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Influence of grain neighbours on the stress-induced martensitic transformation in individual grains studied by synchrotron 3DXRD and Diffraction Contrast Tomography (DCT)
Y. ELHACHI¹, B. MALARD², S. BERVEILLER¹, J. WRIGHT³, W. LUDWIG⁴, X. MOREL¹, D. BOUSCAUD¹, B. PIOTROWSKI¹

1 Arts et Métiers ParisTech, LEM3, 4, rue Augustin Fresnel, 57078 Metz Cedex 03, France. ^b CIRIMAT, 2 CIRIMAT, Université de Toulouse, Toulouse INP, 4 allée Emile Monso 31030 Toulouse, France.

3 ESRF, 71 Avenue des Martyrs, 38000 Grenoble, France.

4 MATEIS, INSA Lyon, UMR5510 CNRS, 345 Avenue Gaston Berger, 69100 Villeurbanne

Abstract

Two synchrotron techniques were coupled to study the behaviour of individual grains of a polycrystal and to correlate this evolution with the 3D microstructure determined by DCT. Results are discussed considering metallurgical features (grain size, crystallographic orientation…) and geometrical ones (location of the grain in the specimen, neighbouring grains…).

Keywords: internal stress, synchrotron, 3D microstructure

Introduction

In shape memory alloys, single crystal analysis has delivered a great deal of useful information furthering the understanding of interfacial motions between parent and product phases, for both uniaxial loading and during temperature changes. Unfortunately, these results cannot be easily extended to martensitic transformation in polycrystalline materials. Strain incompatibilities occurring at grain boundaries and stress transfer between transforming grains strongly influence the transformation kinetics in polycrystals. As a consequence, the macroscopic behaviour differs strongly between polycrystals and single crystals. Therefore, synchrotron techniques have been used to study both morphology and strain-stress state of individual grains embedded in a polycrystal.

Diffraction Contrast Tomography allows the three-dimensional morphology of individual grains to be determined with a spatial resolution of ~1.5µm as well as their positions in the specimen. The 3D-XRD technique gives access to the crystallographic orientation, average position and the stress state of each grain; due to various constraints, internal stresses were determined only in the austenite phase. Previous experiments were performed on four grains embedded in a polycrystal of Cu-Al-Be alloy [Berveiller, 2011] using the 3D-XRD technique, then on one hundred grains [Elhachi, 2015].

In this work, DCT and 3D-XRD technique have been coupled to follow one hundred grains during an in-situ tensile test on a Cu-Al-Be superelastic alloy, considering their morphology and mechanical behaviour.

Materials and experimental technique

The studied alloy was an austenitic Cu-Al-Be alloy (Martensitic transformation start temperature Ms =-100°C) with a mean grain size of 130µm. The specimen is a cylindrical wire of diameter of 0.86mm. In order to follow the stress-induced transformation, an in-situ tensile device was installed on the diffractometer.

The 3DXRD microscopy has been developed to perform structural and crystallographic investigations in bulk materials, for each individual grain of a polycrystalline sample [Poulsen, 2004]. We used the 3DXRD microscope at beamline ID11 of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) in transmission mode. The energy was 80keV ( = 0.155Å), corresponding to a penetration depth in copper of 1.5mm.

The beam size was chosen to ensure that the whole width of the specimen remains illuminated by X-rays during rotation. The beam was 1mm high and 1.6 mm wide for a specimen diameter of 0.86 mm.

Diffraction patterns were recorded on a CCD detector with an effective pixel size of 50µm. We used the rotation method as described by Lauridsen et al. [Lauridsen, 2001]: images were acquired while rotating the specimen around the -axis that was parallel to the tensile axis. At each equidistant step  of 0.3°, a diffraction pattern was recorded. A pair of 114° -ranges were used which corresponded to the incident beam entering the front and back of the load frame device (228º in total). This corresponds to 760 images at each applied load.

For DCT experiments, the sample was continuously rotated through 360° around an axis perpendicular to the incident beam and a series of radiographs are recorded integrating over small angular increments; the detector was placed closely behind the sample [Ludwig, 2008; Johnson, 2008]. Diffraction spots were recorded on the outer part of the detector while the absorption and extinction information carried by the transmitted beam was recorded in the central part.

results

At the initial state, the microstructure of the polycrystal was reconstructed from DCT data in an analysis volume of 0.7mm high. From this technique, the real morphology of individual grains can be determined.



Figure 1: 3D microstructure reconstructed from DCT experimental data (arbitrary colors)

From 3D-XRD experiments, the position of the mass center of each grain can be determined and its volume is estimated from the diffraction intensities. In Figure 2, each dot represents one grain; the size is proportional to the grain volume and the color corresponds to its crystallographic orientation. All grains were matched between both techniques.

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Figure 2: 3D microstructure reconstructed from 3D-XRD experimental data



Figure 3: Stress state (MPa) of the grains at a given loading point

During in-situ tensile test, the evolution of the austenite stress state was followed in each individual grains thanks to 3D-XRD data. Strong heterogeneities were measured: the differences can reach a factor 3 between grains. Moreover, the stress state depends on the crystallographic orientation but also strongly on the local neighbour environment; we observed differences when comparing pairs of grains with the same orientation. In some cases, intergranular interactions inhibited the martensitic transformation. This indicates that Schmid factor is not a sufficient criterion to explain martensitic transformation occurrence. Considering geometric features, grains located at the surface carry lower stress values than grains embedded in the volume, probably due to free-surface effect. However, whatever the difference of mechanical behaviour, when calculating the critical resolved shear stress from the local stress tensor values, we found that all the grains have similar experimental values.

Conclusion

Methodologies have been developed to adapt 3D-XRD and DCT to shape memory alloys. From this original measurement, for the first time, almost 200 grains were followed during stress-induced martensitic transformation from microstructural and mechanical point of view.

These experimental data will benefit to SMA modelling as 3D microstructure will be simulated by finite element modelling in order to compare experimental and simulated data at a fine scale of the microstructure.

References

[Berveiller, 2011]. S. Berveiller, B. Malard, E. Patoor, J. Wright, G. Geandier. Acta Mater, 59, 3636-3645 (2011)
[El Hachi, 2015]. Y. El Hachi, B. Malard, S. Berveiller, J. Wright. Proceedings of ESOMAT 2015 (Antwerp, Sept. 2015). MATEC Web of Conferences 33, 02003 (2015)
[Johnson, 2008] G. Johnson, A. King, M. Gonclaves Honnicke, J. Marrow, and W. Ludwig, J. Appl. Crystallogr. 41, 310 (2008)
[Lauridsen, 2001]. E. M. Lauridsen, S. Schmidt, R. M. Suter and H. F. Poulsen. J. Appl. Cryst.. 34, 744-750 (2001)
[Ludwig, 2008] W. Ludwig, S. Schmidt, E. M. Lauridsen, and H. F. Poulsen, J. Appl. Crystallogr. 41, 302 (2008)

[Poulsen, 2004] H. F. Poulsen, Three-Dimensional X-ray Diffraction Microscopy. Mapping Polycrystals and their Dynamics. Springer, Berlin (2004)