PROGRAMMABLE SYSTEM FOR THE MEASUREMENT OF THE SHEAR MODULUS AND INTERNAL FRICTION, ON SMALL SPECIMENS, AT VERY LOW FREQUENCIES

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PROGRAMMABLE SYSTEM FOR THE

MEASUREMENT OF THE SHEAR MODULUS AND

INTERNAL FRICTION, ON SMALL SPECIMENS,

AT VERY LOW FREQUENCIES

J. Woirgard, Ph. Mazot, A. Rivière

To cite this version:

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PROGRAMMABLE SYSTEM FOR T H E MEASUREMENT OF THE SHEAR MODULUS AND I N T E R N A L F R I C T I O N , ON SMALL SPECIMENS, A T VERY LOW FREQUENCIES

J. Woirgard, Ph. Mazot and A . Riviere

E.N.S.M.A., L a b o r a t o i r e de Mdccmique e t d e P h y s i q u e d e s M a t d r i a w , E.R.A. CURS n 0 1 2 3 , 8 6 0 3 4 P o i t i e r s Cedex, F r a n c e

Abstract. - A programmable system h a s been designed for automatic measurement of t h e s h e a r modulus a n d i n t e r n a l f r i c t i o n , a s a function of frequency, i n a wide frequency r a n g e (10-7 - 100 Hz).

The system incorporates a low cost micro-computer (Rockwell- AIM65) a n d performs d r i v i n g s i g n a l control, response s i g n a l condition- n i n g , analog to d i g i t a l conversion with a high sampling r a t e ( u p to 2 Mhz) and d i g i t a l recording i n s t a t i c RAM memories (16,384 twelve b i t s words p e r c y c l e ) . Before i n t e r n a l friction ( p h a s e l a g ) a n d s h e a r modulus ( a m p l i t u d e ) measurements, t h e recorded s i g n a l i s converted i n t o a fixed frequency s i g n a l (15 Hz) a n d filtered t h a n k s to a h i g h o r d e r , high s t a b i l i t y analog f i l t e r .

Programmed i n a easy to use l a n g u a g e ( B a s i c ) , the system h a s been proved to be very s u i t a b l e for a c c u r a t e measurements on small sized specimens (10 mm i n g a u g e l e n g t h ) a n d to reduce the influence of e x t e r n a l v i b r a t i o n s .

Introduction. - In o r d e r to o b t a i n r e l i a b l e h i g h temperature i n t e r n a l friction measurements, i t i s necessary t o use a v a r i a b l e frequency pendulum of the t y p e introduced by Woirgard (1) a few y e a r s ago.

As a matter of f a c t and since temperature v a r i a t i o n s introduce l a r g e s t r u c t u r a l c h a n g e s , a n d do not influence solely the kinetics of t h e r e l a x a t i o n processes ( t h e r e l a x a t i o n t i m e s ) , i t i s necessary to operate a t well s t a b i l i - zed temperatures a n d to t a k e the v i b r a t i o n frequency a s the p r i n c i p a l experimental parameter.

When such measurements a r e c a r r i e d out on c r y s t a l l i n e specimens, t h e difficulties a r i s e from t h e fact t h a t very small phase l a g s have to b e accu- r a t e l y measured between noisy s i g n a l s a n d on a v e r y wide frequency r a n g e . Due to t h e v e r y low frequencies used (down to Hz) a n d to t h e f a c t t h a t e i t h e r the s t r e s s o r the s t r a i n h a v e to be held constant, i t i s a l s o ne- c e s s a r y to use fully automated a p p a r a t u s .

T h u s , t h e aim of t h i s p a p e r i s to describe a n automated v a r i a b l e frequency pendulum b u i l t about a low cost micro-computer.

Mechanical a p p a r a t u s . - The a p p a r a t u s i s a e v a c u a t e d ( t o r r ) i.nver- 2

ted torsion pendulum which makes v i b r a t e f l a t b a r s (2Ox5xlmm ) hold between tantalum g r i p s 10 mm a p a r t . An overview of t h e a p p a r a t u s i s given i n

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JOURNAL DE PHYSIQUE

f i g u r e 1 a n d t h e d e t a i l of the g r i p s i n f i g u r e 2.

The a p p a r a t u s i s of the isothermal t y p e ( 1 , 2 ) a n d , d u r i n g t e s t s a t f i x e d temperature, the v i b r a t i o n frequency c a n b e v a r i e d between a n d 10 Hz, five o r ten discrete frequencies per decade being commonly used.

I n t h e present arrangement, we use magnetic d r i v e a n d o p t i c a l detec- tion :

a permet magnet, moving i n the field c r e a t e d b y two Helmoltz coils, a n d a s p h e r i c a l minor ( c f . Figure 3 ) , a r e a t t a c h e d to t h e u p p e r g r i p through

t h e extension rod. The coils a r e fed by t h e low frequency a l t e r n a t i n g dri- v i n g c u r r e n t

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60 V

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1 A ) a n d the specimen i s t h u s s e t i n t o forced torsio-

n a l vibrations.

The image of a r e c t a n g u l a r a p e r t u r e i s formed b y t h e s p h e r i c a l mirror on a d i f f e r e n t i a l photodiode ( 3 ) .located a t 500 mm.

The i n t e r n a l friction a n d t h e s h e a r modulus a r e obtained from t h e amplitude r a t i o a n d the p h a s e l a g between the d r i v i n g c u r r e n t i n the coils a n d the o u t p u t of t h e photo-diode.

The moving p a t , a t t a c h e d to the specimen, i s suspended by two f l a t steel ribbons ( 0 . 0 5 ~ 6 mm2 i n cross section) firmly held by two knives a n d attached to a s t r i p (cf. f i g u r e 3 ) , i n a p l a n e p e r p e n d i c u l a r to the specimen one. Thanks to t h a t a r r a n g m e n t , i t i s possible to obtain a high f l e x u r a l stif f n e s s a n d a v e r y low torsional one. The s t r i p s i s a t t a c h e d

,

through a ba- lance arm l y i n g on two knives, to a counterweight which ensures t h a t t h e specimen i s submitted to no a x i a l s t r e s s when t h e temperature is changed. During i n t e r n a l friction measurements, which a r e performed a t fixed tempera- t u r e s , t h e s t r i p i s clamped by a mandrel remotely d r i v e n .

Thank to a s p e c i a l f u r n a c e , with a molybdenum r e s j s t o r , t h e specimen temperature c a n be r i s e d u p to 1800°C. The r e s i s t o r i s located i n a s e p a r a t e vacuum chamber and test c a n be c a r r i e d out with v a r i o u s atmospheres around the specimen. I n the high temperature r a n g e , between 700 C a n d 1700 OC, temperature v a r i a t i o n s do not exceed 0.5 OC.

To e n s u r e t h a t b r i t t l e specimens a r e firmly held a t high temperatures, s p e c i a l g r i p s have been designed (cf. f i g u r e 3 ) . the warmer p a r t s a r e made out of t a n t a l u m a n d out of indium otherwise.

Programming a n d d a t a acquisition system.

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Because of t h e v e r y low frequen- c i e s used a n d due t o the f a c t t h a t t h e v i b r a t i o n amplitude h a s to b e t kept constant, i t i s necessary to perform t e s t s without a n y manual intervention. This c a n be e a s i l y done t h a n k s to a low coast micro-computer

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t h a t offers :

- a 20 columns thermal p r i n t e r

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The system itself comprises :

i ) A frequency a n d amplitude programmable sine generator delivering

+

1.5 A (on 40 ), between Hz a n d 10 Hz, to feed the d r i v i n g coils.

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i i ) A system allowing to digitalize a n d to store the output of the pho-

todiode (16.384 words of 12 bits per cycle) and t o convert i t i n a fixed frequency s i g n a l (15 Hz).

iii) A high performance analog f i l t e r allowing to seperate the s i g n a l

from the e x t e r n a l noise.

i v ) A high performance phasemeter, g i v i n g the phase l a g and the amplitude of the s i g n a l (cf. Figure

4 ) .

Thanks to t h a t arrangment, i t i s possible to determine the i n t e r n a l friction ( t h e phase l a g ) with a n absolute accuracy of about

lo-'

r d a n d the amplitude ( t h e s h e a r compliance) with a relative accuracy better t h a n

Experimental results. - To i l l u s t r a t e the accuracy of the method, some r e s u l t s a r e reported on the following figures : 5-6 and

7.

In f i g u r e 5 a r e shown the spectra obtained between 600°C a n d 900°C in a non equimolar spinel1 single c r y s t a l . It c a n be seen on t h a t figure t h a t a highly thermally activated relaxation peak c a n be observed on a r a t h e r lar- g e temperature range. The exact o r i g i n of t h a t peak, which had not yed been recorded, i s not known.

On figure 6, is shown a cold work peak obtained a t room temperature on a molybdenum specimen. On t h a t f i g u r e i t c a n be seen t h a t the absolute accuracy of the i n t e r n a l friction measurement i s quite comparable to t h a t obtained with more c l a s s i c a l methods.

Finally i n figure 7, obtained a t very high temperatures, on the same molybdenum specimen, i t c a n be seen t h a t very high damping levels c a n be easily determined.

Bibliographie. -

1 - J . Woirgard, Y . S a r r a z i n a n d H. Chaumet Review of

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JOURNAL DE PHYSIQUE 900 COO 300 200 100 F I G .5 - I n t e r n a l f r i c t i o n peaks and modulus d e f e c t obtained a t d i f f e r e n t s p i n e l l e s i n g l e c r y s t a l a t d i f f e r e n t t e m p e r a t u r e s :

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A c o l d w o r k ~ e a l obtained a t room tem- a s in f i e u r e 6.