Bain strain

If this is subjected to the "Bain strain" it becomes an undistorted b.c.c. cell. This atomic "switching" involves the least shuffling of atoms. As it stands the new lattice is not coherent with the old one. But we can get coherency by rotating the b.c.c. lattice planes as well (Fig. 8.8). 

Note that the Bain strain implies a lattice orientation, which from Figure 1 is... 

We now face a dilemma in the case of iron alloys or steels (or in general), the measured IPS is inconsistent with the correct structural change as given by the Bain strain on the other hand, the upsetting produced by the Bain strain is not an IPS. Incidentally, the invariant plane is the habit plane of the martensite plates, as shown in Figure 2. Modem crystallographic theories of martensite formation such as those of Bowles and Mackenzie (1954) (BM) and Wechsler et al. (1953) (WLR) rectify these apparent inconsistencies, so we will proceed to discuss these BM and WLR theories, which are fundamentally identical but differ in mathematical order. 

Modern crystallographic theories suppose that, in addition to the Bain strain (the 3x3 matrix B) and rotation (R) alluded to earlier, a simple shear (S) occurs simultaneously (actually, no temporal sequence is implied by these operations). These three operations taken together are equivalent to the IPS shape deformation (P), or in matrix form... 

Since S is also a shear (but in the opposite direction), its combination with the IPS P produces an invariant line strain (Bowles and Mackenzie, 1954). That is, the combined rotation and Bain strain RB are also the identical invariant line strain (ILS). The ILS reduces to an eigenvalue problem with input data ... 

Najafbadi and Yip (18) have investigated the stress-strain relationship in iron under uniaxial loading by means of a MC simulation in the isostress isothermal ensemble. At finite temperatures, a reversible b.c.c. to f.c.c. transformation occurs with hysteresis. They found that the transformation takes place by the Bain mechanism and is accompanied by sudden and uniform changes in local strain. The critical values of stress required to transform from the b.c.c. to the f.c.c. structure or vice versa are lower than those obtained from static calculations. Parrinello and Rahman (14) investigated the behavior of a single crystal of Ni under uniform uniaxial compressive and tensile loads and found that for uniaxial tensile loads less than a critical value, the f.c.c. Ni crystal expanded along the axis of stress reversibly. 

Morgan, M.G., McKenzie, H., Enright, M.C., Bain, M., and Emmanuel, F.X. 1992, Use of molecular methods to characterize Moraxella catarrhalis strains in a suspected outbreak of nosocomial infection. Eur J Clin Microbiol Infect Dis 11 305-312. 

Alippi, P., Marcus, P. M., and Scheffler, M., 1997, Strained tetragonal states and Bain paths in metals, Phys. Rev. Lett. 78, 3892-3895. 

The X-ray diffraction method can be generalized in the so-called e-sin i method (Clemens and Bain, 1992 Hauk, 1997 Faurie et al., 2004 Thomas et al., 2004). It encompasses the strain measurement as a function of angle >// defined as the angle between surface normal and diffracting plane normal. A series of lattice spacing measurements is carried out for different orientations with respect to the surface normal (Figure L.2). 

A great scientific and atomistic step was taken by Bain (1 ) when he proposed a rather simple, albeit elegant, scheme for f.c.c. austenite to transform into b.c.t. martensite (Figure 1). The Bain distortion relates corresponding unit cells in the two structures and speciHes the upsetting strain, by means of which martensite is formed. This picture is too simple in itself but has remained an integral part of the more sophisticated theories that have ensued. 

It has been known for some time that the formation of martensite causes roughening (in Bain s words) of a prepolished surface, as shown in Figme 2. Careful analysis of the tilted martensite platelets shows, however, that an invariant plane strain (IPS) has occurred (Bowles, 1951). Such a distortion resembles a shear but also includes a volume-change component. In an IPS the displacement of any point is in a common direction and is proportional to its distance from the undistorted and unrotated invariant plane. 

Assumed Bain correspondence (hence the strain axes). 

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