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Multiscale study of phase transformation in shape memory alloys
The superelastic behaviour of a shape memory alloy was studied using high-energy X-ray diffraction imaging techniques. The individual mechanical behaviour of ≈ 180 grains was followed during an in-situ test and the real microstructure was reconstructed. This was then used as input data for finite element modelling: a very good comparison was obtained on more than 95% of the grains.
Shape memory alloys (SMA) exhibit a phase transformation from austenite to martensite under thermal loading, giving rise to the shape memory effect, or mechanical loading (giving rise to superelasticity). This transformation, called martensitic transformation (MT), reverses during unloading; the reversible strain can reach up to 10% in single crystals, which is much higher than in conventional metallic materials . In superelasticity, the actuation stress and the recoverable strain are strongly dependent on microstructural features such as grain size or crystallographic orientations [1-3]: in Cu-based alloys, <100>-oriented grains have the lowest actuation stress and the highest strain, while <111>-oriented grains have the highest actuation stress and the lowest strain. Moreover, Cu-based alloys are strongly anisotropic  their Young modulus varies by a factor 10 between <100> and <111> directions (~20 GPa and ~200 GPa respectively). To predict superelasticity, microstructural features have to be considered, so micromechanical models are required to accurately predict the local mechanical fields within the grain and their effect on superelasticity.
The aim of this work was to study the influence of the microstructure on the occurrence of superelasticity in a Cu-Al-Be SMA at the grain scale. For that purpose, a
coupled approach was developed using high-energy X-ray diffraction (XRD) and finite element modelling (FEM). The experimental part was performed at beamline ID11. As the MT reverses upon unloading, all measurements had to be taken during in-situ tensile tests; in this case, with a cylindrical tensile specimen (diameter of 0.86 mm). First, the initial microstructure was reconstructed in three dimensions using a near-field method, Diffraction Contrast Tomography (DCT), where grain shapes and relative crystallographic orientations were determined, as well as the position in the sample (Figure 113a). About 190 grains were identified in the analysed volume. Then, the average stress and strain tensors in each individual grain were measured by a far-field method, the 3D-XRD technique. As the martensite has a complex crystallographic structure (M18R), it could not be indexed so only the austenite phase was measured. Next, the experimental microstructure served as input data for FEM after meshing (Figure 113c), where a digital twin was built and the tensile test simulated. Very good agreement was obtained by comparing experimental and numerical stress tensors (Figure 114), which was the first time that such a comparison over numerous grains was achieved.
The results confirm the influence of the grain crystallographic orientation on the MT occurrence. The higher stress value (resp. the lowest) in the tensile direction was observed in <111>-oriented grains (resp. <100>), with a factor up to three compared to the applied stress from the elastic domain. Within the grain, the MT occurrence was associated with a stress plateau in the tensile direction and the development of shear components.
However, some grains did not obey this rule: stress heterogeneities by a factor three were obtained in similarly oriented grains. FEM and DCT coupling shows that additional heterogeneities were induced by the neighbouring grains and their own transformation, since
Fig. 113: Representations of the initial microstructure obtained by (a) DCT and (b) 3D-XRD. The centre of each sphere is the centre of mass of the corresponding grain, its diameter is the grain size and its colour is the crystallographic
orientation with respect to the axis of the cylindrical specimen. c) FEM-generated microstructure mesh.