Introduction Reversible plasticity is the main

Introduction Reversible plasticity is the main property of plastic deformation by twinning. It represents the first stage of the mechanical twinning of crystals, elastic twinning [1]. At this stage twinning inclusion is reversible and can completely detwin spontaneously during off-loading. Under a concentrated load, a thin interlayer in the shape of a wedge appears in the crystal; it is a wedge-shaped twin and its crystal lattice is displaced at a certain angle to the matrix. The dimensions of the twin wedge grow proportionally to the external load. If the external load decreases, detwinning of the crystal takes place: the twin decreases in dimensions thus keeping the form of a thin wedge. After unloading it disappears completely, that is, antibiotics the crystal. Elastic twinning is observed in all twinning crystals. The important feature of deformation twin development at the elastic twinning stage is that its dimensions (wedge length L and its width h at the base) change proportionally to the load quantity. After some limit value of applied stress, the twin is wedged and after unloading stays in the crystal. At the stage of residual twinning, detwinning can be observed in response to the action of an external stress of the reversed sign on the crystal [2,3]. Numerous experimental investigations showed that the processes of twinning and detwinning determine the mechanical properties of many technically significant metals and alloys. This stimulates the interest in the study of this phenomenon. Detwinning in crystalline solids is a unique deformation mechanism partially responsible for the shape memory effect [4–7]. In the last years it has been revealed that twinning and detwinning are the important deformation modes in metals and alloys with various crystal structures [8–19]. The metals which have a hexagonal close-packed structure, such as Be, Mg, Zr, and Ti, have aroused great interest. Twinning-detwinning is an important deformation mode in these metals. Detwinning, a reverse twinning process, has been reported in some hexagonal close-packed metals and alloys during loading, unloading or cyclic deformation [20–27]. The detwinning characteristics in magnesium alloys obtained through a cyclic loading test have been studied in detail [28–35]. Detwinning describes the coalescence of a martensite twin into a single martensite crystallite [36,37]. It is stated both experimentally and theoretically that detwinning is a unique deformation mechanism of nanotwinned metals [38–40]. Various theoretical deformation models of crystal twinning-detwinning have been developed [41–46]. Earlier we studied the development of wedge-shaped twins in bismuth single crystals under the action of an increasing concentrated load. In Ref. [47], it was shown that an imprint had several residual wedge-shaped twins after indentation of bismuth single crystals by a diamond pyramid. Their evolution with load growth progressed in different ways. The proportional length and width changing of a wedge-shaped twin was distorted with load growth. Both twins’ growing and their complete stopping while the dimensions of wedge-shaped twins under load remained unchanged were possible. We revealed the cases of a spontaneous size reduction of a twinned wedge with load growth; that was a reversible twinning under load at the stage of residual twinning.
Experimental technique
Results and discussion It was experimentally revealed that the dimensional change of residual wedge-shaped twins of the imprint under repeated crystal indentation with the increased load followed one of the ten modes:
In this situation, an equilibrium state of an isolated elastic twin under load is ensured by elastic and inelastic forces which effect on the length unit of a twinning dislocation in an assembly equal to zero, that is, where are the forces produced by an external load and elastic fields of the dislocation assembly; are the braking forces conditioned by the crystal structure and its defects and also the surface tension forces acting on a twin from a mother crystal.