Modified law of approach for the magnetomechanical model

Sablik, M. J.; Chen, Y.; Jiles, D. C.
May 2000
AIP Conference Proceedings;2000, Vol. 509 Issue 1, p1565
Academic Journal
The behavior of the magnetic response of a ferromagnetic material due to changing stress at constant magnetic field is another variant of magnetic NDE. An example of its use is in measuring changing torque in a steel rod by measuring the magnetic response of the rod as the stresses due to the torque change. Recently, a model was constructed by D. Jiles for the computation of the magnetic response due to changing stresses at constant magnetic field. This model was presented at QNDE three years ago. The key feature was a differential equation known as the “law of approach.” It postulated that the change in the irreversible component of the magnetization with respect to stored elastic energy W due to stress was proportional to the difference between the anhysteretic magnetization and the irreversible component of the magnetization, with the proportionality constant being 1/xi, where xi represents a kind of “relaxation constant” which inversely controls the “rate” at which the material relaxes to the anhysteretic state. Physically, it says that the domain walls distort, move and repin and reconfigure owing to the action of the stress in such a way as to bring the material closer to thermodynamic equilibrium, which is the anhysteretic state. We have found that this is not the whole story. When one reduces the stress, the repinned domain walls do not necessarily climb out of their new pinning position, and hence relaxation to zero stress is not the same as “relaxation” produced by going from zero to some finite stress. There is some distortion and reconfiguration of the walls as one releases to zero stress via the magnetic action of the stress effective field, but this reconfiguration is different from the application process. Thus the “relaxation constant” for the stress release process must be different from the stress application process. Hence, the law of approach has two “relaxatio...


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