The effect of temperature on strain rate sensitivity in an AlMgSi alloy

Acta metall, mater. Vol. 41, No. 11, pp. 3127-3131, 1993

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THE E F F E C T OF T E M P E R A T U R E ON STRAIN RATE SENSITIVITY IN A N A1-Mg-Si A L L O Y C. P. L I N G and P. G. M c C O R M I C K

Department of Mechanical and Materials Engineering, University of Western Australia, Nedlands, WA 6009, Australia

(Received 9 November 1992; in revisedform 22 April 1993) Abstract--The effect of temperature on strain rate sensitivity has been studied in an A1-Mg-Si alloy in the range of dynamic strain ageing. Two regimes of behaviour were observed which depended on the temperature. At low temperatures (T ~<303 K) it was possible to correlate all strain rate sensitivity measurements with a single strain/strain rate/temperature parameter. In the high temperature regime the temperature and strain rate dependence of the strain rate sensitivity deviated significantly from that measured at low temperatures. The two regimes of behaviour were found to correspond with the normal and inverse Portevin-Le Chatelier effect.

1. INTRODUCTION Numerous studies have shown that the occurrence of dynamic strain ageing during plastic deformation is reflected in measurements of strain rate sensitivity [1-3]. Measurements of the flow stress following an abrupt change in strain rate in the regime of dynamic strain ageing exhibit transient behaviour which is associated with the time dependent response of the solute composition at arrested dislocations, Cs, to the abrupt change in the dislocation waiting time at localised obstacles, tw. As a consequence, two different strain rate sensitivities may be measured, the instantaneous strain rate sensitivity, Sj, measured from the instantaneous flow stress change, and the steady state strain rate sensitivity, Sf, determined from the post-transient response [2]. Numerous studies have shown that the occurrence of dynamic strain ageing cause Sf to decrease, with negative values of Sf being a necessary but not sufficient requirement for the onset of the Portevin-Le Chatelier effect [2-4]. Recent studies have shown that dynamic strain ageing phenomena, including the transient effects, can be accurately modelled using constitutive relations which take into account the time dependence of Cs [4-6]. The flow stress equation may be expressed as [5]

a =cri+Si{ln(~o)+H'~C~}

dislocations. Using Cottrell-Bilby strain ageing kinetics [7], modified to include solute saturation [8] gives C~ = Cm(1 -- exp[-- Co(KDt,)"/Cm])

where Cm is the saturation value of Cs, Co is the solute concentration of the alloy, D is the solute diffusion coefficient and K is a constant. In the original Cottrell-Bilby model n =2/3. However, recent studies suggest n = 1/3 [9-11]. As pointed out previously, ta and Cs cannot respond instantaneously to a change in tw. Assuming a first order relaxation process, the rate of change of ta may be expressed as [5] dt~ = (tw - ta)/tw dt

1 OH

Hi=---k T aC~ where H is the activation enthalpy for dislocation motion. A linear dependence of H on Cs and a is implicit in equation (1). The effective solute composition at arrested dislocations is determined by the ageing time, t~, of the

(3)

where it is assumed that the characteristic relaxation time constant equals tw. The Orowan equation may be used to relate t~ and the strain rate f~ tw = -7 £

(4)

where ~ equals pmbL, Pm is the mobile dislocation density and L is the effective obstacle spacing. With conventional tensile tests the machine equation provides a further relation between the constitutive variables

Ca + ~ = V/l

(1)

where tri is the internal stress and

(2)

(5)

where V is the crosshead velocity, l is the gauge length and C is the combined testing machine-specimen compliance. In the limit of quasi-steady state conditions, ta "-~t w and, using equations (1)-(4), the steady-state strain rate sensitivity, [ S f = d a / d ln(£)l,] may be expressed as

3127

/Em+~\. [/E~+~\.-I) Sf: Si{1-#'/PIP2t~)exp[-,~t~)j~ (6)

3128

LING and McCORMICK:

STRAIN RATE SENSITIVITY IN AN AI-Mg-Si ALLOY 82"

where

J

Pl=HiCm

and

P2=~

K'exp

Equation (6) takes into account the possibility of a strain enhanced vacancy concentration, Cv, assisting the diffusion process by letting D =CvD0ex p (-Q/kT), with Cv = K~Em, where Do is the diffusion frequency factor, k is Boitzmann's constant, Q is the activation energy for solute migration and K~ and m are constants. The strain dependence of f~ is accounted for through f~=K2 Ea, where K2 and fl are constants. Combining constants gives K'=KK~K 2Do. The dynamic strain ageing component of the total strain rate sensitivity, (, may be defined as ( S i - Sf)/Si [2]

&m+~\~

F

&m+P'\"-I

C=,a',P~/~- } expL-~/--T- ) J. (7) Ling and McCormick [4] have recently shown that the stress-time curves obtained from the simultaneous numerical integration of equation (1)-(4) accurately model experimental flow stress transients accompanying abrupt increases in crosshead velocity. The numerical modelling enabled the constitutive parameters Si, P~,/'2 and f~ to be determined as a function of strain and strain rate from strain rate sensitivity measurements. In this paper, measurements of the effect of temperature on the strain rate sensitivity in an AI-Mg-Si alloy are reported. Two regimes of behaviour are observed, which correspond to the normal and inverse Portevin-Le Chatelier effect.

2. EXPERIMENTAL Tensile specimens of 3 mm diameter and 30 mm gauge length were fabricated from a commercial 6063 A1-Mg-Si alloy. The specimens were annealed at 800 K for 3.6 ks, air cooled and stabilised at 298 K for 24 h prior to testing. Constant crosshead velocity tests were carried out at three base strain rates of 1.11 x 10 -4, 5.55 x 10 -4 and 1.11 x 10-3s l in the temperature range of 263-373 K using an Instron testing machine fitted with a circulating liquid temperature bath. The specimen temperature was controlled to an accuracy of + 0.1 K. Strain rate sensitivity tests were carried out using a 10:1 increase in cross-head velocity. All measurements were recorded and stored for further processing using a high speed digital acquisition system.

3. RESULTS Typical stress-time curves associated with a discontinuous increase in strain rate are shown in Fig. 1. An initial increase in stress accompanied the increase in strain rate, which was followed by a transient

80' 78'

E = 0.016 58. 56. 54" 52

1 sec

50 Time

Fig. I. Typical flow stress transients accompanying an abrupt increase in crosshead velocity.

period where the stress adjusted to a new quasi-steady state variation with time. As evident in Fig. 1 both the transient variation of the stress and the extent of the transient region increased with increasing strain. The solid curves in Fig. 1 were computed from the numerical integration of equations (1)-(4), as described in Ref. [4]. The procedure enabled values of P~, P2, Si, f~ to be determined for each change of strain rate from which Sf was calculated using equation (6). Values of ~ = ( S i - Sf)/Si were then plotted as a function of X n, X = Em÷ ~/~ for each temperature. For temperatures less than or equal to 303 K (low temperature regime) an excellent correlation between the values of ~ and X n for tests carried out at a single temperature was established with m + j~ = 2 [4] and n = 1 / 3 as shown in Fig. 2. It is seen that approaches zero in the limit of X --* 0 and that all values of ~ lie on the same curve irrespective of the

1.6

1.2 263 K

~,, 0.8

273 K

°'i 0

i

I

1

2

•

283K

O

293 K

• i

303 K i

3

4

1/3

x Fig. 2. Measurements of ~ at low temperatures.

STRAIN RATE SENSITIVITY IN AN A1 Mg-Si ALLOY

LING and McCORMICK: 1.6-

3129

13.0t [i

•

12.5]

•

1.2"

¢~

0.8"

•

/. j~

0.4"

~

/

F /

•

•

t

12.0 z

111,-,

• o

5.55e-4 1.lie-3

11.5

11.0

0.3

0.0

[]

s.sso-5

o

|

0.0

a

0.6

0.9

.3

1.2

3.5

3.7

3.9

1/T X 10 3 (l/K)

X 1/3

Fig. 3. Measurements of ~ at 373 K.

Fig. 5. Effect of temperature on P~.

individual values of E and ~ for tests carried out at a single temperature. Increasing the temperature resulted in an increase in the value of ( at constant X. For temperatures greater than 303 K it was not possible to correlate ( with the constitutive parameter X =Em+'/£ at all strain rates, as shown in Fig. 3 for tests carried out at 373K. At 373K only the results for the two highest strain rates could be correlated with X. At lower strain rates the curves shifted to higher values of X. Replotting the measurements as a function of strain showed that the value of Sf for a given strain actually increased with decreasing strain rate at the lowest strain rate. Similar behaviour was also observed on plotting the strain, %, where Sf = 0, (i.e. ( = 1) as a function of inverse temperature as shown in Fig. 4 for tests carried out at constant strain rate. In the low temperature regime ~0 increases with l/T, as is also evident from Fig. 3. In the high temperature regime E0 reaches a minimum with increasing temperature at T = 353 K. Measurements of the critical strain, E¢, at the onset of serrated yielding as a function of temperature are also shown in Fig. 4. Comparison of the two curves shows that the high temperature regime corresponds with the inverse Portevin-Le Chatelier effect where E~ increases with increasing temperature and decreasing L In the low temperature regime the critical strain

increased with g as E~ z oc~ as reported previously for this alloy [4]. The values of the parameters P~ and P2 were found to be independent of E and ~. In Figs 5 and 6 the values Pt and P2 are plotted as a function of temperature. The values of P~ were independent of T while P2 varied exponentially with 1/T. From the definition of P:, the slope of the curve in Fig. 6 is equal to Q/3k, giving Q = 0.59 eV. The expression for ~r, was obtained by modelling the stress-strain data using a Voce equation [12]. The values of Si and f~ were found to be independent of both d and T over the entire temperature range studied as shown in Figs 7 and 8, respectively. From Fig. 7 it is seen that S~ increases with strain as SiacE°5°. The measurements of f~ increased with strain as f~ocE°68, i.e. ~ = 0.68. Expressions for the constitutive parameters obtained in this study are given in Table 1. 4. DISCUSSION The measurements of strain rate sensitivity show two clearly defined regimes of behaviour which depend on temperature. The low temperature regime T ~<303 K, corresponds to the temperature range over which the normal Portevin-LeChatelier effect was observed, as characterised by ~,~,,+l~ with

I0 °

10 ° Ec

10

I

e~ Eo 10 .2

10 .3

..

2.6

3.0

3.4

3.8

1/T x 1 0 3 ( l / K ) Fig. 4. Effect o f t e m p e r a t u r e on ec, % a n d %.

tO" 1 3.3

3.5 I/T x 103

3.7 (l/K)

Fig. 6, Effect o f t e m p e r a t u r e on P~.

3.9

LING and McCORMICK: STRAIN RATE SENSITIVITY IN AN A1-Mg-Si ALLOY

3130

T a b l e 1. V a l u e s o f c o n s t i t u t i v e p a r a m e t e r s Parameter 1.2

,..,, r~"

f~

263 K

| 0"81f

~

• " • n • A

[0.4 1 1 I

0.0 [ 0.0

4"

•

, 0.1

St (MPa) Pt

283 K 293K 303 K 313 K 333 K 353 K 373 K

P2 (s-l/a)

ai (MPa)

0.2

Plastic S t r a i n

Fig. 7. Measurements of St.

m + fl = 2. In this regime the values of ~ exhibited an excellent correlation with the reduced EN parameter, X , ( x = E m + a / Q in agreement with the E c - ~ measurements. Correlations between ~ and X have been reported in several alloy systems [2--4, 13]. In a previous study on the same alloy [4], ~ was found to be a function of X ~/3 as observed here. However, this functional dependence of ( on X was interpreted as arising from parabolic solid solution hardening behaviour, i.e. oc C]/2 rather than from a one-third time exponent in the diffusion equation [4]. An initial attempt was made to model the present results using C~/2 behaviour, however, it was not possible to correlate the values of ( at different temperatures using a single activation energy. Using n = 1/3 it was possible to model the measurements with a single activation energy, and the value of Q was in excellent agreement with the value obtained from the effect of temperature on E¢. The value of Q is also in good agreement with measurements of the activation energy for solute migration in aluminium [14]. In addition, the n = 1/3 time exponent was found to be superior at low temperatures where the measurement of Sr extended over a wider range of strain. The n = 1/3 strain ageing exponent agrees well with recent measurements of dynamic strain ageing in C u - M n alloys [9]. Springer and Schwink [9] have

0.0006

[]

0.0004

• *

263 K 273 K

0.0002

• • • n • • 4.

283 K 293 K 303 K 313 K 333 K 353 K 373 K

0.0000

0.0

0'.1

Plastic S t r a i n Fig. 8. E f f e c t o f s t r a i n a n d t e m p e r a t u r e o n f~.

0.2

Value 3.63 x 1 0 - 5 + 2 . 1 6

x 10-3~ °'~

0.41 + 2.912~°~° 12.066 1700 exp(-Q /k T) 1/3 38.03 + 129.94[1 - exp(- E/0.056)]

attributed this behaviour to the occurrence of pipe diffusion down forest dislocation as the rate controlling step, such as proposed by Mulford and Kocks [15]. While Springer and Schwink [9] and other [11, 15] discount the possibility of a strain enhanced vacancy concentration accelerating the diffusion process, there is no reason why an excess vacancy concentration will not assist pipe diffusion. As shown in Fig. 8 the variation off~ with strain gave fl = 0.68, independent of strain rate and temperature. The X correlation in the low temperature regime gives m + fl = 2. Thus m = 1.32, in agreement with previous measurements on this alloy, and clearly supports arguments for a strain enhanced diffusion process controlling the kinetics of dynamic strain ageing. The present results show that in the low temperature regime the effect of temperature, strain rate and strain can be combined into a single constitutive parameter g = e x p ( - Q Ik T)e " +~lg. The present results show that the inverse Portevin-Le Chatelier effect is a consequence of the behaviour of ~ at high temperatures and/or low strain rates. In the high temperature regime the measurements of ~ no longer vary as predicted by conventional dynamic strain ageing kinetics valid at low temperatures. Also, as shown in Fig. 4, the variation of E0 and Ec with 1/T show similar departures from their low temperature behaviour, both exhibiting minimum values at high-temperatures. It has been recently shown that the instability associated with dynamic strain ageing does not occur when Sr = 0 is reached, i.e. at E0. Rather, the instability condition is

[5] Sf = - ~ n

(8)

where ~ = da/dE - a. Values of the instability strain, E,, are also plotted in Fig. 4. The values of E, lie between E0 and Ecand exhibit a similar dependence on I/T at all temperatures. It has not been possible in the present study to delineate the reasons for the behaviour of ~ in the high temperature regime. Nonetheless, it is clear from the fact that f~ and Si do not vary with temperature (or strain rate) in the high temperature regime (i.e. retain their low temperature values) that the high temperature behaviour is not due to structural changes, such as precipitation, which could change the nature of the rate controlling obstacles to dislocation motion or the density of mobile dislocations. Rather, it appears that the diffusion controlled kinetics of dynamic strain ageing are altered at high

LING and McCORMICK:

STRAIN RATE SENSITIVITY IN AN A1-Mg-Si ALLOY

temperatures and low strain rates. One possible explanation not accounted for in the present low temperature model is the annealing out of the strain enhanced vacancy concentration [16]. 5. CONCLUSIONS 1. The effect of temperature on strain rate sensitivity measurements show two regimes of behaviour corresponding to temperatures less than or equal to 303 K (low temperature regime) and temperatures above 303 K (high temperature regime). 2. In the low temperature regime the measurements of ( can be directly correlated with a single strain/strain rate parameter, Xn, X = E m + ' / ~ with m+fl=2andn=l/3. 3. In the high temperature regime the measurements do not correlate with X. S~ and D retain their low temperature values indicating that a change occurs to the kinetics of dynamic strain aging at high temperatures. 4. The behaviour of ( at high temperatures directly relates to the occurrence of the inverse Portevin-Le Chatelier effect. Acknowledgement--The authors are particularly grateful to

3131

Professor Y. Estrin for many valuable discussions and for commenting on the manuscript. REFERENCES

1. D. Munz and E. Macherauch, Z. Metallk. 57, 442 (1966). 2. S. H. van den Brink, A. van den Beukel and P. G. McCormick, Physica status solidi (a) 30, 469 0975). 3. H.J. Harun and P. G. McCormick, Acta metall. 27, 155 (1979). 4. C. P. Ling and P. G. McCormick, Acta metall. 38, 2631 (1990). 5. P. G. McCormick, Acta metall. 36, 3061 (1988). 6. Y. Estrin and P. G. McCormick, Acta metall, mater. 39, 2977 (1991). 7. A. H. Cottrell and B. A. Bilby, Proc. Phys. Soc. Conf. B62, 229 (1949). 8. N. Louat, Scripta metall. 15, 1167 (1981). 9. F. Springer and Ch. Schwink, Seripta metall. 25, 2739 (1991). 10. F. R. Brotzen and A. Seeger, Acta metall. 37, 2985 (1989). 11. L. P. Kubin, Y. Estrin and C. Perrier, Acta metall. mater. 40, 1037 (1992). 12. E. Voce, J. Inst. Metals 74, 537 (1947/48). 13. P. G. McCormick, Scripta metall. 12, 197 (1978). 14. P. G. McCormick, Acta metal. 20, 351 (1972). 15. R. A. Mulford and U. F. Kocks, Acta metall. 27, 1125 (1979). 16. G.-C. Lenasson, Scripta metal. 6, 1125 (1972).