Continuum modeling of materials that can undergo martensitic phase transformations
A continuum model for materials that can undergo martensitic phase transformations is developed and applied to the study of several problems that involve such transformations. One of the several advantages of using this continuum model is that the corresponding boundary value problem is in a form th...
| Summary: | A continuum model for materials that can undergo martensitic phase transformations is developed and applied to the study of several problems that involve such transformations. One of the several advantages of using this continuum model is that the corresponding boundary value problem is in a form that permits direct linearization, while retaining finite shape deformations for the martensite phases. The continuum model is used to study several problems dealing with which variant of martensite is preferred during the application of a loading. Among these problems is the case of a uniaxial tensile traction applied to a two-phase cylindrical body, and the case of a hydrostatic pressure applied to a two-phase body that has a finite shape deformation with an infinitesimal dilatation. The results that are obtained correspond with those that have been observed from experiments and with those that might be expected from physical considerations. The next problem that is considered involves the temperature at the interface and quasi-static motions of a two-phase thermoelastic bar. The bar is subject to different temperatures at each boundary and to a mechanical end-loading. The last problem that is considered involves the longitudinal free vibrations of a fixed-free, two-phase bar. The main focus in this problem is the damping behavior of the two-phase bar that is due to the motions of the interface during the free vibrations. A finite-difference numerical routine is used to approximate the displacement solutions for this problem. The damping of the bar is studied as the material coefficients are varied, and the values of the material coefficients that produce the maximum damping are investigated. |
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