TENSION-COMPRESSION ASYMMETRY AND ELASTIC STRAIN INCORPORATED INTO THE SOLUTION OF THE PROBLEM OF MARTENSITIC NONELASTICITY AND DIRECT MARTENSITIC TRANSITION IN BEAMS FROM A SHAPE MEMORY ALLOY UNDERGOING BENDING

In this paper, the problems of cantilever and pure bending of a beam of solid rectangular cross section from a shape memory alloy (SMA) in direct thermoelastic phase end structure transitions are solved. This paper presents database on nonlinear model of SMA straining in phase and structure transitions. In this paper, the propositions of the proportional loading of active processes and of the Bernoulli-Euler hypothesis on a bending problem are accepted. The elastic part of full strain and tension-compression asymmetry of the SMA stress-strain curves is incorporated. A numerical solution of the problem in noncoupled formulation is obtained by a semi-inverse method,. Diagrams of dimensionless neutral surface coordinate and dimensionless beam curving from dimensionless bending moment are shown. In the case of direct transition effect, linear response of martensite volume fraction on dimensionless beam curving and dependence of dimensionless normal axial stress on martensite volume fraction are obtained. Impact tension-compression asymmetry of SMA on the dependence of dimensionless beam flexure on dimensionless axial coordinate in the case of cantilever bending is shown. In the case of martensite nonelasticity effect and in the region of small values of dimensionless bending moment, the dimensionless neutral surface coordinate depends only on the ratio of tension and compression elastic moduli of SMA. Similar results are obtained in the case of direct transition effect and in the region of small values of dimensionless martensite volume fraction.