Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Aerospace Engineering


Engineering Mechanics

First Advisor

Valery I Levitas


In the present study, a scale-free phase-field approach (PFA) is proposed to study solid-solid phase transformations (PT) in shape memory alloys such as NiTi single-crystalline (cubic-monoclinic PT). To characterize the global stress-strain diagram and discrete martensitic microstructures formed during the loading of this class of materials, a thermomechanical model for phase transformation, including the strain-softening and its corresponding strain localization is advanced. Due to the instability point in the local stress-strain curve, a discrete martensitic microstructure (martensitic and austenitic regions separated by a thin transition zone) is formed as a solution to the corresponding governing equations, and no more algorithm is required to track the austenite-martensite interface. The presented phase-field model (in contrast to the traditional phase-field models which are not applicable for micro/macro-scale) is valid for scales greater than 100 nm. Introducing athermal friction (which is the resistance to interface propagation) to phase transition criteria, postpones the phase transformation, and also leads to different magnitudes of hysteresis during the multivariant martensitic phase transformation. A sudden drop in global and local stress-strain diagrams is shown as a consequence of the strain localization. Martensitic microstructures resulted from numerical evaluations in elastic single crystal samples of NiTi are in qualitative agreement with several reported experimentalstudies.Moreover, a scale-independent model is developed to simulate the interactions between the multivariant phase transformations and discrete dislocation bands. In contrast to the previousphase-field approaches, which applications are restricted to the nanoscale, this model can be employed to solve the interactions between dislocation pileups and shear bands in the sampleswith no upper size limit. This model is implemented via Finite Element code to simulate the strain-induced PTs in bi/polycrystalline samples subjected to the compression and shear. The simulations show a considerable reduction in the magnitude of the PT pressure by introducing the plastic shear in comparison to a hydrostatic loading, as it was seen in some experimental results. Also, this model is able to explain the incompletely transformed stationary state andan optimum macroscopic shear strain for the strain-induced synthesis of the high-pressure phases. It is shown that the local transformation-work based phase equilibrium condition is met for thestresses averaged over the entire sample even in complex systems like polycrystalline aggregates. The interfaces, in most cases, are close to the constant pressure and shear contour lines. Theseresults are useful for macroscale modeling of the samples in rotational diamond anvils.


Copyright Owner

Seyyed Ehsan Esfahani Rashidi



File Format


File Size

117 pages

Available for download on Wednesday, June 15, 2022