Strengthening of aluminium-lithium alloys by long-range ordered δ'-precipitates

~

Acta metall, mater. Vol. 43, No. 11, pp. 3983-3990, 1995 Copyright © 1995Acta MetallurgicaInc. ElsevierScienceLtd Printed in Great Britain. All rights reserved 0956-7151(95)00089-5 0956-7151/95 $9.50 + 0.00

Pergamon

STRENGTHENING OF A L U M I N I U M - L I T H I U M ALLOYS BY LONG-RANGE ORDERED 6'-PRECIPITATES

C. SCHLESIERandE. NEMBACHt Institut fiir Metallforschung, Universit~it Miinster, Wilhelm-Klemm-StraBe10, D-48149 Miinster, Germany

(Received 6 December 1994; in revised form 23 February 1995) Abstract--Strengthening of aluminium-rich aluminium-lithium single crystals by spherical, coherent particles of the L 12-long-range ordered 6'-phase has been investigated experimentally and theoretically. The total critical resolved shear stress zt has been measured as a function of the radius r and the volume fraction f of the 6'-particles. r and f covered the ranges 0.0-17.6 nm and 0.0-0.11, respectively. The 6'-particles' contribution Zp to zt is analysed with reference to a model, which had originally been developed for the description of the strengthening effect of L 1z-long-range ordered 7'-particles in nickel-base superalloys. The experimental data zp(r,J) of the present aluminium-lithiumsingle crystals are well represented by this model. The specific antiphase boundary energy of the 6'-particles has been found to be 0.070 -I- 0.020 J/m 2. This value refers to {111}-planes. Zusanunenfassung--Die H/irtung von Aluminium-reichen Aluminium-Lithium-Einkristallen durch kugelfrrmige, kohfirente Partikel der L12-ferngeordneten 6'-Phase wurde experimentell und theoretisch untersucht. Die totale kritische Schubspannung z, wurde als Funktion des Radiusses r und des Volumenbruchsf der ~'-Partikel gemessen, r und f iiberdeckten die folgenden Bereiche: 0.0-17.6 nm bzw. 0.04). 11. Der Beitrag zp der 6'-Partikel zu zt wurde im Rahmen eines Modells analysiert, das urspriinglich zur Beschreibung der Hfirtung von Nickel-Basis-Superlegierungen durch Ll2-ferngeordnete 7'-Partikel entwickelt worden war. Das Ergebnis ist, dab dieses Modell die experimentellen Ergebnisse zp(rd~ gut wiedergibt. Die spezifische Antiphasengrenzenergie der 6'-Partikel wurde zu 0.070 + 0.020 J/m 2 ermittelt. Dieser Wert gilt fiir {111}-Ebenen.

1. INTRODUCTION Aluminium-rich aluminium-lithium alloys combine a low density with high moduli and high strength [1-4]. The latter one derives primarily from fine, coherent, spherical particles of the metastable 6'-phase [1,2,5-12], which has the long-range ordered L12-crystal structure. Crystallographically, this is exactly the same situation as in nickel-base superalloys strengthened by L12-1ong-range ordered 7'-precipitates [8, 13]. In both systems the L12-ordered particles are embedded in an f.c.c, matrix. Because of the particles' order, a perfect matrix dislocation with the Burgers vector (a0/2)(l10} is only a partial dislocation in the precipitates, a0 is the lattice constant of the matrix. The particles' perfect Burgers vector is of the type a 0 ( l l 0 } . In under-aged specimens in which the particles are sheared by dislocations, (a0/2)(ll0}-dislocations glide in pairs. The leading one, D1, destroys the order in the precipitates along the glide plane and creates antiphase boundaries. The trailing dislocation, D2, which glides in the same plane, restores the order and eliminates the boundaries. Figure 1 illustrates this for the AI-Li-alloy Li8.36 described below in Section 2.1.

Since the crystallography is the same for 6'-strengthening of A1-Li-alloys and for V'-strengthening of superalloys, one expects that models of v'-hardening are also applicable to AI-Li-alloys. In this paper it will be shown that this expectation is actually fulfilled. To start with, the ideas on which the models of V'hardening are based are summarized [13-16]. In Fig. 2 the critical configuration of a dislocation pair is sketched. Under the applied resolved shear stress %, D1 is about to break free from a 7'-particle and Zp equals the critical resolved shear stress (CRSS). Li is the average spacing of ?'-particles along Di, d~ is the average length of Di lying inside a 7'-particle. In the critical moment the following balances of forces are established D I : zpbLl + ~ b L l - 7dl = 0

(la)

D2:"rpbLz-ZRbL2 + yd2 = 0.

(lb)

7 is the specific energy of the antiphase boundary. Since dislocations glide on { l l l } - p l a n e s in f.c.c. materials, 7 refers to this type of plane, b is the length of the Burgers vector of either dislocation of a pair: b = (ao/x/2). zR represents the repulsive interaction between D1 and D2. Elimination of ZR from equations (la) and (lb) yields

~ =~{a,/L,-a~/L~}.

tTo whom all correspondence should be addressed. 3983

(2)

3984

SCHLESIER and NEMBACH:

STRENGTHENING OF A1-Li ALLOYS bution [13]. In the peak-aged state L~ equals/-~n [13]. The various models for ),'-strengthening of under-aged specimens differ in what the authors inserted for L~ and for the ratio d:/L2. Raynor and Silcock [14] and Brown and Ham [15] inserted the Friedel [13, 15, 19] length LF for L~

\Fo/

•

(5)

S is the dislocation line tension and F0 the maximum force with which a particle withstands a dislocation. In the present case, F0 of D1 equals 7d~ F0 = vdl = 2Ogrry.

(6)

The term yd~ appears in equation (1 a). Nembach and Neite [13] inserted the Labusch [20] length LL for L~ in equation (2). Thus the finite range w of the interaction force between particles and D 1 is allowed for

1 LL ~-- Cl[1 + C2~7o/LFI Fig. 1. Dislocation pairs in the A1-Li-alloy Li8.36. This high order bright field image has been taken inside a transmission electron microscope under full load. After Refs

(7)

with

w(2sT

~/o = Lm~.k,Fo ]

[10, 11].

"

(8a)

and C2 are numerical constants: C~ = 0.94 and C2 ~ 0.82 [13]. In the case of 7'-hardening w was assumed to be proportional to rr C1

d~ is related to the average radius rr of the intersections between y'-particles and the glide plane; rr is proportional to the average particle radius r d l = 2rr = 2Ogrr.

If the particle radii are distributed as calculated by Wagner [17] and Lifshitz and Slyozov [18], o~r equals 0.82 [13]. The under-aged state is characterized by the condition that Ll is smaller than the square lattice spacing L~n of the particles in the glide plane

f is their volume fraction. The statistical factor Ogq equals 0.75 for the Wagner-Lifshitz-Slyozov distri-

tTp

D2 ~

~,,o~L1

•

©

--;

O

0 L2

(8b)

is an adjustable parameter. The ratio d2/L2 depends on the critical configuration of D2. If D2 is straight, dz/L2 equals f d2/L2 = f .

©

_y -0

Fig. 2. Critical configuration of the paired dislocations D1 and D2, schematically. The image plane is their common {111}-glide plane. Antiphase boundaries are shown hatched.

(9a)

If D2 lies outside of all ordered particles, this ratio vanishes

(4)

L=n = r{nCOq/f ) 1/2.

'd '

w = ~rF = ~mrr.

(3)

dz/L2 = 0.

(9b)

Nembach e t al. [21] strained under-aged single crystal thin foils of the 7'-hardened nickel-base superalloy N I M O N I C PE16 inside a transmission electron microscope and observed the configurations of D 1 and D2 under full l o a d . f was equal to 0.089, this is comparable to f of the present A1-Li-alloys (Table 1). On the basis of these in situ experiments, Nembach and Neite [13] favoured equation (9a). Recent computer simulations performed by Pretorius and R6nnpagel [22] support equation (9b): the antiphase boundaries pull D2 forward until it has left the ?'-particles. Equations (9a) and (9b) are therefore written in a unified form d2/L2 = ~ f

with 0.0 < ~ < 1.0.

(9c)

SCHLESIER and NEMBACH:

STRENGTHENING OF A1-Li ALLOYS

Table 1. Present experimental results for the C R S S ( T = deformation temperature) No.

c,

f

r [rim]

T [K]

z [MPa]

1 2 3 4 5 6 7 8 9 10 lI 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

0.0000

--

------

283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90 283 170 90

5.5 + 0.2 5.9 + 0.5 6.2 + 0.3 9.4 + 0.6 11.8 __+0.2 14.0 _ 0.2 36.7 + 9.1 44.4 + 2.7 47.7 -I- 1.3 36.4 _ 1.7 39.9 + 1.9 37.7 _ 2.8 50.6 _+ 7.5 51.1 + 2.3 49.0 +_ 1.7 59.8 --+_2.4 57.7 + 4.3 55.0 + 2.4 57.9 + 6.4 57.5 _+ 3.9 53.8 ___4.5 58.5 + 7.0 52.7 _ 3.4 48.9 + 1.3 66.6 _ 1.3 69.3 + 2.7 72.2 + 0.8 72.5 + 5.7 71.5 _+ 3.8 80.1 +_ 4.6 82.9 _+ 2.6 81.0 _+ 0.9 84.3 + 1.0 95.0+0.3 86.7 + 4.7 91.3 + 1.9

0.0374

0.0683

0.0836

----0.0322

4.67

0.0374

7.63

0.0592

10.98

0.0592

14.15

0.0592

16.82

0.0592

17.55

0.0926

6.42

0.111

9.42

O.lll

11.97

0.111

15.97

Substituting LL for Ll in equation (2) yields for the CRSS Zp [13]

,hrA

;}

(10a)

3985

Raynor and Silcock's [14] and Brown and Ham's [15] description of ~'-hardening is recovered from equation (10a) by setting ~ equal to zero and ~ equal to 1.0. There remain some minor differences in the statistical factors. Ardell et al. [16] have published a relation, which is similar in structure to equation (10a), but the statistical factors are slightly different. Ardell et al. allowed for the finite extension of the particles. They derived S within the frame-work of linear isotropic theory of elasticity. In Nembach and Neite's [13] treatment the elastic anisotropy is taken into consideration. S is written as

S(O) = gs(O)b21n(Ro/R,).

(11 a)

0 is the angle between the direction of the dislocation and its Burgers vector. Ks has to be calculated as laid down by Barnett et al. [23]. Ro and R~are the outer and inner, respectively, cutoff radii, b = (ao/xf2) will be inserted for R~. There are at least three reasonable choices for no: Lmin [equation (4)], Lr [equation (5)] and LL [equation (7)]. Since D1 is rather strongly bent, Nembach and Neite [13] suggested the use of the geometric mean [S(O = O°).S(O = 90 °) ]~/2in equations (10). This proved to be a suitable average. It will be used in the evaluations presented in Section 3. The elastic stiffnesses C~kneeded for the calculation of Ks(0) have been measured by Miiller et al. [24] at ambient temperature. The variation of Ks with the atomic fraction Csof Li in the matrix and with the temperature T is expressed by

Ks(O,c.T) = Kso(O)[1 + p(O)c~]~p(T)

(1 lb)

with Ks0(0 = 0 °) = 4.38 GPa Ks0(0 = 90 °) = 0.920 GPa

with

p(O = 0 °) = 0.921 A* = 2Cl,~_~--w~~,

(10b)

and A2*

2C1C2o92 /~tOq

(10c)

F o r the Wagner-Lifshitz-Slyozov distribution of particle radii, A* and A2* equal 0.91 and 0.44, respectively. Equation (10a) relates the CRSS to the properties of the ordered particles: r , f , ~ and 4. F o r future reference equation (10a) is rewritten

2bzp

f

F r -p/2 = A~*y3/:L~ j + 7(A2"¢ -- a).

(10d)

Thus one expects a straight line if [2b~p/f ] is plotted vs [r/(fS)] "2. The slope yields ? and the ordinate intercept the term [A2*~ - a]. Unless additional information on a is available, it is not possible to derive ~ from measurements of %.

p(O = 90 °) = 4.55. Ks is assigned the temperature variation of the mean shear modulus [C44(C~1- C12)/2]la of pure A1. Thus one obtains for ¢: ~(283 K ) = 1.000, ~b(170 K ) = 1.064 and ~b(90 K ) = 1.102. The lattice constant a0 is 0.405 nm [25] at 283 K; at 90 K it is about 0.4% smaller. The variation of a0 with cs is negligible. Below measurements of the CRSS of under-aged 6'-strengthened AI-Li-alloys are reported. The data will be discussed in the light of equations (10). Chemical and coherency strengthening [13, 15] are expected to be negligible for such alloys because the specific energy of the 6'-particle-matrix interface is less than 0.02 J/m 2 [26-28] and the lattice mismatch of the two phases involved is less than 10 -~ [29, 30]. The total CRSS zt of actual AI-Li-single crystals comprises not only the zp needed to overcome the long-range ordered 5'-particles, but also the solid solution matrix' contribution z~. Nembach and Neite

3986

SCHLESIER and NEMBACH:

STRENGTHENING OF A1-Li ALLOYS

[13] and Btittner et al. [35] introduced the following empirical relation for the superposition of Zp and z~ z~ = Zpk + ~.

(12)

Since there is no theoretical basis for this equation, the exponent k has to be established experimentally. This is done on the basis of the different temperature (T) dependencies Of Zpand z~. % is only weakly temperature dependent; this is evident from equations (10). zs, however, varies strongly with T because thermal activation is involved, k of under-aged V'-strengthened N I M O N I C PE16 single crystal specimens turned out to be 1.23 [13]. % is experimentally not directly accessible: it has to be derived from equation (12). Labusch [36] has shown that zs is a linear function of c~/3, cs is the atomic fraction of Li in the matrix. Hence z~(c~,T) is written as z~(cs,T) = z~(c~ = O.O,T) + Zoo(T)c~/3.

(13)

At 433 K, c~ in equilibrium with large 6'-particles is around 0.06 [30-34]. If they are small, cs varies with their radius. This will be taken into consideration in the evaluations presented in Section 3.

2. EXPERIMENTS

2. I. Alloys Three different Li-concentrations have to be distinguished: the overall-concentration c, that of the solid solution matrix (cs) and that of the 6'-particles (Cp). Three Al-rich A1-Li-alloys and pure A1 have been studied, the number after Li indicates 100 times c,: Li0.0; Li3.74; Li6.83; Li8.36.

Alloy Li8.36 contains 0.0046 Fe, 3 x 10 -4 Si, 2 × 10 -4 Zr and 10 -4 Mg. Alloys Li3.74 and Li8.36 have been provided by Alcan International Ltd, England. Alloy Li6.83 was melted from high purity A1 and from an A1-0.47Li-master alloy produced by Sumitomo Light Metal Industries Ltd, Nagoya, Japan. 2.2. Specimen preparation Single crystals of 4 mm diameter were grown in BN-crucibles by a zone melting technique. The alloy compositions were checked by atomic absorption spectroscopy. No segregation was detected. The crystals had orientations close to (100~. They were subjected to the following heat treatments in argon filled quartz ampoules: 1.5 h homogenization at 843 K, 0.5 h nucleation treatment at 393 K and 5-672 h Ostwald ripening treatment at 433 K. After the latter treatment the specimens were spark machined to their final dimensions: 1.9 mm diameter and 5 mm length. Since they had been heat treated in the bulk, Li-losses at their surfaces [37] have been avoided. The specimens' orientation was close to (10 2 1~. After the final heat-treatment all specimens of alloy Li8.36 contained some widely spaced plate-like Fe-rich precipitates. Their dispersion was independent of the duration of the 433 K-Ostwald ripening treatment. In Fig. 3 a scanning electron micrograph of such Fe-rich precipitates is presented. 2.3. 6'-particle dispersion In an earlier investigation r and f of the spherical 6'-particles have been established as a function of the duration t of the heat-treatment at 433 K [38]. r and

Fig. 3. Scanning electron micrograph of alloy Li8.36.

SCHLESIER and NEMBACH:

STRENGTHENING OF AI-Li ALLOYS 0.8

f of the present specimens were read from the respective curves. As long as r(t) is less than 9.4 nm, f i n c r e a s e s strongly with t. This is evident in Table 1. f o f a l l o y Li6.83 is between 0.0322 and 0.0592,fofalloy Li8.36 varies between 0.0926 and 0.111.

. . . .

,

. . . .

,

3987

. . . .

'

. . . .

0.6

2.4. Measurements of the C R S S •

The C R S S was determined in compression tests at 90, 170 and 283 K. The resolved strain rate was 1.3 × 10 4 s ~. These temperatures were meant for establishing k of equation (12). The results for z~ of alloys Li0.0 and Li3.74 and for zt of alloys Li6.83 and Li8.36 are listed in Table 1. Each entry is the average over the data taken for 2 3 specimens. The standard deviations of the averages are also quoted. The mean over these deviations amounts to 4.4% for ~ and to 5.9% for z~. Between the final heat treatment and the compression tests, the specimens were stored in liquid nitrogen, except for about 2 h needed for sparkmachining them. z~ of alloy Li3.74 is somewhat higher than to be expected on the basis of the data published by Miura et al. [39]

~

S i n c e f o f alloys Li6.83 and Li8.36 increases with the duration t of the 433 K-treatment, c~ decreases. The lever rule relates c~ to f , ct and cp CI

c~=

--

~

0.4

f = O.lll

0.2

0.059

o

•

T = 283K

[]

•

T = 170K

t, I

0

i

i

i

t

I

5

I

• i

I

t

10

[ r / ( f S )]1/2 3. EVALUATIONS AND DISCUSSIONS

oep

.

T = 90K .

.

.

,

15

.

.

.

.

20

[m2/jlll2

Fig. 4. Present experimental data: [2brp/J]plotted vs [r/(fS)] ~/2. The straight line represents equation (10d) fitted to the data; the three highest ones have been excluded from the fitting routine.

JCp

l-f"

(14)

Cp at 433 K is 0.23 [30, 33]; it is assumed to be independent of t. Inserting c~ into equation (13) yields the C R S S rs of the specimen's matrix. The coefficients zs(c~ = 0.0,T) and r00(T) in equation (13) are derived from the z~-data of alloys Li0.0 and Li3.74. Since r~ of the 6'-particle containing alloys amounts on average to only 25% of z,, the temperature dependence of z, is too weak to derive the exponent k appearing in equation (12) by a fitting procedure. In the case of the 7'-strengthened nickel-base superalloy N I M O N I C PE16 such a fitting procedure yielded for under-aged specimens k = 1.23 [13]. The ratio z/zt and the temperature variation of z, of the latter alloy were high. The system copper-cobalt led to similar results for k [35]. Therefore k of the present A1-Li-alloys is assigned the value 1.23. According to equation (10d) the term [2bzp/f] is plotted vs the term [r/(fS)] 1'2 in Fig. 4. S equals the geometric mean of the line tension of edge and screw dislocations. Lmm of equation (4) is inserted for the dislocation's outer cut-off radius Ro. The straight line represents equation (10d) fitted to the present data. Since the zp-data Nos 7 9 are unreasonably high they have been excluded from the fit. These are the three highest points in Fig. 4. Since they have the smallest particle radii, Tp may have been affected by chemical hardening. Evidently equation (10d) represents all other experimental data well. Their average deviation A from the fitted straight line amounts to 6.7%. This

is well within the combined error limits of %, r a n d f . The specific energy 7 of the antiphase boundary follows from the slope of the straight line: 7 = 0.0627 J/m 2. This value applies to { 111 }-planes. The ordinate intercept yields the term [A*~ - ~t]: 3.8. If the finite range w of the interaction force between the leading dislocation D1 and the 6'-particles is disregarded, vanishes. The positive intercept indicates that ~ is actually finite. Though this intercept is rather sensitive to the evaluations, all of the alternative evaluations listed in Table 2 yield positive intercepts. The reliability of the above result for 7 was checked by trying alternatives for k, S and zs(c~ = 0.0,T) in equations (10d), (12) and (13). The results of these and some other alternative evaluations are compiled in Table 2. The basic evaluations described in the preceding paragraph are repeated in the first line. Evidently all results for 7 are close together. Those obtained for k = 1.00 are quoted in line No. (ii). Since

No. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x)

Table 2. Alternative evaluations Alternative 7 [J/mz] A [%] (A*~ 0.06 evaluated 0.0874 4.8 1.8 Onlydata with.(< 0.06 evaluated 0.0808 7.6 1.7 Data Nos 7-9 included 0.0594 9.8 4.6 z, of Li8.36 reduced by 3 MPa 0.0710 6.5 2.8 S of edge dislocations 0.0495 6.7 4.9 S of screw dislocations 0.0794 6.6 3.0

3988

SCHLESIER and NEMBACH:

STRENGTHENING OF A1-Li ALLOYS

Table 3. Experimentaldata from the literature (s = singlecrystals, p = polycrystals) No. f r [nm] "ct[MPa] "rs [MPa] p or s Reference 101 0.030 2.10 20.0 16.0 p [6] 102 0.067 6.25 56.0 15.0 103 0.090 9.00 72.0 14.0 104 0.120 11.56 88.0 13.5 105 0.140 14.44 98.0 13.0 106 0.150 5.72 91.0 22.0 p [5] 107 0.150 7.81 100.0 22.0 108 0.150 9.59 104.5 22.0 109 0.010 2.00 10.0 7.0 s [7] 110 0.018 3.50 17.0 6.5 111 0.025 5.00 30.0 6.0 112 0.033 8.00 42.5 5.5 113 0.070 15.00 58.0 5.0 114 0.017 6.00 39.4 21.0 p [43] 115 0.058 8.50 111.3 20.0 116 0.059 13.00 132.9 20.0 117 0.130 6.10 50.6 7.6 s [12] 118 0.150 9.10 59.6 7.6 119 0.160 13.10 70.6 7.6 120 0.160 16.50 80.6 7.6

zs of pure A1 turned out to be rather high, as an alternative T~(cs= 0.0,T) was assumed to vanish [line No. (iii)]. Changing Ro from Lm~,to the Friedel length LF [equation (5)] has hardly any effect [line No. (iv)]. If the data obtained for specimens with f > 0.06 [line No. (v)] and with f < 0.06 [line No. (vi)] are evaluated separately, only a short range of the term [r/(fS)] ~/2 is covered in either case. This renders the slopes of the respective straight lines less reliable. The CRSS of alloy Li8.36 is slightly increased by the plate-like Fe-rich precipitates shown in Fig. 3. Their effects on are estimated as follows. If these Fe-rich precipitates were the only obstacles to the glide of dislocations in alloy Li8.36, Orowan's relation as formulated by Kocks [13, 40] would yield a few MPa as CRSS. Therefore as another alternative evaluation, Tt of alloy Li8.36 is rather arbitrarily reduced by 3 MPa. The results of this alternative are presented in line No. (viii) of Table 2: ? is raised by 13 %. Instead of the geometric mean of the line tensions of edge and screw dislocations, their individual line tensions have been tried [line Nos (ix) and (x)]. All ordinate intercepts are positive, even that obtained for Ro = const. = 1000b. This proves that the range w which appears in equations (8) has to be allowed for. Only finite values of w lead to positive ordinate intercepts. The scatter A found for k = 1.00 [line No. (ii)] in Table 2 exceeds A found for k = 1.23 [line No. (i)] by 22%. This result supports the choice k = 1.23. As stated above, it is, however, impossible to derive the o p t i m u m choice of k by an optimization procedure as has been done for N I M O N I C PE16 [13]. Since the ratio z~/~t of the present 6'-strengthened A1-Li-alloys is relatively small, the exact value of k is not very important for them anyway. On the basis of Table 2, it is concluded that ? equals 0.070 _ 0.020 J/m 2. H u a n g and Ardell [8] have compiled published data on 6'-strengthened A1-Li-alloys. These data are reproduced in lines Nos 101-116 in Table 3. There are, however, problems with m a n y of these data. (i) Since

often polycrystals have been investigated, a suitable choice had to be made for the Taylor factor. Possible softening due to 6'-precipitate free zones along grain boundaries has been disregarded [41, 42]. (ii) Furukawa et al. [6] may have overestimated the increase of f with aging time t. (iii) In the case of Sainfort and Guyot's [5] data this variation o f f with t and the ensuing effects on zs have been entirely disregarded. (iv) In the light of the present and of Miura et al.'s [7, 39] zs-data, those listed in lines Nos 106-108 and 114--116 of Table 3 appear to be too high. In lines Nos 117-120, the more recent single crystal data published by Gerold et al. [12] have been added. All data presented in Table 3 are assumed to have been taken at ambient temperature. They and the 283 K-data of Table 1 are plotted in Fig. 5 according to equation (10d). The straight line represents this equation fitted to the data. Since the data Nos 101, 109, 114-116 of Table 3 strongly deviate from all others they have been excluded from the fitting routine. The latter ones are those published by Cassada et al. [43]. Already H u a n g and Ardell observed the strong deviations of these data. Nos 101 and 109 concern those specimens whose average 6'-particle radii are the smallest ones studied by the respective group. In order not to give the present data too much weight, only those taken at 283 K have been included in the analysis. The results for k = 1.23 and R o = = 0.109 J/m 2, A = 15% and [Az*~ - ct] = 0.3. As in Zmin

.

.

.

•

1.2

"E

.

,

s

.

.

.

.

,

.

.

.

.

i

.

.

.

a r e :

.

0

present

I s Gerold

-~A

13 s

Miura

v p

Furukawa

0

p

Sainfort

/x p

Cassada

~ A

-->A

0.8

w

e4

0.4

~ •

0 0

o

,

°

lUll

|

5

,

,

.

111

.

,

10

.--~

.

.

.

.

13

I

15

.

.

.

.

°

20

[ r / ( f S ) Im [m2/J] m Fig. 5. [2bzpff] v s [r/(fS)] 1/2. Data: Furukawa et al. [6], Sainfort and Guyot [5], Miura et al. [7], Cassada et al. [43], after Huang and Ardell [8]; Gerold et al. [12]; s = single crystals, p = polycrystals. The straight line represents equation (10d) fitted to the data; those marked by arrows have been excluded from the fitting routine.

SCHLESIER and NEMBACH:

STRENGTHENING OF AI-Li ALLOYS

the analysis of the present data, the geometric mean of the dislocation line tension of edge and screw dislocations has been used. Evidently equation (10d), which is represented by the straight line describes the data allowed for in the fitting routine, satisfactorily. If k = 1.00 is chosen, the respective results are 0.101 J/m 2, 15%, 0.4. It is evident in Fig. 5 that the data taken by each group cover only a rather small range of the abscissa. This renders it unreliable to derive ~ from the slope of such data. The present data cover the widest range. The second widest one is that of Cassada et al.'s data, which, however, deviate very strongly from all others. If 7 is to be calculated for each group's set of data separately, the respective set has to cover a sufficiently wide range of the abscissa of Fig. 5. It transpires from it that of all data listed in Table 3 only those published by Sainfort and G u y o t [5] and Gerold et al. [12] can be meaningfully analysed. The respective results for 7 are 0.115 and 0.096 J/m2; they have been obtained for k = 1.23, Ro = Lminand the geometric mean of the line tensions. The present data compiled in Table 2 yielded as final result for the antiphase boundary energy ~ of 6'-precipitates in A1-Li-alloys: 0.070 + 0.020 J/m 2. "~ derived from Gerold et al.'s data is only slightly outside this range. The authors themselves gave a higher estimate: 0.165 J/m 2. One reason for this high value of 7 is the high dislocation line tension which the authors inserted. H u a n g and Ardell too derived higher values for 7 from the data Nos 101-116 of Table 3. Again the main reason seems to be the authors' high dislocation line tension. Glazer and Morris [44] obtained y from the onset of the Orowan process: 0.057 + 0.015 J/m 2. Khachaturyan and Morris [45] computed ~ in a second-neighbour interaction model: 0.072 J/m 2. Ardell and H u a n g [46] drew attention to possible short-comings of both approaches. Miedema et al.'s [47, 48] methods of estimating the enthalpies of formation of alloys, leads to the conclusion that 7 of 6'-particles in A1-Li-alloys is by far smaller than ~ of 7'-particles in superalloys. 7 of the latter particles is around 0.25 J/m 2 [13]. Hence the present result 0.070 +_ 0.020 J/m 2 for 6'-particles appears to be reasonable. Nembach et al. [10, 11] tensile tested thin foils of alloy Li8.36 in a T E M and observed the configurations of dislocations under full load. Cross-slip was found to occur rather frequently. Besides the dislocation pairs shown in Fig, 1, there were also unpaired dislocations. Since equations (10) represent the experimental data on the CRSS of the present alloys well, it is not very likely that either process--cross-slip or unpairing of dislocations--has strong effects on the CRSS. 4. CONCLUSIONS 1. Equations (10) which have been meant to describe 7'-hardening of nickel-base superalloys, represent the

3989

present experimental data on 6'-strengthening of AI-Li-alloys well within the limits of error. 2. The { 111}-antiphase b o u n d a r y energy 7 of the L12-1ong-range ordered 6'-particles in AI-Li-alloys has been found to be 0.070 + 0.020 J/m 2. 3. The present experimental data are in reasonable agreement with published ones. The present ones cover, however, a wider range of the term [r/(lS)] 12. This makes the result obtained for 7 more reliable. Acknowledgements--The Minister fiir Wissenschaft und

Forschung des Landes Nordrhein-Westfalen and the Deutsche Forschungsgemeinschaft are thanked for financial support. Alcan International Ltd, England (alloys Li3.74 and Li8.36), Sumitomo Light Metal Industries Ltd, Japan (A1-Li-master alloy), and Vereinigte Aluminium-Werke, Bonn, Germany (high purity A1), provided the indicated materials. This is gratefully acknowledged. REFERENCES

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