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 the shear. Such a morphology can be approximated by an oblate spheroid with semi-axes (r, r, c) with r >> c. The volume and the surface area for an oblate spheroid are given by the relations:

and eccentricity is

For the case in which r >> c, then e -> 1 and S -> 2r². Use this as an approximation. The coherency strain energy per unit volume transformed is:

1. Find expressions for the size and the shape parameters for a coherent critical nucleus of martensite. Use the data below to calculate the values for these parameters.

2. Find the expression for the activation barrier for the formation of a coherent critical nucleus of martensite. Again use the data below.

3. Comment on the likelihood of coherent nucleation of martensite under these conditions. Note that nucleation will proceed at measureable rates if G_N

Data:

_V = 170 MJ/m³ (Chemical driving force at the observed transformation temperature)

= 150 mJ/m² (interphase boundary energy per unit area)

= 2.4 10³ MJ/m³ (strain energy proportionality factor for this case)