Martensitic phase transitions with surface effects

• Main Author: Lusk, Mark T.
• Format: Others
• Published: 1992
• Online Access: https://thesis.library.caltech.edu/4411/1/Lusk_mt_1992.pdf; Lusk, Mark T. (1992) Martensitic phase transitions with surface effects. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NBES-9M76. https://resolver.caltech.edu/CaltechETD:etd-11052004-161432 <https://resolver.caltech.edu/CaltechETD:etd-11052004-161432>

Continuum treatments of martensitic phase transformations are capable of accounting for a variety of important surface effects attributable to the spatially localized interaction of coexisting material phases. Such phenomena are thought to play a critical role in determining the size, shape, and stability of nucleated embryos as well as to affect the conditions under which nucleation events occur. These issues are examined within a purely mechanical context wherein the special properties are modeled as traction and energy fields defined on a two-dimensional abstraction of the interface region. Materials that undergo martensitic phase changes are modeled as having a hyperelastic character in both the bulk and interface. The characterization of such bodies is examined in detail and a representation theorem is presented for describing the interfaces of isotropic, hyperelastic media. A class of isotropic, nonlinearly hyperelastic bulk material is introduced that is capable of modeling the dilatative component of martensitic phase transformations. Such materials are considered within a noninertial setting referred to as The Cylinder Problem. This problem provides a means of exploring a variety of surface effects, and a criterion for nucleation based on energy is presented towards this end. Here nucleation events are modeled as deterministic, temporal shocks that are global in spatial extent. The fundamental development presented does more than capture the desired surface effects. It shows how they are related to specific assumptions regarding interface and bulk constitution. Four different interface characterizations are presented that serve to illustrate this.