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The effect of precipitation hardening on the portevin-le chatelier effect in an AlMgSi alloy
THE EFFECT OF PRECIPITATION HARDENING ON THE PORTEVIN-LE CHATELIER EFFECT IN AN Al-Mg-Si ALLOY D. M. RILEY and P. G. McCORJIICK* School of Xfetaliurgy. University of Nzw South Wales. Kensington, N.S.tV., Australia (Receired 16 .V:zy 1976) Abstract-The influence of precipitation hardening on the characteristics of serrated yielding in an Al-IMg-Si alloy has been investigated. The critical strain at the onset of serrated yielding was increased by ageing and for ageing times longer than 6 hr at 180°C serrated yielding was not observed. The strain ageing time for solute locking was found to increase on ageing for 1 hr and remain constant with further ageing to 1 hr. The exponent of strain. m f /3, in the critical strain-strain rate refation was also increased by ageing. The results are discussed in terms of changes in the matrix solute concentration, the rate controlling obstacles. and the obstacle spacing accompanying the ageing process. Resume--On a etudie I’intluence du durcissement par precipitation sur les caracteristiquer des discontinuites de la contrairte dans un alliage Al-Mg-Si. La deformation critique pour l’apparition de ces discontinuitts augmentait par revenu. et on ne I’observait plus pour des vieillissements a 1SO’C de duree superieure a 6 h. On a trouve que le temps de vieillissement pour le blocage par le solute augmentait pour un revenu dune heure, et restait constant pour un vieillissement allant jusqu‘a 4 h. L’exposant m I- /3 de la deformation dans la courbe deformation critique-vitesse de deformation augmentait aussi par vieiiiissement . On discute ces resultats 6 partis drschangements de la concentration du solute daus la matrice, des. obstacles controlant la vitesse et de l’espacement des obstacles au tours du recuit. Zusammenfassung-Der Einflui3 der Ausscheidungsverfestigung auf die Eigenschaften des ruckweisen FlieDens wurde an einer Al-Xfg-Si-Legierung unterrucht. Durch Altern wurde die kritische Dehnung beim Einsatz des ruckweisen FlieDens vergriioert; bei Alterungszeiten grinder als 6 Stunden bei 1SO’C wurde ruckweises FlieBen nicht beobachtet. Die Reckalterungszeit fur Losungsverfestigung wird gri%er bei einsttindigem Altern und bleibt konstant bei llngerem Altern bis 4 Stunden. Der Reckexponent m + p in der Beziehung kritische Reckung-Reckgeschwindigkeit wurde ebenfalls durch Altern vergrijf3ert. Die Ergebnisse werden auf der Basis von Vednderungen in der Matrixkonzentration geltjster Atome, in den g~ch~vindigke~tsbestimmend~n Hindernissen und in dem den Alterungsprozess begfeitenden H~ndernisabstand diskuriert.
1.
INTRODUCTION
The Portevin-Le Chatelier Effect has been investigated in many alloy systems in recent years [l, 21. Although many of the studies have been carried out in alloys capable of being precipitation hardened. few studies of the effect of precipitation hardening on serrated yiefding have been reported since the early work of Lubahn [3] and Phillips [4]. Lubahn and Phillips found that precipitation hardening delayed the start of serrated yielding to strains higher than that measured in as-quenched samples, and that ageing to near peak strength conditions eliminated serrated yielding [3,4]. Similar effects of precipitation hardening in delaying the onset of serrated yielding have been observed in AI-Nlg [YJ and %Ig-Ag [6] alloys. However, recent work by Lloyd rr nl[7] has shown that the onset of serrated vieldina in a Co-Xi-Cr-Ti super-alloy is decreased by precipitation hardening. * Now at: Department of Mechanical Engineering. University of Western Australia Nedlands. W.A. 6009.
In the static strain ageing fS, 91 - - model _ _ for the Portevin-Le Chatelier effect. the onset of serrated yielding is attributed to the interaction of solute atoms and mobile dislocations temporarily arrested at obstacles in their slip path. Serrated yielding is assumed to initiate when the waiting time, c,, of dislocation arrested at obstacles, is equal to the strain ageing time required for solute locking, r,. The waiting time, t,, may be expressed in terms of the applied strain rate .?c a3
tw-_pLb g ’
(I)
where p is the mobile dislocation density and L is the obstacle spacing. Using the Cottrell-Bilby strain ageing model [IO], r, may be expressed as f,
2
ic,I \
-
cn\3:2
XC0
1
kn?”
L’, C,Do exp( - Q,/kT)
(3
where C, is the local solute concentration at the arrested dislocations required for locking, C, is the 181
IS’
RILEY
.ASD
McCQRMICK:
PRECIPITATES AND THE PORTEVIN-LE
matrix solute concentration of the alloy. x 1 3, U,,, is the solute-dislocation binding energy, C, is the vacancy concentration, 0, is the diffusion frequency factor, and Q,, is the’ activation energy for solute migration, Equating equations (1) and (2), the critical strain. E,, at the onset of serrated flow is expressed as
2.
CHATELIER
EXPERIJIEWT.AL
EFFECT
METHOD
A commercial 6063 Al-Mg-Si alloy containing 0.7:$‘bMg and O.lil/l;Si was used in this study. Cylindrical tensile specimens having a gauge length of 30 mm and a diameter of 4.8 mm were solution treated at 520°C for 3 hr and quenched into water at room temperature. The ageing treatments were carried out at 180% for periods of up to 500 hrs. The grain size was 0.067 mm. The tests were carried out at room temperature using an Instron testing machine. Samples for electron microscopy were held under load after straining for approximately 20 min to allow locking of the dislocations. Foils were prepared by jet machining using a solution consisting of 4 parts acetic acid, 3 parts phosphoric acid, 2 parts nitric acid, and 1 part water at 30 V and 20X. The foils were examined in a Siemens Electron Microscope at 100 kV.
l!jm+SI ’ L.VKU,L)o II E’liTb
expf-Q,;kT)
’
(3)
where K and m are constants in the vacancy concentration-strain relation C, = KE” and N and fl are constants in the mobile dislocation density-strain relation p = X8- In this analysis I. has been assumed to be constant. If L varies with strain, as would be expected when dislocations act as the rate controlling obstacles, the parameter /? includes the combined strain dependence of both p and L, i.e. pL SC8. In alloys exhibiting repeated Type A serrated yielding, it has been shown [II] that measurements of ra may be obtained by increasing the applied strain rate at the initiation of a new Liiders band, causing a decrease in the transit time. r‘, of that band. If the reduction in rL is such that t, < t,, the subsequent yielding will be continuous [12]. Assuming that the transition in the subsequent yield behaviour, from discontinuous to continuous yielding, occurs when tL of the new band equals to, then measurements of tL at the transition give t,. Recent measurements oft, using this or similar yieid transition methods, together with (; measurements, give m = 1.1 and p = 0.9 in a furnace cooled Al-Mg-Si alloy [ll], m = 1.47 and @= 0.93 in an Au-14:/,Cu alloy [13], and m = 1.4 and @= 0.70 in an Al-Mg alloy [14}, in good agreement with measurements of 111and fi using prestrain [lS, 161 and quenching techniques [17]. In terms of the static strain ageing mode1 precipitation hardening may influence the onset of serrated yielding as a result of changes in Co, L and p. Since t, is not dependent on L or p, measurements of both t, and cc should allow the effects of precipitation hardening on serrated yielding to be further clarified. In this paper the effects of precipitation hardening on the serrated yielding behaviour of an Al-Mg-Si alloy are reported. The ageing characteristics of ACMg-Si alloys have been previously studied by Thomas [18]. Ageing at temperatures less than 204’C initially resulted in the formation of coherent needle-shaped precipitates aligned along the < lOO> directions. Precipitate growth occurred along the axes of the needles, with little change in diameter being observed. With further ageing at temperatures greater than 200°C the needles developed into rod-shaped precipitates, increasing in both length and diameter, and at high ageing temperatures plate-shaped precipitates were observed to form from the rods. Deformation in the foils was observed to occur by particle shearing.
3.
RESULTS
Regular Type A serrated yielding, corresponding to the repeated initiation and propagation of single Liiders bands aiong the specimen gauge length, was observed on reaching the critical strain in samples in the as-quenched condition and aged for up to 6 hr at 180°C. Samples aged for longer than 6 hr did not exhibit serrated yielding. Maximum precipitation strengthening occurred after approximately 20 hr at 180°C. The effect of ageing on the stress drop, Aa, accompanying the initiation of rhe Liiders bands and the Liiders strain. Ed, is shown in Figs. 1 and 2. Both A0 and Ed increased with increasing strain, however, increased ageing caused AG to decrease and E,_to increase. Ageing influenced the critical strain at the onset of serrated yielding as shown in Fig. 3. In tests conducted at constant strain rate, ageing resulted in an increase in E, for ageing times up to and including 4 hr. No change in E, was observed on increasing the ageing time from 4 to 6 hours. The values of m + fi
. A.O. . 2hr m
4hr
. 6hr
Otl--I-LI
cxH.3 Fig. 1. Effect of strain and ageing time on the stress drop accompanying
Liiders band initiation.
RILE>
*ND
\\!sCORLfIfX:
PRECiPIT.ATES
A?;D
THE
PORTE’.l?--iE
133
CHATELIER EFFEC? Table !
1.6 2.3 1.3 ‘4 _.
.As quznchsd .\gcd 1 hr .Qed 3 hi Aped I hr
Fig. 2. EtTect of strain and ageing time on the Liiders strain. determined from the slopes of the curv2s in Fig. 3 are shown in Table 1. It is seen that m + p increased from 1.7 in the as-quenched specimens to X-2.4 in the aged specimens. >leasurements of t, wxe made by discontinuously increasing the applied strain rate during the initiation of a new Liiders band. The transit time of the nex band was determined from the relation rL = Ed k. and the yield bchaviour after the passage of the band was judged to be either continuous or discontinuous. In Fig. 4 the yield behaviour is plotted as a function of 1, rL and the strain for the as-quenched specimens. At all strains a transition in the yield behaviour from discontinuous to continuous occurred with increasing 1 rL. The boundary line separating the two regions corresponds with tL = t,. Using equation (1) together nith the vacancy concentration-strain relation the slope of this line gives nz = 1.0. A similar determination of t, for specimens aged l-4 hr is also shown in Fig. 4. Ageing for 1 hr resulted in an increase in
1.13
0.6
!.2 !.’ 1.’
1.1 I.1 1.2
r.l from that measured in the as-quenched specimens. however. no further change in i, occurred on ageing to 1 hr. The value of m for the aped specimens is 1.‘. The Aues of fi dcttrmined from the measurements of vi + fl and nl are given in Table 1. The values of /j for the aged specimens is approrimaislq twice that for specimens in the as-quenched condition. Using equation (1) with t, = I,. the measurements of r, allow the product of (1 and L to be :sperimentally determined at each value of E;. In Fig. 5 curves of pL as a function of strain determined in this manner from the data of Figs. 3 and 4 are shown ior
‘P 07
c\-
0
I
0.2
I
0.5
I
2
c x IO2
Fig. 4. Yield behaviour subsequent to increase in strain rate as a fumction of l/r, and total strain; open figures continuous yielding. solid figures discontinuous yielding.
. 2 hr mShr
:
.ij!lr
-
! ic-3
I i0-c E.
Fig. 5. Effsst
10-3 set
-i
oi strain rate and ageing rime on the critical strain.
IO?: 0.1
./i 0.2
0.3
I
2
3
Fig. 5. E&t
oi strain and ageing time oc pL.
ture deueioped as has &en often observed in quenched AI alioys [lP]. &ring rest&d in the precipitation of coherent rod or needle-shaped precipitates atong the (fW>- direerions similar to that observed by Thomas [ ls]. R’ith ageing the rods grew ~r~~i~y in the (I.@$, directions, such that atter S hr aging at ISO’C the rods were +. l&.2&&in Iengtk witk a diameter of -c X+-i. The disiocation structure after 4?; strain in a sample aged S hr is shown in Fig. 7. Tke precipitate particles appeared to act as Iocal obstacfes to dislocation movement, with the bowing of disiocations around the precipitates being frequently observed. TIte dislocation arrangement in tke aged specimens was more homogeneous than that in the quenched specimens and no evidence of cell formation was observed. 4.
Fig_ 6. Disiocatioo structure of as-quenched specimen, e = 49;. eack keat treatment. For strains less than 296 the asquenched specimens exhibit the highest vaIues of yL and pf, progressively decreases with increased ageing for times up to 4hr. The pL curves for the 4 and 6 hr ageing treatments are the same. The slope of each curve is equal to j? which. as previously indicated, is increased substantially by ageing. For strains greater than 27; it appears that the curves for the as-quenched and 1 hr specimens will cross. Agering aiso intluenced the dislocation structure developed during deformation. In the as-quenched samples irregular dislocation tangles were observed from the start of deformation a shown in Fig. 6. At higher strains a reasonably well defined cell struc-
Fig. 7. Dislocation Structure of specimen aged 8 hr at 180X, c = c,.
DISCL%WW
The serrated yieIding behaviour of as-quenched AIMg-Si alloy has been previously reported[X& 21-j. The value of tn f P determined in the as-quenched specimens from the criticaf strain measurements is in agreement with the value m + ,!3= 1.6 determined previously [Xl], So previous measurements of m have been carried out on this ahoy in the as-quenched condition. althougk nr = 1.1 has been obtained[I 1J in furnace cooled specimens. On ageing the ahoy for one hour m + fl increases From I.6 to 2.3 and. as seen in TabIc I. this is the result of increases in both m and 8. with p exhibiting tke largest increase. The increase in fl on initial ageing may be due to a change in the obstacles controlling dislocation motion. The electron microscopy studies suggest that dislocation motion is limited by disfocation interactions in the as-quenched specimens and by particle interactions in the aged specimens. If disIocations act as the primary obstacles in the asquenched specimens then L shoutd decrease with increasing strain. If it is assumed that L K I -py’, where pr is the total dislocation density, and p r pr, then p x e1.2 for /I L: 0.6 in the as-quenched specimens. In the aged specimens, L would be expected to be determined by the particle spacing and independent of strain, giving p :K 6’ r-lz for the three ageing treatments. It appears therefore that the effect of initial ageing on jI is due to a change in the rate controlling obstacles. rather than a change in the exponent of the mobile dislocation density-strain relation. As shown in Fig. 4 ageing for 1 kr resulted in an increase in t, and m. The increase in t,, may be rationalized in terms of the change in solute concentration accompanying precipitation. Using equation (2) it is seen that 5 x {fC,-COI.lC,j3 ’ and any decrease in CO accompanying precipitation will result in an increase in ta provided Ci remains constant. As the alloy used in tkis study was a commercial one. it was not possible to determine whether the increase in t, is due solely to a change in CO. Since m is also increased somewhat by the initiaf ageing
RILEY
AND
McCORMICK:
PRECIPITATES
AND THE PORTEVIK-LE
treatment, it is likely that the proportionality constant. K, in the vacancy concentration-strain relation is also changed. With further ageing no additional change occurs to I,. indicating that the changes in Co accompanying precipitation are completed by 1 hour. For ageing times longer than one hour it appears that the precipitate growth is competitive and occurs at constant volume fraction of precipitate. Although the kinetics of precipitation in this alloy do not appear to have been studied, considerable evidence exists in other alloy systems[22] for competitive precipitate growth after short ageing treatments. In addition to Cc,, m also remains constant with further ageing. indicating that the vacancy generation process is not influenced by precipitate growth. The effect of ageing on pL directly reflects the shift in the critical strain-strain rate curves and the change in c, with ageing. On ageing for 1 hr both E, and to increase, however the increase in t, is insufficient to account for the change in the E, measurements. With further ageing t, remains constant and the increase in E, can only be rationalized in terms of a decrease in pL. The decrease in pL on ageing may result primarily from changes in L. As indicated previously there appears to be a change in the rate controlling obstacles on initial ageing from dislocations to precipitate particles. A decrease in L should accompany this change in the rate controlling obstacles. On further ageing precipitate strengthening increases causing L to continue to decrease as the precipitate particles become more effective obstacles to dislocation motion. The present results may be compared with the recent measurements of Lloyd et a[.[71 who found that ageing in a Co-Ni-Cr-Ti super-alloy under conditions of constant volume fraction resulted in a decrease in E,. Lloyd et al. showed that the dislocations bypassed the precipitate particles by Orowan looping, indicating that L was equal to the particle spacing, and were able to correlate changes in L with measurements of the increase in particle spacing with ageing. The absence of serrated yielding in specimens aged for longer than 6 hr is not understood and cannot be predicted from the measurements at shorter ageing times. In addition the suppression of serrated yielding by precipitation hardening is not a general feature of all alloy systems as serrated yielding has been observed in Co-Ni-Cr-Ti [7] and Cu-Mn [23] alloys in the peak and over-aged conditions. From equation (3) it is clear that a sufficiently large decrease in pL or C,, would cause E, to increase to beyond the necking strain. The values of pL appear to have levelled out at 6 hr and it would be difficult to rationalize the absence of serrated yielding in specimens aged for longer periods on the basis of a further large decrease in pL. A decrease in Co would be expected to accompany the formation of the equilibrium Mg,Si
CHATELIER EFFECT
185
phase. This, however requires much longer times than 10 hr at lSO’C[lS]. It is possible that in the specimens aged to near peak strength the precipitate particles acting as strong obstacles to dislocation motion impede the formation of Ltiders bands, resulting in discontinuous dislocation motion only on a local scale [24]. It is likely that the absence of serrated yielding in the over-aged specimens is due to the low solubility of Mg,Si. To test this possibility a series of specimens were annealed at 52O’C and given an interrupted cooling treatment by holding at 35OC for 24 hr and at 180°C for 336 hr. Serrated yielding was not observed in these specimens, indicating that the nearequilibrium solute concentration in this alloy is insufficient to cause the degree of dislocation locking necessary for the initiation of discontinuous yielding. Acknowledgements-This work was carried out at the Universities of New South Wales and Western Australia with the financial suppoort of the Australian Research Grants Committee. The assistance of Mr. J. Newby with the electron microscopy is gratefully acknowledged.
REFERENCES I. E. 0. Hall, Yielding Point Phenomena Alloys. Macmillan, New York (1970).
in .Werais and
2. B. J. Brindley and P. J. Worthington, .\fer. Rer. 145, 101 (1970). 3. J. D. Lubahn, Trans. A1:Cf.E 185, 702 (1949). 4. V. A. Phillips, J. Inst. &1er. 81, 649 (1952). 5. K. Matsuura, T. Nishiyama and S. Koda. Trans. JIM 10, 429 (1969). 6. M. Chaturvedi, D. J. Lloyd and K. Tangri. lifer. Sci. J. 6, 16 (1972). 7. D. J. Lloyd, D. W. Chung and M. C. Chaturvedi, Acra Met. 23, 93 (1975). 8. A. W. Sleeswijk, Acra Met. 6, 598 (1958). 9. P. G. McCormick, Acta Met. 20, 351 (1972). 10. A. H. Cottrell and B. A. Bilby, Proc. phJs. Sot. (London) 62, 49 (1949). 11. P. G. McCormick, Acta Met. 22, 489 (1974). 12. J. Friedel, Dislocarions, p. 412. Pergamon Press, Oxford (1964). 13. S. H. van den Brink and P. G. McCormick, Scripta Mer. 8, 1251 (1974). 14. J. A. Taylor and P. G. McCormick. ,Vfar. Sci. Enqr. 21, 35 (l-976). 15. R. K. Ham and D. Jaffrey, Phil Jfag. 15, 247 (1967). 16. A. J. R. Soler-Gomez and W. J. McG. Testart. Phil. Mag. 20, 459 (1969). 17. A. Wijler, M. M. A. Vrijhoef and A. van den Beukel, Acta Met. 22, 13 (1974).
18. G. Thomas, J. Inst. Met. 90, 57 (1961). 19. P. R. Swann, in Elecrron Microscop_v and Strengrh of Crystals (Edited by G. Thomas and J. Washburn). Interscience, New York (1963). 20. P. G. McCormick, Acta Met. 19, 463 (1971). 21. P. R. Cetlin, A. S. Giilec and R. E. Reed-Hill, ,Vfer. Trans. 4, 513 (1973). 22. A. Kelly and R. B. Nicholson, Prog. Mat. Sci. 10, (1963). 23. S. R. Yeomans and P. G. McCormick. to be published. 24. P. G. McCormick, Scripra l\fet. 6, 165 (1972).
1.
INTRODUCTION
The Portevin-Le Chatelier Effect has been investigated in many alloy systems in recent years [l, 21. Although many of the studies have been carried out in alloys capable of being precipitation hardened. few studies of the effect of precipitation hardening on serrated yiefding have been reported since the early work of Lubahn [3] and Phillips [4]. Lubahn and Phillips found that precipitation hardening delayed the start of serrated yielding to strains higher than that measured in as-quenched samples, and that ageing to near peak strength conditions eliminated serrated yielding [3,4]. Similar effects of precipitation hardening in delaying the onset of serrated yielding have been observed in AI-Nlg [YJ and %Ig-Ag [6] alloys. However, recent work by Lloyd rr nl[7] has shown that the onset of serrated vieldina in a Co-Xi-Cr-Ti super-alloy is decreased by precipitation hardening. * Now at: Department of Mechanical Engineering. University of Western Australia Nedlands. W.A. 6009.
In the static strain ageing fS, 91 - - model _ _ for the Portevin-Le Chatelier effect. the onset of serrated yielding is attributed to the interaction of solute atoms and mobile dislocations temporarily arrested at obstacles in their slip path. Serrated yielding is assumed to initiate when the waiting time, c,, of dislocation arrested at obstacles, is equal to the strain ageing time required for solute locking, r,. The waiting time, t,, may be expressed in terms of the applied strain rate .?c a3
tw-_pLb g ’
(I)
where p is the mobile dislocation density and L is the obstacle spacing. Using the Cottrell-Bilby strain ageing model [IO], r, may be expressed as f,
2
ic,I \
-
cn\3:2
XC0
1
kn?”
L’, C,Do exp( - Q,/kT)
(3
where C, is the local solute concentration at the arrested dislocations required for locking, C, is the 181
IS’
RILEY
.ASD
McCQRMICK:
PRECIPITATES AND THE PORTEVIN-LE
matrix solute concentration of the alloy. x 1 3, U,,, is the solute-dislocation binding energy, C, is the vacancy concentration, 0, is the diffusion frequency factor, and Q,, is the’ activation energy for solute migration, Equating equations (1) and (2), the critical strain. E,, at the onset of serrated flow is expressed as
2.
CHATELIER
EXPERIJIEWT.AL
EFFECT
METHOD
A commercial 6063 Al-Mg-Si alloy containing 0.7:$‘bMg and O.lil/l;Si was used in this study. Cylindrical tensile specimens having a gauge length of 30 mm and a diameter of 4.8 mm were solution treated at 520°C for 3 hr and quenched into water at room temperature. The ageing treatments were carried out at 180% for periods of up to 500 hrs. The grain size was 0.067 mm. The tests were carried out at room temperature using an Instron testing machine. Samples for electron microscopy were held under load after straining for approximately 20 min to allow locking of the dislocations. Foils were prepared by jet machining using a solution consisting of 4 parts acetic acid, 3 parts phosphoric acid, 2 parts nitric acid, and 1 part water at 30 V and 20X. The foils were examined in a Siemens Electron Microscope at 100 kV.
l!jm+SI ’ L.VKU,L)o II E’liTb
expf-Q,;kT)
’
(3)
where K and m are constants in the vacancy concentration-strain relation C, = KE” and N and fl are constants in the mobile dislocation density-strain relation p = X8- In this analysis I. has been assumed to be constant. If L varies with strain, as would be expected when dislocations act as the rate controlling obstacles, the parameter /? includes the combined strain dependence of both p and L, i.e. pL SC8. In alloys exhibiting repeated Type A serrated yielding, it has been shown [II] that measurements of ra may be obtained by increasing the applied strain rate at the initiation of a new Liiders band, causing a decrease in the transit time. r‘, of that band. If the reduction in rL is such that t, < t,, the subsequent yielding will be continuous [12]. Assuming that the transition in the subsequent yield behaviour, from discontinuous to continuous yielding, occurs when tL of the new band equals to, then measurements of tL at the transition give t,. Recent measurements oft, using this or similar yieid transition methods, together with (; measurements, give m = 1.1 and p = 0.9 in a furnace cooled Al-Mg-Si alloy [ll], m = 1.47 and @= 0.93 in an Au-14:/,Cu alloy [13], and m = 1.4 and @= 0.70 in an Al-Mg alloy [14}, in good agreement with measurements of 111and fi using prestrain [lS, 161 and quenching techniques [17]. In terms of the static strain ageing mode1 precipitation hardening may influence the onset of serrated yielding as a result of changes in Co, L and p. Since t, is not dependent on L or p, measurements of both t, and cc should allow the effects of precipitation hardening on serrated yielding to be further clarified. In this paper the effects of precipitation hardening on the serrated yielding behaviour of an Al-Mg-Si alloy are reported. The ageing characteristics of ACMg-Si alloys have been previously studied by Thomas [18]. Ageing at temperatures less than 204’C initially resulted in the formation of coherent needle-shaped precipitates aligned along the < lOO> directions. Precipitate growth occurred along the axes of the needles, with little change in diameter being observed. With further ageing at temperatures greater than 200°C the needles developed into rod-shaped precipitates, increasing in both length and diameter, and at high ageing temperatures plate-shaped precipitates were observed to form from the rods. Deformation in the foils was observed to occur by particle shearing.
3.
RESULTS
Regular Type A serrated yielding, corresponding to the repeated initiation and propagation of single Liiders bands aiong the specimen gauge length, was observed on reaching the critical strain in samples in the as-quenched condition and aged for up to 6 hr at 180°C. Samples aged for longer than 6 hr did not exhibit serrated yielding. Maximum precipitation strengthening occurred after approximately 20 hr at 180°C. The effect of ageing on the stress drop, Aa, accompanying the initiation of rhe Liiders bands and the Liiders strain. Ed, is shown in Figs. 1 and 2. Both A0 and Ed increased with increasing strain, however, increased ageing caused AG to decrease and E,_to increase. Ageing influenced the critical strain at the onset of serrated yielding as shown in Fig. 3. In tests conducted at constant strain rate, ageing resulted in an increase in E, for ageing times up to and including 4 hr. No change in E, was observed on increasing the ageing time from 4 to 6 hours. The values of m + fi
. A.O. . 2hr m
4hr
. 6hr
Otl--I-LI
cxH.3 Fig. 1. Effect of strain and ageing time on the stress drop accompanying
Liiders band initiation.
RILE>
*ND
\\!sCORLfIfX:
PRECiPIT.ATES
A?;D
THE
PORTE’.l?--iE
133
CHATELIER EFFEC? Table !
1.6 2.3 1.3 ‘4 _.
.As quznchsd .\gcd 1 hr .Qed 3 hi Aped I hr
Fig. 2. EtTect of strain and ageing time on the Liiders strain. determined from the slopes of the curv2s in Fig. 3 are shown in Table 1. It is seen that m + p increased from 1.7 in the as-quenched specimens to X-2.4 in the aged specimens. >leasurements of t, wxe made by discontinuously increasing the applied strain rate during the initiation of a new Liiders band. The transit time of the nex band was determined from the relation rL = Ed k. and the yield bchaviour after the passage of the band was judged to be either continuous or discontinuous. In Fig. 4 the yield behaviour is plotted as a function of 1, rL and the strain for the as-quenched specimens. At all strains a transition in the yield behaviour from discontinuous to continuous occurred with increasing 1 rL. The boundary line separating the two regions corresponds with tL = t,. Using equation (1) together nith the vacancy concentration-strain relation the slope of this line gives nz = 1.0. A similar determination of t, for specimens aged l-4 hr is also shown in Fig. 4. Ageing for 1 hr resulted in an increase in
1.13
0.6
!.2 !.’ 1.’
1.1 I.1 1.2
r.l from that measured in the as-quenched specimens. however. no further change in i, occurred on ageing to 1 hr. The value of m for the aped specimens is 1.‘. The Aues of fi dcttrmined from the measurements of vi + fl and nl are given in Table 1. The values of /j for the aged specimens is approrimaislq twice that for specimens in the as-quenched condition. Using equation (1) with t, = I,. the measurements of r, allow the product of (1 and L to be :sperimentally determined at each value of E;. In Fig. 5 curves of pL as a function of strain determined in this manner from the data of Figs. 3 and 4 are shown ior
‘P 07
c\-
0
I
0.2
I
0.5
I
2
c x IO2
Fig. 4. Yield behaviour subsequent to increase in strain rate as a fumction of l/r, and total strain; open figures continuous yielding. solid figures discontinuous yielding.
. 2 hr mShr
:
.ij!lr
-
! ic-3
I i0-c E.
Fig. 5. Effsst
10-3 set
-i
oi strain rate and ageing rime on the critical strain.
IO?: 0.1
./i 0.2
0.3
I
2
3
Fig. 5. E&t
oi strain and ageing time oc pL.
ture deueioped as has &en often observed in quenched AI alioys [lP]. &ring rest&d in the precipitation of coherent rod or needle-shaped precipitates atong the (fW>- direerions similar to that observed by Thomas [ ls]. R’ith ageing the rods grew ~r~~i~y in the (I.@$, directions, such that atter S hr aging at ISO’C the rods were +. l&.2&&in Iengtk witk a diameter of -c X+-i. The disiocation structure after 4?; strain in a sample aged S hr is shown in Fig. 7. Tke precipitate particles appeared to act as Iocal obstacfes to dislocation movement, with the bowing of disiocations around the precipitates being frequently observed. TIte dislocation arrangement in tke aged specimens was more homogeneous than that in the quenched specimens and no evidence of cell formation was observed. 4.
Fig_ 6. Disiocatioo structure of as-quenched specimen, e = 49;. eack keat treatment. For strains less than 296 the asquenched specimens exhibit the highest vaIues of yL and pf, progressively decreases with increased ageing for times up to 4hr. The pL curves for the 4 and 6 hr ageing treatments are the same. The slope of each curve is equal to j? which. as previously indicated, is increased substantially by ageing. For strains greater than 27; it appears that the curves for the as-quenched and 1 hr specimens will cross. Agering aiso intluenced the dislocation structure developed during deformation. In the as-quenched samples irregular dislocation tangles were observed from the start of deformation a shown in Fig. 6. At higher strains a reasonably well defined cell struc-
Fig. 7. Dislocation Structure of specimen aged 8 hr at 180X, c = c,.
DISCL%WW
The serrated yieIding behaviour of as-quenched AIMg-Si alloy has been previously reported[X& 21-j. The value of tn f P determined in the as-quenched specimens from the criticaf strain measurements is in agreement with the value m + ,!3= 1.6 determined previously [Xl], So previous measurements of m have been carried out on this ahoy in the as-quenched condition. althougk nr = 1.1 has been obtained[I 1J in furnace cooled specimens. On ageing the ahoy for one hour m + fl increases From I.6 to 2.3 and. as seen in TabIc I. this is the result of increases in both m and 8. with p exhibiting tke largest increase. The increase in fl on initial ageing may be due to a change in the obstacles controlling dislocation motion. The electron microscopy studies suggest that dislocation motion is limited by disfocation interactions in the as-quenched specimens and by particle interactions in the aged specimens. If disIocations act as the primary obstacles in the asquenched specimens then L shoutd decrease with increasing strain. If it is assumed that L K I -py’, where pr is the total dislocation density, and p r pr, then p x e1.2 for /I L: 0.6 in the as-quenched specimens. In the aged specimens, L would be expected to be determined by the particle spacing and independent of strain, giving p :K 6’ r-lz for the three ageing treatments. It appears therefore that the effect of initial ageing on jI is due to a change in the rate controlling obstacles. rather than a change in the exponent of the mobile dislocation density-strain relation. As shown in Fig. 4 ageing for 1 kr resulted in an increase in t, and m. The increase in t,, may be rationalized in terms of the change in solute concentration accompanying precipitation. Using equation (2) it is seen that 5 x {fC,-COI.lC,j3 ’ and any decrease in CO accompanying precipitation will result in an increase in ta provided Ci remains constant. As the alloy used in tkis study was a commercial one. it was not possible to determine whether the increase in t, is due solely to a change in CO. Since m is also increased somewhat by the initiaf ageing
RILEY
AND
McCORMICK:
PRECIPITATES
AND THE PORTEVIK-LE
treatment, it is likely that the proportionality constant. K, in the vacancy concentration-strain relation is also changed. With further ageing no additional change occurs to I,. indicating that the changes in Co accompanying precipitation are completed by 1 hour. For ageing times longer than one hour it appears that the precipitate growth is competitive and occurs at constant volume fraction of precipitate. Although the kinetics of precipitation in this alloy do not appear to have been studied, considerable evidence exists in other alloy systems[22] for competitive precipitate growth after short ageing treatments. In addition to Cc,, m also remains constant with further ageing. indicating that the vacancy generation process is not influenced by precipitate growth. The effect of ageing on pL directly reflects the shift in the critical strain-strain rate curves and the change in c, with ageing. On ageing for 1 hr both E, and to increase, however the increase in t, is insufficient to account for the change in the E, measurements. With further ageing t, remains constant and the increase in E, can only be rationalized in terms of a decrease in pL. The decrease in pL on ageing may result primarily from changes in L. As indicated previously there appears to be a change in the rate controlling obstacles on initial ageing from dislocations to precipitate particles. A decrease in L should accompany this change in the rate controlling obstacles. On further ageing precipitate strengthening increases causing L to continue to decrease as the precipitate particles become more effective obstacles to dislocation motion. The present results may be compared with the recent measurements of Lloyd et a[.[71 who found that ageing in a Co-Ni-Cr-Ti super-alloy under conditions of constant volume fraction resulted in a decrease in E,. Lloyd et al. showed that the dislocations bypassed the precipitate particles by Orowan looping, indicating that L was equal to the particle spacing, and were able to correlate changes in L with measurements of the increase in particle spacing with ageing. The absence of serrated yielding in specimens aged for longer than 6 hr is not understood and cannot be predicted from the measurements at shorter ageing times. In addition the suppression of serrated yielding by precipitation hardening is not a general feature of all alloy systems as serrated yielding has been observed in Co-Ni-Cr-Ti [7] and Cu-Mn [23] alloys in the peak and over-aged conditions. From equation (3) it is clear that a sufficiently large decrease in pL or C,, would cause E, to increase to beyond the necking strain. The values of pL appear to have levelled out at 6 hr and it would be difficult to rationalize the absence of serrated yielding in specimens aged for longer periods on the basis of a further large decrease in pL. A decrease in Co would be expected to accompany the formation of the equilibrium Mg,Si
CHATELIER EFFECT
185
phase. This, however requires much longer times than 10 hr at lSO’C[lS]. It is possible that in the specimens aged to near peak strength the precipitate particles acting as strong obstacles to dislocation motion impede the formation of Ltiders bands, resulting in discontinuous dislocation motion only on a local scale [24]. It is likely that the absence of serrated yielding in the over-aged specimens is due to the low solubility of Mg,Si. To test this possibility a series of specimens were annealed at 52O’C and given an interrupted cooling treatment by holding at 35OC for 24 hr and at 180°C for 336 hr. Serrated yielding was not observed in these specimens, indicating that the nearequilibrium solute concentration in this alloy is insufficient to cause the degree of dislocation locking necessary for the initiation of discontinuous yielding. Acknowledgements-This work was carried out at the Universities of New South Wales and Western Australia with the financial suppoort of the Australian Research Grants Committee. The assistance of Mr. J. Newby with the electron microscopy is gratefully acknowledged.
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in .Werais and
2. B. J. Brindley and P. J. Worthington, .\fer. Rer. 145, 101 (1970). 3. J. D. Lubahn, Trans. A1:Cf.E 185, 702 (1949). 4. V. A. Phillips, J. Inst. &1er. 81, 649 (1952). 5. K. Matsuura, T. Nishiyama and S. Koda. Trans. JIM 10, 429 (1969). 6. M. Chaturvedi, D. J. Lloyd and K. Tangri. lifer. Sci. J. 6, 16 (1972). 7. D. J. Lloyd, D. W. Chung and M. C. Chaturvedi, Acra Met. 23, 93 (1975). 8. A. W. Sleeswijk, Acra Met. 6, 598 (1958). 9. P. G. McCormick, Acta Met. 20, 351 (1972). 10. A. H. Cottrell and B. A. Bilby, Proc. phJs. Sot. (London) 62, 49 (1949). 11. P. G. McCormick, Acta Met. 22, 489 (1974). 12. J. Friedel, Dislocarions, p. 412. Pergamon Press, Oxford (1964). 13. S. H. van den Brink and P. G. McCormick, Scripta Mer. 8, 1251 (1974). 14. J. A. Taylor and P. G. McCormick. ,Vfar. Sci. Enqr. 21, 35 (l-976). 15. R. K. Ham and D. Jaffrey, Phil Jfag. 15, 247 (1967). 16. A. J. R. Soler-Gomez and W. J. McG. Testart. Phil. Mag. 20, 459 (1969). 17. A. Wijler, M. M. A. Vrijhoef and A. van den Beukel, Acta Met. 22, 13 (1974).
18. G. Thomas, J. Inst. Met. 90, 57 (1961). 19. P. R. Swann, in Elecrron Microscop_v and Strengrh of Crystals (Edited by G. Thomas and J. Washburn). Interscience, New York (1963). 20. P. G. McCormick, Acta Met. 19, 463 (1971). 21. P. R. Cetlin, A. S. Giilec and R. E. Reed-Hill, ,Vfer. Trans. 4, 513 (1973). 22. A. Kelly and R. B. Nicholson, Prog. Mat. Sci. 10, (1963). 23. S. R. Yeomans and P. G. McCormick. to be published. 24. P. G. McCormick, Scripra l\fet. 6, 165 (1972).