A new method to quantify the Portevin-Le Chatelier instabilities: application to aluminium-lithium alloys

MATERIALS SCIENCE & ENGINEERING ELSEVIER

Materials Science and Engineering A196 (1995) 79-87

A

A new method to quantify the Portevin-Le Chatelier instabilities: application to aluminium-lithium alloys B. Wack, A. Tourabi Laboratoire Sols, Solides, Structures ([brmerly 1.M.G.), B.P. 53 X, 38041 Grenoble Cedex, France Received 21 December 1993; in revised form 17 October 1994

Abstract

The use of a new method of double strain measurement makes it possible to quantify the macroscopic aspects of the Portevin-Le Chatelier instabilities which appear with some A1 Li alloys and particularly with the former version of the industrial 2091 alloy. Among other parameters, a strain localization ratio which may reach values up to 180 is defined. The results obtained suggest a possible explanation of the decrease in toughness with ageing time of the former version of the industrial 2091 alloy.

Keywords: Mechanical behaviour; Toughness; Alloys; Portevin-Le Chatelier instabilities

1. Introduction The industrial 2091 alloy, in its former version, exhibited a distinct drop in toughness with ageing time ta of the thermal treatment between 6 and 24 h (see Fig. 10 of Ref. [1], or Fig. 2 of Ref. [2]). Furthermore, after a small percentage of tensile deformation, some strain localization effects appear which are characteristic of a P o r t e v i n - L e Chatelier (PLC) phenomenon [3]. The decrease in toughness cannot be explained classically; in fact the material strength seems rather to increase a little with ta, whereas the Young modulus appears to be independent of ta. In order to help understand this situation, a series of systematic experimental tests was conducted, taking great care of the test quality. This was done not only on the 2091 alloy, but also on two simpler model alloys, A1-Li and A I - C u - M g , neither of which exhibit such a drop in toughness. One of the original aspects of the experimental method consists in the use of both a local and a global strain determination for the tensile tests; comparison renders possible quantification of the macroscopic aspects of the PLC phenomenon. However, some of its characteristics are dependent on the ageing time ta and thus suggest a possible explanation of the toughness variation [3]. In the first part of the paper the experimental method is presented, with the definition of the materials tested 0921-5093/95/$09.50 © 1995 - - Elsevier Science S.A. All rights reserved S S D I 0921-5093(94)09716-X

(Section 2). Then the method of determination of the Young modulus and the corresponding results are given (Section 3), as are the results concerning the materials strength and its dependence on t, (Section 4). Finally quantification of the PLC phenomenon is described (Section 5).

2. Experimental method In addition to the industrial alloy, two model materials were studied, one without lithium (denoted A I - C u Mg) and the other without copper and magnesium (denoted A1-Li). As far as precipitation is concerned, the superposition of these two alloys may be roughly considered to be an equivalent alloy of the 2091 series. These materials are elaborated at the Centre de Recherche de Voreppe (Pechiney) in the shape of 1.6 m m thick sheets [1]. The chemical compositions of the three materials are given in Table 1 [4]. After solution treatment (20 min at 527 °C for 2091 and A1-Li alloys and 20 min at 500 °C for A 1 - C u - M g alloy) the materials are water quenched and 2% strained. Further thermal treatment is ageing at 150 °C for a duration ta equal to 6, 12 or 24h. In the 2091 and A1 C u - M g alloys the grains are recrystallized and equiaxed with a diameter of 2 5 - 3 0 ~tm and about 60 ~tm respectively [5].

B, Wack, A. Tourabi / Materials Science and Engineering A196 (1995) 79-87

80

Table 1 Chemical composition (wt.%) of the three alloys

2091 AI-Cu-Mg AI-Li

Li

Cu

Mg

Zr

Ti

Si

Fe

Na

AI

2.0 _+0.06

2.15 + 0.06 2.1 +_0.06 0.006

1.58 ± 0.06 1.35 ± 0.06 0.04

0.08 ± 0.003 0.09 ___0.003 0.095 ± 0.003

0.02 0.02 0.01

0.04 0.04 0.05

0.05 0.03 0.015

0.0004 <0.002

Balance Balance Balance

2.3 ± 0.05

In the A1-Li alloy the grains are flat discs parallel to the rolling plane with a diameter of about 250 gm and a thickness of about 50 ~tm [5]. The form of the tensile sample is suggested by the ISO 50 standard; the length Lg a t the gauge section part is equal to 60 mm and the corresponding width wg is equal to 12.6 mm. The sample axial strain is measured locally by an extensometer in most cases, i.e. ext; for a strain amplitude less than or equal to 2.5%, the measurement base B is equal to 30 mm, and for greater strain amplitude it is equal to 10 mm (Fig. 1). A global axial strain measurement eg~ is also used; it is obtained by the relative displacement of the two sample heads measured by a L V D T displacement transducer. The lateral strain is measured by a second extensometer whose fingers lean on the sample edges [6]. In some cases the local strains are measured with a rosette-type strain gauge glued in the central part of the sample. The tensile stress is determined by taking into account the variation in the sample cross-section. All the tests are strain controlled at constant global strain rate. Three types of strain history are envisaged: type I, monotonic test controlled at a strain rate of 10 -4 s -J (Fig. 2(a));

F

STRAIN /1

.-

2.57. 2Z

A Type /I m3s-

j • J10-4s-t

II

(b)

TIME Fig. 2. The three types of strain history.

type II, monotonic test with increasing strain rate steps of 10 5, 10-4 and 10 _3 s - l (Fig. 2(a)); type III, cyclic test with a first loading of 2.5%, followed by a series o f five cycles between 2.0% and 2.5%, always keeping a tensile state; this test type is controlled at strain rate of 10 -4 s -1 (Fig. 2(b)). Two orientations of the sample are considered, the rolling direction (denoted L) and the transverse direction (denoted T). Thus each test is defined by the material, the ageing time, the orientation and the load history type. All the test results are digitally recorded with a frequency of one measurement point (time, load, starin . . . . ) for an axal strain step of 10 4; some complementary analogue recordings are also obtained. Thus Fig. 3 is an analogue recording, allowing better restitution of the instability phenomena; Fig. 4 is obtained from the digital recording, using a broken line to join the data points.

3. Young modulus The Young modulus is defined as a tangent modulus at the beginning of the loading branch, or just after a load reversal. It is determined by separating the stressstrain curve by branches and by analysing the experimental results in the space Ao-, A~, where e is the axial strain measured locally, so that Fig. 1. The local and global axial strain measurements.

Aa=a--Ra

and

A~=e--R~

(1)

B. Wack, A. Tourabi / Materials Science and Engineering A196 (1995) 79 87 .

.

.

.

.

.

.

.

I

.

81 .

.

.

.

.

.

.

I

. . . .

80

500

m

f

¢¢'j

"d

r3

1

1

0

I

Oo

I

a x i a l strain

Fig. 3. Typical monotonic test of type I (2091 alloy, T orientation, 24 h ageing time, 10 - 4 s -~ strain rate), analogue recording.

•

"

.

.

.

.

.

.

.

I

.

t

,

.

.

.

.

.

.

.

.

I

. . . .

400.

¢¢J

p

.~--,

. . . . . . .

0,,

,

I

. . . . axial strain, ext

O0

.

. 0I2-

. . . .

Fig. 4. Typical cyclic test of type III (2091 alloy, 12 h ageing time, 10 4 s-1 strain rate, (a) L orientation and (b) T orientation), digital recording.

where R 0, Re are the coordinates of the origin or of a reversal state. Using a spline technique it is possible to determine the rigidity modulus ME along each loading branch: M E (Ae) =

dAa/dAe

(2)

and the Young modulus E is defined as [7] E=

lira

ME(Ae)

(3)

~d

Ae~

0.06

Fig. 5. Typical evolution of the rigidity modulus along the loading branches (test of Fig. 4(a)).

and the mean vlaue Ec of the ten measurements on the small branches. (The tangent M E to the stress-strain curve defined by a spline technique is independent of the "length" of this curve, contrary to values obtained with the help of a global polynomial approximation. Owing to the frequency of the digital recording, we recall that the small branches of type III tests are defined by about 50 measurement points.) The difference between the tangent elastic behaviour near the origin and after a load reversal has been confirmed by measurements of the shear modulus with cyclic shear tests on the same material [8]. As foreseen the E 1 and Ec values for each material are independent of the sample orientation on the one hand and of the ageing time t a on the other hand. The results are summarized in Table 2 where the mean values (E~) and ( E c ) of all the tests are reported, as the standard deviation ~re~ and aEc of the individual Table 2 Young moduli and Poisson ratios of the three alloys 2091

A1 Li

AI-Cu

( E t ) (GPa) aE, (GPa) Or (GPa) n

78.5 1.5 0.31 23

76.6 1.3 0.54 6

71.9 1.9 0.67 8

(Ec) (GPa) O'Ec (GPa) O'(Ec> (GPa) n

75.6 1.6 0.35 19

76.2 --3

69.8 --3

(v,) a,.~ or<,., > n

0.309 0.010 0.002 21

0.306 0.011 0.005 5

0.321 0.010 0.004 6

(vc) ~r,. a<,,o> n

0.303 0.008 0.002 18

0.309 --3

0.328

Ae,~0

With tests of type I or II, it is possible to measure only one value of E. However, with tests of type III a group of 11 values may be measured; this allows a more accurate determination of E. Fig. 5 displays a typical result obtained with the 2091 alloy and corresponding to the test of Fig. 4. We notice that the Young moduli of the cyclic loading branches are systematically smaller than the value of the initial loading branch. This property is confirmed by all tests of type III on the 2091 alloy. Consequently we distinguish for each test of type III the value El measured on the first loading branch

.L

-3

Mg

82

B. Wack, A. Tourabi / Materials Science and Engineering A 196 (1995) 79 87

oT *L

0 0"2.5

Table 3 Strengths of the 2091 industrial alloy; parameters of the least square lines

400

ff

350

a (MPa) b (MPa) r n

lib

................

...............

0-0.2, L

0"0.2, T

0-2.s, L

0"2.5, T

2.0 344.0 0.47 5

6.9 330.4 0.73 9

5.6 401.1 0.82 5

8.3 413.0 0.76 9

O

0

1 ' 12

300 6 Fig,

6. Evolution of

the

2 ' 24

T, q (h)

2091 industrial alloy strengths

(Cgl = 10 4S--1).

values and the standard deviation 0- and 0- of the mean values, n being the number of tests. The results concerning E1 are in good agreement with resuits relative to monotonic tests [9,10]. Concerning cyclic tests with the 2091 alloy, we see that the cyclic value Ec is 3.7% smaller than the initial E1 value. For the A1-Li alloy the difference is not significant, whereas for the A 1 - C u - M g alloy the mean value of the three cyclic tests indicates a relative difference similar to that of 2091 alloy. This result suggests a possible explanation related to the presence of Mg atoms. These atoms are essentially in a substitution positions and give, after annealing and ageing at r o o m temperature, intense pinning for the dislocations; if these pinnings are broken by the deformation supported by the material, they may not be easily reinstalled afterwards. Consequently the Mort effect would be less important in the initial state than after a noticeable deformation [11,12]. Complementary tests with 2024-T3 alloy made conspicuous the same phenomenon [13]. The Poisson ratio v is defined, from the curve giving the lateral strain vs. the axial strain, using a similar method as for the Young modulus. We notice that the Poisson ratio also does not show any influence of ageing time, the strain rate and the sample orientation. In addition, there is no significant difference between the initial value vl and the cyclic value Vc (Table 2).

the strength, particularly for the 0-2.5 value. The results also show a small influence of the sample orientation. The inversion of the relative position of the L and T results, 0-'0.2and 0-2.5, indicates a difference in the shape of the loading curves; for the L orientation the loading curve is less smooth in the elbow region, probably owing to the m e m o r y of the initial 2% prestrain in the same direction (Fig. 4). By introducing the dimensionless variable T~, defined by T~ = log ( t , / t o ) / l o g 2

(4)

with to = 6 h, it is possible to summarize the results by the least square line of equation or

%.2 = a T , + b

0-2.5= aTa + b

(5)

The results are indicated in Table 3, n being the number of tests and r the correlation coefficient. For the 0-o.2 value, and the L orientation, the linear variation is not significant and we have to consider a constant value, whatever the value of ta ; the mean value of all the tests is 345.2 MPa. The influence of the strain rate on the 2091 alloy behaviour is displayed in Fig 7 for the T orientation, and we see that it is very small; for the medium strain rate (10 - 4 s - I ) the representative points are the mean values of the results in Fig. 6.

10-5 s-t ~ lO~s-~ o 10-3 sq

%

400 4. Materials strength The strength of the three materials is characterized by two values, i.e. the classical strength 0-o.2 (determined by the intersection of the loading curve with the straight line of slope E containing the abscissa point 0.2%) and a value characterizing the plasticity plateau, which is chosen as the stress 0-2.5 at 2.5% strain. For the 2091 alloy and for the strain rate of 10 4 s-~ the results are summarized in Fig. 6. The increase in the ageing time t~ gives a significant but small increase in

350

8

~o.2

o

0 30O 6

I

2

f

i

12

24

r,

L

t, Oa)

Fig. 7. Evolution of the 2091 industrial alloy strengths (transverse direction). For ~g~= 10-4 s-~ the representative points correspond to the mean values of the tests of Fig. 6.

83

B. Wack, A. Tourabi / Materials Science and Engineering A 196 (1995) 79 87

The results of six tests with the A1-Li alloy (at 10 4 S-1 strain rate and T orientation) are summarized by the following linear regression: (70.2 = 8.0Td + 173.8(MPa)

(with r = 0.99)

(6)

a2.5 = 8.5Ta + 232.3(MPa)

(with r = 0.98)

(7)

-" wt = 1 2 . 5

i !

n=lO

Lb=52.7

Wt

For this alloy the increase in the material strength with ageing time is well marked. In contrast, the strength of the A1 Cu Mg alloy, under the same conditions, appears independent of the ageing time. The mean values for the six tests are (ao.2} --- 217.0 + 1.9(MPa)

(8)

(a25} = 265.7 + 1.9(MPa)

(9)

the error interval is equal to double the standard deviation and gives a confidence level (CL) of 95%.

5. Quantification of the P r o t e v i n - L e Chatelier phenomenon

We have seen (Section 4) that the variation in strength with ageing time cannot explain the decrease in toughness of the 2091 alloy. It is quite the reverse; the increase in ageing time should cause an increase in toughness, which is not the reality. We recall (Section 3) that the Young modulus if found not to vary with ageing time; thus an explanation for the decrease in toughness has to be found elsewhere. Strain localization by the PLC phenomenon appears in monotonic tests (type I) on the plateau of plasticity at a strain of about 5% for the 2091 alloy and at a strain of about 3% and 6% for A 1 - C u - M g and A1-Li alloys respectively. The strain localization also appears, in tests of type II, after a change in strain rate.

~ =/t/3 Fig. 8. Geometry of the sample and the Portevin Le Chatelier bands (dimensions are given in ram). where Wg is the sample width. In our case, with Lg = 60 mm, Wg = 12.6 m m and ~ = zc/3, the theoretical travel is equal to 52.7 m m (Fig. 8). The instabilities related to the PLC phenomenon are manifested clearly on the loading curves (see for example Fig. 9), but appear differently under global strain measurement (Fig. 9(a)) or local strain measurement (Fig. 9(b), (c)). The serrations observed with the global stain measurement are similar to type B Pink's classification [14]. The difference between the two graphs

500 ' I

500 ' I

~

~I ' I ' [ ' I ' I ' 1

I

I

I

I

I

I

1

50O

5.1. M e t h o d o f double strain m e a s u r e m e n t

The strain localization happens in a band of width Wb inclined at an angle c~ of about 60 ° to the sample axis (Fig. 8). During a given time, the dislocations move in this band until saturation; then an adjacent band appears in which the strain localization phenomenon continues. Since the width Wb is small with regard to the sample gauge length Lg, it is reasonable to define an apparent mean velocity Vb of the PLC band parallel to the sample axis. With regard to the observed results, we notice that only one P L C band is active at a time. Generally the band starts at one end of the sample and propagates in the gauge section of the sample. Thus the band may travel a theoretical distance Lb, such that L b = Lg - Wg/tg~

(10)

(c) ~=~ .i=I

[

.01 I

I

I

I

a x i a l strain Fig. 9. Influence of the Potevin Le Chatelier instabilities on a stress-strain curve (2091 alloy, ta = 12 h, T orientation): (a) digital recording with global strain measurement, (b) digital recording with local strain measurement, (c) analogue recording with local strain measurement.

84

B. Wack, A. Tourabi / Materials Science and Engineering A196 (1995) 79-87

0.07

J __/ Ext

_

0

i ~ 0

~ i I 0.07

~i

Fig. I0. Local strainvs. globalstrainof the monotonic testof Fig.9. incites us to compare the two strains (see for example Fig. 10). The global strain egl is obtained by the relative displacement Az of the sample heads and thus takes into account the deformation of the whole sample including the two junction zones of variable crosssection; this introduces the notion of equivalent sample length Lg, greater than the gauge length Lg of constant cross-section: (1 1)

eg, = A z / L'g

The local strain e~t is measured by the extensometer with a base B equal to 10 mm. During a test, three phases may be identified (Fig. 11). At the beginning of the test the global strain evolves more rapidly than the local strain, owing to the compliance of the sample clamps and the quasi-elastic behaviour of the material (phase I). Then the local and the global strains evolve proportionally during the quasi-plastic behaviour (phase II); the equivalent sample length L'g is determined by equating the two strains. The limit between phases I and II corresponds to the elbow of the stress-strain curve. Phase III corresponds to the presence of PLC bands; the graph is constituted

Ext

by broken lines with two alternate and very distinct slopes. Since test is controlled at constant global strain rate, the global strain axis is proportional to time. Thus the steepest slope corresponds to an apparent high strain rate 81 which lasts a time q ; during that time an activated PLC band operates in the measurement base B of the extensometer. The other slope, of apparent strain rate 82, lasts a time t 2 during which the PLC band operates outside of the extensometer measurement base (Fig. 11). We suppose that during propagation of the PLC band the strain rate is homogeneous and constant in the band, and also outside the band of respective values 8b and khb; the width Wb is also supposed to stay constant. From the preceding hypotheses, we have the following relations: Wb B - wb . 81 = -~- eb + ~ ebb

(12)

~2 = khb

(13)

t~ = B / V b

(14)

t2 = (Lb -- B ) / V b

(15)

•

As 8hb is small with regard to 81 and as wb/B is of the order of 0.16, the first relation may be simplified: _

W b.

.

81-- B eb+ehb

Thus the quantities WbSb, ~hb, Vb and L b may be determined by the measured quantities kl, 82, tl and t2: WbSb = B(8, -- 82)

(17)

~hb = ~2

(18)

Vb = B/tl

(19)

Lb = B(1 + t2/t,)

(20)

/4/.

I

II

III

(2 ~ , __---.

,

If the preceding hypotheses are correct, we must check that the global sample displacement rate is equal to the summation of the partial rates L'gSgI = W8b -+- (L'g -- W)Shb

IZ ! ....

(16)

,,.

_

(21)

By neglecting w with regard to L'g and using Eqs. (17) and (18) we obtain Lgt = B - 8g,-~2

(22)

5.2. E x p e r i m e n t a l results ,00s

t (~:~o~-~-0

IOs

t

(~=IOE-,~L s-l) v

Fig. 11. Defination of the measurements parameters related to the Portevin Le Chatelier instabilities.

The interesting quantities which characterize the PLC phenomenon are 8b, ebb, W and Vb. Determination of the quantities Lb and Lg is only of interest for verification of the measurement consistency; we know the theoretical value of Lb on the one hand and the value of

B. Wack, A. Tourabi / Materials Science and Engineering A196 (1995) 79-87

85

Table 4 Parameters of the Portevin Le Chatelier bands, industrial alloy 2091 Test number and type

d r (h) ~gl ( s - I ) el/~gl

~2/~gl t I (s) t z (s) Vb (mm s - t ) Wb~b/~gl (mm) L b (mm) L~, (mm) eb (10 -5)

001, II

001, II

024, II

024, II

006, I

011B, I

025, I

6 10 4 5.2 0.21 11 56 0.91 50 61 63 5.5

6 10-3 5.7 0.19 1.3 5.0 7.7 55 53 68 7.2

24 10 4 5.3 0.28 6.2 28 1.61 50 55 70 3.1

24 10-3 5.3 0.28 1.2 5.0 8.3 50 52 70 6.1

6 10 4 6.7 0.09

12 10-4 5.7 0.24 17 102 0.60 55 70 72

24 10 4 5.4 0.31

L'g is to be compatible with the sample shape and the test results during phase II on the other hand. The PLC instabilities appear clearly during monotonic tests with strain rate steps (type II tests). With monotonic tests at constant strain rate, the PLC instabilities appear only at the end of the test; in that case the quantification is only partial. All the results for the three materials are given in Tables 4 - 6 . The self-consistency of the measurement can be displayed by the representative points of each test, or part of a test, in a n L b , L~ diagram (Fig. 12). We see that the L'g values are well grouped (with the exception of test 063), whereas the L b values are scattered. This result may be explained by the fact that L'g is determined by the strain rate values which are well defined, while the L b values depend on the durations tl and t2, which are less precise. By eliminating test 063, the mean value of the sample equivalent height L'g is ( L g ) = 68.5 4- 10 mm

(n = 13, CL = 66%)

This value is admissible, although it is smaller than the value 76 mm defined at the beginning of the test, during phase II; this difference may be explained by the deTable 5 Parameters of the Portevin-Le Chatelier bands, model alloy A I - L i Test number and type

d r (h) egl ( s - l ) el/egl ~2/~g~ tl (s) t 2 (s) Vb ( r a m s -~) Wb ~b/~g I (mm) L b (mm) Lg (mm) Cb (10-3)

033, II

053, II

034, 1

042, I

054, I

6 10 3 6.2 0.15 1.3 4; 11 7.7 61 40; 85 71 7.9

24 10 3 6.0 0.20 1.6 7.2 6.3 58 55 73 9.3

6 10 4 5.5 0.31 7.9 47 1.3 52 69 75

12 10-4 6.4 0.32 9.9 -1.0 61

24 10-4 5.5 ----

89

--

--58(?) 64

-51 74

crease in the influence of the sample junction zone due essentially to the presence of the localization phenomenon. Concerning the Lb values, we notice their tendency to separate into two groups. The first group of five values defines the following mean value: (Lb) =

54.2 + 0.7 mm

(n = 5; CL = 66%)

This value is to be compared with the theoretical value of 52.7 mm given by Eq. (10); the difference of 1.5 mm may be easily explained, since the latter value is affected by errors concerning the values of Lg, Wg and ~. The second group, with L b values between 61 and 74 mm, contains non-realistic values; these are due essentially to inaccuracy concerning determination of the durations tl and/or t2.

5.3. General properties of the Portevin-Le Chatelier localization bands In a preliminary step we determine the general properties of the PLC localization bands, neglecting here the influence of the ageing time. With the help of the double strain measurements, the strain rate in the band is known only by the product Wb~b (Eq. (17)), but the width wb may be estimated from the graph of the loading vs. local strain (Fig. 9(b), (c)). The stages when the active PLC band is inside or outside the local measurement base are well distinguished, the latter corresponding to a relatively net stress increase during a short (local) strain increase. However, when the PLC band is inside the measurement base, the stress is almost constant for a given strain increase, of about 1%; some distinct serrations then appear which are certainly related to the beginning of activation of each PLC band. (These serrations are also present on the graph F.xt/•gl, but they are less evident.) It is then possible to count the number of bands which cover the measurement base; for the three stages during which the PLC band is in the measure-

86

B. Waek, A. Tourabi / Materials Scienee and Engineering A 196 (1995) 79-87

Table 6 Parameters of the Portevin Le Chatelier bands model alloy AI-Cu-Mg Test number and type

dr (h) ~g~(S 1)

~t/~gE ~2/~g~ t~ (s) t 2 (s) Vb (mm s i) Wb~?b/~gI (ram) L b (mm)

L'g (mm) cb (10 3)

062, lI

062, II

082, II

082, II

063, I

6 10 4 5.6 0.23 9.6 53 1.04 54 65 70 5.2

6 10 3 5.6 0.17 1.8 11.5 5.6 54 74 65 9.8

24 10-4 5.4 0.21 10.2 56 0.98 52 65 66 5.3

24 10-3 5.4 0.21 2.0 9.2 5.0 52 56 66 10.4

6 10-4 4.3 0.23 8.5 44 1.18 41(?) 62 53

m e n t base o f the e x a m p l e o f Fig. 9, the m e a n value o f the n u m b e r o f b a n d s which cover the m e a s u r e m e n t base is 6.3. C o n s e q u e n t l y the m e a n value o f the individual P L C b a n d w i d t h is Wb = 1.6 mm; this value agrees with o p t i c a l o b s e r v a t i o n . F o r lack o f o t h e r precise m e a s u r e m e n t s , we a d m i t this e s t i m a t i o n o f Wb for all the o t h e r tests, o n l y in o r d e r to d e t e r m i n e an e s t i m a t i o n o f 8b . In spite o f the small n u m b e r o f results, a n d a signific a n t spread, we m a y define the o r d e r o f m a g n i t u d e o f a few c h a r a c t e r i s t i c values, intrinsic to l o c a l i z a t i o n b y the P L C b a n d s . R e g a r d i n g the result o f T a b l e s 4 - 6 , it seems r e a s o n a b l e , at a relative u n c e r t a i n t y o f the o r d e r o f 10%, to c o n s i d e r t h a t 8] a n d 82 are r o u g h l y p r o p o r t i o n a l to the g l o b a l strain rate 8g~, with the exception o f 82 for the A 1 - L i alloy. A s a set-off, the a p p a r e n t speed Vb o f the P L C b a n d a p p e a r s to v a r y less r a p i d l y t h a n 8gl. T h e r e f o r e we s u m m a r i z e in T a b l e 7, for the three materials, the m e a n values o f Wb8b, 8b a n d ~hb referred to ~gl, a n d the m e a n values o f Vb for the two g l o b a l strain rates; the r a t i o o f the m e a n value o f 8b to the m e a n value o f ~hb, which m a y be i n t e r p r e t e d as a l o c a l i z a t i o n ratio, is also d e t e r m i n e d . W e see t h a t the r a t i o ~hb/~g] o f the strain rate outside the P L C b a n d to the g l o b a l strain rate is between 0.19 L~ (rnm)

~ o

24

o

AI-Li

+

AI-Cu-Mg

+

24

82

82 .' ÷." 01

,"

52

50

W

(23)

Table 7 Instrinsic parameters of the Portevin-Le Chatelier bands

(Wbib)/~gI (ram)

(ghb)/~gl

(,~b)/(,~hb) (Wb = 1.6 mm) Vb (mm s 1) /"

53

60

Lb ( rmn ) 70

Fig. 12. Measurement scattering of the sample equivalent length Lg and of the travel length Lb of the Portevin Le Chatelier bands.

24 10-4 5.8 0.19 12.5 74 0.80 56 69 69

eb = ~b Vbb

-~

60

12 10-4 5.5 0.15 14.0 84 0.71 54 70 63

083, I

a n d 0.25 d e p e n d i n g o n the material. T h e strain rate inside the P L C b a n d 8b is m u c h higher t h a n the global stain rate 8gl; if we a d m i t the value o f 1.6 m m for the P L C b a n d width, the ratio ib/Sg~ is between 32 a n d 36 d e p e n d i n g on the material. T h u s the P L C b a n d s are c h a r a c t e r i z e d by a l o c a l i z a t i o n r a t i o between 130 a n d 177, the i n d u s t r i a l alloy being c h a r a c t e r i z e d by the smallest value (Table 7). T h e a p p a r e n t p r o p a g a t i o n speed Vb o f the active P L C b a n d is o f the o r d e r o f m a g n i t u d e o f 1 m m s-~ for the g l o b a l strain rate o f 1 0 - 4 s 1. W h e n 891 is m u l t i p l i e d by a factor 10, the a p p a r e n t speed Vb increases only by a f a c t o r between 6 a n d 8, d e p e n d i n g on the material. F i n a l l y a last p a r a m e t e r m a y be defined to c h a r a c t e r ize the influence o f the P L C b a n d on the local beh a v i o u r o f the materials; this is the strain a m p l i t u d e eb p r o d u c e d by an a c t i v a t e d P L C b a n d d u r i n g the time it is s t a t i o n a r y . F o r the simple g e o m e t r y o f o u r sample, this P L C strain a m p l i t u d e eb is defined by

(~b)/~g, (wb = 1.6 mm)

,"

+

2091

4-, ."

fi2

÷ol

/

072, I

(4=10-4s

1)

Vb (mm s ~)

2091

Al Li

Al Cu-Mg

52 (6) _+2.5 32 (6) + 1.6 0.25 (6) -+0.046 130 (6)

58 (4) +4.2 36 (4) ±2.7 0.24 (4) -+0.083 151 (4)

54 (6) _+1.5 34 (6) +0.9 0.19 (6) + 0.029 177 (6)

1.0 (3)

1.15 (2)

0.88 (4)

8.0 (2)

7.0 (2)

5.3 (2)

(~gl = 10--3 S--I)

The number of tests is given in brackets. The error interval corresponds to CL = 66%.

B. Wack, A. Tourabi / Materials Science and Engineering A 196 (1995) 79 87 I ta

'

'

'

'

ta

t IOE-3

hl-Li

increasing =constant

~o~-4 24h fOE-3

6h

,o~-a

~4~

IOE-4

6h

fOE-4

A I -Cu-Mg

s2

increasing

ta=constant

"

:,+,..

,

_4.+,

~__L~

5

2091

,

,

,

t0E-3

fOE-4

24h

IOE-3 I Olg-4

6h

t

!0

Eb(10E-3)

Fig. 13. Evolution of the parameter ~:bfor the three alloys. By introducing Eq. (17) and (19) we have Eb : t, (k, - ~ )

ment. First if we look roughly at only the mean values, independently o f the ageing time and the global strain rate, we see on the one h a n d that the strain rate localization ratio varies between 130 and 180, depending on the material, and on the other hand that the apparent velocity o f the P L C b a n d for the three materials is o f the order o f 1 m m s i for a global strain rate o f 1 0 - 4 s 1. If we look at the results o f the 2091 alloy in m o r e detail, we see that the strain amplitude o f a stationary P L C b a n d diminishes with ageing time. Thus the strong non-linear deformation process, represented by the P L C band, suggests a m e t h o d for explaining the decrease in toughness o f the former version o f the 2091 industrial alloy and gives a new orientation for a further study o f this problem.

(24)

The P L C strain amplitude eb has an evident graphical determination (Fig. 11). The values o f eb for the different materials are given in Tables 4 6. Owing to some uncertainty concerning initiation o f the P L C instabilities in the tests o f type I, we consider here only the results o f type II tests, which are a coherent g r o u p o f experimental data. The corresponding results are displayed in Fig. 13. C o m p a r i s o n o f the results for the three materials suggests a possible explanation for the toughness decrease o f the industrial 2091 alloy in connection with P L C instabilities. A m o r e detailed study would be necessary to base an explanation, but this is b e y o n d the scope o f this paper.

6. C o n c l u d i n g

87

remarks

Accurate determination o f the characteristic values o f the A1 Li alloys shows a t e m p o r a r y instability probably depending on strong dislocation pinnings on magnesium atoms; thus for the 2091 industrial alloy and for the A 1 - C u - M g model alloy the initial Y o u n g m o d u l u s is 3.8% higher than the following cyclic values, whereas for the A I - L i model alloy the initial and the cyclic values o f the Y o u n g m o d u l u s do not show any significant difference. These results, obtained from tensile tests, agree with similar results obtained from simple shear tests [8]. T o confirm the microstructural explanation o f this result, it would be interesting to measure these values again, using the same samples, after a significant resting time. A n o t h e r main point o f this study concerns quantification o f the P L C instabilities; original results were obtained using a new m e t h o d o f double strain measure-

Acknowledgements

The authors would like to thank the Pechiney Research Center o f Voreppe (France) for providing the materials and for financial support t h r o u g h a contract.

References

[1] P. Meyer, Y. Cans, D. Ferton and M. Reboul, in G. Champier, B. Dubost, D. Miannay and L. Sabetay (eds.), Proc. 4th Int. Aluminium Lithium Conj'., Paris, June 1987, in J. Phys. (Paris), C3, 48 (1987) 131. [2] P. Gomiero, Y. Brechet, F. Louchet, A. Tourabi and B. Wack, Acta Metall. Mater., 40(4) (1992) 863. [3] J.-L. Strudel, in P. Groh, L.P. Kubin and J.-L. Martin, Dislocations et DdJormation Plastique, Ecole dYtd d' Yravals, September 1979, Les Editions de Physique, Paris, 1980. [4] P. Gomiero, Thesis, ]nstitut National Polytechnique de

Grenoble, 1990. [5] P. Gomiero, F. Liver, Y. Brechet and F. Louchet, Acta Metall. Mater., 40(4) (1992) 847. [6] A. Tourabi, Thesis, Institut National Polytechnique de Grenoble, 1988. [7] S. Han and B. Wack, Arch. Mech., 38(4) (1986) 439. [8] B. Wack and A. Tourabi, J. Mater. Sci., 28 (1993) 4735. [91 P. Meyer and B. Dubost, in C. Baker, P.J. Gregson, S.J. Harris and C.J. Peel (eds.), Proc. 3rd Int. Aluminium-Lithium Conj'., Oxford, July 1985, The Institute of Metals, London, 1986, p. 37. [10] K. Welpmann, H. Buhl, R. Braun and M. Peters, in G. Champier, B. Dubost, D. Miannay and L. Sabetay (eds.), Proc. 4th Int. Aluminium-Lithium Conf., Paris, June 1987, in J. Phys. (Paris), C3, 48 (1987) 677. [11] Y. Brechet, private communication, 1992. [12] J. Friedel, Dislocations, Pregamon, 1964. [13] B. Wack and A. Tourabi, Etude des propri6t6s m6caniques de l'alliage industriel 2091, Contract report, 1990 (Institute de M6canique de Grenoble, Grenoble). [14] E. Pink and A. Grinberg, Mater, Sci. Eng., 51 (1981) 1.