This study investigated a model theory of the changes in magnetization that a ferromagnetic material undergoes when subjected to an applied uniaxial stress. The description of these effects is shown to be totally different from the description of the changes in the hysteresis curve under a series of constant applied stresses. The main mechanism in the proposed model theory is the unpinning of domain walls by the application of stress, which allows the walls to move and causes a change in the magnetization. This change in magnetization reduces the displacement from the anhysteretic magnetization. In addition, the anhysteretic magnetization itself is changed by the application of stress via the magnetoelastic coupling. It is shown that the effect can be described by an equation in which the rate of change of magnetization with elastic energy is proportional to the displacement of the magnetization from the anhysteretic magnetization. This is termed the 'law of approach'. This law seems to apply when the starting condition of the material is on a major hysteresis loop.

https://iopscience.iop.org/article/10.1088/0022-3727/28/8/001/pdf

Theory of the magnetomechanical effect

A theory of the magnetisation process in ferromagnets, based on existing ideas of domain rotation and domain wall motion is presented. This has been developed via a consideration of the various energy terms into a mathematical description of the process leading to an equation of state for a ferromagnet. The differential equation has been solved and a solution containing terms up to the second order presented, showing the essential features of ferromagnetic hysteresis. The theory has then been used to explain the effects of stress on magnetisation. It has been found that the magnetisation approaches the anhysteretic curve when a ferromagnet is subjected to stress and this is the underlying principle behind such changes in magnetisation. The change of magnetisation with stress can not be predicted solely on the basis of the magnetostriction coefficient except in special cases when the initial (zero stress) conditions of magnetisation lie on the anhysteretic. This condition is also approximately satisfied at higher fields.

https://iopscience.iop.org/article/10.1088/0022-3727/17/6/023/pdf

Theory of the magnetisation process in ferromagnets and its application to the magnetomechanical effect

The evaluation of both applied and residual stresses in engineering structures to provide early indications of stress status and eventual failure is a fast growing area in non-destructive testing. Much work has been done in recent years in the development of magnetic stress measurement techniques for ferromagnetic materials using applied magnetic fields to monitor changes in the magnetic properties of materials, such as variations in the hysteresis curve or Barkhausen emission. But the area of passive field measurement is relatively unexplored. When magnetic metals are strained, they irreversibly transformed from a non-magnetic state to a magnetic state, this is referred to as metal magnetic memory (MMM) or the residual magnetic field (RMF). This paper investigates the phenomena under different circumstances and applies the residual magnetic field technique to stress measurement. A three axis magneto-resistive magnetic field sensor is used to measure the residual magnetic fields parallel to the applied stress and the material surface (Bx) and perpendicular to the material surface (Bz), generated by the magneto-mechanical effect without the application of an external field, using steel samples exposed to stresses. The test results show that without using an applied field, the stresses in a sample can be measured using magnetic field sensing, with Bx showing particularly good correlation. The work concludes that the novel passive field technique including analysis of the magnetic field pattern and magnetic field variation rate, would prove advantageous in certain circumstances, for example in-service inspection of structures with complex geometries. Further research directions are also highlighted.

Residual magnetic field sensing for stress measurement

This paper addresses the modeling of strains and forces generated by magnetostrictive transducers in response to applied magnetic fields. The magnetostrictive effect is modeled by considering both the rotation of magnetic moments in response to the field and the elastic vibrations in the transducer. The former is modeled with the Jiles-Atherton model of ferromagnetic hysteresis in combination with a quartic magnetostriction law. The latter is modeled through force balancing which yields a PDE system with magnetostrictive inputs and boundary conditions given by the specific transducer design. The solution to this system provides both rod displacements and forces. The calculated forces are used to quantify the magnetomechanical effect in the transducer core, i.e., the stress-induced magnetization changes. This is done by considering a “law of approach” to the anhysteretic magnetization. The resulting model provides a representation of the bidirectional coupling between the magnetic and elastic states. It is...

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A Coupled Structural-Magnetic Strain and Stress Model for Magnetostrictive Transducers.

The variability of Young's modulus (the ▵E effect) in giant magnetostrictive Terfenol-D has a significant impact on the performance and modeling of Terfenol-D transducers. In this investigation, Te...

Experimental Investigation of Terfenol-D's Elastic Modulus

Measurements have been made of magnetization curves obtained by applying stresses to various polycrystalline magnetic materials in the presence of a small, constant, magnetic field. The materials examined were nickel, mild steel, and both isotropic and cube textured silicon iron. Residual stray fields were carefully compensated. Both compressive and tensile stresses were applied in the range 0 to 10 kg mm−2. The curves are compared with the theory proposed by Brown in 1949, in which the stress is replaced by an equivalent field, which has been found to be valid at the smaller stresses. There are many features which cannot be reconciled with Brown's analysis, in particular the difference between tension and compression. A tentative explanation is put forward based on discontinuous changes in domain structure.

http://iopscience.iop.org/article/10.1088/0022-3727/3/7/303/pdf

Magnetization changes induced by stress in a constant applied field

It is demonstrated that the response of the magnetization of a single crystal to slow pulsed magnetic fields can consist of a damped precession at microwave frequencies, if the combination of bias and pulsed fields gives rise to a discontinuity in the rotation.

D J Craik

Papers

Magnetization changes induced by stress in a constant applied field

Magnetization dynamics controlled by magnetocrystalline anisotropy