EFFECT OF CRYSTALLOGRAPHIC AND MORPHOLOGIC TEXTURES ON THE ANISOTROPY OF MECHANICAL PROPERTIES OF Al-Li ALLOYS

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EFFECT OF CRYSTALLOGRAPHIC AND MORPHOLOGIC TEXTURES ON THE

ANISOTROPY OF MECHANICAL PROPERTIES OF Al-Li ALLOYS

P. Lipinski, M. Berveiller, A. Hihi, P. Sainfort, P. Meyer

To cite this version:

P. Lipinski, M. Berveiller, A. Hihi, P. Sainfort, P. Meyer. EFFECT OF CRYSTALLOGRAPHIC AND MORPHOLOGIC TEXTURES ON THE ANISOTROPY OF MECHANICAL PROPER- TIES OF Al-Li ALLOYS. Journal de Physique Colloques, 1987, 48 (C3), pp.C3-613-C3-619.

�10.1051/jphyscol:1987371�. �jpa-00226602�

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EFFECT OF CRYSTALLOGRAPHIC AND MORPHOLOGIC TEXTURES ON THE ANISOTROPY OF MECHANICAL PROPERTIES OF A1-Li ALLOYS

P. L I P I N S K I , M. B E R V E I L L E R , A. H I H I * , P. SAINFORT* and P. MEYER* *

L P M M , Institut Supgrieur de Genie Mecanique et Productique, E N I M , Ile du Saulcy, F-57000 Metz,-France

' L M M , Facult6 des Sciences, Universite Mohamed V , Rabat, Maroc

* *

Cegedur-Pechiney. Centre de Recherche et Developpement, B.P. 27, F - 3 8 3 4 0 Voreppe, France

ABSTRACT

A new formulation of t h e self consistent model has been applied t o predict t h e plastic behaviour of A1-Li Alloys. This model enables t o take into account simultaneously the crystallographic texture, the morphology of grains, the internal stresses evolution and t h e anisotropy of intracrystalline hardening. Microscopic observations and analyses of crystallographic textures a r e used t o constitute t h e d a t a for t h e self consistent scheme. As results of such calculations, we present t h e variations of plastic properties versus t h e angle between the tensile axis and rolling direction. Initial Yield point, macroscopic hardening modulus a s well a s transversal plastic flow a r e examined. The direct comparison with experimental results i s given. A satisfactory agreement with numerical results i s observed.

I. INTRODUCTION

The recent development of Al-Li Alloys corresponds t o t h e increasing demand of t h e low density and high strength materials for a i r c r a f t applications. These alloys a r e usualy furnished a s plates or sheets obtained by rolling and exhibit various anisotropies of mechanical properties such a s ^:

-

anisotropy of the yield point

- anisotropy of t h e macroscopic hardening modulus - anisotropy of the transversal plastic flow.

The macroscopic anisotropy is closely related t o t h e anisotropic behavior of t h e single crystal and t h e microstructure of the grains:

-

t h e anisotropy of t h e elastoplastic behavior of t h e single crystal results from t h e crystallographic nature of plastic glide, interactions between the glide systems (reflecting t h e dislocation - dislocation and dislocation - precipitation interactions) and eventually anisot ropy of elastic constants.

- t h e mechanical anisotropy associated with t h e granular aspect of t h e metal is caused by t h e crystallographic texture, morphologic texture (shape of grains) and internal stresses of t h e second order engendred by t h e intragranular incompatibi- lities of t h e plastic strain.

In order t o predict the anisotropic behavior of AI-Li alloys, all t h e micro-physical pheno- mena mentioned above should be taken into considerations.

The modelling of t h e anisotropy of AI-Li alloys was developed by ti. Peters, K. Welpmann and T.H. Sanders [I]. Their model based on the Schmid's law governing t h e activation o f glide systems approached t h e polycrystal by a set of independent grains. This approach neglects different sources of t h e plastic anisotropy of t h e polycrystal excepting for crystallographic texture.

In this paper, we use t h e self consistent method t o predict t h e behavior of A1-Li alloys.

The obtained results a r e directly compared with t h e experimental measurements performed on sheets in 291 alloys. The s h e e t s , of 3.6 mm thickness, have all been tested in t h e

TBx51 temper. First, the fundamental hypothesies o f t h e method a r e rewieved and next,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987371

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C3-6 14 JOURNAL DE PHYSIQUE

the way to introduce the important micro-physical parameters into the model is discussed.

11. MODELLING OF THE SELF CONSISTENT METHOD 1) Single crystal behavior

It is supposed that the crystallographic glide is the main micromechanism of plastic strain of the F.C.C.-crystal. ~ e t ; be a plastic resolved shear strain rate on a g-th slip

+

system characterized by ng unit vector normal t o t h e slip plane and Gg unit vector of slip direction. The plastic strain rate

E

?. resulting from simultaneous slips on active sys-

tems is given by 'J

with .R! =

$

^(&^ng⁺^n: ^my)

'1 1 1

A system g becomes potentially active if the following relation, called Schmid law, is verified :

t g = R.! 0..

c 'J 'J ( 2 )

where the threshold stress .c

E,

named critical resolved shear stress is supposed t o evoluate during plastic strainings. If a linear strain hardening is described by a hardening matrix H ~the critical shear stress rate-on a system labeled h can be expressed by ~ ,

On t h e other ban$, the resolved shear stress rate on a system g is obtained knowing the local stress rate ^T.. by

1J

A system g is activeif simultaneously (2) id verified and

;

is such that

;

^>^0.

Knowing all active systems and the local stress rate, the plastic strain rate may be determined from the above equations

where

If the elastic constitutive law is expressed by the following relation

* e

e . . = Sijkl O k l

'J

the formal constitutive equation for the single crystal may be written down in the form

or, inverting (7), a s

;..

⁼^lijkl

11 €kl

-

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relation

C.. = L.. eff

1, l ~ k l Ekl ( 9 )

Where

k

is the overall strain rate tensor

(k

= < _>), is the overall stress rate tensor

(2

= < >). ,?

and L,;:: is the tensor of the overall instantaneous moduli which reflects both the aniso-

-, ---

tropy of the single crystal and those due t o the microstructure of polycrystal (crystallographic and morphologic texture).

It has been shown [2], that it exists an integral relation linking

Ekl

and

t

kl. This integral equation may be solved using a self consistency hypothesis. The solution of the integral equation can be written as follows :

('J ) = A i j k l n (10)

where Aijkl is the concentration tensor for the strain rate tensor. The components of A depend on ^:

-

the mechanical anisotropy of the polycrystal L eff

-

the behavior of grain 1(n) of a given crystallographic orientation defined by ⁰

-

the shape of grains.

The various method of determination of the tensor A m a y be found in [2]. Here we mention only that the Lin-Taylor [3] model is obtained putting A = I which expresses the homogeneity of total local strain rate. If additionnaly the elastic strain is neglected, the Taylor model [4] is obtained.

In order t o determine the tensor ~ ~ ~ ~ ~ l e t ' s s u b s t i t u t e (10) into (8)

.

1~ = lijkl(n) A ~ ~ ~ ~ ( Q )

Bmn

⁽¹¹⁾

Now, using the averaging operation over the polycrystal volume, the above equation leads to

,eff -

1.

ijkl - V

[

'ijmn'") A m n k ~ ( n ) dV (12)

v

Introducing the orientation distribution function f(n3 such that

dV0

= f(n) d n

v

equation (12), can be rewritten as

This relation takes into account the influences of the crystallographic texture of the polycrystal on the overall behavior of the aggregate. All the sources of the single crystal anisotropy a r e taken into account by this equation. The elastic constant anisotropy is reflected by the tensor siikl, the plastic anisotropy due t o the crystallographic nature of deformation modes is rendered by R tensors and finally the anisotropy of the strain hardening is modelled by the hardening matrix H. The shape of grains (morphological textures) is taken into account by evaluating the A tensor for ellipsoidal inclusions.

111. APPLICATIONS OF THE MODEL TO AI-Li ALLOYS

In order t o perform the numerical simulations, the elastic and plastic properties of the single crystal should be specified. The elastic behavior of the single crystal and conse- quently those of the polycrystal are supposed t o be isotropic and defined by Poisson's

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C3-6 16 JOURNAL DE PHYSIQUE

ration v = 0.3 and LamB's modulus 11 = 3000 daN/mm 2

.

The plastic slip on the twelve easy glide systems of < 111 > (110) type is governed by the Schmid's law. The initial critical shear stress is supposed t o be the same for all glide systems of each grain and equals r o = 12.5 d a ~ / m m ~ . This value is deduced from the experimental data. The hardening rule of the single crystal is described by a constant matrix H composed of two types of terms. The first term modelling the weak interactions between the glide systems is equal t o F(/250. The second term, being 3 times greater reflects the strong interactions between dislocations. This matrix describes well the dislocations - dislocations interactions. The dislocations - precipitate interactions which can considerably modify the single crystal behavior a r e only roughly approached for reason of the lack of numerical informa- tions.

Finally, the shape of grains was estimated using the optical metallography. The results of these observations lead T O the following choice of semi axes of grains :

The same inclusion shape has been chosen for all grains and such that; a-axis indicates the rolling direction b-axis transversal direction and c-axis the normal t o the sheet.

The crystallographic texture was measu red by X-Ray diffraction and analysed using the lrectorial method [5]. The results of these measures are presented in details in another communication at this conference [6]. The numerical simulations have been performed using a certain number of ideal components of the experimental texture. The corresponding weights have been estimated from the orientation distribution function using various standard deviations of integration. The results are presented in Table I.

Standard Goss S Cube Copper Brass

deviation

(%I

(%) (%) (%) (%)

5O 1,04 0 0 0 1 3 8

lo0 1,04 0 0 0,22 6,44

15' 4,46 099 1,28 0,92 9,86

20° 6,08 6,98 3,64 2,61 15,29

TABLE I : Volumic fractions of five ideal texture components.

The experimental tensile tests have been performed a t the room temperature under constant strain rate conditions (

;

⁼ 2 - l 0 - ~ ,-I). Samples were taken from the rolled sheets for various CL angle measured with respect to the rolling direction. The corresponding tension curves are drawn in fig. 1. An important yield point anisotropy is observed and presented on fig. 2. Fig. 3 shows the anisotropy of a hardening moduli defined a s

"/AS and taken for plastic strain internal given by E' = 1% and E' = 2%.

The corresponding numerical results a r e plotted on figs. 4, 5 , and 6. Fig. 4 shows the obtained tension curves (evolution pf c

,, ^-

stress versus EY1

-

plastic strain). Fig. 5

- - - -

presents the influence of the a angle and plastic offset definition on the yield point.

Finally, fig. 6 summarizes the anisotropy of the yield point of three main texture components for two plastic offsets namely E~ = 0.025% and EP = 0.2%.

The comparison of the theoretical and experimental results indicates a good pualitative agreement concerning the evolution of the yield point anisotropy.

Nevertheless, certain differences concerning the hardehing evolution and i t s anisotropy may be remarked.

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rolling and tension directions.

200

0 15 30 45 60 7 5 90

ALPHA IDEGI

Fig 2. Experimental anisotropy of yield points versuscc angles for various plastic offset definitions.

Fig 3. The anisotropy of t h e hardening modulus in func- tion of the tension direction.

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JOURNAL DE PHYSIQUE

Fig 4. Numerical simulations of tension curves for various a -angles.

ALPHA lOEG1

Fig 5. Theoretical evolution of the anisotropy of yield point versus a -angle for four plastic offsets.

Fig 6. The influence of the tension direction on yield p'oint of three ideal texture components

a ) plastic offset E~ = 0.025%

b) plastic offset E~ = 0.2%

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hardening strongly depends on dislocation - precipitate interactions. These interactions have been only roughly modelled in t h e calculations. A more complete study of these problems is undertaken.

REFERENCES

[ I ] M. Peters, K. Welpmann, T.H. Sanders

Texture and anisotropy of tensile properties in Al-Li sheet material. Proc. E-MRS Conf. on "Adv.

a at:.

Res. and ~ e v e l o ~ m e n t for Transport" Strasbourg, France (1985)

[2] P. Lipinski, M. Berveiller

Elasto-plasticity of micro-inhomogeneous metals a t large strains. Submitted for publication

[3] T.H. Lin

Analysis of Elastic and Plastic strains of a F.C.C. Crystal. J. Mec. Phys. Solids, 5, 143 (1957)

[4] G.I. Taylor

"Plastic Strain in Metals". J. Inst. Metals, 62, 307 (1938) [4] G.I. Taylor

"The Mechanism of Plastic Deformation of Crystals". Proc. Roy. Soc. London A145, 362 (1938)

[5] D. Ruer, A. Vadon, R. Baro

Adv. X-Ray Analysis 23, 349 (1980)

[6] ^A. Vadon, C. Laruelle, J.J. Heizmann, Ph. Jeanmarr

Quantitative determination of t h e t e x t u r e of A1-Li Alloys (This conference)