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Athermal resistance to the motion of a phase interface due to a precipitateis investigated. The coupled phase field and elasticity equations are solvedfor the phase transformation (PT). The volumetric misfit strain due to theprecipitate is included using the error and rectangular functions. Due to thepresence of precipitates, the critical thermal driving forces remarkably differbetween the direct and reverse PTs, resulting in a hysteresis behavior. For theprecipitate radius small compared to the interface width, the misfit straindoes not practically show any effect on the critical thermal driving force.Also, the critical thermal driving force value nonlinearly increases vs. theprecipitate concentration for both the direct and reverse PTs. Change in theprecipitate surface energy significantly changes the PT morphology and thecritical thermal driving forces. The critical thermal driving force showsdependence on the misfit strain for large precipitate sizes compared to theinterface width. For both the constant surface energy (CSE) and variablesurface energy (VSE) boundary conditions (BCs) at the precipitate surface, thecritical thermal driving force linearly increases vs. the misfit straincoefficient for the direct PT while it is almost independent of it for thereverse PT. For larger precipitates, the critical thermal driving forcenonlinearly increases vs. the precipitate concentration for the direct PT. Forthe reverse PT, its value for the CSE BCs linearly increases vs. theprecipitate concentration while it is independent of the precipitateconcentration for the VSE BCs. Also, for any concentration, the VSE BCs resultin higher thermal critical driving forces, a smaller hysteresis range, and alarger transformation rate. The critical microstructure and thermal drivingforces are validated using the thermodynamic phase equilibrium condition forstationary interfaces.

Athermal resistance to phase interface motion due to precipitates: A phase field study