Shape Memory Elements in Bending: Influence of the Shape of their Cross-Section

The effect of the shape of the cross-section of a bent prismatic bar on its shape memory recovery moment is investigated. The analysis is based on the mathematical model of the first author (Kafka, 1994a, 1994b, 2001). The area of the cross-section of the bar is assumed to be constant, the shape of the cross-section is varied. The investigated shapes are rectangles with various relations of their sides, and a circular cross-section. It is assumed that the rod is bent above elastic limit and unloaded at room temperature, which results in macroscopic residual stresses giving zero bending moment, and in residual internal variables descriptive of the change of the state of the material. Then, the resulting form is held fixed and temperature of the rod is raised. Due to the increase of temperature there arise recovery stresses resulting in recovery moments. These moments—depending on the shape of the cross-section—are calculated, and in this way the effectiveness of the shape of the cross-section is evaluated. In the case of a rectangular cross-section the effect of the relation of the sides is strongly non-linear, the effect of the circular cross-section is lower by 20% than that of a square cross-section.