Mechanical properties and strengthening of a Ni25Mo8Cr alloy containing Ni2(Mo,Cr) precipitates

Acta mater. Vol. 44, No. 12, pp. 48654880, 1996 Copyright 0 1996 Acta Metallurgica Inc.

Pergamon PI1 S1359-6454(96)00092-4

Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454/96 $15.00 + 0.00

MECHANICAL PROPERTIES AND STRENGTHENING Ni-25Mo-8Cr ALLOY CONTAINING N&(Mo,Cr) PRECIPITATES MUKUL Department

KUMART

of Materials

and VIJAY

Abstract-The

K. VASUDEVAN

Science and Engineering, University OH 45221-0012, U.S.A.

(Received 1 I December

OF A

of Cincinnati,

Cincinnati,

1995; accepted 29 February 1996)

mechanical properties and mechanisms of deformation and strengthening of Haynes Alloy

242l”, a nominal Ni-25Mo&Kr (in wt%) containing Ni*(Mo,Cr) precipitates in a face-centered cubic matrix, are reported. Both solution treated, as well as aged samples (550-75O”C, l-1200 h) were deformed to permanent strains of 1 and 6% in compression and to failure in tension. The deformation structures were observed by transmission electron microscopy. A two-fold increase in strength and tremendous strain hardening are observed as the short-range (SRO) to long-range ordering (LRO) transformation proceeds, although ductility remains high even in well-aged samples. Major contribution to strengthening and strain hardening comes from the precipitation of a high volume fraction of Niz(Mo,Cr) precipitates, with hardening in the solution treated samples and those aged for short periods being associated with the presence of SRO in the matrix. A transition in deformation mode, from glide of unit dislocations in planar arrays to profuse twinning, is observed as a function of aging time and imposed strain, twinning being observed in samples containing Niz(Mo,Cr) precipitates. A semi-quantitative mode1 developed on the basis of precipitate size and mode of deformation (shearing, twinning, bypassing) is able to satisfactorily account for this transition. A presentation and discussion of these results, as well as those of the mechanisms of strengthening and strain hardening, are provided. Copyright 0 1996 Acta Metallurgica Inc.

1. INTRODUCTION Ni-Mo alloys, particularly the N&MO (b) and Ni,Mo (y) compositions, are a class of long-range ordering alloys that have been studied quite extensively in the past, and at least two commercial alloys based on the former composition, Hastelloy B and B2, have seen widespread use because of their excellent corrosion resistance in non-acidic, aqueous media [l]. These compositions exist as a short-range ordered (SRO) structure, c(, above their respective critical temperatures, but transform on slow cooling or isothermal holding of quenched materials below these temperatures to the long-range ordered (LRO) structures, fi and y, respectively. The transformation sequences and mechanisms have been well established through extensive studies in the past. Additions of ternary alloying elements have been shown to have marked effects on phase evolution, with a variety of metastable and stable LRO phases being possible [l,

21. Recently,

242’“,

a new

was

applications. of Ni-25Mo-8Cr

Ni-Mo-Cr

developed The

alloy,

for with

(in wt%)

alloy, gas

Hayne@ turbine

a nominal and

Alloy engine

composition

containing

ordered

SNOW at the Department of Mechanical Engineering, The Johns Hopkins University, 22 Latrobe Hall, 3400 North Charles Street, Baltimore, MD 21218-2686, U.S.A.

Ni2(Mo,Cr) precipitates, combines excellent strength and ductility at room and elevated temperatures with low thermal expansion and good oxidation resistance [3]. The evolution of the LRO body-centered orthorhombic N&MO phase from the initial quenched SRO state has been well characterized through an extensive study and the results are published elsewhere [46]. This ordering process is strongly dependent on temperature and time of aging and has been observed to proceed by a mechanism of continuous ordering at low temperatures (< 725°C) and by a first-order process at higher aging temperatures (750°C). Precipitation of ellipsoidal disks of the Niz(Mo,Cr) phase (PtzMo prototype) was observed to be dense and uniform throughout the f.c.c. matrix, with the volume fraction of the precipitate being about 35%. These microstructural changes are also accompanied by marked hardening. However, apart from two recent reports [7, 81, limited detailed examination of the continuous evolution of mechanical properties and accompanying deformation mechanisms after aging of this alloy has been undertaken. This paper addresses the dependence of mechanical properties and room-temperature strengthening on aging temperature and time. These results will be correlated with transmission electron microscopy (TEM) observations of the deformation

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microstructures and an analytical model based on these observations will be presented. 2. EXPERIMENTAL The Ni-25Mo8Cr (in wt%) material for the research program was obtained from Haynes International, Inc., U.S.A., in the form of machined sheet tensile specimens. Chemical analysis indicated that the actual Ni, MO and Cr levels in the material were near the nominal values and, in addition, -0.04 wt% carbon was present as an impurity. The tensile samples had a gauge length of 56.25 mm, width of 12.5 mm and thickness of 2.25 mm. Prior to tensile testing the samples were solution treated at 1150°C for 24 h under flowing argon, water quenched and subsequently aged at temperatures between 550 and 750°C for times ranging from 1 to 1200 h. The thin oxide layers that had formed on the sample surfaces during heat treatment were removed by polishing on 800 grit emery paper prior to testing. Tensile testing of both unaged and aged specimens to failure was carried out at room temperature at an average strain rate of 6 x 10m3s’. Fracture surfaces were observed in the scanning electron microscope (SEM). Some cylindrical samples, 6.25 mm in diameter and 12 mm in length, were also subjected to similar heat treatments as above. These were subsequently deformed in compression to permanent plastic strains of about 1 and 6% to study the deformation structures in the early/intermediate stages of deformation. Disks for TEM were sliced from the samples tested in parallel to the tensile axis. Those from the compression samples, however, were cut perpendicular to the stress axis. Electron transparent thin foils were prepared by the twin-jet electropolishing technique (T = 290 K, Voltage = 45 V, Current = 70 mA), employing a solution containing 10% perchloric acid, 5% hydrochloric acid and balance acetic acid. The microstructure and deformation structures were observed in a Philips CM20 TEM at an operating voltage of 200 kV utilizing bright field (BF), dark field (DF), weak beam (WB) dark field and selected area electron diffraction (SAED) modes. 3. RESULTS 3.1. Mechanical properties and fractography The optical microstructure of the solution treated and quenched samples consisted of equiaxed grains of f.c.c. c( of average size 100 pm. The presence of many inclusions (average size of 5 pm), determined to be M& eta-carbides by electron diffraction, was also noted. Selected mechanical properties are presented in Fig. 1. Aging at 650 and 700°C led to similar trends in the values of 0.2% yield stress, ultimate tensile strength and strain to fracture. Within 10 h at both temperatures the yield strength increased from the solution treated value of 310 MPa to - 700 MPa

[Fig. l(a)]. Beyond 10 h the yield strength continued to increase slightly and then leveled off to a value of - 800 MPa at 200 h, with no sign of overaging of the alloy at aging times to 1200 h. The ductility shows the opposite trend [Fig. l(c)]. Within 10 h, the ductility dropped from -7O%, for the solutionized condition, to 56 and 36% after aging at 650 and 7OO”C,respectively. Continued aging for longer times at 650°C led to a continuous reduction in ductility to a value of - 36% at 1200 h. At 700°C however, there was only a slight reduction from the value of 36% at 10 h to -32% at 1200 h. Fracture strain was consistently about 34% more than strain at maximum load, except for samples that had been aged for more than 50 h, where little or no necking was observed in the gauge section. The strain hardening exponent, n, calculated using the Ludwig equation [9]: 0 = a0 + kc”, increased, initially, from the value of 0.71 corresponding to the as-solutionized condition to a value of -0.87 after 10 h aging at both temperatures [Fig. l(d)]. Beyond 10 h, the value of “n” increased only slightly and leveled off to a value of -0.94 at and beyond 25 h, with the slight decrease on longer aging most likely due to the greater interparticle spacing, assuming a constant volume fraction of precipitates. The strain hardening observed was quite significant and it was noted that the ultimate tensile strength [plotted in Fig. l(b)] was nearly triple that of the yield strength in the solutionized condition and about double the yield stress of the peak-aged specimens. Similar values of the strain hardening exponent have been reported by others [7]. The behavior of samples aged at 725°C was slightly different from those aged at 650 and 700°C. The initial rapid increase in strength for times to 5 h was similar to that of samples aged at 650 and 700°C but the absolute values were slightly higher [Fig. l(a)], perhaps indicating the faster kinetics of transformation. Beyond 5 h, the strength continued to increase, marginally, to a maximum of - 650 MPa at 50 h, and then dropped slightly at longer times to 1200 h. Interestingly, the yield strengths of samples aged at 725°C for 10 h and longer were somewhat lower than those of samples similarly aged at 650 and 7OO”C,this presumably being associated with precipitation of a lower volume fraction of N&MO precipitates. The changes in ductility with aging time at 725°C [Fig. l(c)] were also different from the behavior of the 650 and 700°C aged samples. The decrease in ductility with aging to 50 h was similar to that of samples aged at 700°C but at longer times, unlike the leveling off to a value of -32% in 700°C aged samples, it continued to drop to a much lower value of - 15% at 1200 h. The strain hardening exponent also increased with aging time to 5 h at 725°C in a fashion similar to those of samples aged at 650 and 7OO”C, but leveled off to a lower value of -0.88 at longer times in contrast with the behavior of samples aged at the latter temperatures [Fig. l(d)].

KUMAR

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MECHANICAL

Strength increase and ductility decrease on aging at 550°C were very gradual, with the values at long aging times being substantially lower and higher, respectively, than those of samples aged at 650 and 700°C. These features were associated with the more sluggish kinetics of ordering at 550°C compared with aging at 650 and 700°C as noted elsewhere [4-61. Aging at 750°C resulted in a small increase in strength to a peak at 10 h and then a decrease to a level marginally higher than those for the unaged specimen. Such behavior is quite typical of overaged alloys containing ordered precipitates. The kinetics of the SRO to LRO transformation, the appearance of LRO domains and the coarsening of NizMO precipitates was noted to be quite rapid at this aging temperature [46]. The strain hardening exponent values exhibited similar trends up to 10 h as of samples aged at the lower temperatures, but in contrast decreased at longer times (50 h) to a value slightly higher than that for the solution treated sample. The ductility remained high for times to 5 h, then decreased abruptly at longer times to 25 h, followed by an increase at still longer times. Fracture of the solution treated sample was fully ductile with extensive dimpling on the grain surfaces

a

1

10

100

,

(,,,,,,

,

( ,1,,,1 , , ,,,,,,

f

600

4

700

1000

, / ,,,, I,

4867

[Fig. 2(a)]. It was predominantly transgranular (with dimpling and void coalescence) in the early stages of aging [Fig. 2(b)], but a gradual reduction in the extent of dimpling to smoother grain surfaces was quite apparent. At longer times, however, a change to a combination of transgranular and intergranular fracture was observed with few dimples within the grains. Representative examples of these changes are shown in Fig. 2 for samples aged at 700, 725 and 750°C for various times. Intergranular fracture, in the form of extensive cracking along grain boundaries, appeared to be associated with formation of secondary particles at the grain boundaries and formation of precipitate free zones near the boundaries. Such discontinuous precipitation observed in samples aged for long periods of time at 700°C and more predominantly in samples aged for intermediate times and beyond at 725 and 750°C can be seen in the TEM micrographs of Fig. 3. These were analyzed to be carbides, different from the inclusions that were present within the grains in the as-solutionized material. Although both the inclusions within the grains and grain boundary particles were determined to be MO-rich cubic carbides, the latter had a lattice constant of

b”

Time (hods)

0.6

OF Nik25Mo-8Cr

Q) 1100 z z 1000 0) + 900 al

-t550°C - - I3 -. 650°C --t 700% - K - 725% + 750% 0

PROPERTIES

’

100

lo (hours) Time

1000

, ,

-

0.1 1 0

C

v, 1

10

100

Time (hours)

1000

0.6 r

do

' 'jlllI1'' '111111'' ' 11I111'' ' 111111'' ' I1

’

100

lo (hours) Time

Fig. 1. (a) Yield strength, (b) ultimate tensile strength, (c) fracture strain (ductility) hardening exponent as a function of aging temperature and time for the Ni-25Mo-8Cr Alloy 242).

1000

and (d) strain alloy (Haynes

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KUMAR and VASUDEVAN:

MECHANICAL

PROPERTIES OF Ni-25Mo-8Cr

Fig. 2. SEM micrographs of the fracture surfaces of failed tensile samples previously in the following conditions: (a) solution treated and quenched; (b) aged at 700°C for 10 h; (c) aged at 700°C for 1200 h; (d) aged at 725°C for 25 h; (e) aged at 725°C for 1200 h; (f) aged at 750°C for 50 h.

1.107 nm, corresponding to the MC (M = MO, Cr, Ni) stoichiometry [lo], whereas the former had a lattice constant of 1.07 nm, corresponding to the M12C structure [lo]. Aging at 725°C was particularly interesting as samples aged for shorter times exhibit fracture morphologies similar in nature to those of samples aged at 700°C for long times, with cracks running along the grain boundaries. However, on long aging at 725°C extensive dimpling was observed on the grain surfaces, but ductilities were much lower than expected, in comparison. The striking feature was the formation of cavities along the grain boundaries,

rather than cracks as seen at shorter aging times. Such behavior can be attributed to sensitization of the grain boundaries due to carbide precipitation, whereas the transgranular fracture was in all likelihood due to the precipitates having coarsened considerably and also being fewer in number. 3.2. Deformation microstructures The results described below shall mainly concentrate on the development of the deformation structures in samples aged in the temperature range of 650-725”C, where the samples were in the peak-aged condition on aging until 1200 h, with a

KUMAR and VASUDEVAN:

MECHANICAL

PROPERTIES OF Ni-25Mo-8Cr

4869

Fig. 3. TEM micrographs and SAED patterns showing grain boundary precipitation of MsC eta-carbides in an undeformed sample aged 50 h at 750°C. (a) and (b) BF images; (c). (d) and (e) are [Ool],~,[II 11, and [112], SAED patterns from the carbides.

brief mention of the samples that were in the overaged state prior to deformation. 3.2.1. Solution treated condition. No ordered particles were observed in this condition [&6], although the presence of quenched-in SRO in the alloy was revealed by the appearance of weak reflections at the characteristic { lfO}ct positions in the SAED patterns [ll]. Deformation to l-2% permanent plastic strain was observed to proceed by crystallographic glide of f( 1 lo), unit dislocations in well-defined intersecting bands on the { 11 l}, planes, these bands indicating highly planar slip (representaTHenceforth, the orthorhombic NilMo lattice will be indexed with reference to the parent f.c.c. lattice and these indices will be referred to by the subscript c. Where no subscripts f.c.c. lattice.

arc present,

the indices again refer to the

tive micrographs are shown in Fig. 4). These undissociated dislocations were determined by stereographic trace analysis to be predominantly mixed in character with their line directions oriented along close-packed cubic directions (( 1 lo),). Furthermore, no evidence for occurrence of cross slip was obtained in any of the grains examined, with the dislocations being quite straight and confined to the primary slip plane. Some tangling of dislocations was observed in samples deformed to failure in tension, although cell formation was absent and the banded structure of the dislocations, similar to that observed at the lower strain level, was retained. Twins were also to be seen, occasionally, near grain boundaries. A complete analysis was not possible owing to the high dislocation densities produced by the large strains the sample had been subjected to before failure.

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Fig. 4. BF TEM micrographs

of the dislocation structures observed in a solutio_nized sample deformed 2% in compression. (a) g = 111, B near_[lOl],; (b) g = 200, B near The set of planar [OOl],; (c) g = 111, B near [loll,. dislocations visible in (a) are invisibk in (b) and (c), giving their b = k l/Z[Oll],.

3.2.2. Aging at 650, 700 and 725°C. The evolution of microstructure and deformation structure was similar in samples aged at these temperatures. In samples that were aged for 5 h the SRO reflections were observed to be more intense than in the solution treated condition and the early stages of LRO could be detected by the appearance of faint N&MO superlattice reflections at the ${220}, and ;{420},

PROPERTIES OF Ni-25Mo-8Cr

positions in the appropriate SAED patterns [&6, 111. All six variants of ellipsoidal disk-shaped NizMo precipitates appeared in the matrix on aging for about 10 h and this is about the time when a large increase in strength was seen [Fig. l(a)]. Aging for longer times leads to a continuous increase in the size of the N&MO precipitates [4-6], but no change in their volume fraction (a micrograph showing the well-developed N&MO precipitates is shown in Fig. 5). Crystallographic glide of f{ 1 lo}, unit dislocations on (11 ljc planes, similar to the solution treated material, was observed on deforming samples aged for short times in compression to ca l-2% plastic strain (Fig. 6) whereas in samples that had been aged for long periods of time (1200 h) thin twins traversing numerous precipitates were observed along with slip by unit dislocations in the matrix. Dissociation of the unit dislocations, mixed in character, though, was rarely seen. Moreover, triplets of unit dislocations, comprising a superdislocation in the presence of ordered N&MO precipitates [12], as expected from the stacking of the glide planes in this structure, were rarely observed. The nature of the interaction between the precipitates and the gliding dislocations could not be determined owing to the fine scale of the particles in the early stages of aging. Observations of the samples deformed to failure under tension, in contrast, revealed that profuse twinning on { 11 l}c planes was the dominant mode of deformation, with pronounced streaking along the (111) axes in the SAED patterns due to the thin twins. This was true for samples aged for 10 h and longer where a high volume fraction of the precipitates were present in the matrix. Examples of deformation twinning are shown by the micrographs in Figs 7 and 8. A uniform distribution of the twins was observed on at least two twinning systems in each grain, with the twins lying on the secondary twinning plane shearing through the twins on the primary twinning plane. Considerable twin thickening was observed, although the twin widths had a wide variation. Twins initiating from the grain boundaries were considerably wider than those which appeared to have nucleated from the precipitate/matrix interface. Twins initiating at the precipitate/matrix interface typically were confined to the precipitates and henceforth will be referred to as “micro-twins,” in contrast to the twins that traversed through the entire grain and in the process of doing so sheared through both the matrix and the ordered domains. Extensive shearing of the precipitates was revealed in the DF images of Figs 7(a)-(c). Furthermore, the evidence from the WB images in Figs S(c)-(d), where fringe contrast characteristic of planar stacking faults with a one-to-one corresponding with the twins imaged in Figs 8(a) and (b), indicated that the formation of such twins was most likely due to the movement of Shockley partial dislocations on successive { 11 l}c planes [ 131.

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Fig. 5. TEM micrographs from a sample aged at 650°C for 200 h showing NilMo precipitates in the f.c.c. matrix. (a) BF micrograph and (b) DF micrograph taken from a Ni2Mo superlattice reflection in the inset [OOl], SAED pattern.

IEvidence of true twinning is illustrated by lsidering the dark field micrographs in Figs 7(at (c)sobtained from the N&MO superlattice reflections ob: served in the B = [112& SAED pattern, and in Fig :s 7(d) and (e), obtained using fundamental twin refl .ections present in the B = [Oil], SAED pattern.

COI

Three out of a possible six variants of NizMo can be imaged in the [112], beam orientation and they are in perpendicular twin relation to each other. Shearing of the precipitate variants imaged in Fig. 7(a) chang ;ed the orientation of the sheared regions of t.he precipitates to match the crystallographic orientati on

Fig. 6. TEM micrographs of the dislocation structures and NLMo domains observed in a sample aged at 650°C for 25 h and &en deformed 1% in compression. (a) BF micrograph, g = 111, B near [112],; (b) BF micrograph,

g = 111, B near [lOI],; (c) DF image from a NizMo superlattice NilMo domains (B near [OOI]).

reflection

showing

fine

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PROPERTIES OF Ni-25Mo8Cr

Fig. 7. TEM micrographs showing the incidence of twinning and shearing of the NLMo precipitates by the passage of these twins in a sample aged at 700°C for 1200 h and then deformed to failure in tension. (a), (b) and (c) are DF images from the perpendicular twin-related NizMo reflections indicated by the arrows in the inset [112], SAED pattern; (d) and (e) are DF images (from fundamental twin reflections, B = [iol],) of twins lying on two planes in the viewed area.

of the variant imaged in Fig. 7(b). Similarly, the sheared regions of the latter are oriented in the manner of the perpendicular twin variant imaged in Fig. 7(c). These observations suggest that shearing of the precipitates leads to a reorientation of the sheared regions such that their orientation relationship with the f.c.c. matrix matches that of a perpendicular twin variant of the original variant, thus establishing that

LRO is preserved during the deformation twinning process (hence crystallographically “true” twinning). It is interesting to note that on deforming samples aged for times 2 10 h (at 650-725”(Z) to about 6% plastic strain some evidence for thin twins extending over several precipitates was obtained. Incidence of twinning was higher in the 1200 h aged samples with all the grains showing twins. Most of the twins in this

KUMAR and VASUDEVAN:

MECHANICAL

case were observed to be lying entirely within the precipitate (Fig. 9), although a few twins stretched from one side of the grain. 3.2.3. Aging at 750°C. Dense precipitation of NizMo by a first-order nucleation and growth process was observed in samples aged up to 10 h, although the volume fraction of the domains was not as high as that observed at the lower temperatures of aging [4-6]. This is about when a peak in strength and strain hardening exponent occurred. At longer times, where the yield and ultimate tensile strength dropped appreciably, overaging occurred rapidly leading to both a considerable reduction in the number of precipitates and nonuniform distribution in the matrix. The deformation structures in these samples consisted of a combination of unit dislocations and micro-twins in each grain, the twins appearing only within the precipitates at a strain level of about 1% and beyond.

4. DISCUSSION The results detailed above provide a general picture of the mechanical properties, deformation mechanisms and work hardening characteristics in the Ni-25Mo-8Cr alloy. In this section an attempt will be made to examine and rationalize these inter-relationships.

PROPERTIES OF Ni-25Mo-8Cr

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4.1. Planarity of slip Dislocation bands indicating planar slip are quite common in N&base superalloys (with disordered f.c.c. matrices) containing large concentrations of alloying elements. This feature was dominant in the present study as well, when the alloy was in the solutionized condition or in the early stages of aging (Figs 4 and 6). Such planar arrays of dislocations (undissociated and in some isolated cases dissociated with narrow separations between the bounding partials) were also observed in samples that were overaged and contained a low volume fraction of coarse precipitates. Apparently, cross slip of dislocations, leading to tangling and cell formation, was inhibited to a large extent. Such a situation would arise if the stacking fault energy (SFE) of the alloy matrix was low enough or if SRO existed in the material. Comparison of the present observations with previous reports [l] on deformation studies in Ni-Mo alloys, primarily confined to the more concentrated alloys (> lO%Mo) where SRO is present, yielded good agreement. The effect of increasing the alloying element (MO) content in these alloys was to restrict the dislocations to the slip plane, indicating that the dislocations were separating into partials and making cross-slip difficult [l]. Also, although wide stacking faults were not observed, it

Fig. 8. TEM micrographs from a sample aged at 700°C for 1200 h and then deformed to failure in tension. (a) and (b) are DF images of twins taken using the fundamental twin reflections indicated by the arrows in the inset B = [Oil], SAED pattern; (c) and (d) are WBDF images showing stacking fault fringes coinciding with the images of the twins in (a) and (b).

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OF Ni-25Mw8Cr

Fig. 9. WBDF micrograph taken from a sample aged at 725°C for 1200 h and then deformed 6% in compression showing stacking faults (also twins) within NizMo precipitates (g = ZOO; B near [OOl],).

was suggested that increasing the MO content lowered the SFE [14]. On the other hand, increase in the MO content also leads to an increase in the degree of SRO [l], this SRO being present in Alloy 242 in the solutionized condition. We can consider the effects of the two factors, namely, the presence of SRO and values of SFE, contributing singly or simultaneously, to planarity of slip. It has been assumed, in general, that reduction in SFE on alloying is the origin of planar slip behavior [15]. Such an explanation is quite plausible since reduction in SFE will lead to extended dislocations, thereby inhibiting the ability of screw dislocations to cross-slip. Similar arguments were put forth to explain deformation structures in binary Ni-Mo alloys that were quenched from a high-temperature annealing treatment [ 11. Although pure Ni has a high SFE (- 150 mJ/m2), it has been well documented that additions of elements like Cr, MO, Al and Ti can substantially lower the value of this parameter [l&19]. The composition of Haynes Alloy 242 does suggest, in lieu of the above argument, that the SFE is much lower compared with pure Ni. It should be noted, however, that the images of the dislocations in the BF imaging mode do not show discernible separation between the partials bounding a stacking fault. The separation into Shockley partials was barely resolvable through WBDF imaging and this indicated that the SFE of

the alloy was of a high enough value to prevent widely spread stacking faults from forming (an approximation suggesting the value of SFE in the matrix to be -75 mJ/m*). A recent comparative study indicated that the driving force behind planarity of slip may not be lowering of SFE [20]. It has been demonstrated, instead, that occurrence of well-developed SRO is necessary to cause planar slip. The correlation between SRO and planar slip follows the argument of Cohen and Fine [21]. The first dislocation moving through the lattice destroys SRO. Since by definition this type of lattice ordering extends for only short distances the dislocations following the first one are unable to restore the order, thereby indicating that the leading dislocation faces a greater lattice resistance than the ones trailing behind it. Instead, an effect termed glide plane softening is observed, whereby slip is localized to a single glide plane and the stress build-up due to the pile-up of dislocations aids in overcoming the resistance to slip. Experimental evidence to prove that SRO rather than SFE was the controlling factor was stressed by a study on N&Fe solid solutions [22], which have high SFE as well as exhibit SRO. The overall dislocation structures were reported [22] to be very similar to the planar arrays occurring in low SFE alloys. Moreover, analysis of data from a number of alloy systems clearly established the fact that planar slip correlates

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with degree of SRO rather than with small values for the ratio of SFE (y) and shear modulus (p), r/p [20]. Also, it was pointed out [20] that when SRO evolves into fully developed LRO, as is the case in single phase ordered Ni-Mo alloys, the dislocation structures change from being planar to those that are normally observed in pure metals (three-dimensional dislocation networks). The same arguments hold on considering the effects of LRO and precipitation of small domains of the ordered phase in the matrix on the dislocation structures. As is well known, the deformation behavior of precipitation hardened alloys results from the interaction between mobile dislocations in the matrix and the particles that act as obstacles to the motion of dislocations. The type of interaction governing deformation is dependent on the structure of the phases present in the system. In cases where the precipitates are simple (not long-range ordered), the resultant coherency strain fields around the particles determine the nature of the interaction with the moving dislocations. However, in systems where precipitates have well-ordered lattices, the interactions are altered considerably owing to the fact that the dislocations shearing through the ordered regions form an antiphase boundary in their wake. Hence, deformation now proceeds by travel of groups of dislocations coupled together, the number of dislocations in the group being decided by the number required to restore order in the superlattice (for example, in the N&MO superlattice a triplet of unit dislocations is required to preserve LRO [12]). As shearing takes place on a single glide plane the resistance to motion of dislocations continually decreases. This can again lead to planar slip since the trailing groups of dislocations have to overcome obstacles that offer increasingly lower resistance until all particles with the activated slip plane are completely sheared. Again, glide plane softening is encountered as the coupling forces binding the dislocation to a group are reduced to a negligible value. It is obvious that such a mechanism becomes increasingly more difficult to operate as the size of the precipitates increases, as the alloy attains a peak aged condition and beyond. This is owing to the fact that the area on the slip plane within the precipitate that is swept by the advancing dislocations increases, thus requiring large stress concentrations at the matrix/ precipitate interface to push the leading unit dislocation through the ordered precipitate. Such a sequence of deformation has been observed in other two-phase ternary Ni-Mo alloys as well, particularly in compositions that are nonstoichiometric to that of an ordered phase [l]. The nature of the dislocation structures was seen to be dependent on the size and amount of the ordered second phase as well as the extent of deformation, quite similar to the findings of the present study on Haynes Alloy 242; witness the dislocation structures observed at low strain levels in samples aged for short times

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OF Ni-25MoG3Cr

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(Fig. 4). It was noticed that as long as the ordered domains (regardless of whether they had the Dl, or PtzMo structure) dispersed in the short-range ordered matrix had a fine size, only single dislocations with no discernible splitting were observed [l]. Such dislocations were seen to have sheared through the fine precipitates, though no stacking faults could be observed in the matrix or the ordered domains.

4.2. Transition in mode of dgformation and ejkt particle size

qf

The deformation mechanisms in Haynes Alloy 242 were sensitive to the prior aging history of the material. In addition to exhibiting a dependence of the aging temperature and time, the mode of deformation, in aged samples, was also a function of the imposed plastic strain. A transition in the mode of deformation from slip to twinning in the presence of ordered particles was reported in earlier studies as well, particularly where the ordered strengthening phase processes tetragonal or orthorhombic symmetry [23, 241. Examples of this are the Ni-base superalloy Inconel 718, where the major strengthening phase has a DOZ2 (1”‘) structure, and NiiMo alloys where the ordered domains, either having a body-centered tetragonal (N&MO) or body-centered orthorhombic (Ni?Mo) structure, are larger than about 100 nm. The transition (from slip to twinning) was explained on the basis of the precipitate size by Sundararaman and co-workers [23] and possible reasons/models for such behavior in the present study, based on their analysis, will be described. No evidence for dislocation looping around the Ni,Mo particles was obtained, although this is a fairly common phenomenon in precipitation-hardened alloys that are in the overaged condition. This can be rationalized on the basis of Fig. 10, in which the calculated values of the critical shear stress associated with different modes of deformation (particle shearing, Orowan looping or precipitate by-passing and shearing of precipitates by twins) are plotted against the Ni2Mo precipitate size. These values are in turn compared with the data obtained from experimental tensile stress-strain curves to determine the regimes in which the various deformation modes will be operative for Haynes Alloy 242, thus providing a semi-quantitative assessment for the observed transition in deformation modes. During the deformation of a two-phase aggregate, consisting of a distribution of hard, ordered precipitates in a softer matrix, two distinct modes of deformation are commonly observed: particle shearing and particle by-passing by creation of loops around the precipitates. The stress required for the process of shearing increases with increasing particle size since the destruction of order over a larger area necessitates higher stresses. The functional relationship between the shear stress and particle size for this

4876

KUMAR

and VASUDEVAN:

450

, , , ,

1 II

s % zl

MECHANICAL

I,

PROPERTIES

1 I I I,

11

OF Ni-25Mo-8Cr

I I,,

I

I,

\ \

.F

350 -

Bypassing

Shearing

\

0

22

44

88

88

110

R (nm) Fig. 10. Calculated values of increment in shear stress, Ar, at 0.2% yield as functions of N&MO particle size for the different deformation mechanisms. Experimentally observed values are marked as crosses in the plot.

mode of deformation

is given by [25]:

were carried out by using the values y = 150 mJ/m’ (calculated from knowledge of the critical transformation temperature), p = 85 GPa [3], f= 0.35 and p = l/6, and the pertinent values for the dimensions of the precipitates are given in Table 1. Increment shear stresses at 0.2% plastic strain, over that of the solution treated value, are also listed in Table 1 and these were calculated by converting the experimental tensile stress to shear stress, assuming a Taylor orientation factor of 3.06 [9]. The stress associated with the precipitate by-passing mechanism, on the other hand, decreases with increasing particle size. A crossover point is observed in terms of the size of the precipitates. Operation of the by-passing mechanism has a smaller stress requirement than the shearing mechanism beyond a critical value of the precipitate size. This is because, for a constant volume fraction, an increase in the mean particle size is accompanied by a concomitant increase in the inter-particle spacing and, therefore, the stress necessary to initiate by-passing would

A~=[$,][{(~)($)l;2jl;2+/1; (1) where Ar is the shear stress increment (over the value of the solutionized material) due to particle shearing, y is the APB energy of the ordered phase, b is the Burgers vector of the shearing dislocation, f is the volume fraction of the ordered phase and I is the dislocation line tension (I = q, p being the shear modulus of the matrix). In the context of ellipsoidal disk-shaped particles, the other parameters that enter the equation are: R, half of the average value of the particle major axis, A, the aspect ratio given by the ratio of the major and minor axes and /I = 0 or l/6, depending on whether all the precipitates belong to the same variant or whether all six variants are present in equal numbers. For deformation to occur by this mode, matrix unit dislocations are expected to take part in the process. Shear stress calculations

Table I, Summary of pertinent values of particle dimensions used in shear stress calculations and experimental stresses

associated with them Aging conditions Solution treated 650C/2SH 650C/200H 650C/1200H 700C/2SH 700C/200H 7OOCil200H

Particle major axis, R (nm) 14.6 61.9 135.9 38.1 14.6 203.4

Particle minor axis (nm)

Aspect ratio, A

Yield stress, 0 (MPal

Shear stress, T (MPal

AZ (MPal

9.4 20.0 34.4 18.5 23.1 50.6

1.55 3.09 3.95 2.06 3.23 4.02

311 698 162 718 721 789 193

101.6 228.1 249.1 254.3 235.6 257.8 259.2

126.5 147.5 152.7 134 156.2 157.5

KUMAR and VASUDEVAN: decrease

A7 = [

according

to the relation

2734

( 2R

MECHANICAL

[26]:

’ .c>

In

(+$)> t2)

l-2A

[

1

where AZ is the shear stress increment associated with precipitate by-passing, v is the Poisson ratio for the matrix, r, is the radius of the dislocation core assumed

to be equal to b, and

The other parameters have the same significance as those in equation (1) above. As described earlier, deformation twinning was observed to occur as a function of precipitate size and applied strain. For this mode of particle shearing to start operating, the stress concentration at the precipitate/matrix interface should exceed the resolved shear stress required to propagate Shockley partial dislocations through the precipitate. Since the growth/broadening of the twin nuclei does not involve disruption of order (assuming that “true” crystallographic twinning occurs), it would be expected that the process of twin growth does not require stresses greater than that required for the nucleation of the twins. Formation of twins in this alloy, which shows a strong tendency for planar slip, is likely to be induced by the stress concentration developed at the front of a dislocation pile-up at the particle/matrix interface. Implicit in such an analysis is the assumption that deformation has proceeded beyond yield and that sufficient slip activity has occurred in the matrix to develop the pile-up lengths necessary to compensate for the low applied shear stresses at this point along the overall flow curve. It is important to realize also that an analysis of this nature cannot be used as a predictive model for the strain levels at which twinning may be initiated; however, it is useful for estimating whether twinning activity is possible, at a stress level corresponding to 0.2% plastic strain, in a sample with a given precipitate size. An estimation of the stresses necessary for twin nucleation can be made by equating the critical stress for twinning, rt, to the critical stress, z,, generated at the head of a dislocation pile-up of length 1, which is sufficient to overcome the obstacle posed by the interface. This critical stress can be expressed as [27]:

where z, is the applied shear stress (or incremental shear stress at yield) and CI is a geometrical factor which assumes a value of 1 and (1 - v) for a pile-up of screw and edge dislocations, respectively. Express-

PROPERTIES OF Ni-25Mo-8Cr

4877

ing 1 in terms of R, A and f, and substituting rt = z,, one obtains the following relationship (for further details regarding the derivations please refer to [23]):

z, = p [%I”*[

{+$}(;)JY

(5)

According to this relationship for constant values of 6, p, tt, f and A, z, should be inversely proportional to 3. Furthermore rt can be estimated from the following relationship [28]:

where y is the SFE of the Ni*Mo phase, c(R) is a function of R, the ratio of the applied stress for twinning to that for slip, and is approximately equal to 2, and b is the Burgers vector of the Shockley partial dislocation. The plot of increments in shear stress as a function of precipitate size is shown in Fig. 10 for various dislocation processes that can be activated in age-hardened alloys. Comparison of the experimental data with the curves obtained through calculations suggests a cross-over in deformation mode at a precipitate size (taken as the major axis of the ellipsoidal precipitates) of approximately 70 nm. This is in good agreement with TEM observations of deformation structures, where twinning at strain levels of l-2% is only seen in well-aged samples where the precipitate sizes are much larger than 70 nm. Below this critical size, the stress required for unit dislocations to shear through NizMo precipitates is smaller than that required to initiate twinning within it. As the precipitates coarsen, the stress required for shearing proportionately increases and beyond a critical value of the precipitate size deformation twinning becomes more competitive, perhaps a mechanism for stress relief in the matrix. A point that needs mentioning is that shear stress increments associated with peak-aged samples are somewhat higher that what are predicted from calculations and this is a good indication of slip activity and work hardening in this matrix prior to nucleation of twins in the precipitates. Secondly, it is also inferred, from Fig. 10, that the critical stresses for twinning are lower than the values associated with Orowan looping/bowing (precipitate by-passing) for the entire range of precipitate size investigated. It is not surprising, therefore, that looping around Ni,Mo precipitates was not in evidence in the present study. In the interest of space a detailed discussion on the nature of the deformation twins and possible dislocation mechanisms for their formation has been excluded, this being the focus of attention of a forthcoming article [29]. It would suffice to say at this juncture that all possible modes of twinning, as defined by Christian and Laughlin [30], were observed to be in operation. The physical implication of the transition in terms

4878

KUMAR and VASUDEVAN:

MECHANICAL

of dislocation motion is that the mode of deformation (in the precipitate and eventually in the matrix) has changed from glide of unit (or super) dislocations to movement of Shockley partial dislocations on adjacent planes. This is governed by the energies of the various faults encountered in ordered phases. Owing to the ordered lattice of the N&MO phase, shear by unit dislocations and subsequent restoration of the ordered structure is possible only by a triplet of unit dislocations connected by strips of anti-phase boundaries (APB) [12]. In turn, the unit dislocations comprising the superdislocation can further dissociate into partials, each pair of partials being connected by a complex stacking fault (CSF). On the other hand, lattice displacements by Shockley partials alone lead to formation of geometrical superlattice intrinsic stacking faults (SISF) where there are no nearest-neighbor violations and long-range order is not disturbed. Since the unit dislocations have a tendency to dissociate in the ordered phase, it is not surprising that there is a lack of evidence for superdislocations in the present study. Rather, there is overwhelming evidence for the formation of SISFs confined within the N&MO precipitates. Eventual overlapping of these stacking faults, lying on adjacent glide planes, would lead to the formation of twins within the precipitates. 4.3. Mechanical properties, strengthening and strain hardening The tremendous increase in yield strength [Fig. l(a)] going from a solution treated sample to one that had been aged for 1200 h in the temperature range 65&725”C can be attributed to the precipitation of a high volume fraction of the strengthening phase, almost 35% with the continuous increase in strength and decrease in ductility being associated with the increasing degree of perfection and size of LRO Ni2Mo domains. The volume fraction of the N&MO precipitates did not diminish with increasing time of aging at the lower temperatures (< 725°C) although the lower values of the yield stress for samples aged at 725°C is almost certainly due to precipitation of a lower fraction of the ordered domains as compared with the samples aged at 650 and 700°C. This was unlike the behavior observed in samples aged at 750°C where after the peak in strength and strain hardening exponent following aging for 10 h the drop in strength at longer times was caused by a considerable reduction in the volume fraction of NizMo precipitates and the fact that the precipitates overaged rapidly in comparison with the behavior at lower temperatures of aging. Ductility followed the opposite trend to that observed for the yield stress and dropped appreciably as soon as distinct Ni*Mo precipitates were observed in the matrix. Nevertheless, the absolute values were quite high even in samples that were in the well-aged condition. The presence of ordered precipitates influenced the

PROPERTIES OF Ni-25Mo-8Cr

fracture mode as well. Fracture was transgranular in the early stages of aging (Fig. 2), but on long aging a combination of transgranular and intergranular fracture was observed. This could be attributed to a combined effect of the ordered precipitates being present in the matrix as well as secondary carbides precipitating on the grain boundaries (Fig. 3). However, on aging at 725 and 750°C where the precipitates were large and few in number, the mixture of transgranular and intergranular mode of fracture could primarily be due to sensitization of the grain boundaries, as extensive dimpling was observed within the grains. Observation of planar slip and the change in deformation mode from slip to twinning has important implications on the twofold increase in strength coupled with significant ductility and high degree of strain hardening. Tremendous work hardening can result as the dislocations get restricted at the precipitate/matrix interface and higher levels of stress are required to initiate slip through the precipitates. The significant levels of ductility suggest that shearing of the precipitates was not a difficult process, provided some critical stress build-up was reached at the interface, and this is corroborated by the fact that no looping of the dislocations around the precipitates was observed. Observations suggest that formation of twins could be a consequence of stacking faults overlapping each other and creating regions which are in twin relation to the surrounding areas (Figs 8 and 9). Such an argument has been invoked earlier to explain the phenomenon of deformation twinning in other tetragonal structures derived from the f.c.c. lattice, like Dl, (Ni,Mo) [24, 311 and DOzz [23, 32, 331. In the following, an assessment will be made of the contributions arising from the various sources that give rise to strengthening in precipitation hardened alloys. At the outset, it should be mentioned that it did not prove possible to isolate and measure the effects from the various strengthening mechanisms that could be operative. Furthermore, there is no a priori to assume that two or more reason mechanisms cannot be operative simultaneously. Solid solution strengthening is a potent mechanism in Alloy 242 owing to the large amounts of solute elements that are part of the chemistry and this is reflected in the yield strength values of the solutionized samples. The presence of SRO is a source of strengthening, as well, as it causes slip to the planar, but it probably has a comparatively minor effect, initially, since it is very weak in the solution treated state. However, the significance of SRO as a source of strengthening increases as it develops in samples representing the early stages of aging. The effect that SRO has on the strength is indirect and is connected to the restriction of slip to planar arrays (see Section 4.1). Presence of SRO and the intermediate value of SFE for the matrix has a profound effect on the work

KUMAR

and VASUDEVAN:

MECHANICAL

hardening characteristics, resulting in ultimate tensile strengths that are almost triple that of the yield strengths. Strain hardening in the solution treated and early aged samples is entirely due to the fact that cross-slip as a stress-relief mechanism is severely restricted. The effects of SRO are aided and abetted by the SFE of the matrix to a great degree. The SFE of the matrix is of such a value that it does not allow formation of wide stacking faults (which may lead to twinning), nor does it allow cross-slip to be active. The operation of either of these mutually exclusive stress-relief mechanisms has been observed to lead to a drop in the strain hardening rates in other single phase f.c.c.-based alloy systems, although there is some controversy over whether twinning leads to softening or hardening [34]. For the sake of argument, it is assumed that twinning has a softening effect until a point is reached where the different twinning systems within a grain start to interact with each other. Since large scale twinning is only observed in samples that contain N&MO precipitates it is safe to say that the work hardening rate (in the solutionized state and in the early stages of aging) is sustained by the interactions between the planar slip bands as the material is strained beyond yield. In age-hardened alloys containing precipitates that have long-range periodicity in their structure, the dominant contributions to strengthening arise due to formation of APBs and destruction of order by the shearing of dislocations, as well as the strain fields arising from the precipitate-matrix lattice misfit. We shall consider first the potential hardening due to coherency strains around the ordered Ni,Mo precipitates. Tanner [35] in his study on the phase transformations in N&V (isostructural with NizMo and NiCr) pointed out that the coherency strains developed around N&V precipitates in a short-range ordered matrix were only of the order - 10-l, even in well-aged specimens, and hence their contribution to the overall hardening of the alloy can be considered rather insignificant. The coherency strains are expected to be the same in the present alloy, in the two-phase condition, since NizMo is isostructural with NizV and has the same lattice dimensions and mismatch relative to the f.c.c. matrix. This is borne out, indirectly, in the present investigation, where misfit dislocations to relieve the coherency strains at the particle/matrix interfaces were observed only in highly overaged samples, typically those aged at 750°C beyond 25 h. Strengthening by ordered coherent precipitates is directly correlated to the APB energy per unit area on the slip plane of the gliding dislocations, as this represents the force per unit length opposing the motion of dislocations as they penetrate the particles. As particle size increases so does the stress required to shear the precipitate. This has been graphically represented in Fig. 10, where an estimate for the strengthening due to the various mechanisms has been plotted. It is clear that when the particles are

PROPERTIES

OF Ni-25Mo-8Cr

4879

smaller than ca 70 nm, the yield strength of the aged samples is directly related to the stresses required for the unit dislocations to shear through the precipitates. This represents the nucleation and early stages of growth of the Ni2Mo precipitates, twinning being observed to be the dominant mode of deformation in peak-aged samples with well-developed Ni,Mo precipitates. The major increment in yield strength over that of the solutionized condition is observed, however, during the transition from SRO to nucleation of LRO N&MO domains through the intermediate states of order (in terms of aging time in the temperature range 650-725’C, this period extends until about 25 h). Once the nucleation event has occurred, assuming all nuclei appear at the same time in the matrix, the yield strength of the aged samples increases only marginally. The contribution of the ordered precipitates to strengthening in age-hardened alloys has been well documented in a number of systems [36]. This conclusion is fairly obvious in the present study as well. However, the effect of precipitation of a high volume fraction of an ordered phase on the strain hardening characteristics has not been investigated before in any detail. Strain hardening is significant in solutionized samples (n N 0.7) and becomes more pronounced as ordering reactions occur in the matrix as a consequence of aging. Calculations for the strain hardening exponent when graphically represented, as in Fig. I(d), show that this parameter attains a maximum value (-0.94) in samples that had been aged for 25 h, beyond which a slight decline is observed. This behavior could be traced in the true stress vs true strain curves from samples aged at the different temperature for various times. Samples in the solution treated condition or aged for short times (< 5 h) exhibited parabolic curves initially where the strain hardening rates are very high and then a gradual decline (in the rate of strain hardening) was observed, finally leveling off to a stage of linear hardening until the UTS was reached. These represent the situations where large scale twinning is not observed even when deformed to failure in tension (total plastic strains well over 40%). As the aging time increased, the parabolic hardening characteristics just after yield became increasingly more pronounced to where the flow curve did not exhibit any linearity. Coupled with this is the fact that the strain to failure also decreased as the aging period is increased. This distinct change could be attributed to fine scale precipitation of the Ni2Mo phase and the onset of twinning. Moreover, it was observed that the strain hardening exponents reached a peak value in samples aged for 25 h, a slight drop being observed beyond this time of aging. This is in all likelihood linked to the fact that as the precipitate size increases, the inter-particle spacing also increases, thus allowing a longer pile-up of unit dislocations at the precipitate/matrix interface and

4880

KUMAR and VASUDEVAN:

MECHANICAL

hence the onset of twinning is pushed to lower global stresses. It can be argued on this basis that twinning cannot sustain the work hardening rate to the same extent that interactions of planar arrays of dislocations can, assuming that twinning is initiated as a mechanism for stress accommodation. While transition in the mode of deformation from slip to twinning may induce the material to exhibit continually declining work hardening rates it does not appear to have any adverse effect on the overall strain hardening of the material; witness the fact that the ultimate tensile strengths of the samples aged beyond 25 h in the temperature range 650-725°C are almost double that of the corresponding yield strengths.

PROPERTIES OF Ni-25Mo8Cr REFERENCES

1. C. R. Brooks, J. E. Spruiell and E. E. Stansbury, Int. Metall. Rev. 29, 210 (1984).

2. K. Vasudevan and E. E. Stansbury, Mater. Res. Sot. Symp. Proc. 62, 337 (1986).

3. S. K. Srivastava and M. F. Rothman, Proc. Symp. High Temperature Materials for Power Systems, Liege, Belgium (1991). 4. M. Kumar and V. K. Vasudevan, Mater. Res. Sec. Symp. Proc. 213, 187 (1991).

5. M. Kumar and V. K. Vasudevan, Kinetics of Ordering Transformations in Metals (edited by H. Chen and V. K. Vasudevan), p. 137. TMS-AIME, Warrendale, PA (1992). 6. M. Kumar and V. K. Vasudevan, Acta mater. 44, 1591 (1996).

I. S. Dymek, M. Dollar and D. L. Klarstrom, Ser. metall. mater. 25, 865 (1991).

5. CONCLUSIONS The major conclusions arising from this study on the mechanical properties and strengthening of an Ni-25Mo-8Cr alloy are:

(1) Yield strength

of the solution treated and quenched samples is governed by solid solution strengthening, effected by the high amounts of alloying addition in Haynes Alloy 242 and the presence of quenched-in-weak short-range order. (2) Tremendous increase in strength in the early stages of aging is associated with intensification of SRO and partial LRO. With an increase in aging time (2 10 h), strength increases are more gradual, but there is a concomitant drop in ductility. This is attributed to precipitation of a high volume fraction (-35%) of NizMo precipitates. (3) Strain hardening is high in the solution treated condition and the alloy strain hardens further on continued aging, followed by a slight decline at long times. The high degree of work hardening is attributed to the difficulty in activating cross-slip, because of the presence of SRO/partial LRO and an intermediate value of the stacking fault energy in the f.c.c. matrix. A transition from crystallographic glide (of (4) planar arrays of unit dislocations) to twinning was observed as a function of.aging time and strain, twinning being observed only in samples that reveal the presence of NizMo precipitates. Strain required to initiate twinning decreased as the aging time increased, a semi-quantitative model predicting that twinning would be the dominant mode of deformation in samples that contain precipitates larger than ca 70 nm.

8. M. Kumar and V. K. Vasudevan, Advances in Physical (edited by S. Banerjee and R. V. Metallurgy Ramaniyan), p. 228. Gordon and Breach, Amsterdam (1996). 9. G. E. Dieter, Mechanical Metallurgy, 3rd edn, p. 288. McGraw-Hill, Inc., New York (1986). 10. A. C. Fraker and H. H. Stadelmaier, Trans. AIME 245, 847 (1969).

11. S. K. Das and G. Thomas, Phys. Stat. Sol. (A) 21, 177 (1974).

12. S. Amelinckx, Dislocations in Solids (edited by F. R. N. Nabarro), Vol. 2, p. 270. North-Holland Publishing Co., Amsterdam (1979). 13. J. P. Hirth and J. Lothe, Theory of Dislocations, p, 739. McGraw-Hill, Inc., New York (1982). 14. T. C. Tiearney and N. J. Grant, Metall. Trans. 13A, 1827 (1982).

15 G. Thomas, Acta metall. 11, 1369 (1963). 16 L. Delehouzee and A. Deruyttere, Acta metall. 15, 727 (1967).

17 P. C. J. Gallagher, Metall. Trans. 1, 2429 (1970). 18 P. S. Kotval, Trans. AIME 242, 1651 (1968). 19. B. E. P. Beeston and L. K. France, J. Inst. Metals 96, 105 (1968).

20 V. Gerald and H. P. Karnthaler, Acta metall. 37, 2177 (1989).

21 J. B. Cohen and M. E. Fine, J. Phys. Radium 23, 749 (1962).

22. H. P. Karnthaler and B. Schiigerl, Strength of Metals and Alloys, p. 205, Pergamon Press, Oxford (1979). 23. M. Sundararaman, P. Mukhopadhyay and S. Banerjee, Acta metall. 36, 847 (1988).

24. L. A. Nesbit and D. E. Laughlin, Acta metall. 28, 989 (1980).

25. J. M. Oblak, D. S. Duvall and D. F. Paulonis, Metall. Trans. 5, 143 (1974).

26. P. M. Kelly, Ser. metall. 6, 641 (1972). 27. J. D. Emburv. Strenptheninn Methods in Crvstals (edited by A. Kelly and R B. Nicholson). Elsevier Science, Amsterdam (1971). 28. N. Narita and J.-I. Takamura, Dislocations in Solids (edited by F. R. N. Nabarro), Vol. 9. North-Holland Publishing Co., Amsterdam (1992). 29. M. Kumar and V. K. Vasudevan, unpublished research (1995). 30. J. W. Christian and D. E. Laughlin, Acta metall. 36, 1617 (1988).

Acknowledgements-The authors would like to gratefully acknowledge the support received from the following agencies during the research program: Haynes International, Inc., Kokomo, Indiana, Oak Ridge Institute of Science and Engineering, Oak Ridge, Tennessee, and University of Cincinnati Research Council. Cincinnati, Ohio. Additional support for one of the authors (MK) from Johns Hopkins University during the writing of this manuscript is also acknowledged.

31. H. P. Kao, K. Vasudevan and C. R. Brooks, Proc. Annual Meeting EMSA.

562 (1986).

32. G. Vanderschaeve and B. Es&g, khys. Stat. Sol. (A) 20, 309 (1973).

33. G. Vanderschaeve and T. Sarrazin, Phys. Stat, Sol. (A) 43, 459 (1977).

34. L. Remy, Metall. Trans. 12A, 381 (1981). 35. L. E. Tanner, Acta metall. 20, 1197 (1972). 36. A. J. Ardell, Metall. Trans. 16A, 2131 (1985).