Abstract:The depth of the effective hardened layer and the extent of the transition layer are critical factors that influence the performance of surface-hardened mechanical components. They constitute significant parameters in the process of quality control for product evaluation. By exploiting the variances in magnetic properties among different structures, a magnetic detection technique can be developed for assessing hardened layers, offering non-destructive and rapid advantages over conventional metallographic observation methods. This method holds promising potential for direct testing and analysis of hardened layers in components. The Boltzmann function is proposed to describe the gradient law of hysteresis characteristic parameters of materials along the depth direction. By discretely layering multi-layered materials and considering the magnetic field coupling between layers, a T(x) hysteresis loop model for multi-layer structural materials is formulated. The hysteresis loops of the hardened layer sample, obtained by cutting them layer by layer, are calculated by using the particle swarm optimization algorithm and the proposed multilayer hysteresis loop model. The accuracy of the model is validated to evaluate its capability in accurately describing the hysteresis loop of multilayer materials, as well as determining and characterizing both the depth of the hardened layer and transition layer.