Shape memory alloys constitutive model extention for considering development of the martensitic elements during phase and structural transformations | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 25 > №4 / 2020 / Pages: 543-562

Shape memory alloys constitutive model extention for considering development of the martensitic elements during phase and structural transformations

Abstract:

The article considers a constitutive model for shape memory alloys (SMA) which allows to take into account the differences between phase and structural transformation. The model reflects the fact that hardening effect is typical for structural transformation, but not for phase transformation. Deformation due to structural transformation is described with the use of loading surface by analogue of the plasticity theory with isotropic hardening. The model describes both phase and structural mechanisms of inelastic deformation, and influence of the first mechanism on the second. The deformed state is determined by one parameter, which can be changed by phase or structural deformation. Inelastic deformation due to structural transformation in the active process is subject to the associated flow rule. The differential condition for the active process and structural deformation is formulated. Tensor increment of the structural deformation is required to be codirectional with the external normal to the loading surface, hardening parameter associated with the structural transformation correspondingly is required to be positive. The article considers the extension of this model to the constitutive equations that allow to take into account development of martensitic elements during phase and structural transformation. It was shown that the model allowed to describe cross-hardening and oriented transformation. Several cases of proportional loading for increasing, decreasing and constant stresses were considered. Deformation plots and loading surface plots were provided for each case. The results for the different material functions determining development of the martensitic elements were compared. If analytical solution was not possible, the Runge-Kutta method was used to solve differential equations for deformation depending on the volume fraction of martensite. It was shown that in the case of constant or linearly increasing stresses, the results for the considered material functions coincided. In the case of decreasing stresses, the deformation values at the end of the process were higher for the material functions taking into account development of the martensitic elements.

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