INTERNAL FRICTION AND HARMONIC GENERATION IN IRON

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INTERNAL FRICTION AND HARMONIC GENERATION IN IRON

V. Coronel, D. Beshers

To cite this version:

V. Coronel, D. Beshers. INTERNAL FRICTION AND HARMONIC GENERATION IN IRON.

Journal de Physique Colloques, 1985, 46 (C10), pp.C10-175-C10-178. �10.1051/jphyscol:19851040�.

�jpa-00225424�

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JOURNAL D E P H Y S I Q U E

Colloque CIO, supplément au n 0 1 2 , Tome 46, décembre 1985 page C10-175

INTERNAL FRICTION AND HARMONIC GENERATION IN IRON

V . F . CORONEL AND D.N. B E S H E R S

Henry Krumb School of Mines, Columbia University, New York.

NY 10027. U.S.A.

Résumé

-

Le 20 kHz dans de Granato-L

f r o t t e m e n t i n t e r i e u r du f e r armco r e c u i t

2

êtG mesure pres de un domaine de deformation a t t e i g n a n t 5x10

".

Le f r o t t e m e n t .ücke dans l ' é t a t aimanté a i n s i que l e f r o t t e m e n t s u i v a n t l a l o i de Rayleigh dans l ' e t a t désaimante o n t 6 t é observés. Des ondes harmoniques, p r o d u i t e s p a r l e s deplacements de d i s l o c a t i o n s e t aussi ceux des p a r o i s de Bloch, o n t é t @ mesurees j u s q u 1 3 l ' o r d r e c i n q .

d b s t r a c t

-

The i n t é r n a l f r i c t i o n o f annealed Armcobiron was measured near 20 kHz f o r s t r a i n amplitudes as h i g h as 5x10

.

Granato-Lücke dampino was observed i n t h e magnetized s t a t e , as was Rayleigh law damping i n t h e demaonetized s t a t e . Harmonic waves produced by t h e motion o f d i s l o c a t i o n s and domain w a l l s were measured up t o t h e 5 t h o r d e r .

1

-

INTRODUCTION

I t i s w e l l e s t a b l i s h e d t h a t t h e main sources f o r t h e

internai-friction

i n ferromag- n e t i c m a t e r i a l s v i b r a t i n g w i t h s t r a i n amplitudes E O up t o =10 a r e o f magnetomechanical o r i g i n /1,2/: stress-induced motion o f t h e domain w a l l s and r o t a t i o n o f t h e magnetization vector, t h e losses being r e f e r r e d t o as-magnetomechanical damping

-

¹

Qm

.

However, Q ~ i s never seen alone. - ~ To separate

O,

from o t h e r c o n t r i b u t i o n s , two measurements must be made on t h e specimen: one i n zero f i e l d w i t h t h e specimen demagnetized, and a n o t h e r - i n a s a t u r a t i n g f i e l d . The corresponding damping values w i l l be r e f e r r e d t o as 4 0 and

os

r e s p e c t i v e l y ; from these one o b t a i n s 9,- by s u b t r a c t i o n : Qm-'=

Co-'-

Qs-l. At frequencies l e s s t h a n 100

Hz,

t h e behavior o f

YmI1

w i t h i n c r e a s i n g f o r i r o n o f v a r i o u s degrees o f p u r i t y i s w e l l known: f o r 10

Sk~~klO-

3 , a l i n e a r r e g i o n ( t h e Rayleigh r e g i o n ) i s seen f o l l o w e d by a peak / 3 / . The mode1 o f Smith and Birchak, SE /4/, based on an exponential d1:tribution o f i n t e r n a l stresses, g i v e s a good d e s c r i p t i o n o f t h e behavior o f Qm vs. E O w i t h t h e slope o f t h e l i n e a r r e g i o n i n v e r s e l y p r o p o r t i o n a l t o t h e square o f t h e i n t e r n a l s t r e s s . The

dislocation

damping nieasurements i n i r o n , again a t frequencies l e s s than 100 Hz /3,5/, show O

'

^{t o be}

-

independent up t o about E O = 10-"fter which i t increases a t a c o n t i j / u a l l y f a s t e r r a t e f o l l o w i n g t h e form described by Granato and L ü c ke(GL) /6/. The ampli tude dependence a r i s e s from non1 i n e a r mechanisms, which

should a l s o generate a c o u s t i c harmonics. Such harrnonics have been measured i n t h e kHz /7/ and KHz /8/ ranges f o r metals o t h e r than i r o n , although i n t h e llHz range o n l y a t very low r o The simultaneous measurement o f damping and harmoni CS provides us w i t h new i n s i g h t s i n t o t h e dynamics o f dornain w a l l s and d i s l o c a t i o n s . b!e r e p o r t here measurements o f i n t e r n a l f r i c t i o n and a c o u s t i c harinonics, up t o t h e 5 t h grder, f o r anneal ed armco Fe, over t h e l a r g e range o f s t r a i n auipl i t u d e s 1 0 - 6 ~ ~ < , 5 x 1 0

".

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851040

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JOURNAL

DE

PHYSIQUE

EXPERIblEI4TAL APPARATUS

The transducer-step-transformer,TST, used t o d r i v e t h e system i n steady s t a t e l o n g i t u d i n a l v i b r a t i o n , and a l s o t o measure t h e dampino o f t h e specimen, has been described i n d e t a i l elsewhere /9/. Our specimens were made o f commercially pure i r o n , armco i r o n w i t h l e s s than 0.1% C content, having a dumbbell shape and, l i k e t h e TST, tuned t o a l o n g i t u d i n a l resonance frequency o f 22.5 kHz. A f t e r machinino, t h e specimens were normalized a t 900°C f o r one hour, then annealed a t 700°C f o r f o u r hours i n an Argon atmosphere, which gave equiaxed p r a i n s o f about 120pm i n averaae s i z e and magnetic domain w i d t h s i n t h e range 10-40pm. A water-cooled s o l e n o i d provided an a x i a l f i e l d up t o 1000 Oe. A small (5 x 5 x 1 mm) LTZ-1 p i e z o e l e c t r i c transducer cemented t o t h e bottom o f t h e specimen r ~ i o n i t o r e d t h e s t a t e o f t h e specimen i t s e l f ; t h i s s i g n a l was f i l t e r e d t o reduce t h e fundamental by 40dB, t o p e r m i t obser- v a t i o n o f t h e small harnonic s i o n a l s w i t h o u t o v e r l o a d i n g t h e spectrum a n a l y t e r .

EXPERIblENTAL RESULTS

The specimen damping and harmonic amplitudes were measured as a f u n c t i o n o f E O f o r b o t h t h e demagnetized and t h e m a g n e t i c a l l y s a t u r a t e d s t a t e s . F i g 1 shows a t y p i c a l curve o f Q vs. E O f o r an annealed specimen i n t h e demagnetized s t a t e ; a l j n e a r r e g i o n i s qeen t o extend up t o E D = 1.0 x 10

",

f o l l o w e d by an u p t u r n i n 4, Iihen t h e s a t u r a t i n g f i e l d i s applied, t h e damping-rerdains a~mplitude-independent up t o

€0.1 x I O - ' + then qiv-ing an amplitude dependence.that, i n a GL p l o t o f l o g ( E ~ Q ~ - ' ) ~ S .

sonq, Fig*2, e x h i b i t s two l i n e a r eegions. The c e s u l t s f o r t h e harmonics a r e shown l n Fig.3, Tor a demagnetized specimen, and i n Fig.4 f o r a m a g n e t i c a l l y s a t u r a t e d speci- nien. The appearance o f 1 t h e . h ~ ~ a n i c s i s n o t accompanied by n o t i c e a b l e changes i n t h e behavior o f e i t h e r O o r Q ; thus f o r a demagnetized specimen t h e harmonics bepin t o appear when

4,

"$s i n t h 3 l i n e a r range w h i l e f o r the'magnetized specimen t h e second harmonic appears i n t h e €O-independent r e g i o n . P l o t s o f l o a A vs. l o g E O

a l l o w us t o t e s t whether t h e n - t h harmgnic e x h i b i t s o r an m-power .lafl dependence on t h e s t r a i n amplitude of t h e form Anaso

.

I n demagnetized specimens t h e second harmonic A2 has 1 . % ~ 2 . 5 , w i t h m c l o s e t o 2.0 i n most cases, whereas f o r t h e t h i r d harmonic A

,

2.0cp$<.?, w i t h m s c a t t e r e d a l 1 over w i t h i n t h e s t a t e d l i m i t s . Khen t h e specimgn i s m a g n e t i c a l i y saturated, t h e power-law r e l a t i o n f o r A i s a t f i r s t 1.7qq2.3, b ü t when ~0'3x10-'+, A departs from t h e power law and e x h q b i t s a broad peak i n t h e r e g i o n o f & p l i t u d e 8ependenee f o r

31

A f o i t h e s a t u r a t e d specimens does n o t e x h i b i t a power law behavior, i n s t e a d a d i p Qn t h e value o f A i s observed i n t h e r e g i o n 1 . ~ x 1 0 - ~ $ ~ 0 $ 2 . 6 ~ 1 0 - ~ . The f o u r t h and f i f t h harmonics we?e a l s o observed b u t , because t h e y d o n l t appear u n t i l ~ 0 ~ 1 . 5 ~ 1 0 - ~ , n o t enough data were c o l - l e c t e d t o c h a r a c t e r i z e them i n d e t a i l .

ANALYSIS OF EXPERIMENTAL RESULTS

Damping

-

The slope 6 of t h e 1 i n e a r r e g i o n i n Fig.1 i s approximately equal t o 25 and compares w e l l w i t R t h e values obtained f o r specimens o f s i m i l a r c h a r a c t e r i s t i c s :

€ 1 ~ ~ 4 0 a t 20 Hz / I O / and ORs30 a t 50 kHz /Il/; a l l o w i n g f o r d i f f e r e n c e s i n heat t r e a t - ment and p u r i t y among t h e specimens conpared, t h e constancy o f OR f o r a frequency v a r i a t i o n g r e a t e r than 10 i s s t r i king. T h i s constancy c o n f i rms t h e h y s t e r e t i c n a t u r e o f t h e magnetomechanical losses i n t h e Rayleigh r e g i o n , s i n c e a n o t a b l e c h a r a c t e r i s t i c o f h y s t e r e t i c behavior should be o f independence frequency. At low

E O , t h e SB mode1 g i v e s

Q-$

4KXs (11,

3 i r

€7

where K i s a constant which depends on t h e h y s t e r e s i s loop, has a maximum value o f 3, dnd i s u s u a l l y of t h e o r d e r of 1 /4/,

X

i s t h e s a t u r a t i o n m a g n e t o s t r i c t i o n , f o r i m n

*

= 7 ~ 1 0 - ~

,

^{c i}i s t h e average of t h e 8bsolute v a l u e o f k t h e i n t e r n a 1 s t r a i n * i n t h e spacimen. Using eR=25, we o b t a i n from eq. ( 1 ) , ~ i = 4 x l O ,which i s f o u r t o e l g h t times l a r o e r than t h e corresponding values f o r h i g h p u r i t y i r o n (12,131 and-1s Yery

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l i k e l y due t o t h e i n t e r n a l stresses produced by t h e i n c l u s i o n s and C - i n t e r s t i t i a l s s i n c e a s i m i l a r s h i f t t o higher E .

-

values has been observed w i t h increased C- content /12/. The slope o f t h e 1:near r e g i o n can thus be used t o make an e v a l u a t i o n o f t h e i n t e r n a l stress. The E O - independence seen f o r Qs-' a t low E O i n Fip.2 i s w e l l known /3,10,12/, and, assuming d i s l o c a t i o n s are t h e main source f o r t h i s damping probably i n d i c a t e s t h a t t h e d i s l o c a t i o n s remain pinned and undergo viscous o s c i l - l a t i o n s ; as increases beyond a c e r t a i n value, t h e r e w i l l be h y s t e r e t i c losses corresponding t o a mechanisrn o f continuous breakaway and r e p i n n i n g o f d i s l o c a t i o n s . The GL mode1 corresponds t o t h i s d e s c r i p t i o n , g i v i n g d i s l o c a t i o n damping o f t h e form

where C and D are constants depending on t h e d i s l o c a t i o n d e n s i t y , t h e d i s t a n c e between i m p u r i t y p i n n i n g p o i n t s , and d i s l o c a t i o n network p i n n i n g p o i n t s . I f eq.(2) i s s a t i s f i e d then l o g ( ~ 0 9 l s ) vs. E O should e x h i b i t a l i n e a r r e g i o n o f negative slope; t h e f a c t t h a t two such regions a r e seen, Fig.2, probably a r i s e s from edge d i s l o c a t i o n s having, f o r t h e same E O , g r e a t e r amplitude o f o s c i l l a t i o n than t h e screws and so t h e r e w i l l be a GL breakaway f i r s t f o r edges and then a t h i g h e r E O ,

f o r screws. The suggestion t h a t t h e amplitude dependent p a r t o f

P-;

cornes from d i s l o c a t i o n s i s r e i n f o r c e d by the a n a l y s i s o f t h e harmonics below.

Harmonics

-

I t i s s u r p r i s i n g a t f i r s t t o see t h a t t h e harmonics f o r t h e demagnetized and f o r t h e m a g n e t i c a l l y s a t u r a t e d specimens do n o t show as d r a s t i c a change as t h e damping, b u t we must remember t h a t t h e damping, being i n h e r e n t l y p o s i t i v e i s t h e sum o f p o s i t i v e c o n t r i b u t i o n s from a l 1 sources, w h i l e t h e harmonic s i g n a l i s a sum o f c o n t r i b u t i o n s w i t h phases from a l 1 t h e sources. The phases being unknown a t present, they might, a t one extreme, be a l 1 t h e same, o r a t t h e o t h e r extreme a l 1 cancel, t h e expected r e s u l t b2ing somewhere b e t ~ e e n ~ t h e s e l i m i t s . Now Our measurements show t h a t A holds f o r ~ 0 > 2 . 5 x l O - almost independently o f t h e s t a t e o f magnetization ^O? t h e specirnen, l e a d i n g us t o a t t r i b u t e t h e second harmonic i n t h i s range t o l a t t i c e anharmonicity /14/; a t h i g h e r E O , E ~ > ~ . ~ X ~ ~ - ' , A shows a broad peak i n a m a g n e t i c a l l y s a t u r a t e d specimen, Fig. 4, suggesting thac t h e d i s - l o c a t i o n motion c o n t r i b u t e s t o A w i t h a d i f f e r e n t phase, which would correspond t o an increase i n d i s l o c a t i o n l o o p ?ength as they breakaway from some p i n n i n g p o i n t s /8,14/. Also t h e d i p seen f o r t h e t h i r d harmonic, Fig.4, appears t o be caused by t h e edge and screw d i s l o c a t i o n s c o n t r i b u t i n g t o Ag w i t h opposite phases and weighing f a c t o r s t h a t l e a d t o c a n c e l l a t i o n a t a p a r t i c u l a r value f o r t h e average d i s l o c a t i o n l o o p l e n g h t Lc, which i s reached as t h e stress-induced breakaway takes p l a c e /8/.

Conclusions

-

The l i n e a r r e g i o n f o r t h e magnetomechanical damping has been observed i n t h e kHz range, the value o f i t s slope both confirms t h e frequency independence o f i t s h y s t e r e t i c nature and allows f o r a n e s t i m a t e o f t h e i n t e r n a l stresses t o be made i n ferr,omagnetic specimens. Harmonics are generated both from magnetomechanical and d i s l o c a t i o n sources, b u t t h e second harmonic i s p r i n e r i l y due t o l a t t i c e anharmoni- c i t y , t h e broad peak f o r A2 and t h e d i p - f o r A seen f o r magnetized specimens, coupled w i t h the GL t y p e o f EO-dependence f o r O

5 ,

i n a i c a t e s t h a t d i s l o c a t i o n s are t h e l i k e l y sources o f these e f f e c t s ,

References:

(1 ) R.Y. Bozorth, Ferrornaanetism, Van Nostrand, Princeton, N. J., 1951, p699 ff.

2 ) P.. Cochardt, Maqnetic Pro o r t i e s o f Metals and A l l o y s ASX, 1958, pp 251-279.

3 ) J.E. Bratina, i n PhysicalPAcoustics, W.P. Mason ed. Vol 111-1, Chap 6, Academic Press, ilew York 1966.

(4) G.W.Smith and J.E. Birchak, J. App Phys, 5174 (1969).

( 5 ) C.F.Burdett, P h i l . Kag.,

3

1459 (1971).

(6) A.Granato and K. Lücke, J. App. Phys., 583 (1956).

( 7 ) i.i.C. Jon, L1. P. blason, and D.N. Beshers, J. App. Phys.

2

5871 (1978).

(8) A. Hfkata e t a l , Phys. Rev., 151 442 (1966).

(9) 2.2. G o t t s c h a l l

,

PhD. Thesis, m u i n b i a U n i v e r s i t y , NY., (1975).

(10) C.Boulanger, Physica 15 266 (1949).

(11) F.P. Higgins and S.H.ëarpenter, iht. Sci. Eg., 173 (1979).

(12) 6.Sumner and K.:!. E n t w i s t l e , J.Jron and Steel I n s t .

192

238 (1959).

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C10-178 JOURNAL DE PHYSIQUE

(13) J . Degauque e t a l . , Phys. S t a t . Sol. ( a ) 45 493 (1 978).

(14) A. Hikata and C. Elbaurn, Phys. Rev.

144

469 (1966).

O 1

strain amplitude X 10 Fi g.1.- Plagnetomechanical darnwing f o r an annealed specimen.

Od LS 2.5

Strain Amplituda x 104

Fig.3.- Harmonic spectrum f o r t h e demagnetized s t a t e . The d e t a i l s Vary with each

run.

Inverse Strain X 10"

Fig.2.- Granato-Lucke p l o t s f o r

annealed and l i o h t l y deforned specimens

Fig.4.- Harmonic spectrum f o r t h e magnetically s a t u r a t e d s t a t e , r e p r e s e n t a t i v e of a l 1 specimens.