A grain size dependent constitutive model of hot deformation Nd-Fe-B permanent magnetic material

To address the lack of available material data for neodymium-iron-boron (Nd-Fe-B) permanent magnets in commercial simulation software such as DEFORM, this study systematically investigates the influence of precursor grain size, regulated through different heat-treatment conditions, on the stress–strain response. A grain-size correction factor is incorporated into the conventional Arrhenius-type constitutive model, leading to the development of a grain-size-dependent constitutive equation specifically for Nd–Fe–B materials. The results demonstrate that the modified Arrhenius model accurately describes the high-temperature rheological behavior over a wide range of temperatures, strain rates, and initial grain sizes. The predicted flow stresses show good agreement with the experimental data, with a correlation coefficient of 0.969 and an average absolute relative error ranging from 8.48% to 10.67%. These findings indicate that the proposed model not only reduces the experimental workload but also significantly improves prediction accuracy, thereby providing a reliable constitutive basis for finite element simulations and process optimization of Nd–Fe–B permanent magnets.