MECHANICAL HYSTERESIS IN INDIUM-THALLIUM ALLOYS

Abstract

Alloys near the composition In-20 at. % Tl are examples of a class of material that has a twinned non-cubic structure and possesses high mechanical hysteresis. The present investigation is concerned with the mechanism by which this high damping is generated. It is well established that the application of stress to the twinned tetragonal structure moves the twin boundaries in the sense that gives partial relief of the applied strain. It is further observed that the boundary movement lags behind the stress during cyclic straining. The strain corresponding to the boundary hysteresis can be deduced from the twin crystallography and the unit cell parameters and agrees with the measured hysteresis. So it is clear that the hysteresis arises from the irreversible boundary movements. The purpose of this investigation was to establish the cause of this irreversible movement. The torsional hysteresis of 2 mm diameter cylinders of polycrystalline In-Tl alloys was measured by plotting torque-twist curves during cycles of stress between constant strain limits over the frequency range 0.004 to 3.0 C/s and for temperatures from - 65 to + 45 °C. The hysteresis loops for 18,20 and 22 at. % Tl reached a maximum area at temperatures which depended on frequency through an activation energy of about 18,000 cal. mole. This is close to the published value for the tracer diffusion of Tl in In of 15,500 cal.mole, which is not a particularly reliable figure because of doubts in the interpretation of the experimental data. The relationship between these two energies suggests that the mechanical hysteresis might be explained by the existence of a force on the twin boundaries caused by an ordering of Tl atoms relative to the orientation of the C axis of the tetragonal cell. If boundaries are suddenly moved at low temperatures the orientation of the C axis will change in the swept-out region and the Tl atoms, which will not have time to jump to the new preferred sites, find themselves in high energy positions. This generates a force which will return the boundaries to their original position when the stress is removed. The rubber-like behaviour at low temperatures is thus explained. At higher temperatures the atoms rapidly move to the newly preferred sites, the boundary is stabilised in the new position, and a permanent deformation results. These mechanical characteristics are reproduced by the model of a Maxwell Solid, comprising a spring and dash-pot in series, and so the possibility that this model reproduces the behaviour of In-Tl was explored. This was done by comparing the hysteresis and the stress relaxation behaviour. When the twin boundaries in the In-Tl alloy are suddenly displaced, the stress required to keep the strain constant steadily relaxes ultimately to zero, as is the case with the Maxwell Solid. It did not prove to be possible to relate the kinetics of stress relaxation, however, to the hysteresis behaviour. The reasons for this will be discussed, in terms of the likely existence of several mechanisms contributing to the deformation behaviour.