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Dislocation-precipitate interaction and cyclic stress-strain behavior of a γ′ strengthened superalloy
Materials Science and Engineering, 34 (1978) 275 - 284 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
275
Dislocation-Precipitate Interaction and Cyclic Stress-Strain Behavior of a 7' Strengthened Superalloy
R. E. STOLTZ* and A. G. PINEAU
Centre des Materiaux, E.N.S.M.P., B.P. 87, 91003 Evry (France) (Received December 10, 1977; in revised form February 21, 1978)
SUMMARY
The cyclic response of WASPALOY, a ~/' strengthened nickel-base superalloy, was measured as a function of 7' precipitate size. Specimens with precipitates larger than the critical size for dislocation looping, 25 nm, cyclically harden to saturation. Samples with smaller, easily shearable precipitates, 8 nm in diameter, harden to a maximum stress, then markedly soften, while those at the critical size soften slightly. Cyclic saturation is due to a dense dislocation substructure which fills the inter-slipband volume. In material with precipitates 25 nm and smaller, shearing of the precipitates, combined with a localization of plastic flow in persistent slip bands, leads to cyclic softening. The marked softening in the 8 nm material is due to the complete mechanical disordering of the precipitates within the slip bands. A model whereby the slip band density is linearly related to the applied strain is proposed to account for the observation that a constant number of cycles to maximum stress exists in the 8 nm alloy.
INTRODUCTION
When a material is subjected to cyclic plastic strains, a series of events takes place which leads eventually to fatigue failure. Though the dividing line between these events is often n o t well-defined, three main processes can be isolated: ( i ) a change in the deformation behavior of the material due to cyclic straining, (2) nucleation of an incipient fatigue crack, (3) the propagation of that crack to a critical length for final failure. Of the three, the me*Present address: Sandia Laboratories, Division 8316, Livermore, CA 94550, U.S.A.
chanical response to cyclic Plastic strains is often the most sensitive to the alloy microstructure. Cyclic response can be measured in a number of ways. The level of the cyclic stressstrain curve indicates whether, in the cyclically stable state, the alloy is stronger or weaker than in the virgin condition. A more detailed approach, however, is through the use of the cyclic response curve, where the applied stress is plotted v s . number of cycles at a fixed plastic strain amplitude. These curves give not only the saturated cyclic flow stress (if saturation occurs}, b u t also the path by which the material arrives at its final flow stress level. Laird [1] has given an excellent review of the various types of cyclic responses observed and a list of the micromechanisms which govern each type of behavior. Briefly, annealed, single-phase materials tend to cyclically harden to saturation, while cold-worked alloys soften to a saturation value. At low plastic strains, carbon steels are seen to cyclically soften, then harden. Dispersion strengthened materials are usually stable, while bulk ordered alloys and alloys strengthened by ordered precipitates show hardening followed by softening. It is the latter phenomenon of hardening followed by softening to which this work is principally addressed. The current theory proposed by Calabrese and Laird [2] for A1-Cu 0" strengthened alloys is based upon a model of precipitate cutting by dislocations, leading to a loss of order strengthening and to overall softening. Direct observation of the interaction between ordered 0" precipitates and dislocations in the A1-Cu alloys investigated in their work was n o t performed. In this work, WASPALOY, a nickel-base superalloy strengthened by spherical, fully coherent precipitates of 7' (Ni3(A1,Ti)) was investigated. Due to the small co-
276 herency strains around the precipitates, the 7' phase can be imaged by dark-field-transmission electron microscopy. The other advantage of WASPALOY is that the size and spacing of the precipitates can be changed (at a fixed volume fraction) without changing the matrix composition. Two heat treatments with equivalent yield strengths were chosen for the major part of the work, one with 8 nm 7' particles which are cut by dislocation pairs, and one with 90 nm particles which are not initially sheared. (The deformation modes of an alloy similar to WASPALOY are reported by Pineau e t al. [3] .) The flow stress vs. number of cycles at various fixed plastic strains was measured and related to the nature of the dislocation-precipitate interactions by optical and transmission electron microscopy.
EXPERIMENTAL
All testing was performed on specimens from a single-swaged bar of WASPALOY. The composition is listed in Table 1, while heat treatments and resulting 7' sizes are given in Table 2. The 1 313 K (1 040 °C) solutionizing temperature was chosen in order fully to dis-
solve the primary 7' and to avoid excessive grain growth. The final grain size determined by a linear intercept method was approximately 60/~m. Fatigue specimens with a cylindrical or hourglass reduced section, 5 mm in diameter, were cut parallel to the axis of the bar. R o o m temperature fatigue testing was done in an Instron modified to cycle between constant total strain limits. The plastic strain was held constant by frequently adjusting the total strain amplitude. Both diametral and longitudinal extensometers, accurate to strains of 10 -4 , were employed. All plastic strains quoted are longitudinal strains, converted, when necessary, from the measured diametral plastic strains. The nature of the fatigue-induced slip bands was studied by both optical and transmission electron microscopy. Fatigued specimens were spark cut for microstructural analysis below the fracture surface in failed samples, and at the minimum cross-section in unfailed specimens. Samples for optical analysis were first electropolished and then etched in a solution of 16 g FeCI3, 9 g (NH4)2S2Os, 100 ml H20, and 60 ml HC1 at 313 K (40 °C). Thin foils from fatigued samples for TEM were dual-jet thinned in a 5% perchloric-acetic acid solution at 290 K (17 °C) and 60 V.
TABLE 1 Composition of WASPALOY (wt. %)
C
Cr
Co
Mo
Ti
A1
Zr
B
S
Si
Cu
Fe
Ni
0.04
19.3
13.9
4.0
3.07
1.37
0.07
0.004
0.003
0.02
0.01
0.01
Bal.
TABLE 2 Heat treatments and resulting 7 ~sizes
diameter (nm)
Experimental Solutionize
Commercial Solutionize
1 313 K (1 040 °C)/ 2 h, oil quench
Age 1 003 K (730 °C)/6 h Age 1 098 K (825 °C)/24 h Age 1 148 K (875 °C)/24 h
1 283 K (1 010 °C)/ 4 h, oil quench
Age 1 123 K (850 °C)/4 h Aircool +
Age 1 033 K (760 °C)/15 h
8 50 90
25
277
RESULTS
Cycle response
Cyclic response curves (stress vs. cycles at a fixed plastic strain amplitude) are given in Figs. 1 and 2 for the 90 nm and 8 nm cases, respectively. While the initial flow stress (at N = 1) is equivalent for the two alloys, the cyclic response is quite different. The 90 nm material, Fig. 1, exhibits an extensive hardening period up to a saturation stress value. The arrows in Fig. 1 indicate the onset of saturation, and show that the lower the plastic strain, the larger the number of cycles to saturation. The final stress drop for ep = 0.50 and 0.83 percent, is due to the formation of macrocracks and we therefore will consider only the behavior up to saturation. By con-
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trast, for the same plastic strains, the 8 nm alloy hardens then sharply softens, Fig. 2. It is interesting that the number of cycles to the m a x i m u m stress, N(amax), indicated by arrows, is approximately the same, 20 - 30, regardless of imposed plastic strain. The final stress drop for the 0.83 and 0.50% tests is due to the nucleation of a macrocrack. Two additional cyclic response tests at ep = 0.50% were run on alloys with 25 nm and 50 nm precipitates sizes. The cyclic response for all four alloys is given in Fig. 3. A normalized stress, ON/OZ,where o l is the stress at the first cycle, is plotted against number of cycles. Only 500 cycles are shown in order to exclude any effects of macrocracking. The 50 nm alloy hardens to saturation in the same number of cycles as the 90 nm alloy, but to a lower saturation stress level. The 25 nm material hardens initially at a faster rate than the other alloys, but reaches a m a x i m u m at approximately 40 cycles, and exhibits only slight softening. M icrostructure
The slip band structure of the 90 nm and 8 nm heat treatments, tested at a plastic strain amplitude of 0.5% is summarized in Fig. 4. After 40 cycles the 90 nm material is still in the hardening stage. Each grain shows the beginning of slip band formation (Fig. 4(a)). The etching response between the slip bands suggests the presence of a uniform deformation network. After cycling to failure, Fig. 4(b)), the slip bands and underlying substructure are more fully developed.
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F i g . 2. C y c l i c response curves f o r W A S P A L O Y with 8 n m ~?' p r e c i p i t a t e s i n d i c a t i n g h a r d e n i n g f o l l o w e d b y softening. The m a x i m u m stress occurs at N ~ 2 5 , r e g a r d l e s s o f p l a s t i c strain.
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278
(a)
(b)
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Fig. 4. Optical mierographs of persistent slip bands in WASPALOY tested at 0.5% plastic strain: (a) 90 nm ~" case, 40 cycles, (b) 90 nm t ease, 1 400 cycles, (c) 8 nm ~? case, 40 cycles, (d) 8 nm 7t ease, 2 500 cycles.
In the 8 nm case, 40 cycles is just past the hardening maximum. Discreet slip bands have formed in the majority of the grains, Fig. 4(c), with no evidence of deformation between the slip bands. At failure, Fig. 4(d), the slip bands have intensified and thickened, but all of the deformation remains confined to the slip band regions. Higher magnification photographs show that the intense slip bands are composed of closely spaced finer bands. It is important to note that all of the above micrographs are from polished and etched regions at the center of the specimen, or from below the surface of fractured specimens, and thus represent the bulk fatigue damage caused by cyclic straining. The major difference in the deformation behavior of the two cases is
in the degree of strain inhomogeneity. A homogeneous substructure is present in the 90 nm specimens, in addition to the persistent slip bands. On the other hand, the absence of slip in the interband regions of the 8 nm samples indicates a strong localization of plastic flow and a highly inhomogeneous mode of fatigue deformation. Thin foils were prepared from the 8 nm and 90 nm samples tested 40 cycles and 1 000 cycles at a plastic strain amplitude of 0.5%. The general observations made by optical microscopy were confirmed by TEM. Figure 5(a) is of the 90 n m alloy tested 40 cycles. A loosely organized primary slip band is shown along with the beginning of activity on a secondary slip system. At this point along the
279
(a)
Shearing of the 8 nm 7' particles results in a much different dislocation substructure when compared with the 90 n m precipitates. After 40 cycles, sharply defined slip bands, often only two or three slip-planes thick, are present. Dislocation activity along each band is n o t uniform across the grain, with a greater density at slip band intersections. After 1 000 cycles, the slip bands are fully developed across the grain, and slip remains confined only in the slip band regions. By tilting the foil to a [110] orientation where the primary [111] slip planes are "edge on", Fig. 6(a) and (b), it can be seen that each macroband is composed of smaller microbands. Using the [300] 7' reflection to image the precipitates, Fig. 6(a), one notes that the ordered precipitates are absent from the micro slip band volume. Care was taken to tilt the foils to verify that no intensity from the [300] 7' spot was present in the slip bands. In Fig. 6(b), from another region in the sample, it can be seen that the slip band channels are swept clean of ~' particles, though, in places, the
(b) Fig. 5, Transmission electron micrographs of the 90 n m 7' case tested at 0.5% plastic strain: (a) 40 cycles, (b) 1 000 cycles.
hardening curve a large fraction of each grain volume is still free from dislocations. By contrast, after cyclic saturation to 1 000 cycles, the dislocation substructure completely fills each grain. Figure 5(b) is of the inter-slipband region. A large number of dislocation interactions have occurred due to the bowing of dislocations around the particles, and a network of dislocation segments extends between each particle. Within the slip bands, the dislocations are more densely arranged, but the gradient of dislocation density is sharply defined between slip band and interband region. As a general observation, saturation occurs once the overall network has filled the grain volumes.
(a)
(b) F!g. 6. Transmission electron micrograph of the 8 nm 9' case tested at 0.5% plastic strain. (a) Dark field view of "edge o n " slip bands, (b) higher magnification dark field view of "edge o n " slip bands, [011 ] zone axis, [300] 7 r reflection.
280
process is not complete (A). The darker regions (B, C) result from residual dislocation contrast, and analysis of these dislocations indicates that they are segments from secondary slip systems extending between the primary bands. Furthermore, contrast experiments show that within each slip band, cyclic deformation leads to dislocation interactions which destroy the usual pair-wise arrangement that exists after monotonic deformation [3]. Two further TEM observations were made on the 50 nm and 25 nm alloys cycled for 1 000 cycles at ep = 0.5%. The dislocation substructure in the 50 nm material was similar to the 90 nm alloy. Dislocation bowing results in coarse slip bands and tangles around the precipitates, along with a dislocation network filling the grain volume between the bands. In the 25 nm alloy, due to the distribution of the 7' particle sizes, both precipitate shearing and bowing is observed locally along the slip plane. (In WASPALOY, 25 nm is the critical size for the shearing-bowing transition [3] .) As with the 8 nm alloy, slip is confined to discreet bands with no overall dislocation network throughout the grains. Dark field microscopy shows, however, that while the precipitates are sheared, fragmented ~' particles still exist after 1 000 cycles within the slip band volume, Fig. 7.
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loys. Figure 8 is a cyclic response curve of the 8 nm alloy, cycled at 0.83% plastic strain, and annealed after partial softening. Annealing was done at 1 003 K (730 °C), the aging temperature of the alloy, in a vacuum furnace backfilled with argon to prevent surface oxidation. Upon retesting in fatigue after annealing, the flow stress is higher, indicating that a large fraction of the strength lost through softening is recovered. During further fatigue cycling the alloy hardens to a higher maximum stress than previously attained, and then again cyclically softens. The n u m b e r of cycles to maximum stress is reduced by the annealing treatments. Optical micrographs were taken of the specimen tested for Fig. 8 (two anneals and cycled to failure) along with a companion specimen tested 110 cycles at 0.83% plastic strain. In the sample tested 110 cycles, Fig. 9(a), a single set of slip bands is present in most grains. By contrast, the alloy annealed twice exhibited the majority of grains with two and three sets of slip traces, Fig. 9(b).
DISCUSSION
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Annealing experimen ts Previous work [2, 4] has shown that short time thermal treatments can significantly affect the behavior of cyclically softened al-
Cyclic response The above results show that the cyclic response of WASPALOY is highly sensitive to the details of the dislocation-precipitate interaction. The two aspects which control cyclic response are: (1) the mechanical stability of the precipitates during reverse plastic straining, (2) the ability of the material to distribute the plastic strains over the grain volume. In the 90 n m and 50 nm 7' alloys, dislocation bowing to form Orowan loops leads to cyclic hardening and stability of the alloys. During reverse plastic straining, the complex dislocation interactions that occur
281
(a)
(b) Fig. 9. Optical micrograph of the 80 nm 7' material tested at 0.83% plastic strain. (a) 110 cycles, (b) cycled and annealed.
around the precipitates, Fig. 5(b), force dislocations o u t of their primary slip plane, creating a "plastic zone" around each particle. The link-up of these zones results in a threedimensional homogeneous substructure, and the eventual cyclic stability of the material. When the precipitates are below 25 nm, the critical size for dislocation bowing, the alloy is no longer able to redistribute the plastic strain throughout the grain volume and cyclic
softening occurs, Fig. 2. A number of other alloys exhibit similar cyclic response behavior, including: other Ni-base alloys strengthened b y 7' or 7" [6, 7] A1-Cu strengthened by 0" [ 2 ] , ordered NiaMn [8] and Cu3Au [9]. Softening is thought to occur in these alloys through a disruption of local, ordered atomic arrangement. This atomic rearrangement results in a reduction locally in the amount of ordered phase and a loss in the order contribution to strengthening [1]. There are interesting differences in the cyclic response curves of these alloys and they can be divided into t w o subclasses: that typified by A1-Cu-0" [2] and that by WASPALOY in Fig. 2. While the number of cycles to maxim u m hardening, N(oma~), in the 8 nm 7' case of WASPALOY and in Udimet 700 [6] is a constant in respect of plastic strain, A1-Cu-0" and the other alloys show an increase in N(Oma~) with decreasing strain. An analysis of the data for A1-Cu-0" (ref. 2, Fig. 2) indicates that the hardening maximum occurs at a critical cumulative plastic strain, N(om~) × % = 65.0%. In A1-Cu-0" alloys, intense slip bands develop from the underlying substructure and, thus, a dense network of dislocation debris exists between the bands. Since softening is due to the repeated shearing of the 0" precipitates, then the onset of cyclic softening should, and does, occur at a constant cumulative plastic strain. In WASPALOY with 8 nm 7' precipitates, all the plastic strain is localized in slip bands from the onset of plastic straining. If the kinetics of hardening and softening processes which govern the cyclic response are the same in each slip band regardless of plastic strain, then, in order to accommodate the higher strains, the number of slip bands must increase linearly with strain. This would account for the fact that the number of cycles to maxim u m hardening is constant. A similar model can explain the behavior of Udimet 700, where Wells and Sullivan [6] observed that all the slip bands necessary to accommodate the fatigue strain are nucleated during the first strain cycle, and that any subsequent plastic flow occurs within the same bands. In order to verify the model that the number of slip bands increases proportionately with plastic strain, three specimens of the 8 nm material were cycled for 100 cycles at 0.83, 0.50 and 0.24% plastic strain amplitude.
282
The samples were then sectioned and the interslip-band spacing, which is inversely proportional to the number of bands per grain, was measured. As shown in Fig. 10, the average spacings are linear with plastic strain. As far as the exact hardening and softening mechanisms that occur within the slip bands, the model of Calabrese and Laird [2, 5] is applicable to the 8 nm WASPALOY. Since the initial dislocation density is low at the beginning of cycling, dislocation generation and interaction lead to a net hardening component. During the hardening stage, jog formation and intersections with secondary slip systems destroy the organized superlattice pair motion and cause the slip bands to thicken. The back and forth motion of this disorganized array of dislocations shears the 8 nm 7' precipitates on each (111) plane so that locally, within the slip band, the amount o f ordered phase is reduced to zero. It is most likely that softening begins at the first strain cycle, so that measurements of the softening component taken from N(oma~) do not account for all the softening that has taken place. The reason WASPALOY reaches its hardening maximum, N(omax) = 25, is, as yet, unclear, though the value of N(amax) should depend upon the size of the precipitates and the grain size. The absence of 7' intensity within the slip band volume, using the [300] 7' superlattice reflection, Fig. 6(b), supports this softening mechanism. The slip bands are intrinsically softer than the alloy in its virgin condition because the hardening c o m p o n e n t due to the ordered second phase is lost. There is some controversy as to the interpretation of dark field micrographs such as Fig. 6(b). Specifically, it is questioned whether the absence of superlattice intensity is due to the absence of an ordered phase, or simply a non-imaging artifact due to local perturbation of the lattice
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by dislocations. The presence of 1" particles along a slip plane within the denuded volume of the slip band (at A in Fig. 6(b)) indicates that if ordered particles are present within the band, they can be imaged. In the denuded region, however, the particles are sufficiently randomly sheared so as n o t to produce any superlattice intensity. Softening during cycling occurs within the slip bands through a progressive shearing of the 8 nm precipitates, which leads to spreading and thickening of the denuded regions. In order for the softening to be complete, however, shearing must occur on each slip plane that intersects the precipitate. In the 25 nm samples, even after 1 000 cycles, the 7' particles can still be imaged within slip bands, indicating that they have not been effectively sheared enough to destroy all the local order. The relative amount of softening is thus less in the 25 nm case compared with the 8 nm material, Fig. 3. Tilting experiments indicate that the occasional Orowan loop, left around the largest precipitates in the slip band, interacts with nearby dislocations on parallel slip planes, thus spreading o u t the shearing action over a wider distance. Instead of being sheared on each slip plane the precipitates are fragmented. Some softening occurs from this fragmentation process because the effective particle radius is reduced, b u t the softening is n o t as complete as in the 8 nm material.
Annealing behavior Since the cyclic softening of the 8 nm 7' takes place at room temperature, no longrange diffusion of the A1 or Ti atoms occurs. (Precipitation does n o t occur below 630 °C [3] .) The mechanical shearing action of the dislocations results in atomic rearrangements over small distances, of the order of a few atom spacings. In this case, short time anneals should re~stablish the local order and recover the softening component. Figure 8 shows the effects of t w o anneals of 10 min/730 °C on the cyclically softened WASPALOY. Similar annealing experiments have been performed on the A1-Cu alloys [ 2 ] , and the behavior of the two alloys is somewhat different. After annealing a cyclically softened A1-Cu alloy, the initial flow stress of the material is reduced. The alloy does, subsequently, harden and then soften, indicating that reordering has taken place, b u t some re-
283 covery in the overall dislocation substructure must have occurred as well. In the case of WASPALOY, no inter-slipband dislocation structure is present. During the thermal treatment the sheared 7' particles coalesce and reorder, but, at the same time, pin the dislocations within the bands. Upon recycling, the flow stress is higher because new, less favorably oriented slip bands on secondary slip systems must be nucleated. (Note that in Fig. 9(b) many grains exhibit three sets of slip traces.) During cycling after heat treating, both the new slip bands and the previously established bands undergo softening, b u t since most of the dislocations necessary for softening already exist in the older bands, the hardening maximum occurs after a fewer number of cycles.
Implication o f cyclic softening in selection of fatigue resistant alloys Numerous reviews on alloy design for fatigue resistance have emphasized the need for materials which resist cyclic softening [10 1 3 ] . The above results demonstrate that in alloys strengthened by ordered precipitates, t w o features are necessary before cyclic softening occurs. First, there must be an instability in the microstructure so that locally, a softer region can develop. Second, the volume of material where the instability occurs must constitute a large fraction of the total volume of material undergoing plastic strain. In the 8 nm case of WASPALOY, the random shearing of the 7' leads to a locally soft region. In addition, all of the deformation is concentrated in the softened region so that both criteria are fulfilled. In the 90 nm material, the alloy is cyclically stable because the dislocations in between the slip bands offset any local softening that may occur within the bands. By comparison, in the A1-Cu-0" alloy [2] the overall dislocation structure is n o t sufficient to overcome the slip band softening, indicating that the degree of strain localization at which softening occurs depends upon the particular alloy. The key feature of all these alloys, however, is that softening and strain localization go hand-in-hand. Materials strengthened by a dislocation structure, such as maraging steels and coldworked copper, also cyclically soften [4, 13]. In these alloys, strain localization is not essential because the softening is due to a re-
arrangement or " s h a k e d o w n " of the preexisting dislocation structure. Though both the precipitation-strengthened- and the substructure-strengthened alloys which cyclically soften should be avoided in fatigue applications due to the loss in strength, the strainlocalized alloy tends to be worse in terms of crack initiation resistance and environment sensitivity due to the localized nature of the fatigue deformation.
CONCLUSIONS The cyclic response (stress vs. number of cycles at a fixed plastic strain) of WASPALOY is a function of 7' precipitate size. Specimens with precipitates larger than the critical size for dislocation bowing (50 nm and 90 nm) cyclically harden to a saturation stress value. Materi.1 with precipitates at the critical size (25 nm) hardens then softens slightly, while those with smaller, shearable precipitates (8 nm) harden to a maximum stress, then markedly soften. The number of cycles to maximum stress is constant with plastic strain in the 8 nm material. Cyclic saturation in the 50 nm and 90 nm alloys is due to a dense dislocation substructure which fills the interslip band regions. In the 25 nm and 8 nm alloys, shearing of the precipitates, combined with a localization of plastic deformation within slip bands, leads to cyclic softening. The marked softening of the 8 nm alloy is due to the complete mechanical disordering of the precipitates within the slip bands. A qualitative model is proposed to account for the constant number of cycles to maximum stress in the 8 nm alloy. The model predicts that the slip band density is a linear function of applied plastic strain and is applicable to other highly strained localized alloys such as Udimet 700.
ACKNOWLEDGMENTS This work was performed at the Centre des Materiaux, ENSMP, Evry, France. The financial support of the French government (CIES) is gratefully acknowledged along with the technical support of A. Hue, G. Baudry and D. Fournier.
284 REFERENCES
1 C. Laird, in R. J. Arsenault (ed.), Plastic Deformation of Materials, Vol. 16, Academic Press, New York, 1975, p. 101. 2 C. Calabrese and C. Laird, Mater. Sci. Eng., 13 (1974) 141. 3 A. Pineau, F. Lecroisey and M. Sindzingre, Acta Metall., 17 (1969) 905. 4 L. F. Van Swam, R. M. Pelloux and N. J. Grant, Metall. Trans., 6A (1975) 45. 5 C. Calabrese and C. Laird, Mater. Sci. Eng., 13 (1974) 159.
6 C. H. Wells and C. P. Sullivan, Trans. ASM, 57 (1964) 841. 7 H. F. Merrick, Metall. Trans., 5 (1974) 891. 8 C. E. Feltner and C. Laird, Am. Soc. Test. Mater., STP 467, 1970, p. 77. 9 K. H. Chien and E. A. Starke, Jr., Acta Metall., 23 (1975) 1 173. 10 J. C. Grosskreutz, Metall. Trans., 3, (1972) 1 255. 11 J. C. Grosskreutz, Proc. Third Int. Conf. Fracture, Munich, PLV-212, 1973. 12 R. M. Pelloux and R. E. Stoltz, Optimization of microstructure for fatigue resistant engineering alloys, 4th Int. Conf. Strength of Metals and Alloys, Nancy, France, 1976. 13 C. E. Feltner and C. Laird, Acta Metall. 15 (1967) 1 621.
275
Dislocation-Precipitate Interaction and Cyclic Stress-Strain Behavior of a 7' Strengthened Superalloy
R. E. STOLTZ* and A. G. PINEAU
Centre des Materiaux, E.N.S.M.P., B.P. 87, 91003 Evry (France) (Received December 10, 1977; in revised form February 21, 1978)
SUMMARY
The cyclic response of WASPALOY, a ~/' strengthened nickel-base superalloy, was measured as a function of 7' precipitate size. Specimens with precipitates larger than the critical size for dislocation looping, 25 nm, cyclically harden to saturation. Samples with smaller, easily shearable precipitates, 8 nm in diameter, harden to a maximum stress, then markedly soften, while those at the critical size soften slightly. Cyclic saturation is due to a dense dislocation substructure which fills the inter-slipband volume. In material with precipitates 25 nm and smaller, shearing of the precipitates, combined with a localization of plastic flow in persistent slip bands, leads to cyclic softening. The marked softening in the 8 nm material is due to the complete mechanical disordering of the precipitates within the slip bands. A model whereby the slip band density is linearly related to the applied strain is proposed to account for the observation that a constant number of cycles to maximum stress exists in the 8 nm alloy.
INTRODUCTION
When a material is subjected to cyclic plastic strains, a series of events takes place which leads eventually to fatigue failure. Though the dividing line between these events is often n o t well-defined, three main processes can be isolated: ( i ) a change in the deformation behavior of the material due to cyclic straining, (2) nucleation of an incipient fatigue crack, (3) the propagation of that crack to a critical length for final failure. Of the three, the me*Present address: Sandia Laboratories, Division 8316, Livermore, CA 94550, U.S.A.
chanical response to cyclic Plastic strains is often the most sensitive to the alloy microstructure. Cyclic response can be measured in a number of ways. The level of the cyclic stressstrain curve indicates whether, in the cyclically stable state, the alloy is stronger or weaker than in the virgin condition. A more detailed approach, however, is through the use of the cyclic response curve, where the applied stress is plotted v s . number of cycles at a fixed plastic strain amplitude. These curves give not only the saturated cyclic flow stress (if saturation occurs}, b u t also the path by which the material arrives at its final flow stress level. Laird [1] has given an excellent review of the various types of cyclic responses observed and a list of the micromechanisms which govern each type of behavior. Briefly, annealed, single-phase materials tend to cyclically harden to saturation, while cold-worked alloys soften to a saturation value. At low plastic strains, carbon steels are seen to cyclically soften, then harden. Dispersion strengthened materials are usually stable, while bulk ordered alloys and alloys strengthened by ordered precipitates show hardening followed by softening. It is the latter phenomenon of hardening followed by softening to which this work is principally addressed. The current theory proposed by Calabrese and Laird [2] for A1-Cu 0" strengthened alloys is based upon a model of precipitate cutting by dislocations, leading to a loss of order strengthening and to overall softening. Direct observation of the interaction between ordered 0" precipitates and dislocations in the A1-Cu alloys investigated in their work was n o t performed. In this work, WASPALOY, a nickel-base superalloy strengthened by spherical, fully coherent precipitates of 7' (Ni3(A1,Ti)) was investigated. Due to the small co-
276 herency strains around the precipitates, the 7' phase can be imaged by dark-field-transmission electron microscopy. The other advantage of WASPALOY is that the size and spacing of the precipitates can be changed (at a fixed volume fraction) without changing the matrix composition. Two heat treatments with equivalent yield strengths were chosen for the major part of the work, one with 8 nm 7' particles which are cut by dislocation pairs, and one with 90 nm particles which are not initially sheared. (The deformation modes of an alloy similar to WASPALOY are reported by Pineau e t al. [3] .) The flow stress vs. number of cycles at various fixed plastic strains was measured and related to the nature of the dislocation-precipitate interactions by optical and transmission electron microscopy.
EXPERIMENTAL
All testing was performed on specimens from a single-swaged bar of WASPALOY. The composition is listed in Table 1, while heat treatments and resulting 7' sizes are given in Table 2. The 1 313 K (1 040 °C) solutionizing temperature was chosen in order fully to dis-
solve the primary 7' and to avoid excessive grain growth. The final grain size determined by a linear intercept method was approximately 60/~m. Fatigue specimens with a cylindrical or hourglass reduced section, 5 mm in diameter, were cut parallel to the axis of the bar. R o o m temperature fatigue testing was done in an Instron modified to cycle between constant total strain limits. The plastic strain was held constant by frequently adjusting the total strain amplitude. Both diametral and longitudinal extensometers, accurate to strains of 10 -4 , were employed. All plastic strains quoted are longitudinal strains, converted, when necessary, from the measured diametral plastic strains. The nature of the fatigue-induced slip bands was studied by both optical and transmission electron microscopy. Fatigued specimens were spark cut for microstructural analysis below the fracture surface in failed samples, and at the minimum cross-section in unfailed specimens. Samples for optical analysis were first electropolished and then etched in a solution of 16 g FeCI3, 9 g (NH4)2S2Os, 100 ml H20, and 60 ml HC1 at 313 K (40 °C). Thin foils from fatigued samples for TEM were dual-jet thinned in a 5% perchloric-acetic acid solution at 290 K (17 °C) and 60 V.
TABLE 1 Composition of WASPALOY (wt. %)
C
Cr
Co
Mo
Ti
A1
Zr
B
S
Si
Cu
Fe
Ni
0.04
19.3
13.9
4.0
3.07
1.37
0.07
0.004
0.003
0.02
0.01
0.01
Bal.
TABLE 2 Heat treatments and resulting 7 ~sizes
diameter (nm)
Experimental Solutionize
Commercial Solutionize
1 313 K (1 040 °C)/ 2 h, oil quench
Age 1 003 K (730 °C)/6 h Age 1 098 K (825 °C)/24 h Age 1 148 K (875 °C)/24 h
1 283 K (1 010 °C)/ 4 h, oil quench
Age 1 123 K (850 °C)/4 h Aircool +
Age 1 033 K (760 °C)/15 h
8 50 90
25
277
RESULTS
Cycle response
Cyclic response curves (stress vs. cycles at a fixed plastic strain amplitude) are given in Figs. 1 and 2 for the 90 nm and 8 nm cases, respectively. While the initial flow stress (at N = 1) is equivalent for the two alloys, the cyclic response is quite different. The 90 nm material, Fig. 1, exhibits an extensive hardening period up to a saturation stress value. The arrows in Fig. 1 indicate the onset of saturation, and show that the lower the plastic strain, the larger the number of cycles to saturation. The final stress drop for ep = 0.50 and 0.83 percent, is due to the formation of macrocracks and we therefore will consider only the behavior up to saturation. By con-
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trast, for the same plastic strains, the 8 nm alloy hardens then sharply softens, Fig. 2. It is interesting that the number of cycles to the m a x i m u m stress, N(amax), indicated by arrows, is approximately the same, 20 - 30, regardless of imposed plastic strain. The final stress drop for the 0.83 and 0.50% tests is due to the nucleation of a macrocrack. Two additional cyclic response tests at ep = 0.50% were run on alloys with 25 nm and 50 nm precipitates sizes. The cyclic response for all four alloys is given in Fig. 3. A normalized stress, ON/OZ,where o l is the stress at the first cycle, is plotted against number of cycles. Only 500 cycles are shown in order to exclude any effects of macrocracking. The 50 nm alloy hardens to saturation in the same number of cycles as the 90 nm alloy, but to a lower saturation stress level. The 25 nm material hardens initially at a faster rate than the other alloys, but reaches a m a x i m u m at approximately 40 cycles, and exhibits only slight softening. M icrostructure
The slip band structure of the 90 nm and 8 nm heat treatments, tested at a plastic strain amplitude of 0.5% is summarized in Fig. 4. After 40 cycles the 90 nm material is still in the hardening stage. Each grain shows the beginning of slip band formation (Fig. 4(a)). The etching response between the slip bands suggests the presence of a uniform deformation network. After cycling to failure, Fig. 4(b)), the slip bands and underlying substructure are more fully developed.
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F i g . 2. C y c l i c response curves f o r W A S P A L O Y with 8 n m ~?' p r e c i p i t a t e s i n d i c a t i n g h a r d e n i n g f o l l o w e d b y softening. The m a x i m u m stress occurs at N ~ 2 5 , r e g a r d l e s s o f p l a s t i c strain.
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278
(a)
(b)
(c)
(d)
Fig. 4. Optical mierographs of persistent slip bands in WASPALOY tested at 0.5% plastic strain: (a) 90 nm ~" case, 40 cycles, (b) 90 nm t ease, 1 400 cycles, (c) 8 nm ~? case, 40 cycles, (d) 8 nm 7t ease, 2 500 cycles.
In the 8 nm case, 40 cycles is just past the hardening maximum. Discreet slip bands have formed in the majority of the grains, Fig. 4(c), with no evidence of deformation between the slip bands. At failure, Fig. 4(d), the slip bands have intensified and thickened, but all of the deformation remains confined to the slip band regions. Higher magnification photographs show that the intense slip bands are composed of closely spaced finer bands. It is important to note that all of the above micrographs are from polished and etched regions at the center of the specimen, or from below the surface of fractured specimens, and thus represent the bulk fatigue damage caused by cyclic straining. The major difference in the deformation behavior of the two cases is
in the degree of strain inhomogeneity. A homogeneous substructure is present in the 90 nm specimens, in addition to the persistent slip bands. On the other hand, the absence of slip in the interband regions of the 8 nm samples indicates a strong localization of plastic flow and a highly inhomogeneous mode of fatigue deformation. Thin foils were prepared from the 8 nm and 90 nm samples tested 40 cycles and 1 000 cycles at a plastic strain amplitude of 0.5%. The general observations made by optical microscopy were confirmed by TEM. Figure 5(a) is of the 90 n m alloy tested 40 cycles. A loosely organized primary slip band is shown along with the beginning of activity on a secondary slip system. At this point along the
279
(a)
Shearing of the 8 nm 7' particles results in a much different dislocation substructure when compared with the 90 n m precipitates. After 40 cycles, sharply defined slip bands, often only two or three slip-planes thick, are present. Dislocation activity along each band is n o t uniform across the grain, with a greater density at slip band intersections. After 1 000 cycles, the slip bands are fully developed across the grain, and slip remains confined only in the slip band regions. By tilting the foil to a [110] orientation where the primary [111] slip planes are "edge on", Fig. 6(a) and (b), it can be seen that each macroband is composed of smaller microbands. Using the [300] 7' reflection to image the precipitates, Fig. 6(a), one notes that the ordered precipitates are absent from the micro slip band volume. Care was taken to tilt the foils to verify that no intensity from the [300] 7' spot was present in the slip bands. In Fig. 6(b), from another region in the sample, it can be seen that the slip band channels are swept clean of ~' particles, though, in places, the
(b) Fig. 5, Transmission electron micrographs of the 90 n m 7' case tested at 0.5% plastic strain: (a) 40 cycles, (b) 1 000 cycles.
hardening curve a large fraction of each grain volume is still free from dislocations. By contrast, after cyclic saturation to 1 000 cycles, the dislocation substructure completely fills each grain. Figure 5(b) is of the inter-slipband region. A large number of dislocation interactions have occurred due to the bowing of dislocations around the particles, and a network of dislocation segments extends between each particle. Within the slip bands, the dislocations are more densely arranged, but the gradient of dislocation density is sharply defined between slip band and interband region. As a general observation, saturation occurs once the overall network has filled the grain volumes.
(a)
(b) F!g. 6. Transmission electron micrograph of the 8 nm 9' case tested at 0.5% plastic strain. (a) Dark field view of "edge o n " slip bands, (b) higher magnification dark field view of "edge o n " slip bands, [011 ] zone axis, [300] 7 r reflection.
280
process is not complete (A). The darker regions (B, C) result from residual dislocation contrast, and analysis of these dislocations indicates that they are segments from secondary slip systems extending between the primary bands. Furthermore, contrast experiments show that within each slip band, cyclic deformation leads to dislocation interactions which destroy the usual pair-wise arrangement that exists after monotonic deformation [3]. Two further TEM observations were made on the 50 nm and 25 nm alloys cycled for 1 000 cycles at ep = 0.5%. The dislocation substructure in the 50 nm material was similar to the 90 nm alloy. Dislocation bowing results in coarse slip bands and tangles around the precipitates, along with a dislocation network filling the grain volume between the bands. In the 25 nm alloy, due to the distribution of the 7' particle sizes, both precipitate shearing and bowing is observed locally along the slip plane. (In WASPALOY, 25 nm is the critical size for the shearing-bowing transition [3] .) As with the 8 nm alloy, slip is confined to discreet bands with no overall dislocation network throughout the grains. Dark field microscopy shows, however, that while the precipitates are sheared, fragmented ~' particles still exist after 1 000 cycles within the slip band volume, Fig. 7.
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loys. Figure 8 is a cyclic response curve of the 8 nm alloy, cycled at 0.83% plastic strain, and annealed after partial softening. Annealing was done at 1 003 K (730 °C), the aging temperature of the alloy, in a vacuum furnace backfilled with argon to prevent surface oxidation. Upon retesting in fatigue after annealing, the flow stress is higher, indicating that a large fraction of the strength lost through softening is recovered. During further fatigue cycling the alloy hardens to a higher maximum stress than previously attained, and then again cyclically softens. The n u m b e r of cycles to maximum stress is reduced by the annealing treatments. Optical micrographs were taken of the specimen tested for Fig. 8 (two anneals and cycled to failure) along with a companion specimen tested 110 cycles at 0.83% plastic strain. In the sample tested 110 cycles, Fig. 9(a), a single set of slip bands is present in most grains. By contrast, the alloy annealed twice exhibited the majority of grains with two and three sets of slip traces, Fig. 9(b).
DISCUSSION
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Annealing experimen ts Previous work [2, 4] has shown that short time thermal treatments can significantly affect the behavior of cyclically softened al-
Cyclic response The above results show that the cyclic response of WASPALOY is highly sensitive to the details of the dislocation-precipitate interaction. The two aspects which control cyclic response are: (1) the mechanical stability of the precipitates during reverse plastic straining, (2) the ability of the material to distribute the plastic strains over the grain volume. In the 90 n m and 50 nm 7' alloys, dislocation bowing to form Orowan loops leads to cyclic hardening and stability of the alloys. During reverse plastic straining, the complex dislocation interactions that occur
281
(a)
(b) Fig. 9. Optical micrograph of the 80 nm 7' material tested at 0.83% plastic strain. (a) 110 cycles, (b) cycled and annealed.
around the precipitates, Fig. 5(b), force dislocations o u t of their primary slip plane, creating a "plastic zone" around each particle. The link-up of these zones results in a threedimensional homogeneous substructure, and the eventual cyclic stability of the material. When the precipitates are below 25 nm, the critical size for dislocation bowing, the alloy is no longer able to redistribute the plastic strain throughout the grain volume and cyclic
softening occurs, Fig. 2. A number of other alloys exhibit similar cyclic response behavior, including: other Ni-base alloys strengthened b y 7' or 7" [6, 7] A1-Cu strengthened by 0" [ 2 ] , ordered NiaMn [8] and Cu3Au [9]. Softening is thought to occur in these alloys through a disruption of local, ordered atomic arrangement. This atomic rearrangement results in a reduction locally in the amount of ordered phase and a loss in the order contribution to strengthening [1]. There are interesting differences in the cyclic response curves of these alloys and they can be divided into t w o subclasses: that typified by A1-Cu-0" [2] and that by WASPALOY in Fig. 2. While the number of cycles to maxim u m hardening, N(oma~), in the 8 nm 7' case of WASPALOY and in Udimet 700 [6] is a constant in respect of plastic strain, A1-Cu-0" and the other alloys show an increase in N(Oma~) with decreasing strain. An analysis of the data for A1-Cu-0" (ref. 2, Fig. 2) indicates that the hardening maximum occurs at a critical cumulative plastic strain, N(om~) × % = 65.0%. In A1-Cu-0" alloys, intense slip bands develop from the underlying substructure and, thus, a dense network of dislocation debris exists between the bands. Since softening is due to the repeated shearing of the 0" precipitates, then the onset of cyclic softening should, and does, occur at a constant cumulative plastic strain. In WASPALOY with 8 nm 7' precipitates, all the plastic strain is localized in slip bands from the onset of plastic straining. If the kinetics of hardening and softening processes which govern the cyclic response are the same in each slip band regardless of plastic strain, then, in order to accommodate the higher strains, the number of slip bands must increase linearly with strain. This would account for the fact that the number of cycles to maxim u m hardening is constant. A similar model can explain the behavior of Udimet 700, where Wells and Sullivan [6] observed that all the slip bands necessary to accommodate the fatigue strain are nucleated during the first strain cycle, and that any subsequent plastic flow occurs within the same bands. In order to verify the model that the number of slip bands increases proportionately with plastic strain, three specimens of the 8 nm material were cycled for 100 cycles at 0.83, 0.50 and 0.24% plastic strain amplitude.
282
The samples were then sectioned and the interslip-band spacing, which is inversely proportional to the number of bands per grain, was measured. As shown in Fig. 10, the average spacings are linear with plastic strain. As far as the exact hardening and softening mechanisms that occur within the slip bands, the model of Calabrese and Laird [2, 5] is applicable to the 8 nm WASPALOY. Since the initial dislocation density is low at the beginning of cycling, dislocation generation and interaction lead to a net hardening component. During the hardening stage, jog formation and intersections with secondary slip systems destroy the organized superlattice pair motion and cause the slip bands to thicken. The back and forth motion of this disorganized array of dislocations shears the 8 nm 7' precipitates on each (111) plane so that locally, within the slip band, the amount o f ordered phase is reduced to zero. It is most likely that softening begins at the first strain cycle, so that measurements of the softening component taken from N(oma~) do not account for all the softening that has taken place. The reason WASPALOY reaches its hardening maximum, N(omax) = 25, is, as yet, unclear, though the value of N(amax) should depend upon the size of the precipitates and the grain size. The absence of 7' intensity within the slip band volume, using the [300] 7' superlattice reflection, Fig. 6(b), supports this softening mechanism. The slip bands are intrinsically softer than the alloy in its virgin condition because the hardening c o m p o n e n t due to the ordered second phase is lost. There is some controversy as to the interpretation of dark field micrographs such as Fig. 6(b). Specifically, it is questioned whether the absence of superlattice intensity is due to the absence of an ordered phase, or simply a non-imaging artifact due to local perturbation of the lattice
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I
0.50
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Fig. 10. Average inter-slip-band spacing, X, v s . applied plastic strain, ep, for the 8 nm case, after 100 cycles.
by dislocations. The presence of 1" particles along a slip plane within the denuded volume of the slip band (at A in Fig. 6(b)) indicates that if ordered particles are present within the band, they can be imaged. In the denuded region, however, the particles are sufficiently randomly sheared so as n o t to produce any superlattice intensity. Softening during cycling occurs within the slip bands through a progressive shearing of the 8 nm precipitates, which leads to spreading and thickening of the denuded regions. In order for the softening to be complete, however, shearing must occur on each slip plane that intersects the precipitate. In the 25 nm samples, even after 1 000 cycles, the 7' particles can still be imaged within slip bands, indicating that they have not been effectively sheared enough to destroy all the local order. The relative amount of softening is thus less in the 25 nm case compared with the 8 nm material, Fig. 3. Tilting experiments indicate that the occasional Orowan loop, left around the largest precipitates in the slip band, interacts with nearby dislocations on parallel slip planes, thus spreading o u t the shearing action over a wider distance. Instead of being sheared on each slip plane the precipitates are fragmented. Some softening occurs from this fragmentation process because the effective particle radius is reduced, b u t the softening is n o t as complete as in the 8 nm material.
Annealing behavior Since the cyclic softening of the 8 nm 7' takes place at room temperature, no longrange diffusion of the A1 or Ti atoms occurs. (Precipitation does n o t occur below 630 °C [3] .) The mechanical shearing action of the dislocations results in atomic rearrangements over small distances, of the order of a few atom spacings. In this case, short time anneals should re~stablish the local order and recover the softening component. Figure 8 shows the effects of t w o anneals of 10 min/730 °C on the cyclically softened WASPALOY. Similar annealing experiments have been performed on the A1-Cu alloys [ 2 ] , and the behavior of the two alloys is somewhat different. After annealing a cyclically softened A1-Cu alloy, the initial flow stress of the material is reduced. The alloy does, subsequently, harden and then soften, indicating that reordering has taken place, b u t some re-
283 covery in the overall dislocation substructure must have occurred as well. In the case of WASPALOY, no inter-slipband dislocation structure is present. During the thermal treatment the sheared 7' particles coalesce and reorder, but, at the same time, pin the dislocations within the bands. Upon recycling, the flow stress is higher because new, less favorably oriented slip bands on secondary slip systems must be nucleated. (Note that in Fig. 9(b) many grains exhibit three sets of slip traces.) During cycling after heat treating, both the new slip bands and the previously established bands undergo softening, b u t since most of the dislocations necessary for softening already exist in the older bands, the hardening maximum occurs after a fewer number of cycles.
Implication o f cyclic softening in selection of fatigue resistant alloys Numerous reviews on alloy design for fatigue resistance have emphasized the need for materials which resist cyclic softening [10 1 3 ] . The above results demonstrate that in alloys strengthened by ordered precipitates, t w o features are necessary before cyclic softening occurs. First, there must be an instability in the microstructure so that locally, a softer region can develop. Second, the volume of material where the instability occurs must constitute a large fraction of the total volume of material undergoing plastic strain. In the 8 nm case of WASPALOY, the random shearing of the 7' leads to a locally soft region. In addition, all of the deformation is concentrated in the softened region so that both criteria are fulfilled. In the 90 nm material, the alloy is cyclically stable because the dislocations in between the slip bands offset any local softening that may occur within the bands. By comparison, in the A1-Cu-0" alloy [2] the overall dislocation structure is n o t sufficient to overcome the slip band softening, indicating that the degree of strain localization at which softening occurs depends upon the particular alloy. The key feature of all these alloys, however, is that softening and strain localization go hand-in-hand. Materials strengthened by a dislocation structure, such as maraging steels and coldworked copper, also cyclically soften [4, 13]. In these alloys, strain localization is not essential because the softening is due to a re-
arrangement or " s h a k e d o w n " of the preexisting dislocation structure. Though both the precipitation-strengthened- and the substructure-strengthened alloys which cyclically soften should be avoided in fatigue applications due to the loss in strength, the strainlocalized alloy tends to be worse in terms of crack initiation resistance and environment sensitivity due to the localized nature of the fatigue deformation.
CONCLUSIONS The cyclic response (stress vs. number of cycles at a fixed plastic strain) of WASPALOY is a function of 7' precipitate size. Specimens with precipitates larger than the critical size for dislocation bowing (50 nm and 90 nm) cyclically harden to a saturation stress value. Materi.1 with precipitates at the critical size (25 nm) hardens then softens slightly, while those with smaller, shearable precipitates (8 nm) harden to a maximum stress, then markedly soften. The number of cycles to maximum stress is constant with plastic strain in the 8 nm material. Cyclic saturation in the 50 nm and 90 nm alloys is due to a dense dislocation substructure which fills the interslip band regions. In the 25 nm and 8 nm alloys, shearing of the precipitates, combined with a localization of plastic deformation within slip bands, leads to cyclic softening. The marked softening of the 8 nm alloy is due to the complete mechanical disordering of the precipitates within the slip bands. A qualitative model is proposed to account for the constant number of cycles to maximum stress in the 8 nm alloy. The model predicts that the slip band density is a linear function of applied plastic strain and is applicable to other highly strained localized alloys such as Udimet 700.
ACKNOWLEDGMENTS This work was performed at the Centre des Materiaux, ENSMP, Evry, France. The financial support of the French government (CIES) is gratefully acknowledged along with the technical support of A. Hue, G. Baudry and D. Fournier.
284 REFERENCES
1 C. Laird, in R. J. Arsenault (ed.), Plastic Deformation of Materials, Vol. 16, Academic Press, New York, 1975, p. 101. 2 C. Calabrese and C. Laird, Mater. Sci. Eng., 13 (1974) 141. 3 A. Pineau, F. Lecroisey and M. Sindzingre, Acta Metall., 17 (1969) 905. 4 L. F. Van Swam, R. M. Pelloux and N. J. Grant, Metall. Trans., 6A (1975) 45. 5 C. Calabrese and C. Laird, Mater. Sci. Eng., 13 (1974) 159.
6 C. H. Wells and C. P. Sullivan, Trans. ASM, 57 (1964) 841. 7 H. F. Merrick, Metall. Trans., 5 (1974) 891. 8 C. E. Feltner and C. Laird, Am. Soc. Test. Mater., STP 467, 1970, p. 77. 9 K. H. Chien and E. A. Starke, Jr., Acta Metall., 23 (1975) 1 173. 10 J. C. Grosskreutz, Metall. Trans., 3, (1972) 1 255. 11 J. C. Grosskreutz, Proc. Third Int. Conf. Fracture, Munich, PLV-212, 1973. 12 R. M. Pelloux and R. E. Stoltz, Optimization of microstructure for fatigue resistant engineering alloys, 4th Int. Conf. Strength of Metals and Alloys, Nancy, France, 1976. 13 C. E. Feltner and C. Laird, Acta Metall. 15 (1967) 1 621.