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of the thermoelastic martensitic transformation V. Prieb and V. Wolff "MFS-Büro Dr. Prieb" Abstract: The hysteresis loop interior of thermoelastic martensitic transformations of TiNi-base shape memory alloys including the transformation with invariant plane is investigated in the partial transformation cycles and discussed. For the transformations with invariant plane the latent hysteresis is negligible small. The dependence of the measured heat on the martensite fraction transformed in the partial cycles is achieved and analyzed. The "invalidity" of the second rule of the thermodynamics is observed in partial cycles of the transformation with invariant plane: at the interrupt of the reverse transformation at a temperature in the interval Tpeak(heating)<T<Af the released heat of the forward transformation measured in the same partial cycle is larger as the absorbed heat of the reverse one. The stability of the two-phase system and connection between the observed energy effects and the dissipation of the elastic energy is analyzed. Introduction: Through the partial transformation cycles of single crystals of Cu-based shape memory alloys the existence of two equilibrium lines was established, which build the internal loop of the latent hysteresis. The analyze of the interior of the hysteresis shows, that the stored as well as the dissipated energy are of the same kind of elastic nature. Dependence of the dissipated energy on the martensitic fraction includes a parabolic term. The energy dissipated within the latent hysteresis is described by a linear term. Although various investigations of the thermoelastic hysteresis and even quantitative estimations of the stored elastic energy and the dissipated energy the establishment of a direct correlation between stored and dissipated elastic energy or between the thermoelasticity and the hysteresis is unique. The extension to different kinds of thermoelastic transformations in several alloys including polycrystals is necessary to generalize the thesis. Several kinds of transformation and hysteresis were investigated by calorimetric measurements for TiNi based alloys. This includes the transformations with invariant plane and therefore minimal hysteresis. This work examines the interior of the hysteresis loops for these transformations. Conclusion: The starting temperatures of the forward and reverse transformation lay along two lines, which are established inside of the hysteresis loop of every transformation. In general they are orthogonal to the temperature axis and parallel to each other and build a loop of the latent hysteresis. The width of the latent hysteresis is from 0°C (B2-B19 inv. and B2-R) up to 35°C (R-B191). The energy of the twin boundaries can be regarded as barrier for nucleation and corresponds to one half area of the latent hysteresis. It is subtracted from transformation energy, so that the measured heat is lower. The transformation passes as a lot of micro-jumps between local states of equilibrium. The breakdown of such stabile groups of martensite crystals during the reverse transformation requires additional energy. If forward or reverse transformation are interrupted not accommodated stress forces the contradictory transformation, which doesn't start at the trajectory building the hysteresis loop, but at the equilibrium line. The stored elastic energy set free from this mechanism of accommodation is dissipated as heat and measured. Such change of mechanisms of accommodation during the thermoelastic transformation should cause a not linear dependence of the measured heat on the fraction of martensite. The mixture of two phases is stabile or meta-stabile in the range of fast martensite growing and instabile at the edge of the hysteresis loops. At the transformation with invariant plane the forward transformation takes place without any barrier just below the equilibrium temperature, what causes the very small latent hysteresis. The "contradiction" the second law of thermodynamics in investigated cases where the radiated heat exceeds the absorbed one can be traced back either to different contributions of dissipated and stored terms of elastic energy, which influence the measured heat, or to discrepancies between the transformation rate and heat removal rate. This situation must be taken into account by calorimetrically measurements of shape memory alloys. More: Article (full script, english) as PDF-file Home |