Materials Science and Engineering, A186 (1994) L 1-L3 L 1

Letter

Modelling of grain rotations during compression deformation of polycrystalline intermetallic L12 compounds

Dierk Raabe lnstitut fiir Metallkunde und Metallphysik, Kopernikusstr. 14, R WTH Aachen, 52056 Aachen (Germany)

Abstract

Grain rotations during compression deformation of L12 compounds were simulated by means of the Taylor theory. The simulations predict a (110) texture for octahedral slip, a (311) and ~210) texture for combined octahedral and cube slip, and a (100) texture in case of dominant cube slip.

I. Introduction

The plastic deformation of intermetallic compounds with L12 crystal structure has been the subject of detailed investigations by Miura et al. [1] and Pope and Ezz [2]. As a result of ternary additions and composi- tional deviations, the mechanical properties, for example the ductility and the temperature for the peak strength, have been considerably enhanced, especially for Ni-based L 12 compounds.

In order to elucidate the anomalous course of the temperature dependence of the strength, i.e. to deter- mine the active slip systems at elevated temperatures, substantial work was carried out on the deformation of single crystals with various starting orientations [1]. The results suggest that in the regime of the positive temperature dependence of the strength, plastic defor- mation is mainly accomplished by slip on {111 }(110) glide systems and that the strength anomaly is caused by locking due to thermally activated cross-slip from primary {111} glide planes to {100} non-glide planes [2]. In correspondence with this cross-slip motion of the entire (110) dislocations, it was found that the critical resolved shear stress (CRSS) depends on the crystal orientation [2]. In the regime above the tem- perature of the peak strength where a negative temperature dependence of strength is observed, the deformation seems to be additionally attained by slip

on {001}(110) systems (cube slip)[1]. In contrast to octahedral slip systems, cube systems are known to obey the Schmid law [1, 2].

In the present study this current knowledge on the plasticity of L 12 single crystals was applied to predict the crystallographic textures of polycrystalline aggre- gates during compression deformation for the follow- ing reasons. First, the texture affects the strength of the material in terms of the Taylor factor. Second, in the field of dynamic recrystallization it can be revealed whether experimentally detected grain orientations are due to certain nucleation mechanisms or to conserva- tive grain rotations. Third, the impact of various types of active slip systems and various CRSS on grain rotations can be elucidated and compared with experi- mental data. Concerning the third advantage of the Taylor type simulations described here, it should be mentioned that the dependence on orientation of the CRSS which was reported from single-crystal deforma- tion of L12 samples to occur in the case of octahedral slip [2] was not taken into account and is discussed in a subsequent work. Since the presented simulations lead, however, to completely different results, which are characteristic for the activated type of slip systems, the main tendency of the texture development can be predicted without consideration of the orientation dependence of the CRSS within the set of 12 { 111 } (110) slip systems.

As shown by Taylor [3], the criterion for selecting the active slip systems in polycrystals is fundamentally different from that which rules the plastic deformation of single crystals. The contributions of octahedral slip on the one hand and cube slip which does not offer more than three linearly independent glide systems on the other hand can be varied quantitatively by changing the corresponding CRSS according to the simulated temperature regime.

For the simulations a Taylor "relaxed constraints" model (RC) which was proposed by Honneff and Mecking is applied [4]. Whereas in the 'Tull con- straints" model (FC) [3] the imposed compression deformation tensor is completely transferred into each grain to allow crystallographic slip, in the RC model some of the external shear components need not to be fulfilled, i.e. they are relaxed permitting local incom- patibilities between adjacent crystals. This assumption is physically reasonable since only a small volume fraction of material is affected if these incompatibilities are conceded locally. Since the compression test is

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L2 Letter

entirely symmetric with respect to the normal axis of the sample, the relaxation of el3 corresponds to that of e23. By decreasing the number of imposed tensor com- ponents in the RC model, the number of active slip systems is correspondingly lowered. The resulting anti- symmetric part of the tensor, i.e. the rotation, is thus changed accordingly. The present simulations were carried out in the deformation range from 10% to 90% with relaxed e23 and e13 tensor components with con- sideration of slip on { 111 } (110) and {001 } (110) glide systems and various ratios of the CRSS.

2. Simulation results and evaluation

As starting texture in the current simulations a set of 936 randomly distributed orientations, each represent-

iii

100 110

Fig. 1. Initial orientation distribution.

111

lO0 3.10

Fig. 2. Orientation distribution after 90% compression deforma- tion, Taylor RC model [3, 4]; relaxation of e23 and e13 tensor components, activation of octahedral slip.

ing a single grain, was chosen. Owing to the high symmetry of the compression test the crystal directions parallel to the compression axis are depicted in inverse pole figures (Fig. 1). First, the orientation changes

(a) 111

100 110

(b) ",11

0

0 0

i00 ii0

l O 0 110

Fig. 3. Orientation distribution after compression deformation, Taylor RC model [3, 4]; relaxation of e23 and e13 tensor com- ponents, activation of octahedral and cube slip, identical CRSS on both types of slip systems: (a) 30%, (b) 60%, (c) 90%.

Letter L3

(a)

i00

iii

0 0

0 0 0

l l C

(b) l ] l

ii0

(c) Iii

t 10G ii0

Fig. 4. Orientation distribution after compression deformation, Taylor RC model [3, 4]; relaxation of e23 and e13 tensor com- ponents, activation of octahedra| and cube slip, CRSS (octa- hedral slip) is five times the CRSS (cube slip): (a) 30%, (b) 60%, (c) 90%.

which result from octahedral slip are inspected (Fig. 2). It can be seen that after 90% compression deformation the grains which reveal a (110) axis parallel to the com- presson axis are the most frequent. Strong scattering can be seen towards the (210) and the (111) axis.

For the prediction of texture close to or above the peak temperature, cube slip is additionally taken into account with a CRSS equal to that of octahedral slip (Fig. 3). After 30% deformation a crystallographic fibre between (210) and (110) and a strong component at (311) with scattering towards (100) is developed (Fig. 3(a)). With ongoing deformation (Fig. 3(b)) the (311) component is increased. After 90% deformation the fibre components are rotated into the (210) axis (Fig. 3(c)). If the CRSS for octahedral slip is assumed to be five times higher than that for cube slip, conditions far above the peak temperature are simulated (Fig. 4). After 30% deformation a fibre between (100) and (110) with a maximum at (100) is developed (Fig. 4(a)). This type of texture is sharpened with ongoing defor- mation (Fig. 4(b)). After 90% deformation a strong (100) and a weak (110) component are stable (Fig. 4(c)).

The results clearly show that a texture transition from (110) to (311) and (210) takes place when octa- hedral slip is accompanied by cube slip. If cube slip reveals a much lower CRSS when compared with octahedral slip the texture consists of a strong (100) component.

A comparison of these simulation results with experimental data cannot be submitted, since no quan- titative results are available at the present time for the following reasons. Since the main results which deviate from predictions for deformation of pure f.c.c. materials are due to the activation of cube slip systems, the simulation results should be compared with experi- mental evidence from high temperature deformation tests. In these experiments it has, however, to be taken into account that dynamic recrystallization occurs. In order to measure the deformed grains only, X-ray or neutron texture analysis which only provide informa- tion about the integral texture of the bulk sample, cannot be applied. A quantitative experimental investi- gation which requires single orientation measurements taken using an electron microscope will be submitted in a subsequent work.

References

1 S. Miura, Y. Mishima and T. Suzuki, Z. Metallkd., 80 (1989) 157, 164.

2 D.P. Pope and S. S. Ezz, Int. Met. Rev., 29 (1984) 136. 3 G.I. Taylor, J. Inst. Met., 62(1938) 307. 4 H. Honneff and H. Mecking, Proc. 6th Int. Conf. on Texture of

Materials, Icotom, Tokyo, ISIJ, 1981, p. 347.