The effect of grain size on the yield strength of Ni3Al

,fcro mefall. Vol. 33, No. 9, PP. 1587-1591. 1985 Printed in Great Britain. All rights reserved

CoPyri&t 0

ooo14160/85 s3.00+0.00 1985 Pcrgamon Press Ltd

THE EFFECT OF GRAIN SIZE ON THE YIELD STRENGTH OF Ni,Al E. M. SCHULSON, Thayer School

T. P. WEIHS, D.

of Engineering,

Dartmouth

V.VIENSfand1.BAKER

College,

Hanover, NH 03755, U.S.A.

(Received IO July 1984; in revised form 4 April 1985) Abstract-Experiments have established that the effect of grain size (d = 2.9-l IOO~m) on the yield strength of Ni,AI at room temperature is given by the relationship or = a, + kd-” where n = 0.80 f 0.05, a,,=93+ l4MPa and k =2080+ lOSMPa.pm am*o.or.The relationship is explained quantitatively in terms of work-hardening which occurs within the Liiders bands which accompany yielding. The Liiders strain, Ed, increases with decreasing grain size according to the relationship Ed= M-O.” where 1 = 8.4 x 10-2~m05r. R&urn&Des experiences ont permis de montrer que I’effet de la taille da grains (d compris entre 2,9 et 1100 pm) sur la limite elastique de N&Al i la tem$rature ambiante est don& par la relation eu = co + kd-” oti n = 0,80 f 0,05, a0 = 93 f 14 MPa et k = 2080 f I05 MPa~pmWfW. Nous exphquons

quantitativement cette relation par l’brouissagc qui se produit dans les bandes de Ltiders qui accompagnent la d&formation plastique. La dkformation de LCiders augmente lorsqu’on diminue la taille des grains suivant la relation e, = Amass, od L = 8.4 x 10-zpm~. Zwammenfassung-Nach Rxperimenten kann der EinfluB der Komgr6Be (d = 2,9 bis 1IOO~m) auf die PlieDspannung von Ni,Al bei Raumtemperatur mit folgender B&hung bescluieben werden: rrr= co + kd -“, mit n = 0,80 f 0,05, a0 = 93 f 14 MPa und k = 2080 f 105 MPa*cmass*ar’5. Dieser Zusammenhang wird quantitativ mit der Verfestigung erkhirt. die in den Ltidersbgndern, welche das PlieDen begleiten, auftritt. Die Liidersdehnung sLsteight mit abnehmender KomgriiBe entsprechend r, = 1 d-O.“, mit I, = 8,4 x IO-* pm”.u,

1. INTRODUCTION

This paper considers the effect of grain size on the room-temperature yield strength of the strongly ordered Ll, aluminide Ni,AI. The work is part of a larger investigation of grain size effects on the mechanical properties of some aluminide intermetallics, but is presented separately because the relationship to be described is a novel one.

2. EXPERIMENTAL

Most specimens were processed from rapidly solidified and consolidated powder. The powder, obtained from Pratt and Whitney Aircraft, West Palm Reach, Florida, was of stoichiometric composition and was consolidated into rod by extruding at elevated temperatures. Table 1 lists the impurities, the extrusion/fabrication schedule and the geometry of the specimens. Multi-stage extrusion was necessaq to produce finely grained aggregates (d < 10 pm).

tPresent address: United Technologies Research Center, East Hartford, Connecticut, U.S.A. fBoundaries of annealing twins were excluded because they appeared not to obstruct slip; i.e. slip lines on deformed surface grains changed direction but did not terminate at twin boundaries.

Specimens were also produced from ingots of stoichiometric composition. The ingots were supplied by United Technologies, East Hartford, Connecticut, and were processed as noted in Table 1. These specimens contained grains which were more than an order of magnitude larger (i.e. d = 9004100~m) than the grains which could be produced through prolonged annealing (100 h/1573 K) of the consolidated powder. from Other specimens were prepared off-stoichiometric (23.9 at.y&) recrystallized single crystals, also obtained from United Technologies. These specimens were processed as noted in Table 1. They allowed a comparison of the strength of medium grained N&Al (9 d d < 80 pm) processed in two different ways. The grain size of the consolidated powder and of the recrystalhxed single crystal was increased by annealing at temperatures between 1073 and 1273 K in a flowing atmosphere of dried and deoxygenated argon. In this way, sixes varying from 2.9 to 80 pm were obtained. When combined with the grain size of the homogenixed ingots, the complete range was 2.9 to 11OOpm. The grain size of every specimen was determined using optical metallography and the method of linear intercepta.$ Prior to and aRer the grain coarsening anneal the material was examined by transmission electron microscopy (TEM) and by X-ray diffraction (XRD).

1587 AM W9A

SCHULSON er al.:

1.588

YlELD STRENGTH

OF N&Al

Table I. Composition and processing of test specimens Composition NiAl

Imuurtties’

(at.%)

iat.%,

Consolidated rapidly solidified powder (RSRP)

75.0

25.0

Ingots

75.0

_2!;0.

RecrystatliZd single crystal

76.1

23.9

Si 0.05 Cr 0.05 Fe 0.05 MO 0.005 c 0.04 0 0.04 N
Not ttttaIyz#l; same starting material as in RSRP. Si 0.05 cr 0.03 co 0.03

Cu 0.008 Pb co.002

Processing and preparation of test specimens Single extrusion: Canned powder under protective atmosphere in 304 stainless steel (62mm 1.D.. S mm wall thickness) sealed and then soaked I b/1533 K, extruded through an area reduction ratio, R. of 25:l; produced rod whose microstructure characterixed by quiaxed and randomly oriented ncrystalhxed grains II to ISpm in dia Doubk extrusion: Canned powders as above; soaked I h/I473 K and extruded tbrougb R = 6:.1, resoaked I h/1373 k and re-extruded through R = 6: 1; produced rod whose microstructure characterixed by equiaxed recrystallimd grains 9 to IO pm in dia Triple extrusion: Product from double extrusion (alloy plus can) m-canned 304 stainless (50mm O.D.), soaked I h/l 123 K and then re-extruded through R = 4.5: I; produced rod whose microstructure characterized by quixed and almost completely recrystaRii grains 2.9pm in dia Test spocimenr Machined dumbbell shaped ten& speeintens2.5 mm dia x 20 mm, eleetropohshed and then armettIed (see text). Ground cytindrical compression specimens 6.1 mm dia x 13.2mm, and then annealed (see text) Ingots, 5 cm dia homogenized at IS23 K for 24 h; grain size 900 to 1IO0pm in dia. machined cylindrical compression spedmcna 12.7 mm dia x 13.3 mm with axis along radial direction of ingot Stieedthin(2.5mm)striphaving{Itl)surfscg{6x25~);rolMa)ong(1.10) in steps of loD/, reduction in area until edge eraeking at overali reduction in area of 59+-4X I”

Cut flat tensile spccimcns (1 x 1.5 x 6.5mm) by elcctro-discharge machining Electropoiishcd and annealed (see text) to produce cguiaxcd grains

*Analyzed by a commercial sounr.

TEh4 revealed [l] that both the as-consolidated powder (whether singly, doubly or triply extruded) and the reerystallixed crystals were highly ordered and were remarkably free from dislocations (i.e. density 2 10sjmq. Anti-phase boundaries were not observed in the consolidated powder, but occasionally were detected either as large loops (2-3pm in dia) or as single wavy boundaries within the most firmly grained (9 pm) product of the recrystallized single crystal [2]. Occasionally, small (< 1 pm) particles of a second phase or phases (identity ~~0~) were found in the consolidated powders. XRD analysis of the asconsolidated powder extruded once at 1533 K and of the once-extruded powder annealed 100 h at 1273 K (which coarsened the grains to around 60 pm in dia) generated (ill}, (200) and {220) pole figures which revealed that these aggregates were comprised of randomly oriented grains. Tension tests were performed at a strain rate of lo-’ s-’ using a floor model Instron machine. Compression tests were performed at the same strain rate using a floor model MTS machine. In this case, the ends of the specimens were lubricated with graphite. 3.

RKSULXS

AND

ANALYSIS

With the exception of the most coarsely grained material (d 2 1 mm) which yielded smoothly, yielding occurred discontinuously. This feature is reminiscent of the behavior of other L12 alloys (N&Fe [3], N$Mn [4], C&Au IS], Zr>Al IS]) and, as noted from visual observations during testing, corresponded to the

propagation of LiIders bands along the gauge. Frequently, a yield drop preceded discontinuous flow (presumably in the better aligned specimens), but owing to its &reproducibility was not characterized in the present study. Figure 1 shows the yield strength, Q,, vs d-“s. For all but the most coarsely grained material, uu was taken as the Liiders band propagation stress which, for a given test, varied by less than f 5 MPa. For the coarsely grained aggregates 4, was taken as the elastic limit. Several points are notewo~hy: (i) Grain refinement is a potent method for strengthening Ni,Al. A decrease in grain size from 1000 to 2.9pm raises the yield strength by approx. nine-fold. In comparison (albeit based upon studies over significantly smaller ranges of grain size), the same refinement is expected to raise the yield strength of the N&based LIZ alloys N&Fe [3] and Ni,Mn [4] by approx. five-fold and to increase the yield strength of elemental nickel [7] by about four-fold. (ii) Within experimental scatter the yield strength in compression is the same as it is in tension, at least over the intermediate range of grain size where both tests were performed (10 < d < 60 pm). This result implies that the strength differential effect evident in single crystals [S, 91 does not affect the yield strength of polycrystalline aggregates of randomly oriented grains, in keeping with the orientation dependence of the sign of this effect. [9]. (iii) The yield strength of the recrystaliized single crystal is similar to the yield strength of the consoli-

. .//lli

SCHULSON et ul.: YIELD STRENGTH OF N&AI Gram 1000

100

sue,

d (pm)

30

10

1589

5

3

/’

.

f6R

Powder, tenmn

l

RSR Powder,

L

R’xd

.

Homoqewed

I

Ssnqle

compressed”

Crystal,

tensnn ,“got,

trystol,

Homoqen~zcd

comprelsto”

tension

wpt,

( Ref

t a01

Ofllf

0112)

P (131

VU48

o(l51

~(16)

-tlTf

I

CM)

compression

I

010

(Gram

030

we 1-O.’

( pm

1

I

t

I

020

ti

040

Ox,

)_a5

Fig. I. Yield strengtb vs (grain size) -0~ for Ni,Al at room temperature. The solid points denote the present

data and the open points, data from the literature. Note the positive curvature.

dated powder, for a given grain size. This result suggests that the method of processing dots not affect this property, in keeping with the observation that both materials were essentially structure fret (Section 2) prior to testing. This remIt also indicates that small deviations to the nickel-rich side of stoichiometry do not significantly strengthen N&AI. (iv) The yield strength does not obey the Hall-Retch relationship; i.e. CT,is not linearly related to d-O”. This point is evident from the positive curvature of the graph, and is strengthened by the observation that the cluster of results obtained from the most coarsely grainal material falls within the range of data [lO-17f previously reported for coarse grained (d = 500-1000 pm) stoichiomettic polycrystals (open points, Fig 1). Rather, the yield strength correlates most strongly with d-‘O*OfoBr, Fig. 2. This dependence was obtained from a regrcssion analysis which was basui upon the equation a,, = u, + kd-”

off-stoichiometric (22.5 at.% Al) N&Al single cry&&t oriented for multiple slip [8], suggesting that the intercept can be viewed as a measure of the resistance of the lattice to dislocation glide. The other observation worth noting is that the Liiders strain,$ +, increased as the grain size decreased, Fig. 3. When subjected to a regression analysis, these data, although fewer than the number of tests owing to the frequent occurrence of premature fracture during yielding, revealed a dependence similar to that noted for Zr, Al [a]; viz.

at.=i J,&O”5.

For Ni,Al I = 8.4 x 10-2~mo-ss, while for Zr,Al I = 5.0 x 10-2pmo.“. This observation is significant because it implies that the yield strength as deEned here corresponds not to the flow stress at a constant strain, but to the flow stress at a plastic strain which incrcascd as the grain size decmascd. In other words,

(1)

Table 2. Regnssion clnalysis bred U,=#o+“-^

and which is summarized in Table 2; a0 = 93 f 14 MPa and k = 2080 f 105 IvIPa~~m”~~w”o”S. Significantly, u. is bracketed by the yield strength of to, values for stoicbiometric crystals are not available. However, given tbat small deviations to the Ni-side of stoichiometry do not lead to significant strengthening, as evident from the prese& data (Fig. l), the corn-parison is considered to be a reasonable one. jet was measured from the length of the plateau on the load-elongation curve.

(2)

n

(h&

0.65 0.70 ‘o:7j

-

_-

__

1800 1890 _

_,980

78.2 : 0.80 93.3 2080 ’ 0.85 106 2190 L~--_-_____~~~~~-----~ 0.90 0.95

119 I30

(Correlation cocmcient)~

(MP:rlny

42.3 61.3

2300 2420

upon

0.974 0.980 ---------1

0.984 0.985 0.984 0.982 0.979

, 4 ’

SCHULSON et 01.: YIELD STRENGTH OF Ni,AI

1590

Gram we, 1000

100 1

30

10

d (pm) 5

3 l

*

900.

so0

_

.

-

i-00-

a” 5

600.

1----11-1

;

. c & g 5L

500-

m i

400-

. /

+ + /=’ I

>300

-

200

-

l’

J

l

.

.

5;’ l

,.. */“=* mo

8

O.?O

020

Q30

040

0.50

(Grain sireBqasa (pml-Osa Fig. 2. Yield strength vs (gmin size)- ‘*. Replotted from data in Fig. 1. Presentdata only.

3.0 c

:

0 .x

20-

E

P ;

e

lo-

2j J

I 5

I 10

I 20

I

I

3040

1

I

60

100

Groin size (pm) Fig. 3. Liiden strain vs grain Size.

because Ed increased as grain size decreased, the attendant strain hardening also increased, thereby raising the yield strength. 4. QIscusIoN

The yield strength is thus viewed as a combined measure of the lattice resistance to dislocation slip plus the work-hardening which results from inter-

actions amongst dislocations within the Liiders bands. A modified view that the yield strength also contains a term re&cting a microstructural feature which either coarsens OT alters during the grain-coarsening anneal is improbable, because the test material was essentially free from microstructural features and from texture (Section 2) and because the yield strength was largely independent of the method of processing. And a view that the “yield &ength” measured the stress requind to propagate, in a crack-opening mode, pre-existing flaws of size proportional to the grain size is untenable, because the yield strengths in tension and in compression are similar for a given grain size, Accordingly, the yield strength may be expressed as the sum uy=cro+aGbfi

(3)

where u, is the lattice resistance, a is a dimensionless constant, G is the shear modulus and b is the Burgers’ vector; pr is the density of the dislocations generated? within the Lfiders band and may be obtained from the relationship

8,= PLb - J’ m

tThat generation and not unpinning of dislocations

OCCURS

during di~ontin~us yielding is evident from the fact that undeformed material is essentially dislocation free (Section 2).

where m is the Taylor orientation parameter. .? is the average distance of dislocation movement and must be less than or equal to one grain in

SCHULSON

er al.:

YIELD

diameter. In view of the planarity of slip [13, 181 in Ni,AI, it is assumed, as others [I91 have done, that

parameter of order unity. Thus, upon combining equations (2) to (5) the

yield strength is given by the relationship

mti

grain size according

to the

J -

B

where 1 = 8.4 x 10-2~mo~5S; (ii) the yield strength-grain size relationship is given by oy = u. + kd-”

d-o’n-

Appropriate values for the constants (G = 78 GPa [20], m = 3.1, b =0502nm, I = 8.4 x lo-* clrn”.“‘, tl = /I = I) reveal that the term modifying d-0.78 equals 930 MPa.~mo77.

The work hardening interpretation of the yield strength is thus in good agreement with the observed grain size dependence (i.e. d-o.78 vs d-““*o.05) and is in rough agreement with the sensitivity of this dependence (i.e. 930 MPa*pmO.‘* versus 2080 f 105 MPa+~m0.s”*0.05). Moreover, it suggests that the reason grain refinement is a more potent strengthener of N&AI than of the other discontinuously yielding nickel-based LIZ alloys (Ni,Mn and Ni,Fe) is that the rate of work hardening at low strains is higher in this material, in keeping with the observation [21] that the hardening rate of polycrystalline Ni, Al at relatively large strains (s = 0.1) is about two to three times the hardening rate of the other materials at the same strain. The analysis, however, should not be accepted without caution, because it implies [through equations (4) and (5)] that pL is proportional to d-‘.JJ, a point which remains to be investigated. Whether other alloys which yield discontinuously and for which the yield strength is taken as the stress to propagate Liiders bands exhibit non-Hall-Petch behavior is not clear. However, it is perhaps significant to note that when data for other Ll, alloys (Cu, Au [5], Zr, Al [6] and off-stoichiometric N&Al containing 24.0 at.% Al and 0.05 wt”/, boron [22]) and data for an f.c.c. ahoy not possessing a superlattice (Cu 0.5 at.% Cd [23]) are subjected to a regression analysis, the largest regression coefficient (r2 > 0.98) is obtained for n values [equation (l)] of around 0.65-0.75. In addition, for the Cu-Cd case a corresponding intercept of co = 25 MPa is obtained instead of the near-zero value derived from a Hall-Petch analysis [23], indicating a lattice resistance term which is more in keeping with expectation based upon the behavior of the elemental metal (i.e. a0 = 25 MPa for copper 1241). 5. CONCLUSIONS From experiments on the effects of grain size (d = 2.9 to 1100 pm) on the room-temperature yield

strength of N&Al it is concluded that: (i) yielding occurs discontinuously and is accompanied by the propagation of Liiders which

with decreasing relationship

1591

(5)

where /l is another dimensionless

bands within

OF Ni,AI

sL = 1 d-ass

f=Bd

a,=uo+aG

STRENGTH

the strain, eL, increases

where n = 0.80 f 0.05, a0 = 93 + 14 MPa and k = 2080 _+ 105 MPa.pm”.“*o”5;

(iii) the dependence of the yield strength on grain size can be explained quantitatively in terms of work hardening within the Liiders bands. Acknowfedgemenrs-The authors wish to thank 0. B. Cavin of the Oak Ridge National Laboratory for the texture analyses and F. D. Lemkey of United Technologies for the N&Al ingots and crystals. This work was supported by the Otlice of Basic Energy sciences of the U.S. Department of Energy through contract No. DE-AC02 8 1ER 10907 and through grant No. DE-FGO2 84ER 45148. REFERENCES 1. I. Baker, J. A. Horton, V. A. Surpmnant and E. M. Schulson. To be published. 2. I. Baker, D. V. ‘Viens and E. M. Schulson, J. Mater. Sci. 19, 1799 (1984). 3. A. C. Arko and Y. H. Liu, Metall. Trans. 51875 (1971). 4. F. M. C. Besag and R. E. Smallman. Acta metall. 18. 429 (1970). 5. S. M. L. Sastry, Mater. Sci. Engng 22, 237 (1976). 6. E. M. Schulson and J. A. Rov. -. Acta metall. 26. 29 (1978). 7. A. W. Thompson. Acta metal/. 23, 1337 (1975). 8. S. M. Copley and B. H. Kear, T.M.S.-A.I.M.E. 239,977 (1967). 9. Y. Umakoshi. D. P. Pope and V. Vitek. Acta metall. 32. 449 (1984). 10. P. A. Flinn, Strengthening Mechanisms in Solidr, p. 17. Am. Sot. Metals, Metals Park, Ohio (1962). 11. R. G. Davies and N. S. Stoloff. T.M.S.-A.I.M.E. 223. 714 (1965). 12. E. M. &ala, Mechanical Properties of Intermetallic Compounds (edited by J. H. Westbrook), p. 358. Wiley, New York (1960). 13. P. H. Thornton,- R. G. Davies and T. L. Johnston, Metall. Trans. 1, 207 (1970). 14. J. A. Lopez and E. F. Hancock, Physica status solidi (a) 5 469 (1970). 15. M. J. Marcinkowski and D. E. Campbell, Or&red Alloys (edited by B. H. Kear, C. T. Sims, N. S. Stoloff and J. H. Westbrook), p. 331. Claiton (1970). 16. K. Aoki and 0. Izumi, Trans. Japan Inst. Metals 19,203 (1978). 17. 0. Noguchi, Y. Oya and T. Suzuki, Metaff. Trans. 12A, 1647 (1981). 18. D. V. Viens, M.E. thesis, Dartmouth College (1983). 19. M. J. Marcinkowski and R. M. Fisher, T.M.S.-A.I.M.E., 223, 293 (1965). 20. F. X. Kayser and C. Stassis, Physica status solidi 64a, 335 (1981). 21. E. M. Schulson and J. A. Roy, Ada metali. 26, 115 (1978). 22. Y. Oya, Y. Mishima, K. Yamada and T. Suzuki, Iron Steel Inst. Japan 20, 1870 (1984). 23. N. Benhood, R. M. Douthwaite and J. T. Evans, Acta mefall. Zs, 1133 (1980). 24. P. Feltham and I. D. Meakin, Phil. Mag. 2, 105 (1957).