Resume：

Advanced high-strength steel (AHSS) has become the ideal material for the automotive industry due to its high strength and ductility, with its superior properties stemming from a multiphase microstructure composed of ferrite, martensite, and residual austenite. However, minor fluctuations in parameters such as temperature and time during manufacturing can significantly alter the microstructure, thereby affecting mechanical properties. To achieve online quality control, non-destructive magnetic testing technology is required. Yet, the magnetic behavior of AHSS is highly sensitive to chemical composition, grain size, and stress state. In practical production, steel plates often endure multi-axis stress, and the strong coupling between magnetic response and mechanical stress may lead to detection deviations (e.g., magnetic permeability shifts or false positives). These interference effects must be eliminated through precise modeling and multi-axis experimental calibration. The Journal of Magnetism and Magnetic Materials published research from the Paris Sackler Laboratory on using online non-destructive magnetic monitoring technology for quality control of steel subjected to multi-axis stress. This study employed an improved biaxial loading experimental setup to investigate magnetostriction behavior of duplex steel (DP steel) under biaxial stress and proposed an equivalent stress model to quantify the impact of multi-axis stress on magnetostriction. Using cross-shaped specimens combined with synchronous magnetic and mechanical measurement techniques, the experiment achieved the first quantitative analysis of non-hysteresis and cyclic magnetostriction under biaxial stress.

Experimental method ：

(1) Loading system: An ASTREE three-axis hydraulic testing machine is employed, equipped with a four-axis independent loading unit (maximum load ±100 kN/axis), achieving a biaxial stress state in the specimen's central region through a cross-shaped fixture (Figure 1).

（2）Sample design: The sample was fabricated from 260 mm × 260 mm DP steel sheet (thickness 1.24 mm) into a cross shape, with two pieces bonded to enhance buckling resistance. EBSD analysis revealed that the material's crystal orientation was nearly isotropic (polarogram strength ≤2.4 times random distribution), and the difference in mechanical and magnetic properties was ≤30 MPa.

（3）Magnetic measurement module: dual soft iron yoke structure (each with 100-turn coils), with a magnetic field strength of up to 14,000 A/m.

Results and discussion

Plotting and interpolating the remanent magnetization and coercive field in the stress plane (recording 25 loading states with average values taken over 5 magnetic cycles) provides a more intuitive understanding of biaxial stress effects on the hysteresis loop. The contour lines differ from those of susceptibility. The biaxial stretching state yields the highest remanent magnetization. When compression is applied along the magnetic measurement direction, the value drops to its minimum, with the contour lines becoming nearly vertical. Conversely, the coercive field gradient highlights the significant influence of stress perpendicular to the magnetic measurement direction. The coercive field gradient peaks along the shear axis (σ1= −σ2), while the biaxial σ1= σ2 configuration results in much smaller variations. Although the remanent induction and coercive force change differently, the coercive force exhibits greater amplitude. This suggests that in the initial approximation, this value governs the magnitude of the magnetization cycle, thereby controlling energy dissipation.

Model construction: Based on multi-scale magnetoelasticity theory, the equivalent stress σₑq is defined to ensure that uniaxial σₑq and multi-axial stress induce the same magnetostriction effect.

The model prediction is consistent with the measured results qualitatively, and the maximum magnetostrictive region is distributed along the stress axis with the slope of 1-2.

Summary:

This study investigates the coupling effects of biaxial stress on magnetic behavior in ferromagnetic materials and optimizes modeling approaches. To address the challenge of signal confusion between stress and microstructure in advanced high-strength steel (AHSS) non-destructive testing, we propose a correction strategy based on a biaxial magnetoelastic model. By improving the experimental setup (enhancing magnetic field uniformity and signal amplitude), we achieve the first high-precision synchronous measurement of hysteresis and magnetostriction under biaxial stress. The results demonstrate significant stress-induced effects on coercive force fields, remanent magnetization induction, and parallel/vertical magnetostriction (e.g., biaxial tensile-compression combinations can induce magnetostriction shifts up to 300 ppm). We further propose a non-unique equivalent stress analytical model, revealing its dependence on magnetostriction tensor components and magnetic field intensity. A linearized formula consistent with experimental observations is derived, providing theoretical guidance for magnetostriction device design (e.g., multi-axis stress combination optimization) and magnetic field intensity selection. The model's applicability is limited to low-to-mid magnetic field ranges, and its extension to shear stress analysis requires integration with magnetization rotation mechanisms.