Vol. 194　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1972

EFFECT OF ELASTIC STRESSES IN A SAMPLE ON THE MAGNITUDE OF THE SECOND HARMONIC OF A HIGH-FREQUENCY FIELD UNDER SUPERPOSITION OF TWO PARALLEL FIELDS OF DIFFERENT FREQUENCIES AND AMPLITUDES

A. M. GRUZNOV, B. B. VINOKUROV, I. G. LESHCHENKO

(Presented at the Second Scientific and Technical Conference of the Faculty of Automation and Computer Engineering)

If a ferromagnetic sample located in a very weak high-frequency field (Fig. 1), with respect to which the sample may be regarded as a linear element, is acted upon by a low-frequency field with an amplitude sufficient to modulate the permeability of the sample, then in the measuring coil there appears a complex spectrum of emf of the form \(n\omega \pm m\Omega\), where \(\omega\) is the frequency of the high-frequency field, \(\Omega\) is the frequency of the low-frequency field, and \(m\) and \(n\) are integers varying from 0 to \(\infty\) [1].

As our experiments have shown, the envelope of the signal in the measuring coil, varying with frequency \(2\omega\), and the envelope of the magnetic-noise signal at frequency \(2\omega\), arising when only the low-frequency field acts on the sample, coincide in shape and in time for any values of the low-frequency field. Both the second-harmonic signal and the noise signal were observed in a frequency band of 10 kc.

It is known that the intensity of noise changes to a great extent if artificial anisotropy is produced in the sample, which depends on elastic stresses [2].

Förster and Wetzel, studying the dependence of Barkhausen jumps on deformation of a sample, found that this dependence can be very strong. Even an insignificant deformation (a cautious touch of the sample by hand) already changes the pattern of the oscillogram of the jumps.

Having information on the influence of elastic stresses on the oscillogram of Barkhausen jumps recorded under quasistatic remagnetization, and data from our experiments showing the existence of a connection between the Barkhausen effect and the second-harmonic signal, we carried out a study of the influence of elastic stresses on the second harmonic.

The experiments were carried out on the apparatus shown in Fig. 1. Wires of various ferromagnetic materials were used as samples: piano steel, nickel, nichrome, permalloy, etc., with a diameter of 0.4 mm and a length of (800–1000) mm. Internal stresses were produced by stretching the wire with a “gate”-type device. The magnitude of the tensile force was fixed according to the readings of a spring dynamometer. In all experiments the elastic limit was not exceeded. The frequency ratio was: \(\Omega/2\pi = 50\) cps, \(\omega/2\pi = 200\) kc. The magnitude of the low-frequency field was varied over wide limits; the magnitude of the high-frequency field was not changed—

…were measured. The average values of the second harmonic were determined from the readings of a V6-1 selective voltmeter.

As is seen from Figs. 2a, 2b, and 2c, which show the experimental results, respectively, for wires of piano steel, nickel, and nichrome, the relative change in the value of the second harmonic averaged over the modulation period is quite large and may in individual cases reach 80% or more.

It is known that even in the absence of an external magnetic field, when elastic stresses act on a ferromagnet, magnetic processes occur in it. Elastic deformation causes a redistribution of the magnetization directions of individual regions. Stretching samples made of materials with positive magnetostriction leads to the growth of domains whose direction of magnetization is close to the direction of stretching, since this direction becomes an axis of easy magnetization. Then, when the direction of stretching coincides with the direction of the external field, the Barkhausen jumps should increase. The opposite picture should be observed when a material with negative magnetostriction is stretched [2]. In [3] we find confirmation of this proposition.

Fig. 1

How does the second harmonic behave? From Fig. 2 it is seen that, for materials with positive magnetostriction, the sign of the increment of the emf of the second harmonic is positive (Figs. 2a, 2c), while for a material with negative magnetostriction (Fig. 2b for Ni) the sign of the increment is negative.

The sensitivity and the form of the dependence of the second-harmonic signal on elastic stresses depend to a considerable degree on the magnitude of the low-frequency field. For nichrome and nickel wires this dependence is, for the most part, hysteretic in character, although at certain values of the biasing field hysteresis is absent. For piano-steel wire the loading and unloading lines coincide at all values of the biasing field of 50 Oe.

The results obtained make it possible to estimate the relative sensitivities of the proposed method. Taking the strain-sensitivity coefficient equal to

\[ S_{\sigma} = \frac{\Delta U_{2\omega}} {\dfrac{U_{2\omega}(\sigma = 0)}{\Delta \sigma}}, \]

where \(\Delta U_{2\omega}\) is the absolute change in the average value of the emf of the second harmonic;

\(U_{2\omega}(\sigma = 0)\) is the value of the emf of the second harmonic under load \(\sigma = 0\); \(\Delta \sigma\) is the increment of the mechanical stress. From the rectilinear portions of the dependences we obtain the following values: for pure nickel, \(S_\sigma = 0.3 \div 1.2\%\!/\mathrm{N/mm^2}\), respectively, for fields of 15 and 90 Oe; for piano steel, \(S_\sigma = 0.1\%\!/\mathrm{N/mm^2}\).

For comparison, let us give the value of the strain-sensitivity coefficient for magnetoelastic transducers, which is expressed either as

Fig. 2

\[ S = \frac{\Delta \mu / \mu}{\Delta l / l} \]

and for nickel has values \(S = (100 \div 300)\), or as

\[ S_\sigma = \frac{\Delta \mu / \mu}{\sigma}, \]

which, on conversion, takes values \(S_\sigma = 0.05 \div 0.15\%\!/\mathrm{N/mm^2}\). For wire strain gauges these values are much lower.

The results obtained make it possible to hope that the proposed method of superposition of two parallel fields of different frequencies and amplitudes can be used as the basis of instruments or devices for measuring elastic stresses and strains in ferromagnetic samples.

REFERENCES

1. L. A. Bessonov. Nonlinear Electric Circuits. “Vysshaya shkola,” 1964.
2. K. P. Belov. Elastic, Thermal, and Electrical Phenomena in Ferromagnets. GITTL, Moscow, 1957.
3. N. N. Kolachevsky. FMM, 11, no. 2, 211–214, 1961.
4. A. M. Turichin. Electrical Measurements of Nonelectrical Quantities. “Energiya,” Moscow–Leningrad, 1966.