Martensitic transformations invariant plane

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

The term invariant-plane strain comes from the fact that the plane of shear in an invariant plane strain is both undistorted and unrotated. Hence the plane of shear is a plane of exact matching of the coherent inclusion and the matrix. In martensitic transformations, this matching is met closely on a macroscopic but not a microscopic scale (see Section 24.3). 

Martensitic transformations involve a shape deformation that is an invariant-plane strain (simple shear plus a strain normal to the plane of shear). The elastic coherency-strain energy associated with the shape change is often minimized if the martensite forms as thin plates lying in the plane of shear. Such a morphology can be approximated by an oblate spheroid with semiaxes (r, r, c), with r c. The volume V and surface area S for an oblate spheroid are given by the relations... 

However, important differences exist. Martensite and its parent phase are different phases possessing different crystal structures and densities, whereas a twin and its parent are of the same phase and differ only in their crystal orientation. The macroscopic shape changes induced by a martensitic transformation and twinning differ as shown in Fig. 24.1. In twinning, there is no volume change and the shape change (or deformation) consists of a shear parallel to the twin plane. This deformation is classified as an invariant plane strain since the twin plane is neither distorted nor rotated and is therefore an invariant plane of the deformation. 

These operations do not occur separately and in any particular sequence but are simply a convenient way to conceptualize the transformation as a series of operations, each of which can be analyzed separately, but which working together produce a martensitic structure containing an invariant plane. As such, they can be imagined to occur in any sequence. For purposes of analysis, it is convenient to imagine that the lattice-invariant deformation occurs first, followed by the lattice deformation, followed finally by the rigid-body rotation. We now show that a lattice-invariant shear by slip followed by the lattice deformation analyzed above can produce an undistorted plane. 

The input data for the model consist of the description of the lattice deformation and the choice of the slip system in the lattice-invariant shear. The model has successfully predicted the observed geometrical features of many martensitic transformations. The observed and calculated habit planes generally have high indices that result from the condition that they be macroscopically invariant. 

Because of the four-fold symmetry of the [001] pole figures in Figs. 24.6-24.9, additional symmetry-related invariant planes can be produced. Also, further work shows that additional invariant planes can be obtained if a lattice-invariant shear corresponding to a = 7.3° rather than a = 11.6° (see Fig. 24.8) is employed [5]. Multiple habit planes are a common feature of martensitic transformations. 

For Nitinol - at the transition Ms, atoms begins to shear uniformly throughout the crystal. As the temperature is lowered the atomic shear continues to increase. At temperature, Mf, the atoms shear to their maximum point and assume a new structure. Thus, between Ms and Mr temperature interval the crystal structure of Nitinol is undefined and belongs neither to austenite nor to martensite . Therefore, thermodynamically, it should be classified as the second-order transformation. This is illustrated in Fig. 3. Conventionally - above Ms temperature, the whole crystal assume a crystal structure identified as austenite . At Ms temperature, a new crystal structure of martensite begins to form through two-dimensional (planar) atomic shear. The two crystal structures of austenite and martensite therefore share an identical plane known as Invariant Plane. As the temperature is lowered, the two dimensional shear (or more correctly, shift ) continue to take place one plane at a time such that the Invariant Plane moves in the direction as to increase the volume of martensite at the expense of austenite . Ultimately, at Mt temperature the whole crystal becomes martensite . Since between Ms and Mf any given micro-volume of the crystal must belong to either the austenite or the martensite , the transformation is of the first-order thermodynamically. This case is pictorially illustrated in Fig. 4. 

At Ms temperature TiNi initiates a uniform (inhomogeneous) distortion of its lattice — through a collective atomic shear movement. The lower the temperature, the greater the magnitude of shear movements. As a result, between Ms and Mr temperature the crystal structure is not definable. In sharp contrast, other known martensitic transformations initiate a nonuniform (heterogeneous) nucleation at Ms and thereafter the growth of martensite is achieved by shifting of a two dimensional plane known as invariant plane [28] at a time. Thus, between Ms and Mr temperature the crystal structure is that of austenite and/or martensite . 

Figure 2. Optical micrograph showing an Fe-24Pt alloy partially transformed to martensite. The surface upheavals caused by martensite formation are analyzed to be an invariant plane strain. Both phases are ordered...

---