Thermally-induced Martensitic Transformation Research Articles

Stability of thermally-induced martensitic transformations in bi-atomic crystals

Some of the most interesting, and technologically important solid–solid transformations are the first order diffusionless transformations that occur in certain equiatomic, ordered, bi-atomic crystals. These displacive transformations include thermally-induced, reversible, proper martensitic transformations as seen in shape memory alloys such as NiTi (where group–subgroup relationships exist between the symmetry groups of the crystal phases) and the reconstructive martensitic transformations seen in certain ionic compounds such as CsCl (where no group–subgroup relationship exists between the phases). In contrast to existing continuum mechanics approaches, the present work constructs a continuum energy density function W( F ,θ) (as a function of a uniform deformation gradient and temperature) of a perfect periodic bi-atomic crystal from temperature-dependent atomic pair-potentials. Equilibrium solutions and their stability are examined as a function of temperature for crystals under no external stress. The full problem is solved numerically, and an asymptotic theory is employed to guide the numerical solution near multiple bifurcation points. Using pair-potentials and enforcing constrained kinematics (uniform deformation of a cubic CsCl-type crystal), lower symmetry crystals, such as orthorhombic, monoclinic, and rhombohedral structures are predicted. The first two of these are unstable within the chosen temperature window for our particular case, while the third is stable for higher temperatures. In addition, a hysteretic transformation was discovered in which the CsCl structure is stable at high temperatures and the NaCl structure is stable at low temperatures. These two cubic phases are connected by an unstable rhombohedral path corresponding to the transformation mechanism proposed by Buerger (1951). The CsCl–NaCl transformation suggested by the numerical results is a reconstructive transformation with a group–nonsubgroup relationship between the symmetry groups of the two phases.

Distinction between Thermal and Stress-Induced Martensitic Transformations and Inhomogeneity in Internal Stress

A concept of inhomogeneous internal stress called shape change stress (SCS) was introduced in martensitic transformations (MTs). The SCS was considered to be required because martensite plates formed on cooling must deform the surrounding untransformed parent. The concept enabled successful elucidation of the reason for the progress of thermally induced MTs (TIMTs) with changing temperature and for that of stress-induced MTs (SIMTs) under constant stress on the basis of the Gibbs phase rule. Decreasing SCS with decreasing specimen size (mass) explained the downward shifts of experimental equilibrium temperatures T* o = (M s + A f )/2 with decreasing specimen mass m so far observed in the TIMTs of some shape memory alloys. Furthermore, the concept that no SCS is generated either in SIMTs or at the ultimate end of m = 0 in TIMTs rationalized the following observation on a monocrystalline Cu-13.4Al-4.2Ni (mass%) alloy. That is, the variations of M, and M f with m converged at the extrapolation to m = 0, and those of As and A f also did; M# s = M# f and A# s = A# f (the superscript # indicates the transformation temperatures at the ultimate end of m = 0). The former coincided with T L (0) where the dependence of transformation stress σ L on temperature was extrapolated to stress zero, and the latter coincided with T U (0) where a similar extrapolation in the case of reverse transformation stress σ U was performed.

On the Three Phase Mixtures in Martensitic Transformations of Shape Memory Alloys: Thermodynamical Modeling and Characteristic Temperatures

We study here the thermally-induced martensitic transformation process of shape memory alloys. Taking the internal energy of phase mixtures as the potential function and introducing coherency energies between martensite and austenite and between different variants of the martensitic phase, we are able to use thermodynamical arguments to obtain hysteresis diagrams which could be measured experimentally. The characteristic temperatures for martensitic transformation, $M_{s,f}$ (martensite start and finish) and $A_{s,f}$ (austenite start and finish) can be identified explicitly and are closely related to the coherency parameters of the coherency energies.

Relationship Between Shape Memory Material Properties and Applications

The shape memory effect has been observed in several material systems: metals, ceramics and polymers. Mainly metallic systems in which a strain-induced or thermally-induced martensitic transformation occurs, have been explored. Also, recent discoveries have shown that shape memory effects in specific systems can also be driven by changes in hydrostatic pressure or magnetic fields. This indicates that not all effects related to the martensitic transformation have been explored yet for use in application. But even in classic systems designers are challenged to better analyse what functions the material properties can really bring about in applications such as actuators, smart materials or medical devices

Crystallography of β2 → γ2′ martensitic transformation in Au-47.5 at.% Cd and Au-47.5 at.% CdCu alloys

The crystallography of the β 2 → γ 2′ stress-induced and thermally-induced martensitic transformations in Au-47.5 at.% Cd and Au-47.at.% CdCu alloys were reexamined by simultaneous measurements was essentially {111} γ 2′ Type I twinning, <121> γ 2′ Type II twining was also found in one case. No difference was found in the crystallography of stress-induced and thermally-induced transformations. Two non-equivalent solutions of the phenomenological crystallographic theory, Type I (+) and (−) solutions, were in excellent agreement with experimental observations. The results for the Type I (+) solution were essentially the same as those previously reported by Lieberman et al., but the agreement between theory and experiment was much better than theirs. Furthermore, (−) solution for Type I twinning and (+) solution for Type II twinning were also found for the first time. Both results show that the phenomenological crystallographic theory applies well in all respects to the present alloy system.

Electron microscopy study of dislocations associated with thermal cycling in a CuZnAl shape memory alloy

The arrangements of dislocations formed during thermally-induced martensitic transformation cycling in a CuZnAl single crystal have been analyzed by transmission electron microscopy. The dislocations were mainly of a mixed type, with bdu = <111> and b = <001> . Two thermal treatments prior to cycling have been considered, finding some differences in the dislocatios distributions and their evolution. These differences are well correlated with those found when studying the thermal cycling of the same alloy by means of calorimetry. Simple considerations show that the evolution of the macroscopic parameters (transformation temperatures, hysteresis cycle shape and position) can be explained semiquantitatively in terms of the free energy changes produced by: (a) the dislocations, when embedded in the ß or in the martensitic phases; (b) stacking faults created in martensite by some of the dislocations appearing during the cycling and (c) the increase in the area of martensite-martensite interfaces.