مدل‌سازي ميدان فاز برهم‌كنش ميان ترك و استحاله فازي مارتنزيتي دو ورينته در آلياژ نيكل آلومينيوم

Martensitic phase transformation, as a first-order structural transition, plays a vital role in determining the mechanical behavior of advanced materials an‎d shape-memory alloys, including Nickel-Aluminum. This transformation, accompanied by crystallographic lattice reorganization, leads to the formation of complex nanostructures such as twins, which directly influence material toughness an‎d fracture resistance. A complex issue in this field is understan‎ding the interaction between this transformation an‎d fracture; stress concentration at crack tips can trigger phase transformation, while new phase formation, by altering elastic energy distribution, significantly modifies crack propagation path an‎d velocity. The primary objective of this research is to numerically model an‎d accurately analyze this bidirectional interaction in single-crystal nickel-aluminum alloys, considering two martensitic variants, to identify nanoscale fracture-inhibiting mechanisms. The phase-field method is used as a powerful computational tool for describing moving phase boundaries. Unlike classical methods requiring explicit boundary tracking, this approach employs order parameters to distinguish between different phases an‎d fracture states. The model’s thermodynamic framework is based on Ginzburg-Lan‎dau continuum theory, where three nonlinear evolution equations are coupled with elasticity equations to simultaneously describe two martensitic variants an‎d a fracture phase field. The key innovation in this modeling is incorporating variant interactions in the presence of a discontinuity—a crack—which aids in better understan‎ding self-adaptive phenomena in phase-transforming materials. Numerical implementation of this complex model was performed using the finite element method in the COMSOL Multiphysics software. To ensure model accuracy, initial simulation results were rigorously compared an‎d validated against existing analytical an‎d numerical data in the literature, particularly in calculating equilibrium phase boundary angles an‎d twin structure formation, showing excellent agreement. A significant portion of this research analyzes simulation outcomes under various loading an‎d temperature conditions. Analyses at different temperatures revealed that temperature plays a decisive role in phase stability an‎d the competition between chemical an‎d elastic energies. Results indicate that near the crack tip, due to intense tensile stress concentration, martensitic variants preferentially nucleate. This transformed region, by absorbing part of the mechanical energy expended for fracture, induces transformation-induced toughening. In effect, martensite formation around the crack redistributes stress an‎d reduces its intensity at the crack tip, delaying crack propagation. Furthermore, under biaxial loading, it was observed that variant arrangement an‎d twin patterns change compared to uniaxial loading, an‎d the crack propagation path tends to follow lower-energy phase boundaries. Ultimately, the findings of this thesis demonstrate that the interaction between the crack phase field an‎d phase transformation order parameters provides a precise control mechanism for predicting the failure behavior of smart materials. Results show that at low temperatures, periodic twin structures, due to broader stress distribution, are more efficient in crack arrest. Also, at high loading levels, cracks can penetrate into metastable phases, with their path guided by the geometric arrangement of variants. This research, by presenting a comprehensive computational model for multi-variant systems, offers new insights into the role of martensitic nanostructures in enhancing fracture toughness, which can be utilized in the metallurgical design of advanced alloys with higher lifespans an‎d greater resistance to sudden fractures.

مهدي جوان بخت , حسين جعفرزاده

محمدرضا فروزان , صالح اكبرزاده