A semi-empirical model for fracture energy evaluation of a Ni₂MnGa magnetic shape memory alloy

Ni₂MnGa magnetic shape memory alloys (MSMAs) experience the shape memory effect due to magnetic field-induced or mechanical stress-induced microstructure reorientation. However, crack initiation and propagation, influenced by the evolving twin microstructure under coupled magneto-mechanical loading, can significantly hamper its function in applications. This study presents a semi-empirical approach to evaluate fracture toughness and fracture energy in Ni₂MnGa using Vickers microindentation. An improved analytical expression is proposed, extending the classical indentation-based fracture model to incorporate magneto-mechanical effects and microstructural evolution through a stress and field dependent exponential term. Experimental results confirm that the transverse magnetic field facilitates crack growth, decreasing the fracture energy, while axial compressive stress impedes crack growth, increasing the fracture energy of the alloy. The proposed empirical relationship provides configuration-specific fracture energy values for the alloy and contributes to identifying loading conditions least conducive to fracture initiation and growth in MSMAs.