Form Effect in Linear Magnetostriction

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Abstract
The influence of the shape of the specimen upon the measured value of magnetostriction is a matter of importance. The classical thermodynamical calculation of Becker applies to specimens in like magnetic fields and consequently compares bodies with unlike intensities of magnetization. In the present paper use is made of the principle of virtual work to make a calculation of the form effect as dependent upon the intensity of magnetization. The form effect for an ellipsoid in an extended uniform field is found to be a constrictive strain of the magnitude ΔA11=−(1−2μ)ENI22, where ΔA11 is the form effect in strain, μ is Poisson's ratio, E is Young's modulus, N is the coefficient of self-demagnetization, and I the intensity of magnetization. Above saturation the form effect is ΔA11=−(1−2μ)ENIs22, where Is is the saturation value of I. The meaning of the term form effect has been expanded to include not only the change in strain in the specimen resulting from the shape of the specimen itself, but also the change resulting from the position of the specimen relative to the magnetizing apparatus. A calculation of the form effect in this extended sense is made for two useful experimental arrangements; one where a specimen is sandwiched between two movable rods and the other where the specimen is situated in the fixed gap of a magnet. For the first case it is found that the form effect depends upon the self-demagnetization of the entire ferromagnetic arrangement and not of the specimen itself. In the second case, the form effect is dependent upon the ratio of gap energy to the volume of the ferromagnetic system and can be small, subject to the qualification that the form effect does not include the effects of any stresses that develop within the gap.

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