Tension-compression asymmetry incorporating in solution the problem of cylindrical bend of the plate from shape memory alloy | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 24 > №2 / 2018 / Pages: 186-206

Tension-compression asymmetry incorporating in solution the problem of cylindrical bend of the plate from shape memory alloy

Abstract:

N this paper the problems cantilever and pure cylindrical bending of plate with solid rectangular cross-section from shape memory alloy (SMA) are solved. Tension-compression asymmetry (TCA) of the SMA stress-strain curves and different elastic modules is incorporated. This paper is database on model of SMA non-linear straining in phase and structure transitions. In this paper proposition of active processes proportional loading are used. So, numerical solution of the problem is obtaining in non-coupled formulation and a slow enough processes are considered. In this paper hypothesis of Kirchhoff-Love in cylindrical bending problem and plane strain hypothesis to second component of the full strain tensor are accept. Dependence of dimensionless neutral surface coordinate, dimensionless normal stress and the compliance of plate from the TCA of stress-strain curves and the difference in elastic modules in case of martensite non-elasticity (MN) and direct transition (DT) are shown. Dimensionless neutral surface coordinate are only depend on ratio of tension and compression elastic modules of SMA in case of small values of dimensionless bending moment (MN) and in case of small values of dimensionless martensite volume fraction (DT). Dependence of the second component of the stress tensor from the first component in implicit form are obtained. Distribution of the elastic and the phase-structure axial strains in plate cross-section are found. Difference in solution of the pure bend of the beam and the cylindrical bend of the similar plate are shown. The low expression nonlinear dependence of the dimensionless plate curvature from the martensite volume fraction is found.

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