Propagation of an heterogeneous precipitation case of φ′ in an A1-4 wt % Cu alloy

Scripta

METALLURGICA

V o l . 15, pp. 3 7 3 - 3 7 8 , 1981 Printed in t h e U . S . A .

Pergamon P r e s s Ltd. All rights reserved

PROPAGATION OF AN HETEROGENEOUS PRECIPITATION CASE OF 0' IN AN AI-4 wt % Cu ALLOY

P. MERLE, F. FOUQUET and J. MERLIN Groupe d'Etudes de M~tallurgie Physique et de Physique des Mat@riaux (ERA 4.63) INSA de LYON Bat. 502 - 20, avenue Albert Einstein - 69621 VILLEURBANNE CEDEX FRANCE -

(Received (Revised

December ii, 1 9 8 0 ) January 22, 1 9 8 1 )

Introduction It is well known that 0' precipitation starts on dislocations and afterwards expands by nucleation of new precipitates in the matrix. This last nucleation is due, according to Lorimer (i), to the stress field of precipitates which are placed in the precipitation front. This sequence has always been described only in qualitative terms ; this paper deals with the methods we have used to study it quantitatively and the results we have obtained. Experimental

procedure

An AI-4 wt % Cu alloy is aged at temperatures between 200 and 275°C after a reversion treatment (2). To describe quantitatively the propagation of the precipitation inside the matrix, we define the quantity ~ (fig. i) such that : ~ V2/(V 1 + V 2) where V 2 is the volume of matrix occupied by the precipitation and V 1 is the volume of residual solid solution. The determination of ~ is made by hardness measurements and is based on the following assumptions :i) the hardness H V of a sample may be given by the relation H V = ~ HV@' + (I - ~) HVS S where HV@, is the hardnes~ of the regions occupied by the @' precipitates and HVSS, the hardness of the residual solid solution ; ii) the copper concentration in domains free from precipitates remains equal to the initial one c o . HV@, cannot be measured directly. As ~, it is an unknown quantity of the p r o b l e m We must also verify the validity of hypothesis i) ; so we made hardness measurements on four different structural states. These states are defined by the following treatments : State 1 : The sample is aged during the time and at the temperature chosen for the formatlon of 0'. The hardness of the sample is : HV'I = ~ HV@' + (i - ~) HVS S (a). State 2 : state i followed by an aging of 3 days at 100°C. In such conditions, GP zones are formed in the domains of residual solid solution. The hardness of the sample is therefore: HV2 = ~ H V~-, + (I - ~) HVG P (b). State 3 : state 2 followed by an aging of I0 days at 130°C. At this temperature, @' is stable and we obtain a progressive transformation GP + 0" in the domains where GP zones are formed. The hardness of the sample is thus : HV 3 = ~ HV] 0' + (I - ~! HV10" (c). State 4 : State 3 followed by an aging of 5-days dt 130 C. The transformation GP ÷ O"is achieved and the hardness of the sample becomes : HV4 = ~ HV@, + (i - ~) HV2@,, (d). To establish these four relations, we assumed that the hardness of domains where 0' has precipitated does not vary during further treatments, i.e. they remain stable between states i and 4. This has been verified by electron microscope studies. Fig. 2 ~ a n d ~ are micrographs obtained with samples in states 2 and 4. We can see that 0" or GP zones precipitations remain localized in domains where 0' has not precipitated. Moreover, hardness measurements which have been done on samples aged 6 h 30 at 225°C, at which stage the 0' precipitation occupies the whole matrix, show that this hardness remains constant when the sample is subject to all the treatments between state i a n d 4 : the supersaturation of copper in the matrix is therefore too small and 0"

373 0036-9748/81/040373-06502.00/0 Copyright (c) 1 9 8 1 P e r g a m o n Press

Ltd.

374

PROPAGATION

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or GP zones cannot form. It can be seen on fig. 2b that the diffusion field of precipitates (revealed by the freu zone around them) is not very extended (200 to 300 A) in comparison with the size of domains of precipitation (a few pm), which justify assumption ii). Experimental

results

The Vickershardnesses HVss, HVGP, HVI@,, , HV2@,, are determined with samples aged according to the treatments described, but without the first sequence of state ]. We have : HVS S = 59, HVG P = 104, HVI@,, = 116, HV2@,, = 124. Tables 1 and 2 give the values of S2 which have been obtained with systems formed with equations (a,b),(a,c),(a,d). The different values which are found are in good agreement, which proves the validity of the assumptions made. Q(t) kinetics are shown on fig. 3 for various temperatures of aging.

.q•Temperature

~ouations~tim e svstems)~ r.

(a -b)

200°C

I

15

20

0.21 I 0,43 0.68 0,9

,

2

10

225"C

0.67

•q

(a -c)

0,17

:.

(a - d)

0,19 0,41 0,67

0,43

0.8B"I

0,37 I I

svste~s~

(a - b ) .~

(a - c ) (a - d)

-

-

20

0.19 !0.4

0,97 'o,17'

0.28 0.46 0.79

1

0.81

1

t il 90

I

9 0.31 0.46 0,82J 1

l 3 I 6

19

15 ~ 30

0,9 'I 1 10,15 0,28 0,43 0.64 I

o.,io, j, io.,, 0,25

i

0.38 0,65 i

1

0,16 0,36 0,67 0,84 "I

0,26 0,33 0,55 0,8 I

1

0,17 0.37 0,68 0.85

0,23 0,35 0,59 0,81

I

Analysis

Table

275°C

40 j 60 0,7

1

I

250°C IO

I 4 16,t

C,2] I0,35 0,47

0.19 0,42 , 0.67! 0.89 0,98

_•.Temperature Equations~'-~----=T-~.

2

I

Table 2

and interpretation

We call ~o the volume fraction occupied by the precipitation directly nucleated on the heterogeneous sites of germination. As the rate of propagation of the precipitation front may be considered as constant (this propagation being due to a succession of identical events), the transformation may be analyzed by mean of an Avrami's equation, if we exclude from this analysis the precipitation nucleated in ~o. We can thus write ; = 1 - (1 - ~o ) exp ( - t/T) ~o is determined by llnearization of the curve in In tlcs corresponding to different temperatures of aging This seems quite acceptable if we refer to mlcrograph are gathered in bands of hellcoTdal dislocations which of the matrix.

(e)

1 - ~ a = f(Int)(fig. 4). For all the kineI ; ~s comprised between 0,13 and 0,15. 5 a obtained on the initial state. Defects are parallel to the (111) glide planes

Model : To determine ~o, we have assumed that the curve ~ (t) derived from an expression like (e), but we can try to obtain directly a theoretical expression for the evolution of ~. Owing to the arrangement of defects revealed by fig. 5a, we can assume that the precipitation expands in the matrix from plane areas of defects (flg.5b). It is thus possible to derive a theoretical expression by developing an analysis similar to that of Cahn, for grain boundary nucleated reactions (3). If N o is the initial density of defect clusters in a plane ~,which give rise to small domains of precipitation, one can consider that the evolution of the number of these clusters is given by N = N o exp (- ~t) where v has a high value (the number of active sites decreases quickly during the first moments of germination). In a plane (P) at a distance y from ('~)

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PROPAGATION

6) t h e " e x t e n d e d a r e a "

OF

(see ref.

HETEROGENEOUS

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3) o c c u p i e d by t h e p r e c i p i t a t i o n

375

will

be :

t - y/V _ y2 of {v2(t- T)2 } No ~ exp (- vt) dT

Se = ~ Sb

if S b is the area of plane (~), v the rate of propagation of the precipitation gives, With ~ = y/vt, and if we extrapolate to high values of ~ : S e = ~ S b N a v 2 t 2 (I - 2 )

if

~

~

1

Se = O

if

{

~

i

front. This

The real volume occupied by precipitation at time t is, for a unit volume of matrix, V r = 2 ~ S r dy, S r being the real surface occupied by precipitation at time t and defined by Se/S = - in (i - St/S) , where S = I S b is the total area of planes of defects in the unit volume. If we identify V r with the quantity (~ - ~o)/(I - ~o ), we find : - ~o I - ~ o

- 2 vtS {i - exp - ~ N

= 1 - exp

o

v 2 t2

it exp ~ N v 2 t 2 ~2 o o

d~

} (f)

Classical expressions like e) with m = l o t 3 area found when N O leads to very high or very low values, and although (f) is strictly different from (e) it can be approximated very correctly by an expression of this kind for any value of N o Comparison with experimental results tance between planes of defects : As S = I/L, by putting 1 - ~o - ~O

= 1 - exp { -

: if t~ is the time for which ~ = I and L is the mean disv = L/t~ (g)

t/t~ = u and ~ =/-NoL , we have 2u

D

"

exp ( - B2 u 2

/ 1 exp o

: 82 u 2 ~2

d~

}

A good agreement (fig. 7) is found with experimental results u n t i l ( ~ - ~ / ( I - ~ o ) = 0,8 if we put ~2 = 13. L can be estimated to about a few ~m, which gives No = 0,5 to 3/~ 2. This is a physically acceptable value, if we bear in mind that N o is the density of clusters of defects. The rate of propagation of the precipitation front can be simply defined by eq. (g) and we can compare the possible values of v with those obtained by Laird and Aaronson (4) for the rate of lengthening V D of isolated O' plates (Table 3)

T('C)

Vn.lO 8 cm/s -(ref.4)

200

0,33

225 250

3,06

275

5,13 Table 3

V 108 cmls L = 2 lJ L : 5 lJ 0,25

0,6

0,8

2

3,5 6

9 20

We have a good agreement for L = 2~ , i.e. in the range of possible values for L. So we can identify the rate of propagation of the precipitation front with the lengthening rate of isolated O' platelets. Moreover the determination of the activation energy with the kinetics ~(t) obtained for different aging temperatures gives 1,1 eV, which is very close to the activation energy of isolated precipitates given by Aaronson and Laird (i eV - fig. 8 ref. 4).

The quantitative model that we have developed seems thus to describe correctly the propagation of the O' precipitation in the matrix and shows that the propagation rate of the precipitation front and the lengthening rate of isolated precipitates have very close values.

References i. 2. 3. 4.

G.W. LORIMER, Proc., of the Fourth Europ. Reg. Conf. on Electr. Micr., Rome (1968) F. FOUQUET and al., Mere. Sci. Rev. Met., 9, 683 (1973) J.W. CAHN, Acta Met., 4, 449 (1956). H.I. AARONSON and C. LAIRD, Trans. of the Met. Soc. of A.I.M.E., 243, 1437 (1968).

376

PROPAGATION

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I'l V2 [e']

,i

FIG. I. Schematic representation of @' precipitation in the heterogeneous stage. V 2 : volume occupied by @', V 1 : volume of residual solid solution.

v, ls,

-T

a

b

FIG. 2. A1 - 4 wt % Cu : a) State 4 b) State 2

1

T('¢:) - 2!S

0,5;

F2f

'

,//.j 0

,

lg'

I

1

250

225

I

I

:.

i

1

I

200

FIG. 3. Propagation kinetics of 8' precipitation in the matrix for various aging temperatures. AI - 4 wt % Cu.

'

D

10

4

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377

in In 1-~o 1-~

7

/

FIG. 4. Determination of ~o by linearization of

,o .,0 7

i In in

q

-I

o

f (In t)

i -

° d'/~ _2

fl° -_0,1 "

,<

.Q°_-0,13/~/=0,15, -3

,

int

i

i

i

3

4

5

6

Fig. 5. a) Defects in samples before reversion b) 0' precipitation for a short aging (70' at 225°C).

378

PROPAGATION

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T = 225"C expe ;

"~precipitation ~z'~ I fr°nt

J

I

~zb

i

o,5 //.~t heoretical 1

FIG. 6.

10

FIG. 7. Comparison between experimental and theoretical propagation kinetics of the 9' precipitation.

4