internal friction and harmonic generation in iron

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. .

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JOURNAL DE P H Y S I Q U E

Colloque CIO, supplément au n012, Tome 46, décembre 1985

page C10-175

INTERNAL FRICTION AND HARMONIC GENERATION IN IRON V.F.

CORONEL AND D.N.

BESHERS

Henry Krumb School of Mines, Columbia University, New York. NY 10027. U.S.A.

Résumé - Le 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 Le f r o t t e m e n t 20 kHz dans un domaine de deformation a t t e i g n a n t 5x10 de Granato-L .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 .

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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 near 20 kHz f o r s t r a i n amplitudes as h i g h as was observed i n t h e magnetized s t a t e , as was demaonetized s t a t e . Harmonic waves produced and domain w a l l s were measured up t o t h e 5 t h 1

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Armcobiron was measured Granato-Lücke dampino 5x10 Rayleigh law damping i n t h e by t h e motion o f d i s l o c a t i o n s order.

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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 ferromaga r e o f magneton 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 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 mechanical o r i g i n /1,2/: t h e magnetization vector, t h e losses being r e f e r r e d t o as-magnetomechanical damping Qm- 1 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 and r e s p e c t i v e l y ; from these one o b t a i n s -9, by w i l l be r e f e r r e d t o as 4 0 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 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 YmI1 w i t h i n c r e a s i n g 10 Sk~~klO3 , 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 independent up t o about E O = 10-"fter which i t 100 Hz /3,5/, show O t o be 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

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

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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 Our specimens were made o f commercially pure described i n d e t a i l elsewhere /9/. 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 dt 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 observ 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 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 curve o f Q 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 specinien. The appearance o f 1 t h e . h ~ ~ a n i ciss 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 ; thus f o r a demagnetized specimen t h e harmonics bepin or Q t o appear when 4, "$s i n t h 3 l i n e a r range w h i l e f o r the'magnetized specimen t h e second harmonic appears i n t h e €O-independent r e g i o n . P l o t s o f l o a A vs. l o g E O a l l o w us t o t e s t whether t h e n - t h harmgnic e x h i b i t s o r an m-power .lafl dependence on t h e s t r a i n amplitude of t h e form Anaso I n demagnetized specimens t h e second harmonic A2 has 1 . % ~ 2 . 5 , w i t h m c l o s e t o 2.0 i n most cases, whereas f o r t h e t h i r d w i t h m s c a t t e r e d a l 1 over w i t h i n t h e s t a t e d l i m i t s . Khen harmonic A , 2.0cp$ ~ . ~ X ~ ~shows 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 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 /8,14/. 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/.

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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 anharmonic 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:

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R.Y. Bozorth, Ferrornaanetism, Van Nostrand, Princeton, N. J., 1951, p699 ff. 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. J.E. Bratina, i n PhysicalPAcoustics, W.P. Mason ed. Vol 111-1, Chap 6, Academic Press, ilew York 1966. G.W.Smith and J.E. Birchak, J. App Phys, 5174 (1969).

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C.F.Burdett, P h i l . Kag., 3 1459 (1971). A.Granato and K. Lücke, J. App. Phys., 583 (1956). i.i.C. Jon, L1. P. blason, and D.N. Beshers, J. App. Phys. 2 5871 (1978). A. Hfkata e t a l , Phys. Rev., 151 442 (1966). 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). C.Boulanger, Physica 15 266 (1949). F.P. Higgins and S.H.ëarpenter, iht. Sci. Eg., 173 (1979). 6.Sumner and K.:!. E n t w i s t l e , J.Jron and Steel I n s t . 238 (1959).

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C10-178

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J . Degauque e t a l . , Phys. S t a t . Sol. ( a ) 45 493 (1 978). A. Hikata and C. Elbaurn, Phys. Rev. 144469 (1966).

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1

Inverse Strain X

strain amplitude 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

Fi g.1.- Plagnetomechanical darnwing f o r an annealed specimen.

Od

LS Strain Amplituda

x

10"

2.5

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.

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.