POLYA~ER MEC HANICS

ACOUSTIC

FATIGUE

I° Electronic

Acoustic

OF

585

POLYMER

MATERIALS

Testing Equipment

Yu. S. U r z h u m t s e v and S. L. Skalozub Mekhanika P o l i m e r o v , Vol. 2, No. 6, pp. 911-916, 1966 UDC 678.7:539.43 A brief description is given of testing equipment developed and built at the Institute of Polymer Mechanics of the Academy of Sciences of the Latvian SSR and intended for investigating the fatigue properties of polymer materfals in a symmetrical tension-compression cycle at a loading frequency of 20 kHz. It is shown that the equipment is suitable for estimating the acoustic parameters of the material (acoustic attenuation coefficient, phase velocity of sound) and the selfheating temperature of the specimen over a broad range of amplitudes of the acoustic displacement throughout the fatigue t e s t . The potential of the equipment is illustrated by describing the results of preliminary tests, The acoustic characteristics have been plotted as functions of time and temperature during the initial period of acoustic loading.

t e r i s t i c s v a r y during the acoustical loading p r o c e s s and t r y i n g to e s t a b l i s h on the b a s i s of these data the nature of the p r o c e s s r e s p o n s i b l e f o r the fatigue f a i l ure of p o l y m e r m a t e r i a l s .

Kn

out °7oo 9

502

§1, P r e m i s e s and p r o b l e m s , Recently, in v a r i o u s b r a n c h e s of technology, t h e r e has been a sharp inc r e a s e in the i m p o r t a n c e of f a c t o r s f o r m e r l y r e g a r d e d as s e c o n d a r y (e. g . , the action of intense a c o u s t i c l o a d s which in a number of e a s e s may cause fatigue damage to p l a s t i c s components and s t r u c t u r e s ) . A r e l a t i v e l y few y e a r s ago high-frequency m e c h a nical fatigue of s t r u c t u r a l m a t e r i a l s did not a t t r a c t much attention, but since the e a r l y s i x t i e s many authors have published r e p o r t s on the effect of acoustic v i b r a lions on the s t r u c t u r e and p h y s i c o - m e e h a n i c a l c h a r a c t e r i s t i c s of v a r i o u s m a t e r i a l s [ 1 - 9 ] , These p r o p e r t i e s v a r y continuously in time d u r i n g the v i b r a t i o n p r o c e s s . A c e r t a i n quantitative change in the p h y s i c o - m e c h a nical p r o p e r t i e s and t h e i r combinations or the a p p e a r anee of v i s i b l e m a c r o d e f e e t s may s e r v e as c r i t e r i a of fatigue f a i l u r e . Of c o u r s e , the r e l i a b i l i t y of the r e corded fatigue c u r v e s will l a r g e t y depend on the a c curacy- with which the m o m e n t of f a i l u r e is e s t i m a t e d in t e r m s of the chosen c r i t e r i o n .

F i g . 1, Block d i a g r a m of e l e c t r o n i c acoustic equipment f o r the acoustic fatigue t e s t i n g of p o l y m e r s . A c c o r d i n g l y , it is worthwhile making a m o r e d e tailed study of how the r h e o l o g i e a l p r o p e r t i e s of s p e c i m e n s and the functionally r e l a t e d acoustic e h a r a c -

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~f60 . . . .

Fig. 2. Graphs of c o r r e c t i o n coefficients for taking into a c count v a r i a t i o n of the working gaps of the c a p a c i t i v e p r o b e s .

Such a study would be valuable in two r e s p e c t s . F i r s t l y , the acoustic c h a r a c t e r i s t i c s (propagation v e l o c i t y and acoustic attenuation coefficient) r e c o r d e d in the initial loading p e r i o d Could s e r v e as s t a r t i n g d a t a f o r c a l c u l a t i n g the propagation of v i b r a t i o n s in p o l y m e r components and s t r u c t u r e s . Secondly, the quantitative e s t i m a t i o n of the v a r i a t i o n of these acoustic c h a r a c t e r i s t i c s during the v i b r a t i o n p r o c e s s wouId help in solving the p r o b l e m of the nature of fatigue f a i l u r e with account for the composition and p h y s i c o c h e m i c a l and s u p e r m o l e c u l a r s t r u c t u r e of the t e s t s u b s t a n c e . F r o m this standpoint the actual method of studying acoustic fatigue using such s t r u c t u r a l l y s e n s i t i v e c h a r a c t e r i s t i c s as the propagation velocity and acoustic attenuation coefficient a c q u i r e s the s i g nificance of a r a p i d method of p h y s i c o - m e c h a n i c a l analysis. A c c o r d i n g l y , the a i m s of our r e s e a r c h , whose r e suits will be r e p o r t e d in this and subsequent p a p e r s , w e r e as follows: 1. to design and build e l e c t r o n i c acoustic t e s t i n g equipment capable of inducing in p o l y m e r s p e c i m e n s u l t r a s o n i c v i b r a t i o n s at a frequency of 20 kHz o v e r the b r o a d e s t p o s s i b l e range of acoustic d i s p l a c e m e n t mnplitudes;

586

MEKttANIKA POLIIVIEROV

2. to c r e a t e the b a s i s of a method of studying the acoustic fatigue of p o l y m e r s (with r e f e r e n c e to compounded r u b b e r specimens) and m e a s u r i n g the acoustic c h a r a c t e r i s t i c s and s e l f - h e a t i n g t e m p e r a t u r e of the s p e c i m e n s during the p r o c e s s of acoustic vibration; 3. to e s t a b l i s h a fatigue f a i l u r e c r i t e r i o n and obtain a r e l a t i o n between the amplitude of the f a i l u r e s t r e s s and the number of c y c l e s .

I 'epor/'X [ Acoustic irradiation time, sec Fig. 3, Time dependence of acoustic c h a r a c t e r i s t i c s and s e l f - h e a t i n g t e m p e r a t u r e in initial period of high-frequency loading. §2. D e s c r i p t i o n of equipment. A block d i a g r a m of the equipment is shown in Fig. 1. It c o m p r i s e s four main channels: an e l e c t r i c o s c i l l a t o r channel; a channet f o r m e a s u r i n g and r e c o r d i n g the amplitudes of the acoustic d i s p l a c e m e n t at the s p e c i m e n input and output f a c e s ; a charmel for m e a s u r i n g and r e c o r d i n g the phase shift between the amplitudes of the input and output v i b r a t i o n s ; and a channel f o r m e a s u r i n g and r e c o r d i n g the s e l f - h e a t i n g t e m p e r a t u r e . E l e c t r i c o s c i l l a t o r channel. The p r i n c i p a l working m e c h a n i s m of the equipment is the e l e c t r i c o s c i l l a t o r and the acoustic s y s t e m , which c o n s i s t s of magnetos t r i c t i o n t r a n s d u c e r - v i b r a t o r , amplitude c o n c e n t r a t o r , adapter, and specimen. The e n e r g y r e q u i r e d to b r i n g the e n t i r e s y s t e m into v i b r a t i o n a l motion is g e n e r a t e d by the ZG-18 type m a s t e r o s c i l l a t o r 1, amplified in the UG-1 type power a m p l i f i e r 2, and fed to the winding of the m a g n e t o s t r i c t i o n v i b r a t o r 5. In o r d e r to obtain maximum a m p l i t u d e s of the acoustic d i s p l a c e m e n t , the frequency of the e l e c t r o magnetic field exciting the v i b r a t o r is tuned to r e sonance with the natural frequency of the e l a s t i c v i b r a t i o n s of the r o d s of m a g n e t o s t r i c t i v e m a t e r i a l [10, 1t]. In our c a s e a t r a n s d u c e r with closed m a g n e tic c i r c u i t s was used to excite longitudinal v i b r a t i o n s . * The e l e c t r i c o s c i l l a t i o n s in the v i b r a t o r coil a r e tuned to r e s o n a n c e by m e a n s of c a p a c i t o r 28. C a p a c i tor 29 s e r v e s for decoupling the c i r c u i t f r o m the constant component. A d c s o u r c e 3 giving an optimal m a g n e t i z i n g c u r r e n t is also connected to the v i b r a t o r coil. The shape of the e l e c t r i c o s c i l l a t i o n s in the v i b r a t o r coil is checked with a type SI-1 o s c i l l o s c o p e 4.

*The working d r a w i n g s f o r the m a g n e t o s t r i c t i o n v i b r a t o r and catenoidal horn w e r e p r e p a r e d at the Moscow Ordzhonikidze Aviation Institute and at the Institute of Metal C e r m a i c s and Special Alloys of the A c a d e m y of Sciences of the Ukrainian SSR.

Accurate tuning of the v i b r a t o r to r e s o n a n c e and good matching of the coil impedance with the a m p l i f i e r output impedance made it possible to obtain sufficiently high s t r e s s in the s p e c i m e n s at an effective a m p l i f i e r (2) power of 200 W. The v i b r a t o r 5 t r a n s f o r m s e l e c t r i c a l into m e c h a nical o s c i l l a t i o n s and by means of catenoidal concent r a t o r 5a, and a d a p t e r 7 t r a n s m i t s the v i b r a t i o n s to the p o l y m e r specimen 8. The end face of the specimen is bonded to the end face of the adapter. This acoustic contact c r e a t e s the optimal conditions for e x t r a c t i n g v i b r a t i o n a l energy from the v i b r a t o r - c o n c e n t r a t o r a d a p t e r s y s t e m and t r a n s m i t t i n g it to the specimen. The c o n c e n t r a t o r 5a s e r v e s to i n c r e a s e the a m p l i tude of the v i b r a t i o n s . Detailed wave a n a l y s e s and c a l culations for c o n c e n t r a t o r s of this type have appeared in the l i t e r a t u r e [12, 13]. The adapter 7 and specimen 8 a r e s e c u r e d to the c o n c e n t r a t o r with a clamp 6. B a s i c a l l y , the function of the a d a p t e r is to e n s u r e smooth t r a n s m i s s i o n of acoustic energy from v i b r a t o r to specimen with minimum l o s s e s . Accordingly, the a d a p t e r is of r e s o n a n t (half-wave) design. Then the r e a c t i v e component of the mechanical impedance of the s o u r c e [14] and the acoustic energy l o s s e s a r e r e duced to l o s s e s due to d i s s i p a t i o n a s s o c i a t e d with the i n e l a s t i c p r o p e r t i e s of the adapter. Approximate adapter calculations w e r e made using a method developed for h a l f - w a v e s p e c i m e n s of tough s t e e l s in fatigue t e s t s at 20 kHz [1]. The exact choice of a d a p t e r d i m e n s i o n s with allowance for the effect of the m a s s of the clamp was made e x p e r i m e n t a l l y . In o r d e r to e n s u r e the p o s s i b i l i t y of m e a s u r i n g v i b r a tions of input amplitude, the d i a m e t e r of the end face of the a d a p t e r in the plane of the joint with the s p e c i men was i n c r e a s e d to 16 ram, the d i a m e t e r of the s p e cimen and the c e n t r a l rod of the adapter being 10 ram. Because of the threaded connection between the a d a p t e r and the r e s t of the acoustic s y s t e m , changing the s p e c i m e n s does not p r e s e n t any s p e c i a l difficulty and does not take much time.

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,

,

20

25

30

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Self-heating temperature F i g . 4. T e m p e r a t u r e dependence of acoustic c h a r a c t e r i s t i c s in i n i t i a l p e r i o d of acoustic i r r a d i a t i o n .

Channel for measuring and recording a m p l i t u d e s of the acoustic displacement at specimen input and output. The amplitudes of the acoustic d i s p l a c e m e n t s at the s p e c i m e n input and output a r e m e a s u r e d with the c o r r e s p o n d i n g c a p a c i t i v e p r o b e s 9 and 10, connected a l t e r n a t e l y by m e a n s of switch 11 to the probe supply b a t t e r y 13 and cathode follower 12. The r e c t i f i e r 14

POLYMER MECHANICS

587

supplies the voltages needed to feed the cathode follower. Beyond the cathode follower the e l e c t r i c a l s i g nal, p r o p o r t i o n a l to the amplitude of the vibration, is amplified by a " T e s l a " type s e l e c t i v e m i l l i v o l t m e t e r 15 and fed to the input of a VK7-3 type peak cathode v o l t m e t e r 18. A PVU-5256 type h i g h - r e s i s t a n c e conv e r t e r 19 and an E P P - 0 9 s e l f - b a l a n c i n g p o t e n t i o m e t e r 20 a r e connected in p a r a l l e l with the v o l t m e t e r i n d i c a tor. The p o t e n t i o m e t e r s c a l e was c a l i b r a t e d d i r e c t l y in units of v i b r a t i o n amplitude (microns) by m e a n s of a m i c r o s c o p e . Since the c a p a c i t i v e p r o b e s a r e switched during the e x p e r i m e n t , p o t e n t i o m e t e r 20 a l t e r n a t e l y r e c o r d s the v i b r a t i o n amplitude l e v e l s in the input and output planes of the specimen. Because the c a p a c i t i v e p r o b e s a r e nonlinear and t h e i r s e n s i t i v i t y v a r i e s with v a r i a t i o n of the gap, c a l i b r a t i o n of the p r o b e s and the subsequent m e a s u r e m e n t s m u s t be c a r r i e d out only at p r e v i o u s l y e s t a b l i s h e d v a l u e s of the working gaps. It is m o s t convenient to set these gaps so that the sens i t i v i t i e s of the p r o b e s a r e equal. The gaps a r e s e t with a m i c r o m e t e r device and p o i n t e r - t y p e d i s p l a c e m e n t i n d i c a t o r s graduated in m i c r o n s . However, the gaps of both p r o b e s change during the e x p e r i m e n t , owing to the i n c r e a s e in the t e m p e r a ture of the s p e c i m e n and the a d a p t e r (due to h y s t e r e s i s e n e r g y l o s s e s ) . In o r d e r to e l i m i n a t e the c o r r e s p o n d i n g systematic error, experimentally recorded relations between p r o b e s e n s i t i v i t y and gap width a r e used to c o n s t r u c t c u r v e s of the c o r r e c t i o n coefficients kin = =fl(Ad), and kout = f2(Ad), where Bd is the change in gap width r e l a t i v e to the initial value (Fig. 2). A s suming in the f i r s t approximation that the d e c r e a s e in the gaps with i n c r e a s e in t e m p e r a t u r e is l i n e a r , we can find Ad f r o m the f o r m u l a r-r

i

Ad=Adf T f _ T i , w h e r e ~df is the d e c r e a s e in the gap at the end of the experiment, T is the variable specimen self-heating temperature, Ti is the initial temperature of the specimen, and Tf its final temperature at the end of the experiment. Channel for measuring and recording phase shift between input and output v i b r a t i o n a m p l i t u d e s , The p h a s e shift between input and output v i b r a t i o n a m p l i tudes is d e t e r m i n e d as the d i f f e r e n c e between the p h a s e s qOin and rPout at the m o m e n t the p r o b e s a r e switched, ~0 = ~0in - ~0out. The p h a s e s q)in and ~Oout a r e m e a s u r e d with a type F 2 - 1 p h a s e m e t e r 21 connected to the output of a m p l i f i e r 15. The " r e f e r e n c e " phase voltage is supplied d i r e c t l y f r o m m a s t e r o s c i l l a t o r 1. An E P P - 0 9 s e l f - b a l a n c i n g p o t e n t i o m e t e r 23 g r a d u a t e d in e l e c t r i c a l d e g r e e s is connected in p a r a l lel with the p h a s e m e t e r i n d i c a t o r a c r o s s a PVU-5256 type h i g h - r e s i s t a n c e c o n v e r t e r 22 in o r d e r to r e g i s t e r the phase shift.

that the t e m p e r a t u r e can be reckoned from 0° C. The t h e r m o - e m f developed by the thermocouple is m e a s u r e d and r e c o r d e d with an E P P - 0 9 s e l f - b a l a n c i n g pot e n t i o m e t e r 17. §3. P r e l i m i n a r y e x p e r i m e n t s . The equipment d e s c r i b e d above was used to p e r f o r m e x p e r i m e n t s on s p e c i m e n s of compounded r u b b e r ( s e r i e s I m a t e r i a [ ) . The chief aim of these p r e l i m i n a r y e x p e r i m e n t s was to d e t e r m i n e the p o s s i b i I i t y of e s t i m a t i n g the acoustic c h a r a c t e r i s t i c s and s e l f - h e a t i n g t e m p e r a t u r e of the s p e c i m e n s and t h e i r v a r i a t i o n during the t e s t - - f r o m the initial s t a g e s to the m o m e n t of acoustic f a i l u r e - and also to deveIop a method of f a t i g u e - t e s t i n g p o l y m e r specimens. The d i m e n s i o n s of the c y I i n d r i c a l t e s t p i e c e s w e r e the same in all the e x p e r i m e n t s (length 6 mm, d i a m e t e r 10 mm). F i g u r e 3 shows the acoustic attenuation coefficient p, the phase velocity v* of propagation of sound, and the s p e c i m e n s e l f - h e a t i n g t e m p e r a t u r e T as functions of the acoustic i r r a d i a t i o n time in the initial loading p e r i o d at an acoustic p r e s s u r e p = 1.2 k g f / c m 2 (118 kN/mZ). In this time i n t e r v a l (10-15 see) t h e r e is an intense i n c r e a s e in s e l f - h e a t i n g t e m p e r a t u r e and a s h a r p l y e x p r e s s e d change in the acoustic c h a r a c t e r i s t i c s . The p e a k vaIue of ~3 c o r r e s p o n d s to a s p e c i men s u r f a c e t e m p e r a t u r e of a p p r o x i m a t e l y +30 ° C. This i s c o n f i r m e d in F i g . 4, w h e r e the c h a r a c t e r i s t i c s a r e plotted a g a i n s t the monotonically i n c r e a s i n g s e l f heating t e m p e r a t u r e . Close to the same t e m p e r a t u r e there i s a c o n s i d e r a b l e (by a f a c t o r of a h n o s t 2) d e c r e a s e in the phase velocity of sound. T h e r e a f t e r the acoustic c h a r a c t e r i s t i c s continue to v a r y with time. The e x p e r i m e n t a l points plotted on the g r a p h s a r e quite r e g u l a r and the s c a t t e r of the r e l a t i v e t e s t r e sults is s m a l l . The coefficient fi was m e a s u r e d on the equipment c o r r e c t to within 10-15% and the phase v e l o c i t y of sound v c o r r e c t to within 3-5~c. SUMMARY F l e c t r o n i e a c o u s t i c t e s t i n g equipment has been d e veloped f o r p u r p o s e s of c r e a t i n g and s i m u l a t i n g i n tense a c o u s t i c loads in p o l y m e r s p e c i m e n s . With this equipment it is p o s s i b l e to m e a s u r e with a c c u r a c y and a u t o m a t i c a l l y r e c o r d changes in the acoustic attenuation coefficient and phase velocity of sound in the s p e cimen and also the s e l f - h e a t i n g t e m p e r a t u r e throughout the e n t i r e t e s t period.

REFI~RENCES 1. V. A. Kuz'menko, Sonic and Ultrasonic Vibrations in Dynamic M a t e r i a l s Testing [in Russian], Kiev, 1963. 2. Io A. T r o y a n , C a n d i d a t e ' s d i s s e r t a t i o n , Kiev, 1962,

Channel for measuring and recording specimen self-heating temperature. The s e l f - h e a t i n g t e m p e r a t u r e of the s p e c i m e n s u r f a c e is m e a s u r e d with a copp e r - c o n s t a n t a n thermocouple, whose hot junction 25 is bounded to the s u r f a c e of the s p e c i m e n , the cold j u n c tion 26 being p l a c e d in a vacuum bottle 24 wi~h ice, so

*The method of d e t e r m i n i n g v and fi will be d e s c r i b e d in l a t t e r i s s u e s of this j o u r n a l .

588 3. V. V. Bolotin, "Acoustic fatigue and related problems," in: Problems of Mechanical Fatigue [in Russian], Moscow, 1964. 4. A. A. Skripnichenko, Zav. lab., 5, 1964. 5. Hart and McClure, Vopr. raketnoi tekhniki, 2, 1960. 6. P. Ulang, J. Aeoust. Soe. A m e r . , 34, g. P a r t i, 1161, 1962. 7. Langenecker, Raketn. tekhn, i kosm., i, 1963. 8. Tormi and Britton, Raketn. tekhn, i kosm., 8, 1963. 9. Ryan and Coates, Raketn. tekhn, i kosm., 6, 1964.

MEKHANIKA

POLIMEROV

10. L. Bergmann, Ultrasound [Russian translation], Moscow, 1957. 11. L. D. Rozenberg, V. F. Kazantsev, L. O. Makarov, and D. F. Yakhimovieh, Ultrasonic Cutting [in Russian], Moscow, 1962. 12. L. G. Merkulov, Akust. zh., 3, 1957. 13. I. I. Teumin, Ultrasonic Vibratory Systems [in Russian], Moscow, 1959. 14. Yu. I. Iorish, Vibrometry [in Russian], Moscow, 1963. 20 May t966

Institute of Polymer Mechanics, AS Latvian SSR, Riga