Magneto-Mechanical Coupling under Rotational Magnetization: From Multi-Scale Modeling to Non-Destructive Stress Evaluation in Ferromagnetic Steels

Residual and applied stresses strongly influence the magnetic behavior of ferromagnetic steels through magnetoelastic coupling. Classical magnetic techniques (e.g., Barkhausen noise, incremental permeability) under unidirectional configurations provide indirect stress indicators but are limited by anisotropy and irreversible domain-wall mechanisms [1].

Recent advances, such as Magnetic Rotational Permeability (MRP [2]), reveal that rotational magnetization enables access to alternative magnetization processes (notably 90° domain wall motion, coherent rotation), offering new routes for stress-sensitive magnetic signatures.
However, the quantitative link between the measured electrical response (induced voltage, complex impedance) and the mechanical stress state remains only partially understood. Bridging this gap requires a combination of accurate constitutive equations (for instance based on multi-scale magneto-mechanical approaches), advanced simulation (for instance based on the finite element method), multiphysical characterization of materials and precision instrumentation.

The objectives of the PhD project are :

_ Exploit a multi-scale model for magneto-mechanical coupling in steels under rotational magnetization conditions, linking local stress to domain-scale magnetic energy and macroscopic magnetic permeability.

_ Implement the coupled constitutive equations using GetDP [3] or COMSOL Multiphysics to simulate the rotational magnetization under stress.

_ Develop and optimize rotational magnetization-based eddy-current instrumentation capable of detecting small stress-induced magnetic variations in the near-surface region.

_ Design coils and excitation protocols optimized for surface stress sensitivity (by controlling field amplitude, frequency, and penetration depth).

_ Implement MRP measurements under controlled stress (uniaxial and residual).

_ Validate the model with experimental MRP data.

_ Identify and calibrate magnetic indicators correlating with residual stress.

_ Establish a quantitative correlation between electrical signatures (complex voltage, permeability tensor) and mechanical stress distribution in the top layer of steels.

_ Propose non-destructive testing procedure for stress quantification using rotational magnetization.

International Framework

Expected Outcomes

A validated magneto-mechanical model predicting magnetic rotational permeability under stress.

A quantitative NDT protocol for surface residual stress evaluation.

A new generation of MRP-based sensors with enhanced sensitivity to magnetoelastic effects.

Double degree diploma INSA - Lyon (France) / Tohohu University (Japan)

The PhD candidate will spend at least 1 year in Japan and 1 year in France.

_ Electrical engineering

_ Material science