NON-LINEAR INTERACTION BETWEEN ULTRASONIC SHEAR WAVES AND DISLOCATIONS IN ALUMINIUM

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NON-LINEAR INTERACTION BETWEEN

ULTRASONIC SHEAR WAVES AND DISLOCATIONS

IN ALUMINIUM

Y. Wang, W. Britton, R. Stephens

To cite this version:

NON-LINEAR INTERACTION BETWEEN ULTRASONIC S H E A R W A V E S A N D D I S L O C A T I O N S

IN A L U M I N I U M

Y.T. Wang, W.G.B. B r i t t o n and R.W.B. S t e p h e n s

Chelsea CoZZege (University o f London), England

A b s t r a c t . - S h e a r w a v e s a t a f r e q u e n c y o f L . 8 3 I<Bz h a v e b e e n -rap- a g a t e d a l o n g t h e 1 1 0 0 7 a x i s o f a n a l u m i n i u m c r y s t a l o f h i g h p u r i t y . T h e s e c o n d a n d t h i r d h a r m o n i c s a r i s i n g f r o m t h e i n t e r a c t - i o n b e t w e e n t h e u l t r a s o n i c w a v e s a n d d i s l o c a t i o n s h a v e k e e n m e a s - u r e d a t s m a l l b i a s s t r e s s e s . Up t o a s t r e s s o f 3 . 2

x

1 0 d y n . t h e s e c o n d h a r m o n i c a m p l i t u d e i n c r e a s e d a n d r e a c h e d a maximum b u t o n t h e o t h e r h a n d t h e t h i r d h a r m o n i c s h o w e d a g r a d u a l d e - c r e a s e . B o t h t h e s e c o n d a n d t h i r d h a r m o n i c s w e r e v e r y s e n s i t i v e t o t h e a p p l i e d b i a s s t r e s s . A m a r k a d d i f f e r e n c e was f o u n d i n t h e r e s p o n s e o f t h e s e c o n d h a r m o n i c g e n e r a t i o n t o f u n d a m e n t a l w a v e s o f d i f f e r e n t a m p l i t u d e . O b s e r v a t i o n s h a v e b e e n made o f t h e e f f e c t o n t h e h a r m o n i c a m p l i t u d e s a r i s i n g f r o m t h e p r e - s t r e s s i n g o f t h e s p e c i m e n . I n t r o d u c t i o n . - T h e s e e x p e r i m e n t s h a v e b e e n u n d e r t a k e n w i t h t h e o b j e c t - -> -i v e o f g a -i n -i n g f u r t h e r -i n f o r m a t -i o n o n d -i s l o c a t -i o n d y n a m -i c s -i n c r y s t a l s a s a r e s u l t o f o b s e r v a t i o n s on h a r m o n i c g e n e r a t i o n b r o u g h t a b o u t by t h e i n t e r a c t i o n b e t w e e n u l t r a s o n i c w a v e s a n d d i s l o c a t i o n s . A s e c o n d s o u r c e o f i n t e r e s t a r i s e s i n t h e p o s s i b l e a p p l i c a t i o n o f t h e s e e x p e r - m e n t s t o n o n - d e s t r u c t i v e t e s t i n g

(NDT)

s i n c e t h e m a g n i t u d e o f t h e g e n e r a t e d h a r m o n i c s r e f l e c t s t h e n a t u r e o f t h e c o n i l g u r a t i o n o f t h e d i s l o c a t i o n s a n d t h e p r e s e n c e o f o t h e r d e f e c t s w h i c h s t r o n g l y i n f l u e n c e m a t e r i a l s t r e n g t h . A l m o s t u n i v e r s a l l y , p r e v i o u s w o r k e r s ( 1 - 1 ) h a v e e m p l o y e d l o n g i t u d i n a l w a v e s w h i c h i n v o l v e , f o r t h e s e c o n d h a r m o n i c , b o t h t h e a n h a r m o n i c i t y o f t h e l a t t i c e a n d d i s l o c a t i o n i n t e r a c t i o n o f c o m p a r a b l e m a g n i t u d e s . I n t h e c a s e o f t h e t h i r d h a r m o n i c t h e e f f e c t o f t h e l a t t i c e i n h a r m o n i c i t y i s much s m a l l e r t h a n t h a t d u e t o d i s l o c e t i o n s H e n c e t h e u s e o f l o n g i t u d i n a l w a v e s t o s t u d y t h e t h i r d h a r m o n i c a v o i d s t h e c o m p l i c a t i o n o f t h e l a t t i c e c o n t r i b c t i o n . The a d v a n t a g e o f ~ i s i n g s h e a r w a v e s i s t h a t i n some c a s e s t h e a n - h a r m o n i c i t y o f t h e l a t t i c e w i l l make n o c o n t r i b u t i o n t o t h e s e c o n d h a r m o n i c

( 5 ) .

G e d r o i t s e t a 1

( 5 . 6 )

o b s e r v e d s e c o n d h a r m o n i c s o f s h e a r w a v e s i n some s i n g l e c r y s t a l s a n d f o u n d t h a t t h e h a r m o n i c s w e r e s e n -

C5-390 JOURNAL DE PHYSIQUE

driving amplitude as that used in obtaining the results presented in

Fig.2.

-

( B ) m

amplitude dependence of the

harmonlc upon the fundamental amplitude.

Q

Theory predicts that the amplitudes

0.01

.

of the second and third harmonics should

be proportional to the square and cube

"0

;

2 l l

bias stress

of the fundamental amplitude respect-

ively (2). The experimental results are

Fig.3 :The changeAo(,

of the

in close agreement with this pre-

attenuation of the fundamental

wave with bias stress.

diction as seen in Fig.L. The foll-

owing empirical relations were

obtained

: -

a n d ~ ~ ~ ~ ~ : ' ~ ~ , w h e r e

A1, A2& A3are the amplitudes of the

fundamental ,second harmonic and

third harmonic respectively. The

deviation from the third power law

can be explained in terms of the

.

relation between the third harmonic

amplitude and the dislocation loop

length, vhich will be increased by

the fundamental wave driving-force,

because of the breakaway of the dis-

locations from weak pinning points.

The most probable czuse for the dev-

iation of the second harmonic would

F i g e L

The between

be the amplitude-dependent attenuat-

the deviations A A , and

AA,

of the second and Lthird shdar

ion of the fundamental wave, as

harmonic amplitudes respective-

ly with changes

P A ~

of the

discussed in

( 3 ) .

fundamental wave.

(C) The effect cif pre-stress upon the amplitude of the harmonics.

It was found that the pre-stress on

h

specimen, which was much

less than the stress required for plastic deformation, caused a marked

modification of the change of amplitude of the second shear harmonic

with the applied stress. The preliminary measurements are presented

in Fig.5. It can be noted that,after the specimen was subjected to a

6

6

CS-392 JOURNAL DE PHYSIQUE

Siriwatayakorn ( 8 ) has discussed the possibility of the residual bias

stress arising from pre-stressin!. c a u s i ~ z a finite value for

X

in the

relation (l), even though the lattice contribution is expected to be

zero. His calculation pointed out that t1:e dependence of the magnitude

and position of the second harmonic maximum on the loop length of the

dislocations was quite sensitive to the value of

X.

This behaviour of

second harmonic generation with respect to gre-stressing was also ob- served in the present experiments.

(D)

The effect of the fundamental wave drivinp amplitude on the

amplitude of the harmonics.

The effect of bias stress on the magnitude of the second harmonic should be affected by the driving amplitude of the fundamental wave because ultrasonic stress waves can cause un-pinning of dislocations from weak pinning points, as shown in the measurement of the third

harmonic for longitudinal waves

( 3 ) .

In Fig.6 the curves show the

change of the second harmonic with bias stress for different amplitudes of the fundamental.Again it was found that the second harmonic was considerably influenced by the driving amplitude.

Acknowledgement. The authors express their thanks to

Dr. Siriwatayakorn for his great help during the course of this work. References.

(1)

A.Hikata, B.B.Chick, C.Elbaum, J.App1.Phys.z (1965) 229,

(2) A.Hikata, C.Elbaum,Phys.Rev.a (1966)

469

(3) A.Hikata, F.A.Sewel1, C.Elbaum,Phys.Rev.l51

(1966)

4 4 2 ,

( 4 )

C.R.Scorey,

Acts

Metallurgica,g,(1970)

81.

(5) A.A.Gedroits, L.K.Zarembo, V.A.Krasilnikov,Soviet Phys.-Doklady,

(7)

S.Siriwatayahorn,W.G.B.Britton,R.W.B.Stephens, Proc. 1nst.Acoust.

April 1980,