesting that the interstitial content was not affected appreciably.
VOL.
21,
1973 RESULTS
The effect of temperature and orientation
(a)
Under tensile loading conditions it is possible to apply shear stresses on the (lOiO}(l~lO) systems of hcp crystals while maintaining those on the basal slip systems at zero. This is achieved by keeping the tensile axis perpendicular to the C-axis of the crystal. The situation in reverse, however, is geometrically impossible i.e. finite shear stresses cannot be applied on a basal system while those on all the prism systems remain zero. Alternatively, suitable orientations may be chosen such that the Schmid factor on one system is sufficiently high relative to the other in order for slip to be induced on the desired plane. An attempt has been made earlierc2) to induce basal slip at 78 and 295°K in suitably oriented Zr crystals tested in tension. -No basal slip however was observed. The crystals yielded due to twinning when the angle between the basal plane and the tensile axis (xB) exceeded 35 and 45” at 78 and 295”K, respectively. Prismatic slip was responsible for plastic flow in other orientations. In the present work a crystal with xB = 53” was deformed at 723OK. The stress-strain curve is shown in Fig. 1. The ratio of the Schmid factor for basal slip to that for the most favourable prismatic slip (SJS,) was 2.85. Serrated plastic flow was observed over the entire stress-strain curve. Optical examination of the deformed specimen did not show twin markings whereas slip lines corresponding to the most favourably oriented prism plane were observed. Further evidence that prismatic slip occurred was obtained from a lattice rotation measurement. The tensile axis was found to rotate towards the (1120) direction which constituted a part of the geometrically _E < y”
Zr-
PRISMATIC SLIP T=723”K
.E I.2 -
z
E I-
m
LO-
lo@
% ;0439 ?I 0 0.6 ! : o.40
Ilicq
[oooz 01
0.2
03
SHEAR STRAIN
Fro. 1. Resolved shear stress VB. shear strain curve of a crvstal deformed at 723°K bv Drismetic slin. The ratio of*Sohmid factors on the most* favourable basal system to the prism system wsa 2.86 at yield (~8 = SO’).
AKHTAR:
BASAL
SLII?
IN
3
ZIRCONIUM
Figure 5 shows the slip lines on a specimen deformed to fracture (Y = 1.2) at 1073°K. The waviness of slip Iines suggests cross slip. From two surface analysis these wavy traces were found to be parallel to the trace of the basal plane. The initial and final positrons of the tensile axis are shown in the unit triangle in Fig. 6. It is apparent that the tensile axis has moved towards the [1120] corner. This is co~istent with deformation due to basal slip. Note that the lattice rotation would be towards [ZlIO] had single prismatic slip taken place. From the initial and final orientations, the shear strain expected(n) from base1 slip only would be 1.17. Since the experimental error in the dete~ination of orientations is &2”, this value of 1.17 may at best be considered
FIG. 2. Resolved shear stress vs. shear strain curves (assuming baaal slip) of cry&& deformed between 29582PK. The orientations are shown in the unit triangle.
most favoured prism system. Serrated yielding has been observed earl%&‘*) in polycrystalline Zr when deformed in the vicinity of 7OO’K. Three more crystals having Schmid factor ratios (SB/SP) between 4 and 6.5 were tested at 295,523 and 823’K. The results are shown in Fig. 2, as resolved shear stress vs. shear strain curves assuming basal slip. Lightly deformed specimens were examined rne~~o~~hi~~y. This examination showed that the onset of plastic flow occurred due to twinning in each case. Optical micrographs of specimens deformed at 523 and 823’K to fracture and subsequently polished to remove slip markings are shown in Figs. 3(a) and (b) respectively. Using the two surface method the twins in Fig. 3(a) were identified as being of the type At 823”K, however, (1121) as well as (iOi2) twins were observed. Another set of crystals having a Sohmid factor ratio (~~~~~) of about 5 were tested between 873 and 1073°K. The results are plotted as resolved shear stress vs. shear strain curves assuming {0002}(ll2O) slip and are shown in Fig. 4. All these crystals yielded smoothly, although the specimen tested at 873°K twinned after about 5 per cent shear strain as indicated by the successive load drops. Subsequent optical examination of this crystal revealed a small number of twins.
(1OiZ).
(b) Slip lines amd lattice rotation The crystals deformed between 973 and 1973°K were examined optically and their o~entations were determined again in order to determine the lattice rotation.
(b)
FIG. 3. (a) Twins of the type jlOi2) in specimen deformed at 623°K and lightly polished. (b) {lOf2) and {llirl) twins shown at a and b, respectively in a specimen deformed at 823’K and polished lightly.
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METALLURGICA,
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I;liio]
ZIRCONIUM BASAL SLIP
86Wz+ z4cmT(L
U-5--1023*K
200“-I--1073.K
[OOOZ] FIG. 4. Resolved shear stress vs. shear strain curves for basal slip in specimens deformed between 8?3-1073°K at an unresolved strain rate of 1.66 x IO-” see-l, The initial orient&ions are shown in the unit triangle.
accurate within 10 per cent. From the stress-strain curve the strain at fracture was 1.2. Therefore qualitatively it may be concluded that the majority of the dislocation activity has occurred on the basal planes. An in~~t~g feature of the stress-strain curves of crystals tested at 923 and 973°K is an abrupt work softening at an intermediate strain. This phenomenon was observed at a shear strain of approximately 0.75 at 923’K and 0.95 at 973’K. In interrupted tests at 973’K it was observed that the plastic flow occurred uniformly over the entire gauge length before the load drop. At the load drop the specimen thinned locally and the narrow region gradually spread over the rest of the crystal in the post load drop region. In a crystal deformed to a shear strain of 1.27 at 973°K the thinner region constituted approximately
FIU. 5. Siip lines on a specimen deformed to fracture (y = 1.2) at 1073°K. Note the wavy nature of slip.
IDlid
FIG. 6. Tensile axis of a crystal before the test (a) and Lattice rotation towards 10 13°K. [IIZO] c&&r is consistent with baaal slip.
8ftAX fracture fb) 8t
4 of the gauge length. X-ray diffraction patterns of the deformed crystal were taken at the thin region as well as at the part associated with the uniform elongation. Two orientations along with that of the undeformed crystal are shown in Fig. 7. The initial rotation of the tensile axis towards [ll%!O] is consistent with basal slip. From lattice rotation the shear strainor) associated with basal slip between orientations a and b would be 0.97 which is approximately the shear strain at which softening occurs in the stress-strain curve (Fig. 4). Surface deformation markings at the two regions of the deformed crystal are shown in Fig. 8. The two surface technique confirmed basa1 slip below y = 0.97. A similar analysis of the thin region revealed that the two sets of wavy intersecting traces [Fig. 8(b)] correspond to the {9002} plane and the 1st order prism plane having the highest Schmid factor ({OliO} in Fig. 7).
Fm. 7. Lattice rotation in a specimen exhibiting work softening at 973°K. (8) Tensile axis of the undeformed crystal, (b) before neck growth y = 0.97, (c) in the narrow region y = 1.27.
AKHTAR:
BASAL
SLIP
IN
5
ZIRCONIUM
would be interesting to evahmte the effect of basal slip on the ease of glide on the prism plane which constitutes the cross slip system (having.the common slip vector). It is also not clear why prismatic slip should lead to work softening. (c) The critic& resolved shear stress The CRSS for basal slip is plotted against temperature in Fig. 9. First, deviation from linearity was taken as the yield criterion. Suitably oriented crystals were also deformed by prismatic slip and these data are also included in Fig. 9. Below 850’K the CRSS for basal slip could not be determined because of interference from twinning. In basal slip the CRSS decreases rapidly up to a,pproximately 1000°K followed by a moderate lowering up to 1113°K. A similar behaviour is observed in prismatic slip, however, the yield stress remains less temperature sensitive than in basal slip. The ratio of the CRSS on the two slip systems, which is a measure of their relative ease decreases from 3 at 850’K to 1.12 at 1100°K indicating that prismatic slip continues to be the slip mode operative at the lowest stress level at any temperature. (d) The eSfect of strain rate Differential strain rate change experiments were carried out between 86%1113’K by alternating the cross head speed between 0.002 and 0.01 in./min using push button selectors. Strain rate cycling was carried out between yield and onset of non-homogenous plastic flow. (b) Fro. 8. Slip lines on a speaimen deformed to y = 1.27 at 973°K. (a) Basal slip in the region of uniform plastio flow. (b) Basal and prismatic slip in the neck region.
These observations therefore suggest that the load drop is associated with the operation of prismatic slip in addition to basal glide. It should be noted here that the prismatic plane under consideration is not the cross slip plane in basal glide, i.e. the Burgers vector in prismatic slip is (2iiO) while that for basal slip being (1120) (Fig. 7). The resolved shear stress on the most favoured prism system at the onset of load drop (orientation b in Fig. 7) was calculated as 278 g/mms. The CRSS for prismatic slip in annealed crystals is 280 f 10 g/ mm2 (Fig. 9). It is apparent that the two stresses are equal within experimental scatter, suggesting that extensive deformation due to basal slip has no latent hardening effect on this specific prism system. It
2 I RCONIUM
SINGLE CRYSTALS 0 I I .-0AsAL
SLIP O-PPRISUATIC YIP
I : 8 I 0 I I
i 0 800
Fro.
900
IoOo TEYPERATURE *I(
II00
9. The critical resolved shear stress vs. temperature for basal and prismatic slip.
ACTA
M~TA~L~~~~CA,
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1
*
ot
02
t
c34 05 03 SHEAR STRAIN -
1
CM
Q-7
I otl
Fro. 10. A&iv&on volume vs. shear &IT& for basal slip et temper&ama between 868-1113°B,
The activation volume ‘CTwas e~~~~~ted using the relationship : V=@kT (11 where lc is the Boltzm~nn constant, 21 is the ~rn~r~tu~ of defo~&tiou and
&Inj
B=d7_
in “IX,
(2)
?ZZTZshear strain rate ;
T = flow stmss. The dependence of the a&ivation volume on both strain and tern~r&tu~ is ill~str&ted in Fig. 10. No change in V OGCWSup to a shear strain of approxim&te~y 0.3. However, ztn increase with strain is observed at higher stmins in tests conducted above 973’K. The activation volume at yield increases gredually between 868 and 973’K rendrapidly thereafter to &tain tbv&e of 1600 @ at 1113’K. In order to make & more detailed ex~min&tion of the effect of strain rate on the flow stress at a constant temperature, a cry&& was deformed at various cross head speeds between 0.0002 tand 2 i~./min at 1073’K. Since there is practiclally no work hsrdening st 1073°K (Fig. 4), it was observed that the stress required for flow s,t 8 certain rate was almost exactly reproduced if this rate was re-estiblished a.fter some intermediate r&es. That is, one could cycle brtck sod forth &mong various strain-rates a;nd always come brtck to the same stress for s given r&e. This behaviors however was not followed once prismatic slip set in. For this
1973
-2
-3
Fro.
*o
21,
-I 0 LOG,IC.H.SPEED~
I
2
II. Flow stress vs. strain r&6 at T = 1073°K plotted on a log-log so&.
z~e8son the test w&s ~onfmed to y = 0.2.
The results are showu on a log I vs. log (cross head speed) plot in Fig. 11. The d&a follow ~p~ro~rn~tely 8 lines,r relationship with a gr&ieut of 113.46. (e) Th eptdiw
of state
The CRSS vs. tempemture d&s are replotted 1 as log r vs. - in Pig. 12 (basal slip). A straight line is T oboist sugg~ting thhatan rhesus type refstionship is obeyed. From Fig. 11 it is clear that the fiow stress itt s cons&& temperature is related to 113.48 power of the strain rate (assuming cross head speed to be pro~~ional to strain rate), The data of Fig. 11 are replotted as T vs. (cross head spe~d)~‘s.~s in Fig. 13,
s-4 Z tR~UNlUM t
i/T
in lO‘*‘K”’
Fxa. 12. Th0 logari~m of CRSS vs. l/T strain rate,
at constant
AKHTAR:
BASAL
SLIP
The value of the stress exponent la can also be estimated from the results of the strain rate cycling experiments conduced over a range of tem~r&tures (Fig. 10). These results are replotted as rl/rz vs. shear strrtin in Fig_ 14; where rr is the flow stress corresponding to a cross head speed of 0.01 ~~.~rn~ and 7%that at 0.002 in/mm Although & large scatter is observed at high strains the rat-io r1/r2 at, yield appears to be independent of temperature and hrts a value equal to 1.52. From equation (3) one may write at constant temperature,
\ 1200 ZIRCONIUM
e /
ln ~~~~~= n In (+e) * 06 (CROSS
HEAD
I
‘
0.8 SPEED)“*.‘*
I.0
I
7
IN ZIR~O~I~~~
t
1.2
(4)
The value of % thus determined is 3.85 which is slightly higher than the stress exponent of 3.48 determined from Fig. 11.
FIG, 13. Belowstress vs. 113.48 power of the aross hesd speed at T - 1073’K. Note the straight line passes through the origin.
Note that the straight line passes through the origin, From Figs 11-13 therefore one may write an empirical equation relating the flow stress to temperature and strain rate as follows : p = &&-Q/tl
(3)
where 3 is 8 constant; Q is s, constant having the ~rne~o~ of energy and independent of T and 3; n is a dimensionless quantity. The slope of the straight line in Fig. 11 is equal to f/n from which ?t oomes out to be 3.48. The gradient of the straight line in Fig. 12 is Q/n and has a value of 0.424 eV, which gives a. v&e of & - 1.48 eV.
0 -973 *K o- I023’K A - IO73 *K
SHEAR
STRAIN
y
Fxa. 14. The ikw stress ratio vs. shear strain in crystals tested & 923, 973 and 1023’K. The strain rate ~8% changed by & factor of Ike.
Fm. 16. Dislocation structure in a specimen deformed to y = 0.16 at 973%.
Dislocation structures have been examined in thin foils of two identical cry&& deformed to y = 0.15 at 973’K. Flat tensile specimens having dimensions of 4 x I x 25.4 mm were used. The specimens were cooled rapidly by lowering the fugue imm~i&tely after the test and allowing He to enter the vacuum system. The technique of foil preparation hapl been described efsewhere.@~ Thin foils were examined in an electron microscope with an accelerating voltage of 100 k’v. Figure 15 shows the disloo&ion structure in a foil having the basal planes ~e~en~cu~&r to the foil surface. The dis~oc&tion lines lie &long the traces of the basal planes with small segments inclined to these
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1973
traces. A rudimentary network was observed in some regions of the foil as shown in Fig. 16. Another foil with its surface nearly parallel to { 1012) exhibits segmented dislocation lines (Fig. 17). Small dislocation loops are also seen. Hydride plates, which presumably were formed during foil preparation are observed lying parallel to the traces of the {lOiO} planes. DISCUSSION
The dislocation mechanism responsible for basal slip in Zr will be examined in this section. The likely processes to be considered are Peierls’, climb, intersection and cross slip. Of these, Peierls’ mechanismo2) can be ruled out on the grounds that the observed activation volumes are higher (>200 ZG) than those associated with the lattice friction process (-c 100 as). The process of climb of edge-dislocations is also unlikely since the requirement for this is an activation volume of b3. The Hirsch-Warrington modelus) of vacancy diffusion at jogs in screw dislocations requires an activation energy equal to that of self diffusion. For Zr the activation energy for self diffusiono4) is 2.2 eV which is higher than the observed activation energy of 1.48 eV. The experimental data are also inconsistent with the dislocation intersection mechanism.(15Js) The apparent activation energy U for this process is defined as:
FIQ. 17. Electron micrograph of a specimen deformed to y = 0.16 8t 973°K. Foil surfece nearly parallel to { 1012). Note hydride plate at A.
From the measured activation volumes (Fig. 10) and the CREEL temperature data (Fig. 9) U has been calculated for a series of temperatures as shown in Table 1. A decrease in U with increasing temperature TABLE 1. Apparent activation energy at different tempcratures assuming intersection as the rate determining process
U(r) Temperature
V (in. cm*)
(9 868 973 1023 1053 1073 1113
= TV
0.795 1.18 2.4 3.376 4.06 5.4
x x x x x x
lo-‘0 lo-‘@ lo-‘O lo-‘0 lo-‘0 lo-a@
(dyn/cmY’K) 1.08 0.62 0.216 0.12 0.07 0.03
x x x x x x
106 10” 106 106 10’ 10”
(eV) 4.65 3.75 3.31 2.67 1.9 1.12
(and decreasing 7) is apparent. This is inconsistent with the intersection model which requires a linear increase in U with temperature. (a) cross s&l Single crystals of hexagonal metals which normally deform by basal slip (e.g. Mg and Zn) can undergo prismatic slip along a (1120) direction when tension is applied parallel to the basal plane.07*ls) Friedelos) has suggested that under no applied stress the dislocations remain split into partials on the basal planes. Under applied stress these dislocations recombine and screw components cross slip onto the prism plane thereby enabling glide to occur on {lOTO} planes. This process of cross slip is thermally activated with an activation energy U such that :oD) 26/2R3/2~~/2 Fm.
16. Rudimentary network in the same foil as in Fig. 17.
u=u,+
3b 7
(6)
AKHTAR:
BASAL
where C, = the energy to form a ~onst~~tio~ on the dissociated dislocation on the basal plane ; R = the energy to recombine a unit length of the two partials ; T = applied shear stress on the prism plane ; b = Burgers vector; F = line tension. The explicit shear strain rate 3 for the process is given by(17a1s) . y=
25/9R3/2r1/2
ilAb%+ 8Rr
=P
31j
7
kT
(7)
where A = average area swept out/process ; 2. = total lengthiu~t volume of screw dislocations on the operative prism plane ; v = frequency factor; k = Boltzmann constant. Equations (6) and (7) were originally derivedc19’ for prismatic slip in materials where basal slip operates at a relatively low stress. The situation in Zr however is that prismatic slip is the easier of the of lattice two slip modes, although caleulatio~ friction stress and strain energy@@) indicate that basal slip should be easier than prismatic. It has been suggested therefore that the ease of prismatic slip in Zr and Ti is possibly a result of a lower stacking fault energy on the prism planes.(m) A low value of stacking fault energy on the prism planes of Zr has in fact been obtained expe~menta~y~z) (56 ergs~cm2). It is likely therefore that in Zr and Ti the dissoeiated dislocations on the prism planes must recombine over a critical length large enough to be able to cross slip onto the basal plane and expand under applied stress. Physically, therefore, the Friedel cross slip model(lB) should be applicable to basal slip rather than prismatic slip in Zr. An impo~ant consideration in apply~g equations (6) and (7) is to maintain the shear stress on the cross slip system constant. Experimentally this is achieved simply by applying tension parallel to the basal plane in Zn(l*) and Mg’17) so that the resolved shear stress always remains zero on the basal plane. Geometrically however one cannot apply finite shear stresses on the basal plane, keeping those on all three sets of prism planes at zero under conditions of tensile loading as has been pointed out earlier. However, the particular prism plane which cont,ains the slip direction for basal glide (the cross slip plane) is of importance. In all specimens which deformed by basal slip in the present investigation the cross slip plane was initially at an angle of nearly 0” to the tensile axis ((1~00) plane in Fig. 7). For example in
9
SLIP IX ZIRCONIUM
all &y&als sho\nmfn Fig. 4 this angle was less than 3”. Therefore shear stress on the cross slip system remains zero at least at the onset of flow. It should be noted that with increasing deformation in basal slip the shear stress on the cross slip plane continues to increase due to lat.tice rotation. (b) The re~~~v~~m~~anc~ of li, a& R It has been pointed out by FriedeW that the exact variation of the yield stress with temperature and strain rate will depend on which of the two terms in the activation energy U predominates. For not too widely dissociated dislocations UC will be small compared with 25/2R3i2~1Jz~3rb. Therefore one would expect T cc I/T
(8)
For more widely dissociated dislocations the constriction energy U, will be predominant. As a result j=C.$.
oxp f - U,IkT)
(9)
where C is a constant. The experimental data follow an equation of state of the type. 9 = BPaM exp (-&/kT) which is similar to equation (9) with the difference that T~*~* instead of 72 is observed. A 73 relationship has been observed earlier in the case of prismatic slip in Zn.cLs) Impurities have been observed to raise the stress exponent in Zn.(ls) However, whether this is the reason for a high exponent in Zr has not been determined yet. Equating the experimentally determined & = 1.48 eV with U, and using the relationship :c21) Gb% u, = 30
(10)
where d is the width of the stacking fault (on the prism planes in the present case) and substituting the shear modulus of Zr at 295’K. d i;
d
112
( 1 ]ogT;
= 11.5
from which d -cII
b
11
This value of the stacking fault width is in fair agreement with that arrived at from the dislocation dynamics of prismatic slip(2) in Zr.
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METALLURGICA,
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‘8 7-2
900
I 1000 TEMPERATURE OK
FIG. 18. Log T vs. temperature
8 Ii00
for bad
slip.
Finally it should be noted that the cross slip model of Schoeck and Seeger(22*m)is not applicable to the present results. This model of cross slip predicts that the stress at the onset of cross slip 7 is related to the test temperature through an equation of the form(24) In T = ln (0) -
BT
(11)
where l3 is a constant and T(O) is the flow stress at the onset of cross slip at 0°K whereas the CRSS for basal slip in Zr follows a In ~tc :
relationship (Fig. 12).
The data of Fig. 12 are plotted as log 7 vs. T in Fig. 18. It is apparent that the data do not follow a linear relationship. Furthermore, the strain rate dependence of the flow stress in basal slip of Zr is not consistent with the dictates of the Schoeck and Seeger mode1.(22r23) According to this model: ln 7 = ln
T(0)
-
A kT
ln
(h/P)
(12)
where y0 is a constant. From equation (12) one may write for strain rate change at constant temperature ln TI/T2 =
TA ln CPl/li2)
(13)
where T1 and T2 are the flow stresses at strain rates of y1 and yz. Therefore for a fixed y1/y2 the change in TJT~ will depend on the test temperature if Schoeck Seeger model is applicable. However Fig. 14 shows that between 973 and 1073°K the ratio TJT~ at the onset of basal slip is independent of temperature. Work softening
above y = 0.1 at 923°K:
Work softening at an intermediate strain (y N 0.8) which is associated with the operation of prismatic
VOL.
21,
1973
slip (Burgers vector different from that, in basal slip) has been discussed earlier. Although it’ is not yet clear as to what mechanism would lead to softening, the phenomenon itself is perhaps responsible for the lowering of the work hardening r&e above y fl 0.1 in crystals tested at 923°K. Rapid work hardening is observed in basal slip in these crystals which leads to an increased resolved shear stress (RSS), on the most highly stressed prism slip system. As lattice rotation takes place t’he crystal reorients more favourably for prismatic slip. The (RSS), at y = 0.1 in Fig. 4 reaches a value of 0.24 kg/mm2 while the CRSS for prismatic slip at, 923’K is 0.36 kg/mm2. It is likely, therefore, that localised prismatic slip would occur at regions of high stress concentration thereby leading to the softening observed between y = 0.1 and 0.75. Above y = 0.75 exceeds the CRSS and extensive prismatic NW, slip is observed. Micro-twinning may also contribute to softening of this kind although twins were not detected on the surface of the deformed crystal. CONCLUSIONS
1. Suitably oriented single crystals deformed by basal slip at temperatures above 85O“K. Below this temperature twinning and prismatic slip precede basal slip. 2. Prismatic slip continues to be the easiest slip mode at all temperatures, although the relative ease of basal slip increases with increasing temperature. 3. Non basal slip vectors and slip planes other than basal and 1st order prism were not observed et any temperature in the range of orientations investigated. 4. It is proposed that basal slip in Zr occurs by the recombination of dissociated partial dislocations on the prism planes followed by cross slip. 5. An activation energy of 1.48 eV was obtained for basal slip, which yields a stacking fault width of llb on the prism planes at room temperature. This is in good agreement with the spacing of partial dislocations arrived at from the kinetics of prismatic slip. ACKNOWLEDGEMENTS
The author is grateful to Mr. R. Palylyk for experimental assistance and to Prof. E. Teghtsoonisn for his constructive criticism of the manuscript. REFERENCES 1. E. D. LEVINE, Trans. Japan. Imt. Metals. 9, Suppl. 832 (1968). 2. A. AKHTAR and E. TEQHTSOONIAN, Acta. Met. 19, 655 (1971). 3. P. Soo and G. T. HIWINS. Acta Met. 16.177 (1968). 4. D. MILLS md G. B. CRAIG, Tram. k&l. Sot‘. AJ1M.E. 242, 1881 (1968).
AKHTAR:
BASAL
SLIP
5. W. R. TYSON, Can. me&K Q. 6, 301 (1967). 6. R. E. REED-HILL and J. L. MARTIN, Tpalls. metall. SOC.A.I.M.E. 250,780 (1964). 7. D. G. WESTLAKE, J. nucl. Mater. 13, 113 (1964). 8. J. I. DICKSON and G. B. CRAIG, J. nucl. Hater 40. 346 (1971). 9. E. D. LEVINE, Trans. metall. Sot. A.I.M.E. SB, 1558 fl966~. \----,10. B. RAMASWAXY and G. B. CRAIG, Trans. metall. Sot. A.I.sM.E. 289. 1226 (19671. 12. Ji E’. DORN and S. ]~.UXAK, Trans. metall. Sot. A.I.X.E. 230, 1052 (1964). 13. P. B. HIRSCE and D. H. WARRINGTON, Phil. Xag. 6, 735 (1961).
IN
ZIRCOSIUM
11
14. V. S. LAYASHENKO, V. X‘. BYKOC and L. 1’. P_~rtrr;or, Fizika iVet&. 8? 362 (1959). 1.5. .I. SEEGER, D+.slocations and Mechanical Propertim of Crystals, pp. 243-329. John Wiley (1955). 16. Z. S. BASINSKI, Phil. Nag. 4, 393 (1959). 17. P. WARD FLYNN, J. MOTE and J. E. DORS, !Fmw. metall. Sot. A.I.M.E. 221, 1148 (1961). 18. J. J. GILMAX, J. Metals 8, 1326 (1956). 19. J. FRIEDEL, Internal Wress and Fatigue in _Vetal.e, p. 238. Elsevier (1959). 20. W. R. Tysox. A& Net. 15. 674 fl967t. 21. A. PI’. STRCIR,‘P~OC. Plays.-,&. B&, 42f (195-l). 22. G. SCROECKand A. SEEGER,Proc. Bristol Cbzf. Phys. See., p. 340 (1955). 23. P. HAASEX. Phil. Muo. 3. 384 (1958). 24. H. WOLF, 2. Xaturf. b& 180 (196Oj.
SLIP
IN ZIRCONIUM*
A. AKHTARt Single crystals of Zr heve been deformed in tension between 295-l 113°K with a range of orientetions. First order prismatic slip continues to be the easiest slip mode, although the rel8tive ease of besel slip incresses with temperature. Extensive b8s81 slip is observed above 850°K in orient&ions unf8voumble for prismatic slip, whereas twinning precedes slip et lower temperatures. Non-basel slip vectors 8nd slip planes other then {OOOZ} 8nd (1010) were not detected et any tempereture within the renge of orientetions investigated. The critical resolved shear stress for basal slip ~8s found to be temper&me and stmin rete dependent. An equ8tion of state of the form: p = BP exp (-Q/kT) with 8 stress exponent equal to 3.48 snd 8n ectivetion energy of 1.48 eV ~8s obeyed. It is proposed that the mechanism of besctl slip involves recombination of extended dislocetions lying on the prism plenes followed by cross slip. On the basis of this model 8 partid dislocetion spacing of 1lb on the { 1010) planes is obt&ned, which is in good sgreement with 8n earlier estimate of the stecking fault energy from the mechanics of prismetic slip. GLISSEMENT
DANS
LE
PLAN
DE
BASE
DANS
LE
ZIRCONIUM
Des monocristeux de zirconium de differentes orientations ont et& deform& en tmction entre 295 et 1113°K. Le glissement prismetique de premier ordre continue 8 6tre le mode de glissement le plus facile, bien que 18 fecilite reletive du glissement de bese sugmente 8vec la temp6rature. Un glissement importsnt dans le plen de bese est observe eu-dessus de 860°K d8ns lea orient&ions defevorables pour le glissement prismatique, elors que le m&clage p&o&de le glissement aux temperatures plus basses. Des vecteurs de glissement non basal et des plens de glissement autres que {0002} et { 1010) n’ont 66 observes 8 eucune des temper8tures pour les orientetions 6tudi6es. L’auteur 8 trouve que l8 cission critique pour le glissement d8ns le plan de bese depend de la temp&&ure et de 18 vitesse de deformation. Le phenombne obeit 8. une equation d’etat de la forme: 3 = BP exp (-Q/kT) d8ns laquelle l’expossnt de 18 contrainte est de 3,48 et l’energie d’aativation de 1,48 eV. L’euteur propose que le m&nisme du glissement dens le plen de bese comprend 18 reoombineison des dislocations dissooibs se trouvent sur les plans prismatiques, suivie d’un glissement d&i& D’apms ce modele, on obtient tm especement des dislocations ptvtielles de 115 sur les plans {lOTO}, ceci Btant en bon 8ocord 8vec un calcul enterieur de l’energie de faute d’empilement 8 pertir de la m&mique du glissement prismatique. BASISGLEITUNG
IN
ZIRKON
Zr-Einkrist8lle verschiedener Orientierungen wurden zwischen 295 und 1113°K im Zugversuch verformt. Obwohl die Basisgleitung mit zunehmender Temperatur immer leichter erfolgt, bleibt die erste oder prismatisahe Gleitung der leichteste Gleitmechanismus. Ausgedehnte Basisgleitung wird oberhelb 850°K in Krist8llen beobechtet, deren Orientienmg fur prismatische Gleitung ungimstig ist; d8gegen erfolgt bei tieferen Temperaturen erst Zwillingsbildung und d8nn Gleitung. Bei den untarsuchten Orientierungen und Temperaturen wurden nur Besisgleitvektoren und {0002}- und {lOTO}Gleitebenen beobachtet. Die kritische Schubspennung ftir Bssisgleitung ist temperatur- und gesch. windigkeitsabhiingig. Folgende Gleichung gilt: p = BrRexp
(-Q/kT)
D8bei ist der Spannungsexponent 3,48 und die Aktivierungsenergie 1,48 eV. Es wird vorgeschlagen, daB bei der B&sisgleitung die euf Prismenebenen aufgesp8ltenen Versetzungen zun&ohst eingesohntirt werden und denn quergleiten. Auf der Grundlage dieses Modells wird eine Versetzungseufspaltung von 1lb euf den { lOTO}-Ebenen ebgeleitet. Diese Aufspaltung ist in guter Obereinstimmung mit einer frtiheren Abschiitzung der St8pelfehlerenergie 8us der Mechanik der prismatischen Gleitung.
INTRODUCTION
The low temperature dislocation mechanism,(i) work hardeningf2) and interstitial solution hardening’3-5) of Zr in prismatic slip have been examined in some detail in the past. Such information, however, is lacking for basal slip of Zr, although rather limited evidence to suggest dislocation motion on the basal planes have been published.‘2*6*) The low temperature CRSS for basal slip of Ti on the other hand has been studied in some detail and a rate controlling mechanism has been proposed.@)
Slip in hexagonal close packed metals primarily occurs in the direction of greatest atomic-density, revealing that the Burgers vector of the active slip dislocations is of the type a/3 [1120], while the two most commonly observed slip planes are the basal (0002) and the 1st order prism (lOiO} planes. Prismatic slip is readily observed in Zr and Ti, both having an axial
ratio
of nearly
1.58.
* Received Meroh 14, 1972; revised M8y 8, 1972. t Department of Metallurgy, The University of British Columbie, V8iWOUver 8, C8n8d8. ACTA 1
METALLURGICA,
VOL.
21, JANUARY
1973
1
The
object
deform
single
of
the
crystals
present
investigation
of Zr in tension
over
was
to
a range
ACTA
2
METALLURGICA,
of strain rates, temperatures and orientations and to examine unusual slip systems. Optical examination of surface deformation markings, lattice rotation and electron microscopy of thin foils have been used as additional aids to interpretation. EXPERIMENTAL
METHODS
Crystal bar zirconium has been used in the present study. Single crystals were grown from the melt using an electron beam %oating zone technique and cooled through the a 2 /l transformation (1135°K) in a controlled fashion to yield up to 20 cm lengths of a - Zr crystals.(s) An attempt was made to obtain the .desired orientations through seeding. However little success was achieved due to the recrystallization of the seed in the process of a + p transformation. As an alternative, therefore, a large number of crystals was grown at random without seeding and the desired orientations were selected from these 4.5 mm rods. The as grown crystals were annealed at 1093’K under a dynamic vacuum of less than 2 x 10m6mm of Hg for 5 days. Tensile specimens having a gauge length of 2.54 cm and circular cross section were obtained using a spark erosion lathe. Electra polishing was carried out at -50°C under a potential difference of 20 V in a 5% perchloric acid +95% methanol solution to remove the spark damaged layer. In order to assess the difference in interstitial content of one batch of crystals from another, two tensile specimens suitably oriented for prismatic slip were chosen from each batch and tested at 78OK. The CRSS measured was 2.6 f 0.2 kg/mm2 in each case, suggesting that the interstitial content was reproducible from one batch to another. From the earlier published datac2) this CRSS of 2.6 f 0.2 kg/mm2 at 78’K is equivalent to approximately 120 ppm interstitial oxygen in zirconium. Tensile tests were carried out on a floor model Instron. A dynamic vacuum of less than lo4 mm of Hg was maintained during all test,s conducted above room temperature. Resistance heating was used to attain temperatures up to 1113°K and controlled to within k2”. The maximum duration of any test including the time required to attain the desired temperature was less than 6 hr. In order to determine whether the interstitial content was affected in this process, one crystal oriented for prismatic slip was subjected to 84O’C at lo4 mm of Hg for 6 hr in the testing apparatus, cooled and subsequently tested at 78°K. The CRSS still remained below 2.8 kg/mm2, thereby suggesting that the interstitial content was not affected appreciably.
VOL.
21,
1973 RESULTS
The effect of temperature and orientation
(a)
Under tensile loading conditions it is possible to apply shear stresses on the (lOiO}(l~lO) systems of hcp crystals while maintaining those on the basal slip systems at zero. This is achieved by keeping the tensile axis perpendicular to the C-axis of the crystal. The situation in reverse, however, is geometrically impossible i.e. finite shear stresses cannot be applied on a basal system while those on all the prism systems remain zero. Alternatively, suitable orientations may be chosen such that the Schmid factor on one system is sufficiently high relative to the other in order for slip to be induced on the desired plane. An attempt has been made earlierc2) to induce basal slip at 78 and 295°K in suitably oriented Zr crystals tested in tension. -No basal slip however was observed. The crystals yielded due to twinning when the angle between the basal plane and the tensile axis (xB) exceeded 35 and 45” at 78 and 295”K, respectively. Prismatic slip was responsible for plastic flow in other orientations. In the present work a crystal with xB = 53” was deformed at 723OK. The stress-strain curve is shown in Fig. 1. The ratio of the Schmid factor for basal slip to that for the most favourable prismatic slip (SJS,) was 2.85. Serrated plastic flow was observed over the entire stress-strain curve. Optical examination of the deformed specimen did not show twin markings whereas slip lines corresponding to the most favourably oriented prism plane were observed. Further evidence that prismatic slip occurred was obtained from a lattice rotation measurement. The tensile axis was found to rotate towards the (1120) direction which constituted a part of the geometrically _E < y”
Zr-
PRISMATIC SLIP T=723”K
.E I.2 -
z
E I-
m
LO-
lo@
% ;0439 ?I 0 0.6 ! : o.40
Ilicq
[oooz 01
0.2
03
SHEAR STRAIN
Fro. 1. Resolved shear stress VB. shear strain curve of a crvstal deformed at 723°K bv Drismetic slin. The ratio of*Sohmid factors on the most* favourable basal system to the prism system wsa 2.86 at yield (~8 = SO’).
AKHTAR:
BASAL
SLII?
IN
3
ZIRCONIUM
Figure 5 shows the slip lines on a specimen deformed to fracture (Y = 1.2) at 1073°K. The waviness of slip Iines suggests cross slip. From two surface analysis these wavy traces were found to be parallel to the trace of the basal plane. The initial and final positrons of the tensile axis are shown in the unit triangle in Fig. 6. It is apparent that the tensile axis has moved towards the [1120] corner. This is co~istent with deformation due to basal slip. Note that the lattice rotation would be towards [ZlIO] had single prismatic slip taken place. From the initial and final orientations, the shear strain expected(n) from base1 slip only would be 1.17. Since the experimental error in the dete~ination of orientations is &2”, this value of 1.17 may at best be considered
FIG. 2. Resolved shear stress vs. shear strain curves (assuming baaal slip) of cry&& deformed between 29582PK. The orientations are shown in the unit triangle.
most favoured prism system. Serrated yielding has been observed earl%&‘*) in polycrystalline Zr when deformed in the vicinity of 7OO’K. Three more crystals having Schmid factor ratios (SB/SP) between 4 and 6.5 were tested at 295,523 and 823’K. The results are shown in Fig. 2, as resolved shear stress vs. shear strain curves assuming basal slip. Lightly deformed specimens were examined rne~~o~~hi~~y. This examination showed that the onset of plastic flow occurred due to twinning in each case. Optical micrographs of specimens deformed at 523 and 823’K to fracture and subsequently polished to remove slip markings are shown in Figs. 3(a) and (b) respectively. Using the two surface method the twins in Fig. 3(a) were identified as being of the type At 823”K, however, (1121) as well as (iOi2) twins were observed. Another set of crystals having a Sohmid factor ratio (~~~~~) of about 5 were tested between 873 and 1073°K. The results are plotted as resolved shear stress vs. shear strain curves assuming {0002}(ll2O) slip and are shown in Fig. 4. All these crystals yielded smoothly, although the specimen tested at 873°K twinned after about 5 per cent shear strain as indicated by the successive load drops. Subsequent optical examination of this crystal revealed a small number of twins.
(1OiZ).
(b) Slip lines amd lattice rotation The crystals deformed between 973 and 1973°K were examined optically and their o~entations were determined again in order to determine the lattice rotation.
(b)
FIG. 3. (a) Twins of the type jlOi2) in specimen deformed at 623°K and lightly polished. (b) {lOf2) and {llirl) twins shown at a and b, respectively in a specimen deformed at 823’K and polished lightly.
ACTA
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600.
METALLURGICA,
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I;liio]
ZIRCONIUM BASAL SLIP
86Wz+ z4cmT(L
U-5--1023*K
200“-I--1073.K
[OOOZ] FIG. 4. Resolved shear stress vs. shear strain curves for basal slip in specimens deformed between 8?3-1073°K at an unresolved strain rate of 1.66 x IO-” see-l, The initial orient&ions are shown in the unit triangle.
accurate within 10 per cent. From the stress-strain curve the strain at fracture was 1.2. Therefore qualitatively it may be concluded that the majority of the dislocation activity has occurred on the basal planes. An in~~t~g feature of the stress-strain curves of crystals tested at 923 and 973°K is an abrupt work softening at an intermediate strain. This phenomenon was observed at a shear strain of approximately 0.75 at 923’K and 0.95 at 973’K. In interrupted tests at 973’K it was observed that the plastic flow occurred uniformly over the entire gauge length before the load drop. At the load drop the specimen thinned locally and the narrow region gradually spread over the rest of the crystal in the post load drop region. In a crystal deformed to a shear strain of 1.27 at 973°K the thinner region constituted approximately
FIU. 5. Siip lines on a specimen deformed to fracture (y = 1.2) at 1073°K. Note the wavy nature of slip.
IDlid
FIG. 6. Tensile axis of a crystal before the test (a) and Lattice rotation towards 10 13°K. [IIZO] c&&r is consistent with baaal slip.
8ftAX fracture fb) 8t
4 of the gauge length. X-ray diffraction patterns of the deformed crystal were taken at the thin region as well as at the part associated with the uniform elongation. Two orientations along with that of the undeformed crystal are shown in Fig. 7. The initial rotation of the tensile axis towards [ll%!O] is consistent with basal slip. From lattice rotation the shear strainor) associated with basal slip between orientations a and b would be 0.97 which is approximately the shear strain at which softening occurs in the stress-strain curve (Fig. 4). Surface deformation markings at the two regions of the deformed crystal are shown in Fig. 8. The two surface technique confirmed basa1 slip below y = 0.97. A similar analysis of the thin region revealed that the two sets of wavy intersecting traces [Fig. 8(b)] correspond to the {9002} plane and the 1st order prism plane having the highest Schmid factor ({OliO} in Fig. 7).
Fm. 7. Lattice rotation in a specimen exhibiting work softening at 973°K. (8) Tensile axis of the undeformed crystal, (b) before neck growth y = 0.97, (c) in the narrow region y = 1.27.
AKHTAR:
BASAL
SLIP
IN
5
ZIRCONIUM
would be interesting to evahmte the effect of basal slip on the ease of glide on the prism plane which constitutes the cross slip system (having.the common slip vector). It is also not clear why prismatic slip should lead to work softening. (c) The critic& resolved shear stress The CRSS for basal slip is plotted against temperature in Fig. 9. First, deviation from linearity was taken as the yield criterion. Suitably oriented crystals were also deformed by prismatic slip and these data are also included in Fig. 9. Below 850’K the CRSS for basal slip could not be determined because of interference from twinning. In basal slip the CRSS decreases rapidly up to a,pproximately 1000°K followed by a moderate lowering up to 1113°K. A similar behaviour is observed in prismatic slip, however, the yield stress remains less temperature sensitive than in basal slip. The ratio of the CRSS on the two slip systems, which is a measure of their relative ease decreases from 3 at 850’K to 1.12 at 1100°K indicating that prismatic slip continues to be the slip mode operative at the lowest stress level at any temperature. (d) The eSfect of strain rate Differential strain rate change experiments were carried out between 86%1113’K by alternating the cross head speed between 0.002 and 0.01 in./min using push button selectors. Strain rate cycling was carried out between yield and onset of non-homogenous plastic flow. (b) Fro. 8. Slip lines on a speaimen deformed to y = 1.27 at 973°K. (a) Basal slip in the region of uniform plastio flow. (b) Basal and prismatic slip in the neck region.
These observations therefore suggest that the load drop is associated with the operation of prismatic slip in addition to basal glide. It should be noted here that the prismatic plane under consideration is not the cross slip plane in basal glide, i.e. the Burgers vector in prismatic slip is (2iiO) while that for basal slip being (1120) (Fig. 7). The resolved shear stress on the most favoured prism system at the onset of load drop (orientation b in Fig. 7) was calculated as 278 g/mms. The CRSS for prismatic slip in annealed crystals is 280 f 10 g/ mm2 (Fig. 9). It is apparent that the two stresses are equal within experimental scatter, suggesting that extensive deformation due to basal slip has no latent hardening effect on this specific prism system. It
2 I RCONIUM
SINGLE CRYSTALS 0 I I .-0AsAL
SLIP O-PPRISUATIC YIP
I : 8 I 0 I I
i 0 800
Fro.
900
IoOo TEYPERATURE *I(
II00
9. The critical resolved shear stress vs. temperature for basal and prismatic slip.
ACTA
M~TA~L~~~~CA,
VOL.
I.9
1
*
ot
02
t
c34 05 03 SHEAR STRAIN -
1
CM
Q-7
I otl
Fro. 10. A&iv&on volume vs. shear &IT& for basal slip et temper&ama between 868-1113°B,
The activation volume ‘CTwas e~~~~~ted using the relationship : V=@kT (11 where lc is the Boltzm~nn constant, 21 is the ~rn~r~tu~ of defo~&tiou and
&Inj
B=d7_
in “IX,
(2)
?ZZTZshear strain rate ;
T = flow stmss. The dependence of the a&ivation volume on both strain and tern~r&tu~ is ill~str&ted in Fig. 10. No change in V OGCWSup to a shear strain of approxim&te~y 0.3. However, ztn increase with strain is observed at higher stmins in tests conducted above 973’K. The activation volume at yield increases gredually between 868 and 973’K rendrapidly thereafter to &tain tbv&e of 1600 @ at 1113’K. In order to make & more detailed ex~min&tion of the effect of strain rate on the flow stress at a constant temperature, a cry&& was deformed at various cross head speeds between 0.0002 tand 2 i~./min at 1073’K. Since there is practiclally no work hsrdening st 1073°K (Fig. 4), it was observed that the stress required for flow s,t 8 certain rate was almost exactly reproduced if this rate was re-estiblished a.fter some intermediate r&es. That is, one could cycle brtck sod forth &mong various strain-rates a;nd always come brtck to the same stress for s given r&e. This behaviors however was not followed once prismatic slip set in. For this
1973
-2
-3
Fro.
*o
21,
-I 0 LOG,IC.H.SPEED~
I
2
II. Flow stress vs. strain r&6 at T = 1073°K plotted on a log-log so&.
z~e8son the test w&s ~onfmed to y = 0.2.
The results are showu on a log I vs. log (cross head speed) plot in Fig. 11. The d&a follow ~p~ro~rn~tely 8 lines,r relationship with a gr&ieut of 113.46. (e) Th eptdiw
of state
The CRSS vs. tempemture d&s are replotted 1 as log r vs. - in Pig. 12 (basal slip). A straight line is T oboist sugg~ting thhatan rhesus type refstionship is obeyed. From Fig. 11 it is clear that the fiow stress itt s cons&& temperature is related to 113.48 power of the strain rate (assuming cross head speed to be pro~~ional to strain rate), The data of Fig. 11 are replotted as T vs. (cross head spe~d)~‘s.~s in Fig. 13,
s-4 Z tR~UNlUM t
i/T
in lO‘*‘K”’
Fxa. 12. Th0 logari~m of CRSS vs. l/T strain rate,
at constant
AKHTAR:
BASAL
SLIP
The value of the stress exponent la can also be estimated from the results of the strain rate cycling experiments conduced over a range of tem~r&tures (Fig. 10). These results are replotted as rl/rz vs. shear strrtin in Fig_ 14; where rr is the flow stress corresponding to a cross head speed of 0.01 ~~.~rn~ and 7%that at 0.002 in/mm Although & large scatter is observed at high strains the rat-io r1/r2 at, yield appears to be independent of temperature and hrts a value equal to 1.52. From equation (3) one may write at constant temperature,
\ 1200 ZIRCONIUM
e /
ln ~~~~~= n In (+e) * 06 (CROSS
HEAD
I
‘
0.8 SPEED)“*.‘*
I.0
I
7
IN ZIR~O~I~~~
t
1.2
(4)
The value of % thus determined is 3.85 which is slightly higher than the stress exponent of 3.48 determined from Fig. 11.
FIG, 13. Belowstress vs. 113.48 power of the aross hesd speed at T - 1073’K. Note the straight line passes through the origin.
Note that the straight line passes through the origin, From Figs 11-13 therefore one may write an empirical equation relating the flow stress to temperature and strain rate as follows : p = &&-Q/tl
(3)
where 3 is 8 constant; Q is s, constant having the ~rne~o~ of energy and independent of T and 3; n is a dimensionless quantity. The slope of the straight line in Fig. 11 is equal to f/n from which ?t oomes out to be 3.48. The gradient of the straight line in Fig. 12 is Q/n and has a value of 0.424 eV, which gives a. v&e of & - 1.48 eV.
0 -973 *K o- I023’K A - IO73 *K
SHEAR
STRAIN
y
Fxa. 14. The ikw stress ratio vs. shear strain in crystals tested & 923, 973 and 1023’K. The strain rate ~8% changed by & factor of Ike.
Fm. 16. Dislocation structure in a specimen deformed to y = 0.16 at 973%.
Dislocation structures have been examined in thin foils of two identical cry&& deformed to y = 0.15 at 973’K. Flat tensile specimens having dimensions of 4 x I x 25.4 mm were used. The specimens were cooled rapidly by lowering the fugue imm~i&tely after the test and allowing He to enter the vacuum system. The technique of foil preparation hapl been described efsewhere.@~ Thin foils were examined in an electron microscope with an accelerating voltage of 100 k’v. Figure 15 shows the disloo&ion structure in a foil having the basal planes ~e~en~cu~&r to the foil surface. The dis~oc&tion lines lie &long the traces of the basal planes with small segments inclined to these
ACTA
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1973
traces. A rudimentary network was observed in some regions of the foil as shown in Fig. 16. Another foil with its surface nearly parallel to { 1012) exhibits segmented dislocation lines (Fig. 17). Small dislocation loops are also seen. Hydride plates, which presumably were formed during foil preparation are observed lying parallel to the traces of the {lOiO} planes. DISCUSSION
The dislocation mechanism responsible for basal slip in Zr will be examined in this section. The likely processes to be considered are Peierls’, climb, intersection and cross slip. Of these, Peierls’ mechanismo2) can be ruled out on the grounds that the observed activation volumes are higher (>200 ZG) than those associated with the lattice friction process (-c 100 as). The process of climb of edge-dislocations is also unlikely since the requirement for this is an activation volume of b3. The Hirsch-Warrington modelus) of vacancy diffusion at jogs in screw dislocations requires an activation energy equal to that of self diffusion. For Zr the activation energy for self diffusiono4) is 2.2 eV which is higher than the observed activation energy of 1.48 eV. The experimental data are also inconsistent with the dislocation intersection mechanism.(15Js) The apparent activation energy U for this process is defined as:
FIQ. 17. Electron micrograph of a specimen deformed to y = 0.16 8t 973°K. Foil surfece nearly parallel to { 1012). Note hydride plate at A.
From the measured activation volumes (Fig. 10) and the CREEL temperature data (Fig. 9) U has been calculated for a series of temperatures as shown in Table 1. A decrease in U with increasing temperature TABLE 1. Apparent activation energy at different tempcratures assuming intersection as the rate determining process
U(r) Temperature
V (in. cm*)
(9 868 973 1023 1053 1073 1113
= TV
0.795 1.18 2.4 3.376 4.06 5.4
x x x x x x
lo-‘0 lo-‘@ lo-‘O lo-‘0 lo-‘0 lo-a@
(dyn/cmY’K) 1.08 0.62 0.216 0.12 0.07 0.03
x x x x x x
106 10” 106 106 10’ 10”
(eV) 4.65 3.75 3.31 2.67 1.9 1.12
(and decreasing 7) is apparent. This is inconsistent with the intersection model which requires a linear increase in U with temperature. (a) cross s&l Single crystals of hexagonal metals which normally deform by basal slip (e.g. Mg and Zn) can undergo prismatic slip along a (1120) direction when tension is applied parallel to the basal plane.07*ls) Friedelos) has suggested that under no applied stress the dislocations remain split into partials on the basal planes. Under applied stress these dislocations recombine and screw components cross slip onto the prism plane thereby enabling glide to occur on {lOTO} planes. This process of cross slip is thermally activated with an activation energy U such that :oD) 26/2R3/2~~/2 Fm.
16. Rudimentary network in the same foil as in Fig. 17.
u=u,+
3b 7
(6)
AKHTAR:
BASAL
where C, = the energy to form a ~onst~~tio~ on the dissociated dislocation on the basal plane ; R = the energy to recombine a unit length of the two partials ; T = applied shear stress on the prism plane ; b = Burgers vector; F = line tension. The explicit shear strain rate 3 for the process is given by(17a1s) . y=
25/9R3/2r1/2
ilAb%+ 8Rr
=P
31j
7
kT
(7)
where A = average area swept out/process ; 2. = total lengthiu~t volume of screw dislocations on the operative prism plane ; v = frequency factor; k = Boltzmann constant. Equations (6) and (7) were originally derivedc19’ for prismatic slip in materials where basal slip operates at a relatively low stress. The situation in Zr however is that prismatic slip is the easier of the of lattice two slip modes, although caleulatio~ friction stress and strain energy@@) indicate that basal slip should be easier than prismatic. It has been suggested therefore that the ease of prismatic slip in Zr and Ti is possibly a result of a lower stacking fault energy on the prism planes.(m) A low value of stacking fault energy on the prism planes of Zr has in fact been obtained expe~menta~y~z) (56 ergs~cm2). It is likely therefore that in Zr and Ti the dissoeiated dislocations on the prism planes must recombine over a critical length large enough to be able to cross slip onto the basal plane and expand under applied stress. Physically, therefore, the Friedel cross slip model(lB) should be applicable to basal slip rather than prismatic slip in Zr. An impo~ant consideration in apply~g equations (6) and (7) is to maintain the shear stress on the cross slip system constant. Experimentally this is achieved simply by applying tension parallel to the basal plane in Zn(l*) and Mg’17) so that the resolved shear stress always remains zero on the basal plane. Geometrically however one cannot apply finite shear stresses on the basal plane, keeping those on all three sets of prism planes at zero under conditions of tensile loading as has been pointed out earlier. However, the particular prism plane which cont,ains the slip direction for basal glide (the cross slip plane) is of importance. In all specimens which deformed by basal slip in the present investigation the cross slip plane was initially at an angle of nearly 0” to the tensile axis ((1~00) plane in Fig. 7). For example in
9
SLIP IX ZIRCONIUM
all &y&als sho\nmfn Fig. 4 this angle was less than 3”. Therefore shear stress on the cross slip system remains zero at least at the onset of flow. It should be noted that with increasing deformation in basal slip the shear stress on the cross slip plane continues to increase due to lat.tice rotation. (b) The re~~~v~~m~~anc~ of li, a& R It has been pointed out by FriedeW that the exact variation of the yield stress with temperature and strain rate will depend on which of the two terms in the activation energy U predominates. For not too widely dissociated dislocations UC will be small compared with 25/2R3i2~1Jz~3rb. Therefore one would expect T cc I/T
(8)
For more widely dissociated dislocations the constriction energy U, will be predominant. As a result j=C.$.
oxp f - U,IkT)
(9)
where C is a constant. The experimental data follow an equation of state of the type. 9 = BPaM exp (-&/kT) which is similar to equation (9) with the difference that T~*~* instead of 72 is observed. A 73 relationship has been observed earlier in the case of prismatic slip in Zn.cLs) Impurities have been observed to raise the stress exponent in Zn.(ls) However, whether this is the reason for a high exponent in Zr has not been determined yet. Equating the experimentally determined & = 1.48 eV with U, and using the relationship :c21) Gb% u, = 30
(10)
where d is the width of the stacking fault (on the prism planes in the present case) and substituting the shear modulus of Zr at 295’K. d i;
d
112
( 1 ]ogT;
= 11.5
from which d -cII
b
11
This value of the stacking fault width is in fair agreement with that arrived at from the dislocation dynamics of prismatic slip(2) in Zr.
ACTA
10
Zr-BASAL
METALLURGICA,
SLIP
‘8 7-2
900
I 1000 TEMPERATURE OK
FIG. 18. Log T vs. temperature
8 Ii00
for bad
slip.
Finally it should be noted that the cross slip model of Schoeck and Seeger(22*m)is not applicable to the present results. This model of cross slip predicts that the stress at the onset of cross slip 7 is related to the test temperature through an equation of the form(24) In T = ln (0) -
BT
(11)
where l3 is a constant and T(O) is the flow stress at the onset of cross slip at 0°K whereas the CRSS for basal slip in Zr follows a In ~tc :
relationship (Fig. 12).
The data of Fig. 12 are plotted as log 7 vs. T in Fig. 18. It is apparent that the data do not follow a linear relationship. Furthermore, the strain rate dependence of the flow stress in basal slip of Zr is not consistent with the dictates of the Schoeck and Seeger mode1.(22r23) According to this model: ln 7 = ln
T(0)
-
A kT
ln
(h/P)
(12)
where y0 is a constant. From equation (12) one may write for strain rate change at constant temperature ln TI/T2 =
TA ln CPl/li2)
(13)
where T1 and T2 are the flow stresses at strain rates of y1 and yz. Therefore for a fixed y1/y2 the change in TJT~ will depend on the test temperature if Schoeck Seeger model is applicable. However Fig. 14 shows that between 973 and 1073°K the ratio TJT~ at the onset of basal slip is independent of temperature. Work softening
above y = 0.1 at 923°K:
Work softening at an intermediate strain (y N 0.8) which is associated with the operation of prismatic
VOL.
21,
1973
slip (Burgers vector different from that, in basal slip) has been discussed earlier. Although it’ is not yet clear as to what mechanism would lead to softening, the phenomenon itself is perhaps responsible for the lowering of the work hardening r&e above y fl 0.1 in crystals tested at 923°K. Rapid work hardening is observed in basal slip in these crystals which leads to an increased resolved shear stress (RSS), on the most highly stressed prism slip system. As lattice rotation takes place t’he crystal reorients more favourably for prismatic slip. The (RSS), at y = 0.1 in Fig. 4 reaches a value of 0.24 kg/mm2 while the CRSS for prismatic slip at, 923’K is 0.36 kg/mm2. It is likely, therefore, that localised prismatic slip would occur at regions of high stress concentration thereby leading to the softening observed between y = 0.1 and 0.75. Above y = 0.75 exceeds the CRSS and extensive prismatic NW, slip is observed. Micro-twinning may also contribute to softening of this kind although twins were not detected on the surface of the deformed crystal. CONCLUSIONS
1. Suitably oriented single crystals deformed by basal slip at temperatures above 85O“K. Below this temperature twinning and prismatic slip precede basal slip. 2. Prismatic slip continues to be the easiest slip mode at all temperatures, although the relative ease of basal slip increases with increasing temperature. 3. Non basal slip vectors and slip planes other than basal and 1st order prism were not observed et any temperature in the range of orientations investigated. 4. It is proposed that basal slip in Zr occurs by the recombination of dissociated partial dislocations on the prism planes followed by cross slip. 5. An activation energy of 1.48 eV was obtained for basal slip, which yields a stacking fault width of llb on the prism planes at room temperature. This is in good agreement with the spacing of partial dislocations arrived at from the kinetics of prismatic slip. ACKNOWLEDGEMENTS
The author is grateful to Mr. R. Palylyk for experimental assistance and to Prof. E. Teghtsoonisn for his constructive criticism of the manuscript. REFERENCES 1. E. D. LEVINE, Trans. Japan. Imt. Metals. 9, Suppl. 832 (1968). 2. A. AKHTAR and E. TEQHTSOONIAN, Acta. Met. 19, 655 (1971). 3. P. Soo and G. T. HIWINS. Acta Met. 16.177 (1968). 4. D. MILLS md G. B. CRAIG, Tram. k&l. Sot‘. AJ1M.E. 242, 1881 (1968).
AKHTAR:
BASAL
SLIP
5. W. R. TYSON, Can. me&K Q. 6, 301 (1967). 6. R. E. REED-HILL and J. L. MARTIN, Tpalls. metall. SOC.A.I.M.E. 250,780 (1964). 7. D. G. WESTLAKE, J. nucl. Mater. 13, 113 (1964). 8. J. I. DICKSON and G. B. CRAIG, J. nucl. Hater 40. 346 (1971). 9. E. D. LEVINE, Trans. metall. Sot. A.I.M.E. SB, 1558 fl966~. \----,10. B. RAMASWAXY and G. B. CRAIG, Trans. metall. Sot. A.I.sM.E. 289. 1226 (19671. 12. Ji E’. DORN and S. ]~.UXAK, Trans. metall. Sot. A.I.X.E. 230, 1052 (1964). 13. P. B. HIRSCE and D. H. WARRINGTON, Phil. Xag. 6, 735 (1961).
IN
ZIRCOSIUM
11
14. V. S. LAYASHENKO, V. X‘. BYKOC and L. 1’. P_~rtrr;or, Fizika iVet&. 8? 362 (1959). 1.5. .I. SEEGER, D+.slocations and Mechanical Propertim of Crystals, pp. 243-329. John Wiley (1955). 16. Z. S. BASINSKI, Phil. Nag. 4, 393 (1959). 17. P. WARD FLYNN, J. MOTE and J. E. DORS, !Fmw. metall. Sot. A.I.M.E. 221, 1148 (1961). 18. J. J. GILMAX, J. Metals 8, 1326 (1956). 19. J. FRIEDEL, Internal Wress and Fatigue in _Vetal.e, p. 238. Elsevier (1959). 20. W. R. Tysox. A& Net. 15. 674 fl967t. 21. A. PI’. STRCIR,‘P~OC. Plays.-,&. B&, 42f (195-l). 22. G. SCROECKand A. SEEGER,Proc. Bristol Cbzf. Phys. See., p. 340 (1955). 23. P. HAASEX. Phil. Muo. 3. 384 (1958). 24. H. WOLF, 2. Xaturf. b& 180 (196Oj.