Angular Dependence of the Magnetic Properties of Steels Under the Action of Uniaxial Stress
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ANGULAR DEPENDENCE OF THE MAGNETIC PROPERTIES OF
STEELS
UNDER THE ACTION OF UNIAXIAL STRESS D. A. KAMINSKI', D.C. JILES', S.B. Biner, and M.J. SABLIK*" *Center for NDE, Ames Laboratory, Iowa State University, Ames, IA. 50011 ** Southwest Research Institute, San Antonio, TX. 78228-0510 ABSTRACT
Angular dependence of structure sensitive magnetic properties such as coercivity and permeability has never been adequately explained by a quantitative physical model or theory. The present study investigates the angular dependence of magnetic properties of materials with different microstructures. Measurements were taken under compressive and tensile uniaxial stress. The materials investigated were plain carbon steels with compositions of 0. 1% - 0.8% carbon. Alloy steels with compositions of 2.25 % Cr and 1.0 % Mo were also investigated. The effects of uniaxial stress on permeability along the direction of the stress can be described by including an effective field H. given by: Ho =
3a ( dX / dM ) ( cos 2 4 - v sin 2 ) /(2po )
Experimental results are compared to model using Ho. INTRODUCTION
For materials with positive differential magnetostriction (dX/dM), such as iron at low field strengths, permeability increases with tensile stress along the field axis, and decreases with compressive stress along the same axis [1]. In a material with a negative (dX/dM), such as nickel, permeability decreases with tensile stress along the field axis and increases with compressive stress. The change in the permeability depends on the stress, angle of magnetization and the value of (dX/dM). Iron exhibits a positive (dX/dM) at low applied fields and a negative (dX/dM) at high fields. The point at which the cross over from one behavior to the other is called the differential Villari reversal point. The reversal in sign of (dX/dM) depends on the applied stress, field and angle of magnetization. The Villari reversal is also sometimes called the Ewing reversal. Measurements of magnetization are macroscopic averages over a large number of domains with different orientations and therefore analysis on the basis of single domain magnetostriction is inappropriate [2]. In a recent paper [3] it has been shown how to incorporate the effects of coaxial stress and magnetic field into an effective magnetic field. The effective magnetic field is given by [4] Hf = 1/4t
(dA/dM)r
(1)
where A is the Helmholz free energy of the system. Following the previous analysis this effective field can be written as Hef = H + otM + Ho
(2)
where ot represents the self coupling of the magnetization resulting from the exchange Mat. Res. Soc. Symp. Proc. Vol. 291. @1993 Materials Research Society
510
interaction, and Ho = 3cr (aX/aM)T / (2/Ao)
(3)
is the equivalent field due to stress. If polycrystalline iron is considered to behave isotropically on the macroscopic scale, then under the action of a uniaxial stress a the strain e((k) as a function of angle 4) from the stress axis will be [5] e(k) = e( ( cos 2(k - v sin 2 ) )
(4)
which is the strain ellipsoid
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