HARMONIC GENERATION ASSOCIATED WITH NONLINEAR INTERNAL FRICTION IN A HIGH-DAMPING Mn-Cu ALLOY

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HARMONIC GENERATION ASSOCIATED WITH NONLINEAR INTERNAL FRICTION IN A

HIGH-DAMPING Mn-Cu ALLOY

Z.- L. Pan, I. Ritchie

To cite this version:

Z.- L. Pan, I. Ritchie. HARMONIC GENERATION ASSOCIATED WITH NONLINEAR INTER-

NAL FRICTION IN A HIGH-DAMPING Mn-Cu ALLOY. Journal de Physique Colloques, 1987, 48

(C8), pp.C8-347-C8-352. �10.1051/jphyscol:1987851�. �jpa-00227155�

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JOURNAL DE PHYSIQUE

Colloque C8, supplement a u n012, T o m e 48, decembre 1987

HARMONIC GENERATION ASSOCIATED WITH NONLINEAR INTERNAL FRICTION IN A HIGH-DAMPING Mn-Cu ALLOY

Z.-L. PAN and I.G. RITCHIE

Materials Science Branch, Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establishment, Pinawa, Manitoba, ROE 1L0, Canada

~e'srlrne'

-

On a observi la gsniration d'harmoniques dans un alliage commercial 'a amortissement 6leve'a base de Mn-Cu \a l'aide de la

technique de l'oscillateur composite h la frkuence fondamentale d'environ 40 kHz. Les amplitudes des 2e, 3e et

se

harmoniques, reprdsentees respectivement par A,, A, et A,, augmentent en fonction de l'amplitude de dsformation des vibrations, E, lorsque l'alliage est

1"etgt d'amortissment Sieve'. A, est proportionnelle 'a c2 tandis que A, a E

dt

^1.6

<

^m

⁵

^{1.9 pour}^E

⁵

¹^x ^{et 5.2}

<

^m

<

^{5.6 pour}^o⁾

1 x lo-'. A, est insignifiante pour toutes les zprouvettes. Pour les gprouvettes 'a l16tat d'amortissement faible (apr'es trempe), on n'a observg aucune variation importante de A,, mais A, gtait beaucoup plus faible et A, 'etait presque n'egligeable. Dans d'autre m'etaux tels que le zirconium pur et les alliages de Zn-Al, on n'a observe' que A,. I1 est probable que la ggne'ration de A, dans l.es alliages

>

amortissement ilevi est associ'ee au mouvement des parois antiferromagdtiques.

Abstract

-

Harmonic generation has been observed in a commercial high- damping Mn-Cu based alloy using a piezoelectric, composite oscillator technique at about 40 kHz. Amplitudes of the 2nd, 3rd and 5th harmonics, denoted by A,, A, and A,, respectively, increase with the vibra- tional strain amplitude, c, when the alloy is in a high-damping condition. A, is proportional to c2, while A, o: cm where 1.6

5

m

5

^{1.9 for}

c

<

¹x lo-' and 5.2

<

^m

<

5.6 for c

>

¹x 10". A, was negligible in

all of the specimens tested. For specimens in a low-damping condition (after quenching) no significant change in A, was noted, but A, was significantly smaller and A, was almost negligible. In other metals, such as pure zirconium and Zn-A1 alloys, only A, was observed. It is probable that generation of A, in high-damping Mn-Cu alloys is associated with the movement of antiferromagnetic domain houndaries.

I

-

INTRODUCTION

When an initially sinusoidal stress wave propagates through a solid with a nonlinear response, the propagating wave pattern is slightly distorted harmonically. If this distorted waveform is transformed from the time domain to the frequency domain using a waveform spectrum analyzer, harmonic components are revealed and the phenomenon is referred to as harmonic generation.

The simultaneous measurement of internal friction and harmonic generation is recog- nized as a method to provide more information about the mechanisms of vibration damping in materials. Previous workers [I-51 have employed ultrasonic pulse tech- niques at MHz frequencies, to observe harmonic generation caused by lattice anharmonicity and dislocation motion. Wang, Britton and Stephens 161 reported second- and third-harmonic generation due to the dislocation motion in an aluminium single crystal subjected to a small applied bias stress. Beshers et al. 17-111 have shown that substantial generation of acoustic harmonics may occur in the kHz range of frequency in Armco iron and brass at sufficiently high strain amplitudes. The amplitude dependence of the harmonics was attrihuted to lattice anharmonicity in the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987851

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C8-348 JOURNAL DE PHYSIQUE

lower amplitude range and to long-range motion of dislocations in the higher amplitude range. The process of magnetostriction, e.g., the stress-induced movement of Bloch walls, has been mentioned as a third source of harmonic generation by Beshers et al. 1101.

An Mn-Cu based alloy was investigated in the present work. It has been shown that the high damping state of this alloy is associated with the presence of the antiferromagnetic tetragonal phase 1121. The stress-induced motion of antiferromagnetic domain walls gives rise to a strongly amplitude-dependent damping associated with some other nonlinear phenomena, such as soft resonance curves 1131. Therefore, it is expected that the stress-induced motion of antiferromagnetic domain walls will also give rise to harmonic generation. Indeed, harmonics up to the fifth in the kHz range were observed in this Mn-Cu alloy when the strain amplitude was higher than 1 x lo-'.

This paper is limited to a report of the observation of harmonic generation in the antiferromagnetic Mn-Cu alloy. The characterization of the damping and dynamic Young's modulus changes as a function of temperature and strain amplitude, caused by different thermomechanical treatments, will be published elsewhere [13).

I1

-

EXPERIMENT AND RESULTS

A piezoelectric ultrasonic composite oscillator technique (PUCOT) with a fundamental frequency of 40 kHz is used in the present work 1131. In addition to the normal PUCOT equipment, a spectrum analyzer is used to observe the harmonic generation of the vibrating composite oscillator system. A two-stage, high-pass filter with a cut-off frequency of 70 kHz is inserted between the input of the spectrum analyzer and the output of the preamplifier of the gauge voltage. This reduces the amplitude of the signal with fundamental frequency (c 40 kHz) by 30 dB. Then the small signals with harmonic frequencies of c 80 kHz, c 120 kRz and c 200 kHz are readily analyzed without overloading the spectrum analyzer. The harmonic amplitudes are monitored,

together with the drive voltage, gauge voltage and frequency.

The specimens were cut from a submarine propeller blade (200 kg) cast from a

commercial Mn-Cu based alloy called SONOSTON 1131. The chemical composition (wtX) of SONOSTON is as foll.ows: Mn 52.4, Cu 38.3, A1 4.36, Fe 3.16, Ni 1.42, C 0.095,

Si 0.07. The cross-sectional dimensions of the specimens tested were 3 x 3 mm. The faces of the samples were carefully machined and the length of each sample precisely matched to resonate with the quartz crystals.

In order to check the measurement system, the quartz crystal pair, i.a., a two- component oscillator without any specimen, was first tested alone. No harmonic generation above the background noise level was observed for strain amplitudes, E, up to 1.6 x 10". It was essential. to verify that the harmonic signals appearing from the three-component set-up were in fact coming from the specimen rather than from electronic distortions in the instrumentation or other extraneous causes. Towards this end, the harmonic generation of a specimen of a die-cast 2 ~ 2 7 % A1 allov was analyzed. The Zn-77X A1 alloy can be considered as almost linear in its damping vs.

vibration amplitude behaviour at frequencies

*

40 kHz 1131. The third harmonic amplitude, A,, is approximately equal to one third (or less) of the second harmonic amplitude A, (i.e., typical behaviour of a linear solid). No fourth and fifth harmonic amplitudes above the noise level could be distinguished in this linear specimen. These results can be used as a basis for the comparison of harmonic generation in other, nonlinear specimens.

The internal friction, Young's modulus and harmonic amplitudes for a heat-treated SONOSTON specimen are shown in Figure 1, as a function of vibration strain amplitude.

The heat treatment chosen was two hours at 700 K, followed by slow (furnace) cooling.

The results for "as-received" specimens are similar to those in Figure 1. It has been shown that the "as-received" and heat-treated specimens are both in a high damping state which yields markedly nonlinear, internal friction phenomena 1131. The harmonic amplitudes, A,, A, and A,, all increase with strain amplitude. The third harmonic amplitude, & , is higher at a strain amplitude E = 1.5 x lo-' than A2 by a factor of 2, while the fifth harmonic, AS, is only observed when E

2

¹^x^lo-'. ^No

fourth harmonic or harmonics higher than the fifth were observed.

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By plotting log An vs. log E, an approximate power-law relation of the form

is obtained. The plots for A, and As of SONOSTON specimens are shown in Figures 2 and 3, respectively. The second harmonic, A,, yields 1.9

<

^m

<

2.7, with an average m close to 2.3 in the "as-received", heat-treated, quenched and aged SONOSTON specimens, but two different regions of behaviour are observed for the third harmonic, A,.

When E

<

1 x lo", 1.6

<

^m

<

1.9; whereas when r

>

1 x 10", 5.2

<

^m

<

^5.6. ^{For the}

smaller fifth harmonic, not enough data have yet been obtained to characterize it in detail, but the exponent, m, of A, is close to that of A,.

In an "as-quenched" specimen the damping and Young's modulus is amplitude independent (as shown in Figure 4) and the third harmonic, A,, is much lower than that of the heat-treated specimen in Figure 1. No fourth or higher harmonics are observed in the

"as-quenched" sample, and the results are similar to those of the linear specimen of 2 ~ 2 7 % Al. It is particularly interesting to note that, after aging the "as- quenched" specimen for more than three months at room temperature, the third harmonic, A,, increased to a much higher amplitude and a small-amplitude fifth harmonic appeared. Thus, the harmonic pattern of the quenched and aged specimens began to resemble that of an "as-received" specimen. In other words, quenching from 1070 K suppresses the odd harmonics, while subsequent aging at room temperature

progressively returns the odd harmonics to their original level. A comparison of the amplitude dependence of A, in SONOSTON specimens subjected to different treatments is shown in Figure 5.

IIT

-

T)ISCITSSION

Prgvious studies 112,131 have shown that, at temperatures below the ~ 6 e l point (about 80 C) in "as-received" SONOSTON, the high damping state is highly nonlinear and caused, at least in part, by the stress-induced movement of antiferroma~netic domain walls. Reshers 1101 has given a Fourier analysis of magnetomechanical damping in ferromagnetic materials. When the cyclic stress is given by T = r sin wt, the corresponding strain is

where R, = (a

+

^BT~)T~;far odd n, An = (-1)P4~~~/~~(n2

-

4), where p = (n-I)/%, and all other coefficients are zero. These equations show that the strain harmonics (odd only) are always out of phase with the driving stress and the coefficients, A rapidly decrease with n. Presumably, the antiferromagnetic domain wall motion in n' SONOSTON is similar to the Rloch wall motion that gives rise to magnetomechanical damping in ferromagnetic materials and, therefore, their Fourier analyses have the same form. If this is the case, it is expected that only odd harmonics will be generated by antiferromagnetic domain wall motion and A, will have a very much lower amplitude than A,. These expectations coincide with the experimental results in the present work.

No measurable fourth harmonic was observed in any of the SONOSTON specimens, while the amplitudes of the second harmonic are approximately the same in the specimens with different thermomechanical treatment (except for the "as-quenched" specimen).

Thus, a significant component of the second harmonic in SONOSTON at room temperature cannot be attributed to antiferromagnetic domain wall motion. We have to attribute A,, at least in part, to the other principal sources of harmonic generation: lattice anharmonicity and dislocation motion. From the log A, vs. log E plot (Figure 2), the exponent, m, of the second harmonic amplitude as a function of strain ampljtude is approximately equal to 2.3. This is close to the experimental value (2.0) obtained by previous investigators.

In the "as-quenched" specimen, the paramagnetic, high-temperature structure was retained to a large extent. Consequently, A, was much smaller than its counterparts in the other SONOSTON specimen, and no other odd harmonics were observed. But, after aging the "as-quenched" specimen for a few months at room temperature (below the N6el

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JOURNAL

DE

PHYSIQUE

point), some of the antiferromagnetic phase developed, causing the third harmonic to increase again. The third harmonic amplitude at a strain amplitude e = 1.5 x In-' is 4.8 (arbitrary units) in the heat-treated specimen, 4.0 in the "as-received"

specimen, 0.8 in the "as-quenched" specimen, and 3.5 in the quenched and aged (three months) specimen (see Figure 5). Therefore, it appears that the third harmonic amplitude is very sensitive to the antiferromagnetic structure. In fact, the fraction of antiferromagnetic phase is largest in the heat-treated specimen and lowest in the

"as-quenched specimen". The heat-treated specimen was slowly cooled from 700 K, and thus well annealed. Consequently, we expect the heat-treated specimen at room temperature to he characterized by a low density of dislocations, well anchored by immobile impurities. This further strengthens the evidence that antiferromagnetic domain wall movement is responsihle for the third (and other odd power) harmonic generation, rather than dislocation motion, in this specimen.

In log

A,

vs. log e plots (Figure 3) of harmonic generation in the heat-treated specimen, there are two regions; the exponent m is approximately equal to 1.7 in region e

<

¹x 10-' and 5.4 in region e

>

^{1 x lo-'.} This implies that different mechanisms are responsible for the third-harmonic generation in the different strain- amplitude regions. At the lower strain amplitudes, the applied stress causes a small oscillation of the antiferromagnetic domain walls about their original positions.

This is analogous to the Rayleigh region in magnetomechanical damping. In the higher strain-amplitude range, the applied stress exceeds the local resisting force, so that breakaway of domain walls from pinning points begins to occur. This causes the surface area of the freely vibrating domain walls to increase rapidly. We suggest that this unpinning of the antiferromagnetic domain boundaries gives rise to the rapid increase in both A, and the damping with strain amplitude. A similar mechanism involving the interaction of antiferromagnetic domains with pinning points has been suggested for the peak of damping as a function of strain amplitude observed in SONOSTON at low frequencies

(*

⁵Rz) 1121. However, the details of this mechanism remain ohscure. The movement of domain boundaries by the formation of step-rings (analogous to kink-pair generation on dislocations), as discussed by various workers (14,151, and the interaction of the steps with pinning points, probably contribute to both the amplitude-dependent damping and harmonic generation.

TV

-

CONCLUSION

Third-harmonic generation, associated with the stress-induced motion of antiferromagnetic domain walls, is observed in the commercial Mn-Cu based alloy SONOSTON. In specimens containing almost no antiferromagnetic structure that are quenched from 1070 K, the third and other odd harmonics are almost suppressed. The second harmonic in SONOSTON is attributed, at least in part, to lattice anharmonicity and dislocation motion. It would appear that the measurement of harmonic generation offers another avenue for understanding the high damping characteristics of SONOSTON and similar materials, which are of considerable engineering interest 1131.

V

-

ACKNOWLEDGEMENTS

Stimulating correspondence with Professor D.N. Reshers is ~ratefully acknowledged.

One of the authors, Z-L. Pan, a visiting scientist from the Institute of Metal Research, Academia Sinica, Shenyang, People's Republic of China, wishes to express his appreciation for the support of Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establishment.

VI

-

REFERENCES

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2

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⁷¹⁹⁶⁵⁾2 2 9 . 141 HIKATA A., SEWELL F.A. Jr. and ELBAUM C., Phys. Rev.,

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151 THOMPSON R.B., BUCK ^0.and THOMPSON D.O., J. Acoust. Soc. Am.,

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66

(1985) C10-171.

CORONEL V.F. and BESHERS D.N., J. de Phys.,

46

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46

(1985) C10-409.

PAN 2-L., SPRUNGMANN K.W., SCHMIDT H.K. ANT) RITCHIT I.G., this conference proceedings.

SUMINO K., Acta Metall.,

3

(1966) 1607.

LINES M.E. and GLASS A.M., "Principles and Applications of Ferroelectrics and Related Materials", Clarendon Press, Oxford, 1977, pp. 108-111.

Figure 1 Harmonic amplitudes (arbitrary units), damping and Young's Modulus as a function of vibration strain amplitude in a heat- treated SONOSTON specimen (two hours at 700 K followed by furnace cooling).

Strain Amplitude. x loS

0 0

Figure 2 Log A, vs. log e plot for

"as-received" (*) and heat- treated (0) SONOSTON specimens.

- -

-I a

3 :- so

z 2~

e

-

2 ^7- 8 -Jz

N -

'-10.00 -9.60 -8.00 -8.50 LOG S T R A I N AMPL.

1

0 XJ

f

^-

%TI 0 0 CIC

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JOURNAL DE PHYSIQUE

4 8 12 16

Strain Amplitude, 6 x l o S 0

0

4 8 12 16

Strain Amplitude. 6 x 10'

o As-received 0

A Ouenchcd 0

-

Quenched and Oped 00

0 Heal treated

2. y:

0 s

"

&:**

=

.0&5

&

,

80 O O AA

oa 0-0

L

,

^A ^A ^{, A}

Figure 3 Log A, vs. log e for heat- treated (0) and quenched and aged (*) SONOSTON specimens.

i 4-

A L I0

a 9.

g- z

8- q _:-

8

J

Harmonic amplitudes (arbitrary units), damping and Young' s Modulus as a function of vibra-

tion strain amplitude in an

"as-quenched" SONOSTON specimen.

'-110.00 [email protected] -r.oo -8.60 LOG S T R A I N AMPL.

m

316

mo rn