PSI - Issue 69

Nadezhda M. Kashchenko et al. / Procedia Structural Integrity 69 (2025) 89–96

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S and the relative change in volume δ on θ, at Z=0, R=1200a (a is the lattice parameter of the γ phase; the origin is the center of the segment Λ 1 , vertical lines separate the regions of dominance of the shifts S 1 or S 2 , L 1 = 7 × 10 3 a and L 2 =10 4 a ). We also present numerical data for unit vectors of characteristic directions at θ = 15º: N ║ [0.4133 0.4125 0.8118] ( ≈ 0.52º from [112]); S 1 ║[0.4075 0.5389 "0"."7" "3"7" "2" ] ( ≈ 8.77º from [11 2" ]); ξ 3 ║[ 0" ". "7" "8"1" "2" 0.6186 0.0834] ( ≈ 8.17º from [1 1" 0]). It is easy to verify that a change in the Z coordinate for close values of R and θ, at least in the interval: − ! /4≤ Z≤ ! /4 , is not accompanied by a noticeable change in the orientation of the ξ 3 direction collinear to the long axis of the NBC in the form of an elongated rectangular parallelepiped. This means that the results presented above for the case of Z = 0 are also preserved for Z from the interval − ! /4≤Z≤ ! /4 . Then the emerging SM crystals in the form of a narrow plate ("needle") will have one of the sides with a size of at least L 1 /2. The formation of SM with habits {112} is caused mainly by the influence of the elastic fields of the segments Λ 1 ║ <1 1" 0> of the DNC. Similarly, the formation of SM crystals with habits of the {17 14 12} type is mainly due to the elastic fields of the Λ 2 ║ <1 2" 1> DNC segments. In order to determine the choice of the DNC* initiating the lateral growth of SM crystals with the habit (112), we note that when the crystal growth starts in the elastic field of the segment Λ1, a faceted crystal with segments Λ 1 * ║ [1 1" 0] and Λ 2 * ║ [1 1 1" ] should arise. As the direction of the Burgers vector b *, we choose the previously found direction of the macroshear b * ║ S 1 ║ [0.4075 0.5389 0" "."7" "3"7" "2" ]. We also consider that the first rapidly occurring stage of the SM crystal formation leads to a crystal with segment lengths L 2 < L 1 . Then, for L 1 * = 5000 a , L 2 * = 3000 a , R = 1000 a , Z = 0, we find that for the maximum value of the shift S 2 * at θ* ≈ 177 º , the orientation of the habit plane [0.41014 0.40551 0.81691]* is selected, which is ≈ 0.19 º with the (112) plane and ≈ 0.53 º with the previously calculated habit (0.4133 0.4125 0.8118). In addition, the direction of the macroshift S 2 * ║ [0.45089 0.50807 "0". "7" "3" "3"8" "7" ] deviates from the previously calculated b* ║ S 1 by ≈ 3.06 º . Conclusion The obtained result shows that layer-by-layer growth of the transverse size of the crystal (lateral growth) is possible, corresponding to the practical absence of layers of residual austenite between successively arising layers of martensite, parallel to the habit plane. It is this variant that corresponds to the occurrence of IES at θ* close to ± 180 º (in the case under consideration θ* ≈ 177 º ). Note that the formation of a stack of crystals with significant layers of retained austenite, similar to the stack in Fig. 3(b), is possible in the elastic fields of dislocation nucleation centers in the presence of a maximum tensile strain in the region of angles θ close to ± 90º, as noted in [Kashchenko et al. (2024)]. It is useful to keep in mind that the ideology of using DNC* to describe the lateral growth of martensite crystals has also justified itself in the description in [Kashchenko (2024)] of the (110) faces of SM crystals. The apparent "continuous" face growth (observed experimentally) can be interpretated as a rapid, discontinuous growth alternating with prolonged pauses. This interpretation offers new insights into the dynamic mechanism governing martensite lateral growth in shape-memory alloys. Acknowledgements The authors express their gratitude to the participants of ESOMAT-2024 for discussing part of the results of the work. References Baur, A., Cayron, C., Logé, R., 2017. Variant selection in surface martensite. Journal of Applied Crystallography, 50, 1646-1652. Georgieva, I. Ya., Izotov, V. I., Khandarov, P. A., 1970. Study of the morphology and structure of surface martensite. Industrial Laboratory 6 , 695. Haush, G., Warlimont, H., 1973. Single crystalline elastic constants оf ferromagnetic face centered cubic Fe-Ni invar alloys. Acta Metallurgica 21, № , 401 - 414. Kashchenko, M. P., 2010. Wave Model of Martensite Growth upon the γ-α Transformation in Iron-Based Alloys, 2nd ed. NITs Regul. i Khaotich. Dinamika, Izhevsk. Inst. Komp’yuternykh Issledovanii, Izhevsk [in Russian]. Kashchenko, M. P., Chashchina, V. G., 2011. Dynamic model of supersonic martensitic crystal growth.Physics-Uspekhi 54, № 4, 331 - 349.