IMPROVING THE DUCTILITY OF INTERMETALLICCOMPOUNDS BY PARTICLE-INDUCED SLIP

HOMOGENIZATION

Ian BakerThayer School of Engineering, Dartmouth College, Hanover, NH 03755

(Received March 5, 1999)(Accepted March 15, 1999)

Introduction

Many high-symmetry intermetallic compounds which possess the five independent slip systemsrequired for general plastic flow, e.g. L1o-structured, L12-structured and B2-structured compounds,show low ductility at ambient temperature, even when tested in vacuum as high-purity, slow-cooled,carefully machined, electropolished specimens. This brittleness is not like that of a ceramic in whichfracture is essentially elastic. Instead, under tension, fracture typically occurs either in the Lu¨ders regionfollowing yielding or after a few percent plastic strain. And, under compression, such materials canoften exhibit substantial shortening prior to failure. Thus, one may ask, what is the cause of this lowductility? High strain-rate sensitivity and large slip vectors do not occur in these compounds, and bothdifficult nucleation and glide of dislocations do not seem important sources of the brittle behavior [1].Extrinsic factors such as the environment, impurities, surface finish, the “pest” problem and cooling rateeffects may exacerbate ductility problems [2] but are often not the root cause. Intrinsic factors, such asdifficult slip transmittal across grain boundaries, poor grain boundary cohesion, low cleavage strengthand the production of sessile dislocation locks (which act as crack nucleation sites), often have a rolein the brittle behavior. But, here we suggest that restricted cross-slip and intense planar slip are the keyfeatures of brittle fracture in high-symmetry intermetallics.

Intense planar slip can lead to crack nucleation from dislocations pile-ups at low overall strains, eventhough locally substantial plasticity occurs, producing either intergranular fracture, transgranularcleavage on the slip plane or transgranular cleavage on some other plane. (Evidence for the role ofintense local slip in intergranular fracture has been observed in polycrystalline Ni3Al where good-quality selected-area electron channeling patterns were obtained from the surface of the gage offractured tensile specimens but not from the fracture surface [3]. Similar observations have been madein FeAl [4].) Intense planar slip also probably enhances the water vapor-induced embrittlement thatoccurs in many aluminides and silicides by rapidly transporting hydrogen into the material. (This is,presumably, why single crystals of Fe-40Al strained in air fracture at 0.6% elongation but with 6.6%reduction in area at the fracture surface [5].) Hydrogen may also increase the slip planarity. Intenseplanar slip occurs in intermetallics when dislocations are restricted to their original slip plane becauseof: dissociated dislocation cores; the need to recombine dislocation partials prior to cross-slip; orslip-plane disordering [6]. (Since slip-plane disordering reduces the anti-phase boundary (APB) energy

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on the slip plane, cross-slip would require that the dislocations move onto a plane with a higher APBenergy.)

A Possible Solution

The general approach to this problem is to prevent intense planar slip, by dispersing slip to other slipplanes or, possibly, other slip systems, and to limit the length of dislocation pile-ups. One possiblesolution is to reduce the grain size. The potential solution considered here is the introduction offinehard incoherentparticles. Note that soft shearable particles increase slip planarity, and large particlesact as stress concentrators and crack nucleators, so both are undesirable. A fine, hard particle dispersioncould improve ductility through a number of mechanisms, for example:

● By homogenizing slip through rapid work-hardening on an active slip plane. This will cause slip tobe transferred toparallel but inactive planes before sufficient pile-up formation occurs to nucleate acrack [7].

● By homogenizing slip through the activation ofadditional slip systems around the particles. Thatadditional slip systems are activated by fine particles is suggested by the absence of the easy glideregion in the stress-strain curves of dispersion-hardened f.c.c. Cu-SiO2 single crystals [8].

● By limiting the length of dislocation pile-ups. The interparticle spacing may define the pile-up lengthby defining the stress required to cause dislocations to loop between particles, see Figure 1(a).Alternatively, a small amount of compressive strain can be used to produce a cell structure (whichwill define the pile-up length) whose size will be related to the interparticle spacing [9], see Figure1(b).

The first two micromechanisms have been observed in disordered alloys [10], whereas the thirdmechanism, i.e. limiting the pile-up length by particles, is possible but has not been observed. Whetherthese mechanisms can improve the ductility of otherwise low ductility intermetallics is unclear. Notethat in a ductiledisorderedalloy, the role of particles is quite different; i.e. they act as nucleation sitesfor voids. Increasing their volume fraction, f, decreases the failure strain,ef, but from a high level. Forexample, the relationship shown in equation (1) is well established for copper polycrystals:

ef 5 0.5 ln [=(p/6f) 2 =(2/3)1 en] (1)

Figure 1. (a) View normal to slip plane showing dislocations piling-up at particles before looping around them. (b) A dislocationcell structure, formed after a few percent strain in compression. In both cases, the interparticle spacing defines the pile-up length.

DUCTILITY OF INTERMETALLIC COMPOUNDS410 Vol. 41, No. 4

where en is the strain to nucleate voids at particles (;0.1–0.2 for copper). For copper alloys,ef fallsfrom ;1.5 with f 5 0.01 to near zero when f. 0.25 (an extremely large volume fraction) [10].

Will This Solution Work?

We may ask, does the introduction of a fine dispersoid improve the ductility of intermetallics? Theevidence is mixed. Seybolt [11] first noted that a fine dispersion distributes slip more homogeneously,reduces stress concentrations and, hence, might lead to an improvement in ductility. Thus, he added 5%of 0.2–0.3mm particles of Y2O3 to nickel-rich NiAl polycrystals. Unfortunately, rather than improvingthe ductility, this dispersion raised the brittle-to-ductile transition temperature from 300°C to 450°C.This may have been because the large volume fraction of particles more than doubled the yield strengthand because some larger (.0.5mm) Al2O3 particles, which arose from the ball-milling plus extrusionprocessing route, were present. Also, the nickel-rich polycrystals he used are significantly more brittlethan stoichiometric NiAl, typically failing before yielding under tension [4]. Using similar processing,Dollar et al. [12] obtained very fine (0.5mm) grains in polycrystalline stoichiometric NiAl by incor-porating large volume fractions of Al2O3 particles which limited grain growth. The particles weresmaller in this case (10 nm within the grains and 0.1mm on the grain boundaries) but, again, noroom-temperature tensile ductility was reported. A fundamental problem with NiAl is that the,100.{011} slip provides only three independent slip systems.

The effects of fine particles in FeAl, which has sufficient independent slip systems,,111.{110},for general plastic flow in a polycrystal, are more promising. Strothers and Vedula [13], Morris andMorris [14] and Maziasz et al. [15] have all observed considerable increases in the ductility ofpolycrystalline iron-rich FeAl when, respectively, fine Y2O3, ZrB2 or ZrC particles were introduced.(Note that Maziasz et. al. [15] attributed the excellent ductility in their powder processed Fe-36Al (15%in air, 28% in oxygen) to the fine grain size and the ZrC particles acting as sources of mobiledislocations. However, Fe-36Al is not as brittle as more aluminum-rich FeAl, showing 15% elongationin oxygen [16].) These ductility improvements could even be obtained in air, indicating that the watervapor-induced environmental embrittlement that occurs in FeAl can be ameliorated. These ductilityimprovements in FeAl are encouraging but it is not clear whether they arose due to the particlesper se,i.e., by the micromechanisms noted earlier, or due to the particle-induced grain refinement thatoccurred, which has been shown to improve the ductility of FeAl [17]. The boron present may also havehelped, since it is known to improve the ductility of Fe-Al at room temperature [16].

A Model for Particle-Induced Ductilization of Intermetallics

Let us develop a simple model for particle-induced ductilization of intermetallics using the followingassumptions:

1. Transgranular cracks nucleate with a length comparable to that of dislocation pile-ups. (Althoughfracture (crack propagation) in brittle intermetallic polycrystals can be either by transgranularcleavage or intergranular fracture, crack nucleation probably involves dislocation pile-ups andtransgranular cracks.)

2. The interparticle spacing on the slip plane defines the pile-up length.3. Once a crack nucleates, it propagates either transgranularly or intergranularly, with little further

increase in stress, i.e. fracture ensues.

DUCTILITY OF INTERMETALLIC COMPOUNDS 411Vol. 41, No. 4

We can estimate the fracture stress,sF, when the dislocation pile-up constitutes a crack, using theGriffith equation:

sF 5 F 2Eg

p~l 2 2r s!G 1/ 2

5 F4G~1 1 n!g

p~l 2 2r s!G 1/ 2

(2)

Where E is Young’s modulus, G is the shear modulus,n is Poisson’s ratio,g is the surface energy andthe surface-to-surface interparticle spacingl 2 2rs is also the crack length or dislocation pile-up length(where rs is the particle radius andl is the center-to-center interparticle spacing).

Equation (2) indicates that the fracture stress increases continuously as the interparticle spacingdecreases. Thus, we also might expect the failure strain to increase continuously as the interparticlespacing decreases. However, fine particles also increase the global yield strength,sy, which for alooping mechanism, can be described by:

sy 5 so 1aGb

~l 2 2r s!(3)

Whereso is the lattice resistance,ro is the dislocation inner cut-off (“core”) radius,b is the magnitudeof the Burgers’ vector, anda ' 1

Let us assume that particles do not change the work-hardening rate and that it is linear. (In practice,at small strains, the work-hardening rate is higher, but after a few percent strain it is similar to that ofthe particle-free alloy [10].) The failure strain,ef, can be estimated from the difference betweensF andsY (equation (2) and (3) divided by the work-hardening rate,u, i.e.

ef 51

u HF4G~1 1 n!g

p~l 2 2r s!G 1/ 2

2 so 2Gb

~l 2 2r s!J (4)

Using some typical values for Fe-40Al, i.e. G5 94 GPa [18],n 5 33,so 5 200 MPa [19],g 5 1Jm22,u 5 5GPa [20] and using rs 5 20 nm, the fracture strength and global yield strength (Figure 2) and thefracture strain (Figure 3) can be plotted as a function of (l 2 2rs)

21/2.From Figures 2 and 3, some novel and interesting points emerge

1. Above a certain interparticle spacing,lmax, the particles have little effect on ductility and fractureoccurs before yielding, i.e.sF , sY.

Figure 2. Graph of yield strength,sY, and fracture strength,sF, as a function of (l 2 2rs)21/2.

DUCTILITY OF INTERMETALLIC COMPOUNDS412 Vol. 41, No. 4

2. Below a certain interparticle spacing,lmin, the particles increasesY more than they increasesF.Hence, again,sY , sY and brittle fracture occurs. (It may seem odd that the interparticle spacingcan be too fine for good ductility. However, as shown in equation (1), in disordered alloys, theductility decreases as the volume fraction of particles increases, that is, as the interparticle spacingdecreases.)

Both lmin andlmax can be obtained by settingsF 5 sY, i.e.

lmax, lmin 5G

soHF ~1 1 n!g

psoG 1/ 2

6 F ~1 1 n!g

pso2 bG 1/ 2J 2

1 2rS (5)

3. Betweenlmin andlmax, the particles enhance the ductility i.e.sY , sF, with the maximum failurestrain occurring atlcrit, which can be estimated fromd(sF 2 sY)/dl 5 0, i.e.

lcrit 5pGb2

g~1 1 n!1 2rS (6)

Using the values noted above for Fe-40Al, we obtainlmin 5 56 nm,lmax 5 3.49mm, andlcrit 5 95nm. These are well within the range of typically achievable interparticle spacings. According to thisanalysis, atlcrit we would expect (from equation 4)ef 5 13%. Thus, this simple model suggests thatsignificant ductility can be obtained in a brittle intermetallic if fine hard particles homogenize slip andreduce the lengths of dislocation pile-ups. Whether this occurs in practice is unknown. The analysis alsoimplies that simply adding fine particles, as has been done previously, may or may not improve ductilitythe ductility of an intermetallic, depending on the particle dispersion parameters.

Acknowledgments

This research was sponsored by the Division of Materials Sciences, U.S. Department of Energy undercontract DE-FG02-87ER45311 and the National Sciences Foundation through grant DMR 9812211with Dartmouth College. Professors H.J. Frost and E.M. Schulson of Dartmouth College are thankedfor helpful comments.

References

1. I. Baker and P. R. Munroe, J. Metals. 40, 28 (1988).2. I. Baker and E. P. George, Metals Mater. 8, 318 (1992).

Figure 3. Graph of failure strain,ef, as a function of (l 2 2rs)21/2.

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3. E. M. Schulson, D. A. Davidson, and D. V. Viens, Metall. Trans. A. 14A, 1523 (1983).4. P. Nagpal and I. Baker, Mater. Characterization. 27, 167 (1991).5. M. V. Nathal and C. T. Liu, Intermetallics. 3, 77 (1995).6. J. A. Horton, I. Baker, and M. H. Yoo, Phil. Mag. 63, 319 (1991).7. G. Lutjering and S. Weissmann, Acta Metall. 18, 785 (1970).8. R. Ebeling and M. F. Ashby, Phil. Mag. 13, 805 (1966).9. M. H. Lewis and J. W. Martin, Acta Metall. 11, 1207 (1963).

10. J. W. Martin, Micromechanisms in Particle-Hardened Alloys, pp. 82, 105, 113, Cambridge University Press, Cambridge,UK (1980).

11. A. U. Seybolt, Trans. Am Soc. Metals. 59, 860 (1966).12. M. Dollar, S. Dymek, P. Nash, and S. J. Hwang, Metall. Trans. 24A, 1993 (1993).13. S. D. Strothers and K. Vedula, Prog. Powder Metall. 43, 597 (1987).14. D. G. Morris and M. A. Morris, Acta Metall. Mater. 39, 1771 (1991).15. P. J. Maziasz, D. J. Alexander, and J. L. Wright, Intermetallics. 5, 547 (1997).16. C. T. Liu, E. P. George, P. J. Maziasz, and J. H. Schneibel, Mater. Sci. Eng. A258, 84 (1998).17. D. J. Gaydosh, S. L. Draper, R. D. Noebe, and M. V. Nathal, Mater. Sci. Eng. A150, 7 (1992).18. M. R. Harmouche and A. Wolfenden, Mater. Sci. Eng. 84, 35 (1986).19. I. Baker, P. Nagpal, F. Liu, and P. R. Munroe, Acta Metall. Mater. 39, 1637 (1991).20. Y. Yang and I. Baker, Intermetallics. 6, 167 (1998).

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