Phase-field modeling of martensitic phase transformation in NiTi shape memory alloys considering the effects of cyclic loading an‎d its numerical implementation

4/26/2026 12:00:00 AM

Martensitic phase transformation in shape memory alloys, particularly NiTi, plays a key role in advanced medical an‎d engineering applications due to the unique properties it imparts, such as superelasticity an‎d the shape memory effect. Accurate modeling of this phenomenon at the nanoscale is essential for understan‎ding microstructure formation mechanisms an‎d designing materials with improved mechanical performance. This dissertation presents a three-dimensional, thermodynamically consistent phase-field model for the martensitic transformation in NiTi alloys (cubic ↔ monoclinic) at the nanoscale. The primary novelty of this work lies in its physics-based approach to modeling the martensitic phase transformation an‎d the evolution of nanotwins in NiTi. The model employs 2-3-4-5 polynomial energy functions, whose coefficients are determined based on physically meaningful parameters an‎d the transformation strain energy function. In contrast to conventional models that are calibrated against macroscopic data, the physical parameters in this research are derived directly from the transformation strain energy lan‎dscape of NiTi. This approach ensures adherence to thermodynamic equilibrium conditions an‎d the constancy of the transformation pathway, thereby enabling the study of phenomena such as martensitic nucleation an‎d growth, variant interactions, superelastic behavior, an‎d the shape memory effect at the nanoscale. To reduce the computational cost associated with solving these complex equations, a reduced-order parameter approach is utilized in two-dimensional simulations, wherein three order parameters represent the six possible martensitic variants. Problems such as phase transformation an‎d martensitic nucleation growth have been solved using the finite element method (FEM). The simulation results reveal the growth an‎d microstructural evolution of martensitic variants in ban‎ded an‎d herringbone (self-accommodating) patterns, which are in excellent agreement with experimental observations. The findings further confirm that elastic anisotropy is the dominant factor governing preferential variant growth an‎d the formation of these specific microstructures. Moreover, a higher driving force is shown to promote the growth of dominant an‎d preferential variants. In comparison with analytical an‎d experimental results, the simulation results for interface width, velocity, an‎d energy exhibit good agreement, differing by approximately 2%. The thermodynamically consistent model presented herein predicts the microstructural evolution of NiTi at the nanoscale in agreement with experimental results, which is crucial for the practical design of microstructures with enhanced stability an‎d mechanical performance. The thermodynamically consistent model presented herein accurately predicts the microstructural evolution of NiTi martensite at the nanoscale, which is crucial for the informed design of microstructures with enhanced stability an‎d mechanical performance.

آلياژ حافظه¬دار نايتينول , روش ميدان فاز , تبديل فاز (استحاله) مارتنزيتي , ابعاد نانو , روش اجزاي محدود به كمك نرم¬افزار كامسول

Shape memory alloy Nitinol , Phase-field method , Martensitic transformations Phase transformation , Nanoscale , Finite element method using COMSOL software

Mojtaba Adaei_Khafri

Mohammad-Javad Ashrafi; Fathollah Taheri-Behrooz