The Correspondence Theory and Its Application to NiTi Shape Memory Alloys

Cyril Cayron

doi:10.3390/cryst12020130

Abstract

Martensite crystallography is usually described by the phenomenological theory of martensite crystallography (PTMC). This theory relies on stretch matrices and compatibility equations, but it does not give a global view on the structures of variants, and it masks the relative roles of the symmetries and metrics. Here, we propose an alternative theory called correspondence theory (CT) based on correspondences and symmetries. The compatibility twins between the martensite variants are inherited by correspondence from the symmetry elements of austenite. We show that, for the B2 to B19′ transformation, there is a one-to-one relation between the specific misorientations and the specific inter-correspondences between the variants. For each type of misorientation, the twin of its junction plane can be predicted without calculating the stretch matrices, as in PTMC. The rational elements of the twins do not depend on the metrics; all the transformation twins are thus “generic”. We also introduce the concept of a weak plane that permits to explain the junction planes for polar pairs of variants for which the PTMC compatibility equations cannot be solved. The predictions are validated by comparison with experimental Transmission Kikuchi Diffraction (TKD) maps.

Highlights

Shape memory alloys (SMA) such as nickel-titanium (NiTi) are widely used in stents, springs, actuators, sensors and connectors
When the bar is bent at room temperature, the austenite is first deformed elastically and becomes unstable; the austenite grains are progressively transformed into martensite variants that are well-oriented in the stress field
We have investigated the possibility of other weak twins of axis [211]B19 that would be inherited by correspondence from [011]B2, and we found by increasing the tolerances in GenOVa that, besides the 213 B19, a weak plane 111 B19 could be possible

Summary

Introduction

Shape memory alloys (SMA) such as nickel-titanium (NiTi) are widely used in stents, springs, actuators, sensors and connectors Their astonishing mechanical properties directly result from the crystallography of the austenite (A) to martensite (M) phase transformation [1,2,3,4]. The bar is soft at room temperature and can be bent at low force; it keeps its deformation when the stress is released, with nearly no elastic return. This unusual plastic behavior comes from the fact that the deformation is not mediated by dislocations but by variant reorientation under stress. When the stress is released, the bar comes back to its initial austenite state and to its straight shape in a way that looks like elasticity but with a larger amplitude

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