Stress field around precipitates: direct measurement and relation with

include either theoretical or measured stress fields around precipitates. In order to ... The shear stress acting on the dislocation is 50 MPa. maps, from which we ...
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Materials Science and Engineering A319– 321 (2001) 270– 273 www.elsevier.com/locate/msea

Stress field around precipitates: direct measurement and relation with the behavior of dislocations J. Douin a,*, P. Donnadieu b, T. Epicier c, G.F. Dirras a,d, A. Proult e, J.F. Silvain f a

b

LEM, CNRS/ONERA, BP 72, 29, A6enue De La Di6ision Leclerc, 92322 Chaˆtillon cedex France LTPCM-ENSEEG-INPG, Domaine Uni6ersitaire BP 75, 38402, Saint Martin d’He`res cedex, France c GEMPPM, INSA, Bat 502, 69621, Villeurbanne cedex, France d Department of Mechanical Engineering, Johns Hopkins Uni6ersity, Baltimore, MD 21218, USA e LMP, BP 179, 86960 Futuroscope cedex, France f ICMCB, A6. Dr Schweitzer, 33608, Pessac cedex, France

Abstract Use of digital processing of HRTEM images to determine stress fields around precipitates is exemplified in the case of aluminum alloys. Behavior of dislocations in these stress fields is simulated and compared to experimental observations. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Stress; Precipitates; Dislocations

1. Introduction Studies on structural work-hardened materials are usually focused on identification and determination of morphologies and orientations of precipitates in a matrix. While of interest, these data are usually not sufficient to tackle the mechanical properties of these materials. The mechanical properties of structural work-hardened materials are essentially governed by the local stress fields around the precipitates, the effective range of these fields and their interactions. In particular, the stress field associated with the presence of a precipitate in the matrix plays a significant role on the mechanical properties by changing the ability of movement of dislocations in the matrix, even at distance from the precipitates. This is particularly true in the case of nanometric precipitates, but stands for larger inclusions generating long-range stress fields. Direct determination of lattice distortions is possible using digital processing of High-Resolution Transmission Electron Microscopy (HRTEM) images of materi* Corresponding author. Tel.: + 33-1-46734442; fax: + 33-146734155. E-mail address: [email protected] (J. Douin).

als. The technique based on the use of Fourier transformations gives a direct experimental determination of the displacement field around the inclusion, from which the stress field can be extracted. Such a technique has been successfully employed to characterize stresses at interfaces but, to the authors’ knowledge, this is the first time it is used for precipitates. The influence of the measured stress field on the movement of dislocations has been subsequently studied by computer simulation. The program allows to include either theoretical or measured stress fields around precipitates. In order to compare simulated and observed behavior of materials, the properties of dislocations were also studied by conventional weak-beam Transmission Electron Microscopy (TEM) on plastically deformed samples.

2. Stress field measurement In order to measure the strain field around a nanometric precipitate, we first image the matrix using HRTEM in the close vicinity of the precipitate in the best imaging conditions. To test our experimental conditions, we have used two different microscopes (a Jeol 2010 operating at 200 kV with a Field Emission Gun

0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 1 0 3 - 0

J. Douin et al. / Materials Science and Engineering A319–321 (2001) 270–273

and a Jeol 4000 FX operating at 400 kV). The chosen materials are the 6056 and 6061 aluminum alloys. After a T6 heat treatment, these alloys are known to present a high density of precipitates whose diameters range

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from 2 nm for the 6056 alloy to 100 nm for the 6061 alloy. From HREM images of the matrix close to precipitate seen end-on, we then extract atomic displacement

Fig. 1. (a) HREM image of two precipitates in a 6056 aluminum alloy (directions of electrons: [001]). The distance between two atomic columns (white spots) is 0.202 nm; (b) and (c) atomic displacement fields, respectively ux and uy. A linear scale is used: a black pixel indicates no displacement while a white pixel corresponds to 0.2 nm. The moire´ contrasts at the location of the precipitates are artifacts and have no physical meaning.

Fig. 2. (a) Simulated HRTEM image of an aluminum matrix with a spherical precipitate 2 nm in diameter (elastic misfit between the matrix and the precipitate: 2%; defocus of the image − 83 nm, multi slice method). No distortion of the atomic planes can be seen directly; (b) and (c) corresponding displacement fields, respectively ux and uy (contour plot).

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J. Douin et al. / Materials Science and Engineering A319–321 (2001) 270–273

Fig. 3. (a) Simulated interaction of a dislocation segment with a perfectly coherent precipitate. The dislocation is pinned between two points; (b) movement of the same segment in the absence of the precipitate. The shear stress acting on the dislocation is 50 MPa.

maps, from which we deduce strain and stress maps. The first step is done by image processing of the HRTEM images using the Semper program. The extraction of the displacement maps from HRTEM images is based on the calculation of the information related to the phase of the image parallel to a chosen diffraction vector. This is done by centering an aperture around a chosen reflection in the Fourier transform of the HRTEM image, then performing an inverse Fourier transform. Details of this procedure can be found in [1]. In the reciprocal space, the information of the displacement field of the fine scale precipitation is contained within a Brillouin zone. In order to get information in the direct space, it is thus necessary to choose the size of the aperture as the width of a Brillouin zone. As the contribution of the precipitate to the Fourier transform of the image may exceed the Brillouin zone, it is also mandatory to remove the precipitate from the HRTEM image before processing. This is made by using a mask centered on the precipitate, and the mask is chosen gaussien to decrease the edge effects on the Fourier transform. Finally, the magnification of the image must be chosen in order to get sufficient sampling (in the order of 0.01 nm per pixel). The general method to transform the images phase into displacement fields can also be found in Hytch et al. [1]. As the precipitates in the 6056 aluminum alloy are usually found parallel to a Ž001 direction, we choose the (200) and (020) diffraction vectors for the processing, resulting in the extraction of components of the displacement fields ux and uy, respectively parallel to the [100] and [010] directions. The result of such an image processing is exemplified in Fig. 1.

In the case of the simplest spherical precipitate in an isotropic matrix, the radial displacement at a distance r from the center of the precipitate is inversely proportional to r 2 (see for example [2]). The simulation presented in Fig. 2a corresponds to a precipitate 2 nm in diameter, and the parametric misfit between the matrix and the precipitate was fixed to 2%. The simulation in Fig. 2a clearly exemplifies that a direct visual examination of the image would not allow to point out the atomic displacements when the precipitate has a small size (typically less than 3 nm in diameter) and when the misfit is low (less than 3%). However, numerical treatment of the image in Fig. 2a allows the extraction of the displacement fields (Fig. 2b–c). This justifies the use of the phase image method.

4. Numerical simulation of the movement of dislocations in the vicinity of precipitates The precipitation process usually strongly modifies the mechanical properties of the alloy. This is directly related to the influence of the stress field generated by

3. Vaildation of the stress field measurement method In order to validate our calculations, we have simulated HRTEM images of a deformed Al matrix around a nanometric precipitate.

Fig. 4. Microstructure of a 6061 aluminium alloy deformed plastically of 2% in compression at room temperature (weak-beam image). Notice the frequent loops attesting on the activation of the Orowan process (TEM Jeol 200 CX operating at 200 kV).

J. Douin et al. / Materials Science and Engineering A319–321 (2001) 270–273

the nanometric precipitates on the movement of the dislocations. We have thus developed a simulation of moving dislocations in the experimental stress field obtained by the technique described above. As one of the important parameters governing the interaction of dislocations and precipitates is the character of the dislocation in the vicinity of the precipitate, a continuous model describing the dislocation as a set a moving points, and thus allowing any character for the dislocation, has been developed. The chosen approach was develop by Bacon [3] and Foreman [4]. It consists in describing a dislocation as a set of points linked by straight segrnents of dislocations rather than a set of segments with given characters. The trajectory of each point is calculated at each time step of the calculation, allowing the dislocation to bow continuously and adopt whatever configurations temporarily minimizing its energy. In the present state, the simulation allows to study the influence of a non-uniform stress field, either defined analytically or determined experimentally (Fig. 3).

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erties of dislocations in an aluminum alloy by direct TEM using the weak-beam technique. The observed microstructure of the heat-treated 6061 alloy is usually not uniform. Some areas are dominated by precipitates adopting a lath shape while in other areas cylindrical needles are mainly found. After 2% plastic deformation, the dislocations are found pinned on the precipitates and we observed numerous dislocations loops resulting from the activation of the Orowan process (Fig. 4). It is worth pointing out that this process was the one that the above simulation using experimentally measured stress field was predicting.

Acknowledgements This work for supported by the ‘Programme mate´ riaux’ of the French National Center for Scientific Research (CNRS).

References 5. Deformation mirostructure of a 6061 alloy: comparison with simulation To compare the predicted and the experimental behaviors of dislocations, we have also studied the prop-

[1] M.J. Hytch, E. Snoeck, R. Kilaas, Ultramicroscopy 74 (1998) 131. [2] M.S. Duesbery, N.P. Louat, K. Sadananda, Phil. Mag. A 65 (1992) 311. [3] D.J. Bacon, Phys. Stat. Sol. 23 (1967) 527. [4] A.J.E. Foreman, Phil. Mag. 15 (1967) 1011.