Experimental and computational studies on the stress-dependent magnetic property of silicon steel are on-going. A physical magnetization model, an energy-based multiscale magnetization model called multi-domain particle model (MDPM) 1, was developed, which successfully predicted the stress-dependent properties of silicon steel without using measured stress-dependent data. To avoid measurement under arbitrary combination of stress and magnetization directions, several stress models have been developed. This study examines two of them by comparing with the MDPM. One is the equivalent stress (ES) theory 2 and the other is the stress decomposition (SD) method 3. The latter assumes that the stress effect can be decomposed into its principal directions. A rotational single sheet tester applied a compressive stress to a non-oriented silicon steel sheet in the rolling direction (RD, φ=0). A magnetic field was applied along φ = 0 or π/4. Fig. 1 shows the measured stress dependence of hysteresis loss w_x in the RD when the amplitude of B_x is 0.5, 0.7 and 1.0 T, where B_y has only a small effect on the stress dependence of w_x . It supports the assumption of stress decomposition. BH loops under the excitation angle of π/4 were simulated using the MDPM, where the directions of stress and applied magnetic field are denoted by φσ and φH. Fig. 2 shows BH loops as below: reference, blue lines φ_H=π/4 and φ_σ=0 with σ = −40, −80 MPa, ES theory, green lines φ_H=φ_σ=π/4 with σ = −10, −20 MPa based on the ES theory, SD, brown lines synthesized loops of φ_H=φ_σ=0 with σ = −40, −80 MPa and φ_H=φ_σ=π/2 with σ = 0, and modified SD, red lines synthesized loops of φ_H=φ_σ=0 with σ = −40, −80 MPa and φ_H=φ_σ=π/2 with σ = +40, +80 MPa. The ES theory roughly predicts the stress dependent loops along φ = π/4, but fails to predict decomposed loops along φ = 0, π/2. The SD fails to reconstruct loops along φ=π/2 because a compressive stress along φ=0 acts as a tensile stress along φ=π/2. The modified SD roughly predicts the stress dependent loops in all the directions by giving tensile stresses along φ=π/2.
References
1 T. Matsuo, Y. Takahashi, K. Fujiwara, J. Magn. Magn. Mater., vol. 499, 166303, 2020. 2 M. Rekik, L. Daniel, O. Hubert, IEEE Trans. Magn., vol. 50, 2001604, 2014. 3 M. Nakano, et. al, IEEJ Trans. Ind. Appl., vol. 129, pp. 1060–1067, 2009.

Comparison of measured loss increase Δw_x with φ_H = 0, π/4 and φ_σ = 0.

Simulated BH loops along (a) φ = π/4, (b) φ = 0, and (c) φ = π/2.