High temperature cyclic deformation of precipitation hardened alloy—II. Fully coherent precipitates

HIGH TEMPERATURE CYCLIC DEFORMATION OF PRECIPITATION HARDENED ALLOY-II. FULLY COHERENT PRECIPITATES SHRIK.LC’T

P. BHATt and CAiiPBELL

LAIRD

Department of bletallurgy and Materials Science. University of Pennsylvania. Philadelphia. PA 19104, U.S.A. (Receiced

14 February

1979; in

retisedform

4 JUW

1979)

experimental investigation into the cyclic stress-strain behavior of an Alilqb Cu alloy aged to contain 0”. as a function of temperature is reported. Tests are carried from room temperature up to the aging temperature of the alloy. At all temperatures this microstructure cyclically hardens to a peak and then continually softens. By analysing the hysteresis loops. it is shown that the component of the friction stress due to the precipitates goes through a peak. Structural observations on specimens cycled at room and higher temperatures are examined under various mechanisms suggested in the literature for cyclic softening in these alloys. Using the unidirectional hardening theories for ordered precipitates for cyclic straining conditions, it is shown that both hardening and softening are predicted by considering dislocation interactions with ordered precipitates. Abstract--An

R&m&-Nous prCsentons une etude exptrimentale du comportement 6 la diformation cyclique d’un aliiage A1-4T0 Cu vieilli pour contenir du 0”. en fonction de la tempt?rature. Les essais sent effect&s depuis la temperature ambiante jusqu’B la temperature de vieillissement de I’alliage. A toutes tempiratures. la microstructure durcissait cycliquement, passait par un pit, puis s’adoucissait continuellemenr. L’anaiyse du diagramme d%yst&se montre que la composante de la contrainte de frottement diie aux prtcipites passe par un pit. Nous avons examini la structure d’&hantillons deform& cycliqucment h I’ambiante et B haute temperature, B la lumiire des divers mecanismes proposbs dans la Iitterature pour I’adoucissement cyclique de ces alliages. En utilisant les theories du durcissement unidirectionnel dans les pr&ipit& ordonnis pour une diformation cyclique, nous montrons que le durcissement et I’adoucissement peuvent etre p&us. en considirant les interactions entre dislocations et pr&ipit&. zyklische Spannungs-Dehnungsverhalten der Legierung Al-4% Cu. enthaltend 0”. wird in AbhIngigkeit von der Temperatur (von Raumtemperatur bis zur Auslagerungstemperatur) untersucht. Bei allen Temperaturen verfestigt sich diese Mikrostuktur bis zu einem Maximum und entfestigt sich anschliel3end kontinuierlich. Die Auswertung der Hystereseschleifen zeigt, da13 die Komponente der von den Ausscheidungen herriihrenden Reibungsspannung durch ein Maximum IIuft. Beobachtungen der Struktur von Proben. die bei Raumtemperatur und bei hiiheren Temperaturen zyklisch verformt worden waren. werden mit verschiedenen. in der Literatur ftir zyklische Entfestigung vorgeschlagenen Modellen verglichen. Unter Benutzung der Verfestigungstheorien fiir einsinnige Verformung geordneter Ausscheidungen wird gezeigt, da0 bei der zyklischen Verformung sowohl Verfestiaung als such Entfestigung auf der Basis der Wechselwirkung von Versetzungen mit geordneten AusschGdungen vorhergesagt werden ktinnen. Zusammenfassung-Das

1. IhTRODUCTION In a companion publication [I] (hereafter referred to as Part I), it is demonstrated that an A1-4% Cu alloy aged to contain 0’ and subject to high temperature cycling rapidly reaches saturation even up to 0.56 of the matrix melting temperature. However, with continued cycling numerous changes in morphology of the platelike 0’ precipitates take place depending on the temperature and strain amplitude and eventually the 0’ precipitates transform to 8. In the present work, we report the cyclic stress-strain behavior of an A1-4% Cu alloy, aged to contain B”, as a function of temperature. A room temperature this microstructure shows work hardening to a peak stress and then gradually softens until fracture [Z]. This fatigue softening is t Present address: Inland Steel Research Laboratories, 3001 East Columbus Drive, East Chicago, IN 46312, U.S.A. 4.H.

27 12-c

attributed to some form of localized damage which occurs in the metastable precipitates and leads to the formation of persistent slip bands where plastic strain is assumed to be concentrated. Various mechanisms suggested for precipitate degradation are (a) overaging [3,4], (b) reversion or re-solution [3-81, (c) aging disorderinhomogeneities [9, 101, (d) precipitate ing[Z], and (e) Ostwald ripeningcll]. Indirect evidence has been presented in support of these mechanisms in the references quoted above. Bret and Doherty [12] used chemical analysis of the PSBs with the hope of discriminating these various mechanisms. However, the results ruled out only (a) and (c). Calabreve and Laird [2] have pointed out the questionable nature of the evidence advanced in support of mechanism (b). Fournier and Pineau Cl33 have obtained direct evidence in support of the precipitate disordering mechanism, (d), in Inconel 718. However, such direct evidence is lacking in AI-CU alloys. experimental difficulty stemming from the small size of the pre-

1873

1874

BHAT

AND

LAIRD:

II FULLY COHERENT PRECIPITATES

CUMULATIVE

STRAIN,

EAhrp -

Fig, 1. Cyclic response curves for the 0” structure: (a) Plastic strain amplitude = 0.001; (b) Plastic strain amplitude = 0.01.

cipitates. Therefore, for this alloy. we stiU have to depend on indirect evidences. Most of the previous studies on Al-Cu alloys were carried out at room temperature. We report here new results of cycling the 8” microstructure at high temperatures. Emphasis is placed on bulk deformation aspects; suriace observations related to crack nucleation have been reported elsewhere [ 141. 2. EXPERIMENTAL

PROCEDURE

Details of the test apparatus, material preparation, and the techniques for structural observation are described in Part I El, 15j. The @”~~os~ucture was produced by aging for 5 h at 160°C foLiowing a 30 s solution treatment at 545°C used to control the grain size (0.1 mm). Structural characterization of microstructures containing 8’ is treated adequately in the literature [16-191 and was repeated routineiy here for purposes of con~oi~ng and checking the microstructure. The test temperatures chosen for the present investigation were ambient, 100°C and 160°C corresponding to 0.32.0.40 and 0.46 of the matrix melting point. The highest test temperature was chosen to equal the aging temperature of the ahoy. The tests were not carried out at stih higher temperatures because structural changes attendant on heating alone would have

been rapid enough to obscure the eff~s strain.

of cyclic

3. RESULTS 3.1 Phettomenological experiments Cyclic response curves obtained at the three test temperatures and the two strain amplitudes at each temperature are plotted in Figs. l(a) and (h). The two strain amplitudes used were 0.001 and 0.01 giving typical lives of less than 10,000 cycles at room temperature. The flow stress values plotted are the averages of the peak tensiie and compressive stresses in each cycle. These cyclic response curves are unique in one respect; at all temperatures and strain amplitudes tested, they show work hardening to a peak stress and then gradual softening until fracture whereas pure metals and alloys show work hardening and then saturation [2OJ. This softening occurs by a gradual decrease in both the tensile and compressive parts of the cycle and is different from the fina crack related asymmetric softening. In Table 1 the peak cyclic flow stresses are summarized as a function of temperature and strain amplitude. Monotonic properties, the yield stress and the UTS, are also included for comparison. It is clear from this table that the hardening produced by cychc plasticity is quite pronounced compared to monotonic hardening at all

Monotonic proper&s

temperatures. Indeed the peak cyclic flow stresses exceed elen the UT5 by as much as Z-3036. 3.2 Srrucrurai obserwtions The aging treatment given to the alloy produces a homogeneous dispersion of 6“. and no aging eiTects such as precipitate free zones were observed except at grain boundaries. The @“ precipitates form as discs along the : it%; planes of the matrix and are about 25-30nm in diameter and about 25 nm distance apart. After cycling many changes were observed and the principal features are described as follows. 3.2. I Room rernperurtrrr cyling. The predominant effect of cycling was tht formation of several deformation bands i3 each grain. usually extending across the entire grain. For example. when the alloy was cycled at O.IYOplastic strain amplitude for 4500 cycles the resulting bands were about 0.2-0.25 m wide and 2 pm apart [Fig. 2(a)]. These bands consist of densely packed iragmented dislocations. Sensitivity of these bands to the iocal diffraction conditions is illustrated in Figs. Ztb) and (c), taken from the same area as that in Fig. I(a). The apparently empty band in 2(b) is brought to strong contrast in 2(c) after a smafl tilt. (Relative tilt of oniy O.S’f. Very often a tiit of 1’ or less was found sufficient to change the contrast from that of the matrix to that of the band. When observed under appropriate diffraction conditions, both the matrix and the bands were seen to be composed of a homogeneous dispersion of fragmented dislocations. Because of their small size, it is difficult to make out the preciss interaction between the precipitates and dislocations and after heavy deformation the strain fields of the disiocations overshadow those of the precipitates. However, no evidence for overaging or reversion as suggested by some previous investigations [_%7] was ever found. It appears safe to conclude from these observations that the deformation bands observed here are merely regions that are misoriented to the matrix by about 1’. These obsemations arr entirely cons&rent with those of Calabrese and Laird [Z]. Deformation bands were also seen after room remperature tensile deformation, Fig. 3. again, structurally thr bands and the matrix were similar in det,lils except for a small mis-orientation [cf. Figs. 3(bi (c)

and (d)]. fn this ease, however, neither the sands nor

the matrix were as hcaviiy packed with ?a_pented dislocations as were bands formed by cycling. 3.2.2. Hot stage microscopy. It was pointed out in Part I that in situ observations using the technique of hot-stage microscopy were very helpful in eiccidating the role played by the high temperature during cyclic deformation [l]. In the beIief that the hot-stage woutd also be useful here, a sample cut from the bvcimen cycled at O.ly/; piastic strain amplitude and at room temperature was selected for study. Figure Aa) shows a typical area prior to heating. Heating the sample for times up to 1 h at 100°C did not bring about any significant change. I-Iowever, the dislocation sructure within the band was found to have undergont annealing to some extent [cf. Fig. qb) and ‘]icf]. C& increasing the temprature to 160°C. the first tu nuclei were detected in about 20 min of heating [Fig. 4s: 3. Figure qd) and (e) correspond to a total annealing time of 30 min at 16O’C (in addition to 1 h at 1OO’C~Figure 4(d) shows an area where previously there had been a deformation band whereas Fig. 3(e) corresponds to a region away from the band. The noteworthy features of these micrographs are; fat @’transforms to @ without independent nucleation of B’ {except. perhaps. rarely); (bf the newly formed 8’ precipitates X=X fairly uniformly distributed throughout the matrix and the band; and (c) the B precipitates show a predominance of one habit plane. 3.2.3. Elevated temperature cycling. The buik deformation structure after cycling at 100°C w= almost identical to that at room temperature. Cycling even at 160°C resulted in deformation bands. %‘ith &crease in test temperatures. the bands were much Gder, e.g. w 0.6 w at 0.17: plastic strain amplitude [Fig. S(a)]. The band itself was primarily composed of densely packed fragmented, dislocations [Fig. 5!5t]. The complexity of the structures resulting from e&e high temperature cycling. and hence the extreme msirivity to the diffraction conditions are iilusrrared in Figs. 5{c-e). Although in most areas the heat?- dislocation tang&g obliterates the contrast from precipitates, often the diffraction pattern condxd the (ZOO} streaks from 0” and extra satellite SF:< irom 8’. Very careful tilting. particularly in thin rs-@ens of the foil, brings ti” [Figs. S(c)] or 0 [Fig. 51d!] into

Fig. 2. ial Microstructure

containing 6” cycled at ‘+

= 0.001 and at room temperature for 4500 cy :les,

showin? intense deformation bands and dislocation debris beween them. (bi and id illustrate the sensitivity of the band to local diffraction condition. Apparently empty band in fbf comes to st:rong contrast condition in (c) after a relative tilt of 0.5’.

tensile dJormation showing an intense Fig. 3. Microstructure containing 0” after room temperatur: delormation band and the effect of small tilts on the appearance of thz dislocation structure. The position of micrographs Ibl. (cl and (d) with respect to the appsrently rtnpiy band ars marked in [al.

better contrast. In Fig. 5(d) it is seen that, just as in the foils cycled at room temperature and subsequently heated, the /Y formed predominately on one habit. Occasionaliy, however, it was found that B precipitates growing along two independent directions meet across a diffuse region and in such areas 0’ plates with two orientations could be identified. One such area is shoNn in Fig. j(e).

sis of the hysteresis loops obtained during the life of a specimen is presented, as follows. The analysis adopts the concepts advanced by Kuhimann-Wilsdorf and Laird [2 I. 221 for copper single crystals. According to these authors, the friction stress (Go) and the back stress (gB) [2.3] for dislocation behavior in fatigued metals can be obtained irom the hysteresis loops as follows: OF=

4. DIS~SSIOS

GE f -

Gs

2

and The cyclic response curves of the A!-& alloy containing 0”. along with many other age-hardened alloys. exhibit first. hardening to a peak and then continuous softening. As noted in the introduction, the softening is attributed to some form of localized damage to the precipitates. It was also noted that structural observations and the interpretation of such observations used in support of some of the mechanisms are controversial [ZJ. For a ‘better understanding of the role of the precipitates during cycling. an analy-

where bE is the end or the maximum stress within a IoOp, and (TVis the stress at which reverse plastic deformation begins. For copper single crystals. these authors have demonstrated that crBand a major part of Go (equal in magnitude to ae) have a similar dependence on cumulative strain and that both come to an abrupt saturation after a transient. The behavior of the loop

187s

BWhf .ANDLAlRD:

fl FULLY COHEREST

Fig. 4. Hot-stage microscopy of the microstructore

PRECIPITATES

containing 6” and cycled at room temperatures (a)

Before heating;(b) structure of the baud after 1 h heating at 160°C; (c) 160°C. and 20 m.in of heating; (d) and (e) correspond to 30 min of heating at 160°C. (d) near the tract of a pre-existig @j area away Gem the deformation bands.

patches in copper at strains corresponding to the plateau and below is treated in terms of a Taylor dislocation lattice, which is used to determine the origin of the back stress and its connection with the friction stress (its major component). Jog-dragging and dispersed point defects make a small but additional contribution to the friction stress [22,24,25]. An attempt to extend these concepts to two-phase

deformation band;

alloys ‘is not str~ghtforward because the dislocation structures are different from those in homophase single crystals. However, the basic principles of the method should apply to exploring the role of the precipitates in contributing to the ‘ii-iction’ stress. By analysing the hysteresis loops for polynystalline nickel [26] we have verified that the main findings for pofycrystals agree with those for copper single crys-

Fig. 5. Microstructure containing 0” and cycled at 160°C showing intense deformation bands
tafs. Accordingly. we are confident of the suitability of

the merhod in its extension to poiyxystalline material. The hysteresis loops obtained for the specimen cycled at 17; plastic strain amplitude. and room temperature were analysed according to equation f 1) and the results are presented in Fig. 6. Several points may be noted. As in pure metals, Go comes to an abrupt

saturation after .a transient and remains practicalI>unchanged for the rest of its Me. It is particuiarl: noteworthy that Go remains constant even aider the macroscopic stress response of the alloy sho=s a Iarge softening. On the contrary, fiF continues 13 in232ase ever3 after c8 attains a saturation. However. Gr e%entually reaches a peak and begins to soitcn spaic, roughly corresponding to the macroscopic sok:ning.

BHAT

ASD

LAfRD:

II FULLY

COHERENT

PRECIPlT.ATE.5

400 I

f

x-x-x--+

0

j

/xyx-

0.01

0. I CUMULATIVE

-x_L.j

I

I

I

IO

STRAIN +

Fig. 6. Friction stress (oF) and black stress (a,) extracted from the hysteresis loops for the micrpstructure containing 0” cycled at room temperature and at a plastic strain amplitude of IX. Only the tension half of the hysteresis loops w&r used for this plotting.

Now, from the work of Kuhlmann-Wilsdori and Laird [21,22]. it is reasonable to assume that 4yU’$?Pirate should be roughly equal to oa and show a similar cycle dependency to that of oB (neglecting the jog-dragging and point defects contributions to CJ~).It then follows from Fig. 6 that only the component of the friction stress due to the precipitates Prc’ipi*3’e) goes through the peak during cycling. (OF

4.2 Siytrificance of strw.xural ohsrrrurions The predominant effect of cycling at room temperature or above is the formation of several deformation bands per grain. Detailed microscopy after cycling and after tensile straining has revealed that these bands are retions that are misoriented to the matrix by a few degrees. and are not regions devoid of precipitates as suggested in many previous investigations [S-7,27]. When observed under appropriate diffraction conditions, both the bands and the matrix reveal similar structural details. Although dislocation strain fields often obliterate those of the precipitates, no reduction in size of the 6” within the band (as compared to precycled material). was observed. This result is quite different from that of Wilhelm et al. [X] in Al-Zn-Mg, who did claim a reduction in the size of the precipitates. In addition, our hot-stage microscopy has not revealed any preferential nucleation site (0” aside, of course) for transformation to 0’. Thus, even if there is a strain localization and a change in the precipitate structure of 0” in the bands, it is not significant enough to change the kinetics of the transformation of 8” -+ 0’ with respect to that occurring in the matrix. In passing. the potency of the cyclic straining in inducing transformation to a more stable phase is emphasized. Similar cyclic strain enhanced transformation has been noted in Part I for &-0[1]. 4.3

Cylic

harden&

und sofbzning mrchauisms

The quantitative analysis of the cyclic hardeningsoftening mechanisms in age hardened alloys still

elude us because many mechanisms can play a role [2]. However, the hysteresis loops’ analysis presented in 4.1 suggests that only the friction stress due to the precipitates changes with cycling. This then rules out aging-inhomogeneity and reversion of 6’ into solid solution as being general mechanisms for the observed cyclic response, because reversion would only require a decrease of u~“‘Pitntc and not an initial increase with cycling as observed. Again, structural observations presented rule out reversion and overaging as possible mechanisms. It therefore appears most promising to examine the results in terms of the ‘order’ within the precipitate. Both cyclic hardening and softening are predicted by considering dislocation interactions with ordered precipitates. Because unidirectional hardening concepts have been found useful in understanding cyclic response [29-311 an attempt to apply the hardening theories of ordered precipitates to cyclic conditions is offered as follows. Gleiter and Hombogen [32] and Hombogen [33] have reviewed the hardening contribution from ordered precipitates. Applying the usual criterion of dislocations by-passing or penetrating the particles, we find that for the aging conditions employed here the slip dislocations penetrate the 0” particles [lj]. The additional stress (AT) needed to force the first dislocation through the particle is given by [33]

where d is the particle diameter and D the interparticle spacing. Note that usually, this equation is written in terms of volume fraction. However, it is recognized here that only for spherical particles ~3~1 we approximate djD =j’,‘3 where f is the volume fraction. Plate-like precipitates act as much more effective barriers to dislocation motion than equiaxed particles and therefore, the simple expression in terms of volume fraction is unsatisfactory. For the treatments given. d: D = X0& aging

BHAT A?;D LAIRD:

If FULLY COHERENT

@’ = 50 x 10-JJm-‘, and G.2 = 2.7 x 10” m-:. Substitution of these values &es 7APB

N

Ar = 36.75 MPa, or Ao = 112-45 MPa (using the Taylor factor), This essentially yields the increase in flow stress due to order in the particles. In considering what happens when the specimen is cycled, we have to consider two additional factors. Firstly, as shown by Dahlgren [34] the first dislocation to penetrate will sio&ificantly alter the energy-distance situation for the next dislocation, which will be forced to ‘hop’ on to the next available parallel slip plane. Therefore, it would not be possible for dislocations to cancel antiphase boundaries or to retrace their paths when the strain is reversed. Instead they tend to deform the precipitate at a distance away from the original cutting plane. Because new paths are being carved both in the forward and the reverse portion of the cycle, the stress needed to impose the applied strain may well continue to be represented by equation (2). In these polycrystals, as more and more grains begin to deform the hardening contribution to the overall flow stress increases, partly due to Schmid factor effects and partly due to the precipitate strength. In addition, the hardening due to the & contribution increases, because the dislocation density is increasing by mechanisms of statistical storage [35]. However, the dislocation density tends to saturate and also eventually all the grains become deformed. We envisage that most of the precipitates are penetrated all along their lengths and thus reach the maximum in flow stress. To consider what happens on continued cycling, we must take account of the following additional factor. Hornbogen [33] has pointed out that the local shear stress for ordered particles decreases as the number of dislocations n > 1 pass through the same slip plane, i.e. . Thus as more and more dislocations pass through an already opened channel, the ordering contribution decreases. Of course, in cycling, reversed motion of dislocations maintains the average geometry of the 8’ plates, even when the Hornbogen softening becomes operative. It should be emphasized that because of the Dahlgren hopping of dislocations the plates are not considered to be sheared in two but rather ‘scalloped’ along their length, thus maintaining the average geometry of the plates. The ultimate consequence of these cutting processes would be a disordered crystal structure of the plates [2]. In order to check for the accuracy of predicted stress values we need information about the hardening contributions

other than that due to order [equa-

PREClPITATES

1881

tion (2)], namely chemical hardening and the etTects of coherency strains, and modulus differences between matrix and precipitate. A lead to this can be found in the experiment by Calabrese and LairdCZ] in which they cycled an N-4% Cu alloy immediately after it was quenched to room temperature. The peak flow stress at 1% plastic strain was reported as 324MPa. Present results for 8” for the same strain amplitude give a value of 374 MPa. To a first approximation, all the hardening contributions other than that of ordering can be assumed to be the same in the two studies. Therefore, the increase in 300~ stress due to ordering is found to be ar teust 50 MPa, but it may well be hi&ter because Calabrese and Laird actually found evidence of cyclic-strain-induced-precipitation in the solid solution. In view of the uncertainties in this comparison it is considered that the value of the flow stress increment computed from equation (2) (112MPa) and the measured value (50MPa) are in fair agreement. It is worth noting that in equation (2). the only temperature dependent term is the modulus. The modulus corrected peak flow stresses are listed in Table 1. The results, in accordance with equation (2). show that the peak cyclic stresses (after correction) are independent of temperature. 4.4 Cyclic strain induced nansformarion of d The disordering of the 0” due to cyclic deformation also appears to influence the subsequent formation of 6’. One of the surprising observations both in hotstage microscopy and in high temperature farigue was that of stacks of 8’ of one habit. The effects of directional external stress imposed during transformation in promoting or retarding the formation of particular variants of !3’have been discussed by many authors [36-381. In fact, Stobbs and Purdy [39] suggest that the stacks are a feature of initial nuciearion and growth even in the absence of any stress biasin effects. However, all these studies refer to direct formation of 0’ from the matrix during aging It is unlikely that, after heavy cold work, 6’ would nucleate in the matrix independent of the pre-existing 8’. .4 more likely explanation lies in the deformation of 0”. When the microstructure containing 0” is cycled. dislocations of three different Burgers vectors are represented. However, one of them will be in the habit plane of precipitate and con~quently does not cause disorder in that plate when a dislocation of that Burgers vector passes through the precipitate [40,41]. The dislocation of the other two Burgers vectors are effective scramblers. It is likely that one of the sets of dislocations predominates in density because it is the primary set. When dislocations of this set are stored through interactions with 8” and other dislocations, they are often close to 0” plates. Although the precise interaction of the scrambling dislocations with the precipitates is not known, we assume that different amounts of edge and screw components will be adjacent to the plates with different habit planes_ Now, the

BHAT

1882

AND

LAIRD:

II FULLY COHERENT

6’ transformation is the relief of the excess coherency strain of 8”. Sin&z edge dislocations are most effective in relieving this strain, it is possible that the 0” plates with the highest proportion of adjacent edge components are the first to transform to 0’ and thus lead to the predominance of one habit plane in any given stack. It must however be pointed out that the 0’ observed here are in their early stages of growth and perhaps a more uniform population would evolve in the manner suggested by Stobbs and F’urdy [39] and Lorimer [42], if the opportunity for complete aging was given.

PRECIPITATES

first step in the B’-

5. SUMMARY AND CONCLUSIONS (1) At all temperatures and strain amplitudes tested, the microstructure containing 0” cyclically work hardens to a a peak and then gradually softens until fracture. The temperature dependence of the peak stress can be explained by the temperature dependence of the shear modulus. (2) Deformation bands that are mis-oriented to the matrix were observed in cycled materials at all temperatures. In addition, at the highest test temperature 8” was found to transform to 0’ in stacks of predominantly one habit. (3) By analysing the hysteresis loops along the lines suggested by Kuhlmann-Wilsdorf and Laird [22], it is shown that only the precipitate friction stress component goes through the peak during the life of a specimen. It is argued that this analysis in conjunction with structural observations rules out many of the mechanisms suggested in the literature for explaining cyclic response of this class of material. (4) It is suggested that both hardening and softening could be predicted by considering the interaction of dislocations with ordered precipitates. Quantitative agreement of the measured and computed values is fair. (5) Predominance of one habit in the newly formed 0’ is attributed to the accumulation of a higher proportion of adjacent edge components on any given set of 0” during the complex disordering processes due to cycling.

REFERENCES 1. S. P. Bhat and C. Laird, Acta merall. 27,000 (1979). 2. C. Calabrese and C. Laird, Mater. Sci. Engng 13, 141 (1974). 3. T. Broom, J. A. Mazza and V. N. Whittaker, J. Inst. Metal!. 86, 17 (1957). 4. R. F. Hanstock, J. Inst. Metal/. 83, 11 (1954). 5. A. J. McEvily, J. B. Clark, E. C. Utley and W. E. Hernstein, Trans. Metall. Sot. AlME 227, 1903 (1963). 6. R. K. Ham, Can. Metall. Q. 5, 61 (1966). 7. J. B. Clark and A. J. McEvily. Acta metall. 12, 1359 (1964). 8. C. A. Sutbbington, Acta metall. 12, 931 (1964). 9. C. Laird and G. Thomas, Int. J. Fructure Mech. 3. 81 (1967). 10. A. R. Krause and C. Laird, Mater. Sci. Engng 2, 331 (1967). 11. C. M. Sargent and G. R. Purdy, Scripra metall. 8, 569 (1974). 12. S. Bret and R. D. Doherty, Mater. Sci. Engng 32. 2.55 (1978). 13. D. Fournier and A. Pineau, Metall. Trans. A 8, 1095 (1977). 14. S. P. Bhat and C. Laird, in Fatigue Mechanisms (edited

by J. T. Fong). ASTM STP 675 (1979). In press. 15. S. P. Bhat, Ph.D. Thesis, Univ. of Pennsylvania, Philadelphia (1978). 16. R. B. Nicholson and J. Nutting, Phil. Msg. 3, 531 (1958). 17. &. B. Nicholson, G. Thomas and J. Nutting, J. Inst. Metall. 87. 429 (1958-1959).

18. A. Kelly and R: B. Nicholson, Prog. mater. Sci. 10, 193 (1963). 19. V. A. Phillips, Acra metall. 23, 751 (1975). 20. C. Laird, in Work Hardening in Tension and Fatigue (edited by A. W. Thompson), p. 150. AIME (1977). 21. D. Kulmann-Wilsdorf and C. Laird, Mater. Sci. Engng 27, 137 (1977).

22. D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci. Engng 37 (2). 111 (1979). 23. A. H. Cottrell, Dislocafions and Plastic Flow in Crystals, p. 111. Oxford (1953). 24. D. Kuhlmann-Wilsdorf, Mater. Sci. Engng. To be Published. 25. D. Kuhlmann-Wilsdorf, Mater. Sci. Engng. To be Pub lished. 26. S. P. Bhat and C. Laird, Unpublished research, University of Pennsylvania (1979). 27. S. P. Lynch, Metall. Sci. 9, 401 (1975). 28. M. Wilhelm, M. Nageswararao, and R. Meyer, in Fa‘atigue Mechanisms (Edited by J. T. Fong), ASTM STP 675 (1979). In press. 29. C. E. Feltner and C. Laird, Acta merall. 15, 1633 (1967). 30. S. P. Bhat and C. Laird, Fatigue Engng Mater. Srructures 1.59 (1979).

31. S. P. Bhat and C. Laird, Fatigue of Engng Mater. Structures 1, 79 (1979).

32. H. Gleiter and E. Hombogen,

Mater.

Sci. Engng 2,

285 (1967/68).

Acknowledgemen&-This work was supported by the National Science Foundation under Grant No. DMR 73-07.541 and DMR 7621926 and by a grant from Alcoa Foundation. This research is related to that carried out in the Materials Failure Thrust area of the Laboratory

for Research on the Structure of Matter, and we gratefully acknowledge both the provision of testing facilities and the help of Mr. R. de la Veaux, Mr. R. G. White and Mrs. N. Y. C. Yang. We wish to thank Drs. R. Sankaran and D. KuhlmannWilsdorf for their critical reading of the manuscript.

33. E. Hornbogen, Proc. 3rd Int. Co& Strength of Metals and Alloys,-Cambridge, p. 108. (1973). S. Dahlaren. Metall. Trans. 7A. 1401 119761 M. F. ishdy, in Strengtheninb Methods in Crystals (edited by A. Kelly and R. B. Nicholson), p. 137. Elsevier (1971). 36. W. F. Hosford and S. P. Agarwal. Metall. Trans. 6A, 487 (1975). 37. R. Sankaran, Merall. Trans. 7A, 770 (1976). 38. T. Eto, A. Sato and T. Mori, Acta metall. 26, 499 (1978).

39. W. M. Stobbs and G. R. Purdy. Acra metall. 26, 1069 (1978).

BHAT

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