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Trace analysis of the shape strain predicted by the Phenomenological Theory of Martensite Crystallography (PTMC) and variant selection prediction. (A) EBSD map of the grain with red arrows indicating the traction direction. The dashed lines indicate the normal to the habit plane of variant α 4. (B) Pole figure of the normals to the habit planes (green) and the shear directions (yellow) predicted by the BCC model. (C) Pole figure of the normal to the habit planes (green) and the shear directions (yellow) predicted by the BCT model. (D) < 110 > γ experimental pole figure.
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Variant selection is commonly observed in martensitic steels when a stress is applied to the material during transformation. Classically, the selection phenomenon is modelled considering the work of the shape strain in the applied stress field. This shape strain is generally calculated by using the Phenomenological Theory of the Martensite Crystall...
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... verification of the habit plane prediction is then performed by studying an austenite grain selected from the EBSD map presented in Figure 3. The grain is shown in Figure 5A with the austenite in blue and the martensite in Euler color coding. In Figure 5B,C respectively, the shape strains predicted by the PTMC calculations for the BCC and BCT models are shown for all four variants in Figure 5A. ...
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... grain is shown in Figure 5A with the austenite in blue and the martensite in Euler color coding. In Figure 5B,C respectively, the shape strains predicted by the PTMC calculations for the BCC and BCT models are shown for all four variants in Figure 5A. The normals to the predicted habit planes are marked in green and the shear directions are marked in yellow. ...
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... grain is shown in Figure 5A with the austenite in blue and the martensite in Euler color coding. In Figure 5B,C respectively, the shape strains predicted by the PTMC calculations for the BCC and BCT models are shown for all four variants in Figure 5A. The normals to the predicted habit planes are marked in green and the shear directions are marked in yellow. ...
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... midrib is considered as the habit plane of the martensite and a trace analysis is performed to verify the PTMC predictions. As an example, the normal to the habit plane of the red variant α 4 is marked with dashed lines in Figure 5. Our analysis clearly indicates that the BCT model does not predict the observed habit plane. ...
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... the contrary, the BCC model which fails to account for the variant selection seems to correctly predict the habit planes. From Figure 5, we can see that selected habit planes almost contain the traction direction. Hence, the shear resolved on it is almost zero, which explains why the criterion based on the work of the shape strain associated with the BCC model is not able to account for the variant selection. ...
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... seems, however, that even though the thermomechanical treatments are different, the results of Chiba et al. have similarities with ours. As illustrated in Figure 5A, we also observe that four variants form preferentially, these variants belonging to the same plate group. The variant coupling in plate groups is frequently observed in lenticular martensite [19][20][21]. ...
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... are defined in terms of habit plane orientation, as the group formed by the variants having their habit planes that cluster around a given < 110 > γ direction of the parent crystal. An illustration of such a cluster is proposed in Figure 5D,B where squares are drawn to indicate the < 110 > γ direction and the associated habit plane normals, respectively. In terms of lattice orientation, the plate group is crystallographically defined in reference [20] and illustrated with the yellow Kurdjumov-Sachs variants in Figure 6A. ...
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... appears that this criterion accounts very well for the variant selection observed in our sample. Figure 8 illustrates the selection phenomenon for the grain in Figure 5A with the austenite in blue and the martensite in Euler color coding. Figure 8A presents the experimental pole figures of the grain. ...
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... Simulation movies showing at the atomistic displacements during the fcc-bcc transformation could be proposed for the first time. The variant selection of martensite in steels was also quantified with the interaction work between the lattice distortion and the external stress [65,66]. Mathematically, the interaction work is the product , where is the matrix of the external stress field, and is the deformation matrix calculated from the distortion matrix F by . ...
Martensite crystallography is usually described by the phenomenological theory of martensite crystallography (PTMC). This theory relies on stretch matrices and compatibility equations, but it does not give a global view on the structures of variants, and it masks the relative roles of the symmetries and metrics. Here, we propose an alternative theory called correspondence theory (CT) based on correspondences and symmetries. The compatibility twins between the martensite variants are inherited by correspondence from the symmetry elements of austenite. We show that, for the B2 to B19′ transformation, there is a one-to-one relation between the specific misorientations and the specific inter-correspondences between the variants. For each type of misorientation, the twin of its junction plane can be predicted without calculating the stretch matrices, as in PTMC. The rational elements of the twins do not depend on the metrics; all the transformation twins are thus “generic”. We also introduce the concept of a weak plane that permits to explain the junction planes for polar pairs of variants for which the PTMC compatibility equations cannot be solved. The predictions are validated by comparison with experimental Transmission Kikuchi Diffraction (TKD) maps.
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Transformation-induced plasticity in a ceria-stabilized-zirconia based composite was studied in four-point bending, with particular emphasis on nucleation and growth of tetragonal-to-monoclinic transformation bands. They initiated on the side in tension at a given value of stress and grow in size and number with increased applied load. The spacing between them was related to samples’ thickness: thicker samples led to a smaller number of larger/deeper bands. Residual stresses around indentations, placed on the tensile surface of some samples, triggered transformation bands nucleation but had no significant effect on the final total number of bands. A simple stress shielding model suggests that wide bands hinder adjacent thinner bands to propagate and expand because of stress shielding around them. Nucleation of a given transformation band is thus related to: (i) stress concentrations at the surface, (ii) geometry (stress-field inside the sample) and (iii) a shielding effect from the bands already present.
Variant selection during the A1→L10 transformation in a polycrystalline red gold alloy close to equiatomic Au-Cu composition has been extensively studied by Electron Back Scattered Diffraction (EBSD) in our previous work. The use of a mathematical description of the lattice distortion and the maximal work criterion allowed us to quantify the degree of selection. With the same approach, we investigate here an interesting shape distortion effect, discovered twenty years ago in equiatomic AuCu-Ga. The shape distortion of thin samples placed in bending condition and then heat-treated under stress is studied in details. The singular shape memory effect and the remarkable distortion amplification, which we call TADA effect, are explored by monitoring the sample radius of curvature and the advancement of the transformation. The underlying mechanisms of variant selection are revealed by EBSD analysis across the samples. The experimental crystallographic variant selection distribution is compared with the expected profile calculated with the Euler-Bernoulli beam theory. The good agreement demonstrates that variant selection during the transformation is at the origin of the macroscopic distortion of red gold alloys. The TADA effect was found to occur when external stresses are released, and strongly depends on the stress at the initial stage of the transformation. This unusual effect is assumed to result from the persistence of variant selection throughout the transformation.
A shape-memory effect is known to appear in red gold alloys with compositions close to Au–Cu. The aim of this paper is to study by electron backscatter diffraction (EBSD) the variant selection in the A1 → L1 0 transformation occurring under stress, in bending conditions. The L1 0 domains are successfully identified by this technique despite the c / a ratio being close to unity. The orientation relationship between the cubic and tetragonal phases is determined by a careful analysis of the EBSD data. The distortion of the lattice for each variant is then modelled and calculated from the experimental orientations. The mechanical work associated with the transformation is computed from the lattice distortion by neglecting the obliquity. Finally, the distribution of this mechanical work is compared with the case of a uniform distribution of all variants, in order to evaluate the extent of variant selection. The maximal work criterion, often used for martensitic transformations, enabled quantification of the variant selection phenomenon.
