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Nucleation barriers for the cubic‐to‐tetragonal phase transformation in the absence of self‐accommodation
Author(s) -
Knüpfer Hans,
Otto Felix
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800179
Subject(s) - martensite , tetragonal crystal system , nucleation , scaling , austenite , phase (matter) , materials science , diffusionless transformation , surface energy , elastic energy , cubic crystal system , accommodation , crystallography , thermodynamics , condensed matter physics , physics , mathematics , chemistry , metallurgy , microstructure , geometry , optics , quantum mechanics
The austenite‐to‐martensite phase transformation is characterized by the creation and growth of small nuclei of the new martensitic phase. Within a geometrically linear description and including an interfacial energy, we show that the minimal energy scales like V 11 13in the volume V of the nucleus for V ≫ 1 when primarily only two martensite variants are present. This complements the findings in [Knüpfer, Kohn, Otto, CPAM 2012] where it has been shown that the minimal energy of the transient nuclei has the lower scaling V 9 11if all three martensite variants are present. The higher scaling of the minimal energy is related to a failure of self‐accommodation. The proof requires new analytical ideas and tools.
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