TY - JOUR

T1 - Using eigenmoduli and eigenstates to evaluate the possibility of martensitic phase transformations

AU - Annin, B. D.

AU - Ostrosablin, N. I.

AU - Ugryumov, R. I.

N1 - Funding Information: This work was carried out within the framework of the Basic Research Program of the Siberian Branch of the Russian Academy of Sciences (Project code III.23.3.1) and with partial support from the Russian Foundation for Basic Research (Project code 19-01-00511 A). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/9

Y1 - 2021/9

N2 - The possibility of phase transitions (martensitic transformations) in shape-memory alloys is evaluated using the concept of eigenmoduli and eigenstates from the linear theory of elasticity. For alloys with cubic and hexagonal lattices, the matrices of elastic moduli and compl are given and expressions for their eigenmoduli and eigenstates are written. For cubic and hexagonal phases, the specific strain energy is presented as the sum of six independent terms corresponding to six orthogonal eigenstates. It is shown that depending on the ratio of eigenmoduli, there are six types of materials (alloys) with cubic and hexagonal symmetry. The specific strain energies in the cubic and hexagonal phases are compared. If the strain energy is greater in the hexagonal phase than in the cubic phase, the alloy can tend to return to its original state with lower energy. In addition, the strain energies in different phases can be compared using the formulas of the tensors closest in the Euclidean energy norm to cubic and hexagonal tensors. The energies are compared for some values of elastic constants.

AB - The possibility of phase transitions (martensitic transformations) in shape-memory alloys is evaluated using the concept of eigenmoduli and eigenstates from the linear theory of elasticity. For alloys with cubic and hexagonal lattices, the matrices of elastic moduli and compl are given and expressions for their eigenmoduli and eigenstates are written. For cubic and hexagonal phases, the specific strain energy is presented as the sum of six independent terms corresponding to six orthogonal eigenstates. It is shown that depending on the ratio of eigenmoduli, there are six types of materials (alloys) with cubic and hexagonal symmetry. The specific strain energies in the cubic and hexagonal phases are compared. If the strain energy is greater in the hexagonal phase than in the cubic phase, the alloy can tend to return to its original state with lower energy. In addition, the strain energies in different phases can be compared using the formulas of the tensors closest in the Euclidean energy norm to cubic and hexagonal tensors. The energies are compared for some values of elastic constants.

KW - compliances

KW - cubic and hexagonal lattices

KW - eigenmoduli and eigenstates

KW - elastic moduli

KW - shape-memory alloys

KW - specific strain energy

UR - http://www.scopus.com/inward/record.url?scp=85122297487&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=47556047

UR - https://www.mendeley.com/catalogue/1e3d53fd-ce32-3c15-8543-ff6a8b64f7f2/

U2 - 10.1134/S0021894421050011

DO - 10.1134/S0021894421050011

M3 - Article

AN - SCOPUS:85122297487

VL - 62

SP - 709

EP - 716

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 5

M1 - 1

ER -