PSI - Issue 69

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

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2. Basic provisions of the dynamic theory of formation of martensite crystals The dynamic theory of MT is based on the concept of the controlling wave process (CWP). Despite the existence of the review [Kashchenko and Chashchina (2011)] and monographs [Kashchenko and Chashchina (2009, 2012), Kashchenko (2010)], which remain relevant, it seems appropriate to briefly dwell on the key ideas developed mainly by the authors of the article to facilitate the assimilation of a large volume of information. 1. First, the martensitic transformation (MT) exhibits clear signs of a first-order transition, suggesting a heterogeneous nucleation mechanism for the new phase. However, despite extensive investigation, no nucleation sites have been observed. The formation of the (CWP) implies the emergence of an initial excited state (IES) – a spatially localized oscillatory process. 2. The heterogeneity of the initial crystal formation stage is evident from the emergence of the initial excited state (IES) within a localized region of the elastic deformation field near a dislocation nucleation center (DNC). This region takes the form of an elongated rectangular parallelepiped, with edges aligned along the eigenvectors of the DNC’s elastic deformation tensor (Fig. 5a). Notably, two of these deformations exhibit opposite signs, while the third is zero. 3. During cooling, the transformation initiates at the M s temperature, which lies below the phase equilibrium temperature T 0 , indicating that the process occurs under non-equilibrium conditions. 4. The formation of the initial excited state (IES) involves discrete atomic jumps within a localized region, followed by intense oscillations around new equilibrium positions. This process generates wave beams that carry information about the elastic field characteristics in the IES domain. 5. The wave beams transport a critical deformation threshold that destabilizes the initial phase within their superposition region. This process establishes a prototypical martensite crystal structure in the form of a plate, with thickness d ~ λ₁,₂/2, where λ₁ and λ₂ represent the wavelengths of the nearly orthogonal wave beams (Fig. 5b).

Fig. 5. Scheme of the origin and wave control of the growth of a martensite crystal: (a) – the region of localization of the NWS in the elastic field of a dislocation is shaded; (b) – wave model of crystal growth control. The habit plane is generated by the moving intersection line of the wave fronts and aligns with a linear combination of the wave velocities. Consequently, its orientation is determined solely by the elastic properties of the parent phase. In the simplest case, the normal vector N to the habit plane can be expressed as:

(1)

, where n 1,2 are unit vectors along the velocities v 1 and v 2 , and the ratio of the velocity moduli is found from the Christoffel equation for a given set of values of the elastic moduli of the austenite phase.