Mechanical hysteresis caused by pseudotwinning in In–Pb alloys with concentrations of 6, 8, and 11.6 at.% Pb is investigated in the temperature range 1.7–180 K. The parameters of the hysteresis are estimated: the thermodynamic stress τT responsible for the reversibility of plastic deformation (superelasticity) and the friction stress τf characterizing the resistance exerted by the crystal lattice and its defects to the motion of twin boundaries. It is shown that the parameters of the mechanical hysteresis are determined by athermal processes: the fraction of the sample that has gone into the twin (or, on unloading, to the parent) orientation depends solely on the value of the applied stress. With increasing lead concentration the value of τT increases and τf decreases. One of the main conditions for the appearance of superelasticity is the inequality τTf. The hardening of superelastic alloys under cyclic loading is investigated (up to 300 cycles). In alloys with 8 at.% Pb the cyclic loading leads to a slight expansion of the hysteresis loop. For the alloy with 6 at.% Pb there is typically a strong distortion of the hysteresis loop, with the appearance of a transition-hardening part with a large coefficient of work hardening. An analytical description of the cyclic deformation diagrams of a superelastic alloy is proposed.

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