Measurement of magnetostrictive tensor components ... - IEEE Xplore

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MEASUREME” OF MAGNETOSTRICTIVE TENSOR COMPONENTS USING ... system of equations that can either be solved via a non-linear regression walysis ...
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MEASUREME” OF MAGNETOSTRICTIVE TENSOR COMPONENTS USING ELECTRONIC SPECKLE PATTERN INTERFEROMETRY (ESPI) M. L. Storch, A. D.Rollett, M. E. McHenry Camegie Mellon University Pittsburgh, PA. 15213 Introduction Magnetostriction is defined as the change in shape of a material upon the application of a magnetic field 111. This is a small effect, generating strain on the order of p‘arts per million, and for most calculations can be safely neglected. However, for premier soft magnetic materials such as equiatomic iron cobalt alloys, other sources of losses have been minimized to the point that magnetos@ictive losses may become significant. Due to the small s u e of the effect, magnetostriction has been, at hest, difficult to measure in the past. Typically, strain gauges, with their associated problems, were the measurement technique of choice. More recently, other techniques have heen developed, but all of them are simply extensions or variations on the linear strain measurement provided by the strain gauge technique. Here we will present work which utilizes electronic speckle pattern interferometty to measure the local displacement field of a sample resulting from the application of a known field. Knowing the local displacement field it is possible to calculate the local strain tensor and we will show that it is possible to calculate the components of the magnetostrictive tensor from the local strain tensor.

‘I3

= %I

‘23

= %2 = 2 h h 3 M 4 4

=2hlh3MW

These relations me valid locally for each paint on the sample. This leads to an overdetcrmined system of equations that can either be solved via a non-linear regression walysis to find the components of the magnetostrictive tensor. In which case we get a measurement of the averaged bulk response, or we can solve on a local basis and observe the local differences in the magnetostrictive response. A map of local strain tensor components resulting from an applied field of nominally lOOOe for a 6 n i l coinmercial Hiperco 50 foil (49% Fe, 49% CO,2%V) obtained from Carpenter Technologies is shown in figure I.From this we can see that ESPI is capable of resolving the diffetence in magnetostrktiye strains from features as small as the domxin size in the material

Electronic speckle Eatem interferometry Electronic speckle pattem interferometry (ESPI) is a technique utilizing a solid state laser and a CCD camera to capture the speckle interfereme patterns produced on a surface 121. ESPI is a differential technique that allows for resolution of displacements down to 30nm. The system measures the difference between a reference and a displaced state by measuring a shift in the phase of the speckle interference pattem. Because this is a differential technique, any sample motion or transient noise is automatically subtracted. This makes it an ideal technique to measure relatively small magnetostrictive strains while remaining insensitive to noise. Calculation of mametostrictiqn Magnetostrictive strain a~ conventionally written as a Taylor series expansion in direction cosines, but can he expressed as a fourth rank tensor property [3]. The following expression relates the magnetostrictive tensor and the field to the strain in a magnetic material due to magnetostriction = M&4 (1) This equation takes the same form as that used for describing elasticity [41 and, in fact, we can make the same symmeuy arguments to limit the number of independent tensor terms to three in a cubic material. If we then expand eqn. 1 we get the following relations for the components

Figure 1-Local strain tensor components of a 6 mil Hiperco 50 foil References 111 B. D Cullity, “Introduction to Magnetic Materials”, Addison-Wesley Publishing Company, 1972 [21 R. Jones & C. Wykes, “Holographic and Speckle Pattern Interfemmetq” , Cambridge University Press. 1989 [31 R. R. Birss, “Symmetry and Magnetism”, Noah Holland Publishing Company- Amsterdam, 1964 [4] Dieter, “Mechanical Metallurgy”, McGraw-Hill Series in Materials Science and Engineering, 1986