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Nanoscience and Technology: An International Journal
ESCI SJR: 0.228 SNIP: 0.484 CiteScore™: 0.37

ISSN Imprimir: 2572-4258
ISSN En Línea: 2572-4266

Nanoscience and Technology: An International Journal

Formerly Known as Nanomechanics Science and Technology: An International Journal

DOI: 10.1615/NanoSciTechnolIntJ.2018026744
pages 165-181


Ilya V. Mishustin
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russia


The behavior of shape memory alloys (SMAs) depends substantially on the type of stress-strain state. For example, under active tension and compression of initially chaotic martensite, the martensitic inelasticity curves differ both in absolute values and in shape. A flat sloping section of the curve like on yield plateau is present under tension and is absent in the case of compression. A nonlinear model of polycrystalline SMA phase-structural deformation that takes into account the martensite nanostructure is proposed using the hypothesis of heterogeneous strain hardening of a representative volume and an analogue of the incremental plasticity theory with isotropic and translational hardening to describe the structural transformation. Two dimensionless parameters proportional to the ratio of deviator's third invariant to the cube of intensity of the inelastic strain tensor and active stress tensor are introduced to take into account the type of strain and stress state, respectively. The parameter of martensitic volume isotropic hardening is lifetime maximum of the ratio of inelastic strain intensity to its limit value corresponding to the current strain state type. The material function of translational hardening depends on the full stress intensity and stress state type. The test modes of SMA loading to the determination of the functions used in the model are described. Special cases of SMA martensitic inelasticity in a homogeneous stress state and corresponding simplifications of the basic equations are considered. The first case relates to the proportional loading of a specimen, the second one relates to the axial tension–compression and torsion of a thin-walled cylindrical rod.