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ltraso nic insp ect ion of m ater ia ls w ith

coa rse gra in an iso t rop ic s t ructures

I . N . E rm o l o v a n d B . P . P i l i n

D u r i n g t h e u l t ra s o n i c t e s ti n g o f c o ars e- g ra in e d a n i s o t ro p i c m a t e r i a ls s t ru c t u ra l n o i s e d u e

t o s c a t t e r i n g o f u l t ra s o u n d b y i n h o m o g e n e i t i e s c a n b e p ro d u c e d wh i c h m a y i n t e r f e re

wi t h t h e d e t e c t i o n o f f l a ws i n t h e m a t e r i a l . T h i s p a p e r re v i e ws t h e t h e o re t i c a l d e t e rm i n a -

t i o n o f s t ru c t u ra l n o i s e a n d d e t a i l s s o m e o f t h e m e t h o d s d e v e l o p e d t o i n c re a s e t h e

s igna l- to -no ise ra t io in u l t rason ic tes t ing o f coarse-gra ined m ater ia l . A l tho ug h the prob lem

o f s t ru c t u ra l n o i s e ha s n o t b e e n c o m p l e t e l y o v e rc o m e i t is s u g g e st e d t h a t t h e m e t h o d s

descr ibed here represent a s ign i f ican t advance towa rds i ts so lu t ion .

N o t a t i o n

V r

V m i n

Vn

D

f

X

C

n

f

Sa

t B

ds A

dSB

d r

fi

6s

6a

Z

T

k

N

p

a

F

/ o

Po

Pno

electr ic s ignal o f f law

minim um e lec t r ic s ignal s ensed by s e t

electric noise signal

average grain size

u l t ra sonic f requency

wave length

ul t ra sonic ve loc i ty

in tens i ty o f no i se

intens i ty of f law s ignal

a rea of p i ezoe lec t r i c e l emen t i e p rob e a rea )

d i s t ance f rom a po in t A of the probe to a po in t B

o f m e d i u m

e l e m e n t a r y a r e a a ro u n d p o i n t A

e l e m e n t a r y a r ea a r o u n d p o i n t B

w i d t h o f e le m e n t a r y v o l u m e a r o u n d p o i n t B

a t t e n u a t i o n f a c t o r

d i s s ipa tion fac tor

a b s o r p t i o n f a c t o r

a c o u s ti c i m p e d a n c e o f m e d i u m

ul t ra sonic pu l se dura t ion

w a ve n u m b e r

l ength o f nea r f i e ld

d i s t ance f rom prob e axi s to po in t B

probe rad ius

foca l d i s tance o f focus ing probe

amp l i tude o f emi t t ed acous t i c s ignal

roo t -mean-square of the s t ruc tura l no i s e ampl i tude

in the far f ie ld

n o i se a m p l i t u d e , d i r e c t p r o x i m i t y t o t h e p r o b e

The authors are both with the Ultrasonics Laboratory CNIIT MASH

M o s c o w P r o fe s s o r E r m o l o v is

international advisory editor for NDT

international for the Soviet Union.

P n F

K

, o f

ds

d

S f

qout

q n

A

l

lo

\ 2 r /

J l

W

noise ampl i tude in foca l p l an of focus ing probe

coef f i c i en t

acoust ic s ignal of f law

diame te r o f sphe r i ca l f law

diamete r o f cy l indr i ca l f law

area of d i s c - form f l aw

signal- to-noise ra t io a t the accumulator output

s ignal- to-noise ra t io of the accum ulato r input

w i d t h o f t h e m a i n l o b e o f d i r e c ti v i ty f u n c t i o n o f

p r o b e

accum ula t ion in t e rva l

s t ruc tura l no i s e co r re l a t ion in t e rva l

f u n c t i o n d e t e r m i n e d p a t t e r n o f p r o b e

F i r s t o rde r Bessel func t io n

coef f i c i en t

pow er of the e mi t t ed pu lses

In order to detect f laws in any materia ls us ing ul t rasonic

inspec t ion , two condi t ions m us t be me t : 1 the s igna l p ro-

d u c e d b y a f la w V f ) m u s t b e s t ro n g e r th a n t h e m i n i m u m

s ignal Vmin) s ensed by the amp l i f ie r o f the f l aw de tec tor ;

and the f law s ignal must be s t ronger than the noise s ignal

Vn). That is ,

Vf > Vmin

and Vf > Vn 1)

In the case o f u l t ra sonic inspec t ion o f coa rse -gra ined

mate r i a l s t he s econd condi t ion cannot usua l ly be me t be -

cause of the h igh l eve l o f s t ruc tura l no i s e . Thi s s t ruc tura l

no i se i s due to s ca t t e ring of u l t ra sound a t t he boun dar i e s o f

e l a st i cal ly inhom ogeneo us c rys t a l s o f the ma te r i a l . 2 S ignal s

produced by s t ruc tura l i nhomogene i t i e s , r each ing the

rece ive r a t t he s ame ins t an t , a re kno wn to in t e r fe re w i th one

NDT INT ERN ATI ONA L DECEMBER 1976 275

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a n o t h e r a n d , d e p e n d i n g o n t h e p h a s e s, c a n e it h e r a m p l i f y

o r a t t e n u a t e o n e a n o t h e r . A s a r e s u lt o f a r a n d o m p h a s e

r e l at i o n s h ip a n d d e p e n d i n g o n t h e p r o p e r t i e s a n d n u m b e r

of c r ys ta l l i t e s r e spons ib le f o r the s ca t t e r ing o f u l t r a sound ,

s t r uc tur a l no i se m a y take the f o r m o f ind iv idua l , c lea r ly

de f ined pu lses which can eas i ly be conf use d wi th f l aw sig-

na l s . I n add i t ion , the ene r gy of the use f u l s igna l p r oduced

by a f law d im in i shes due to d i s s ipa t ion of u l t r a sound , w i th

a r e su l tan t dec r ease in the s igna l -to - no ise r a t io .

S t r u c t u r al n o i s e h o l d s a u n iq u e p o s i t i o n a m o n g t h e w h o l e

va r ie ty o f no i se occur r ing in the cour se o f u l t r a son ic inspec -

t ion . I f the cha r ac te r i s t i c s o f m agne t ic , e lec t r i ca l and o the r

no ise d i f f e r s subs tan t ia l ly f r o m tho se o f the use f u l s ignal s

and a r e in no way as soc ia ted wi th them , the s t r uc tur a l no i se

c h a r a c te r i st i c s w i ll h a v e m u c h i n c o m m o n w i t h t h o s e o f t h e

f law signa ls . F or exam ple , the f r equ ency sp ec t r a o f a f law

s ignal and r eve r be r a t ion no ise a r e sim i la r in m a ny r e spec t s .

The in tens i ty o f s t r uc tur a l no i se va r ie s d i r ec t ly wi th the

a c o u s t i c p o w e r l ev el o f t h e e m i t t e d p u l s e . F l u c t u a t i o n s o f

the s t r uc tur a l no i se enve lope have a dur a t ion of p r ac t i ca l ly

the s am e or de r o f m ag ni tude a s tha t o f the s igna ls p r o duc ed

by a f l aw. All th i s m a te r ia l ly a f f ec t s the d i s c r im ina t ion of

f law signa ls aga ins t the bac kgr o und of s t r uc tur a l no i se .

This pape r p r esen t s a sur vey of s tud ies conce r ned wi th s t r uc -

t u r a l n o is e a n d e l a b o r a t i o n o f m e t h o d s d e v e l o p e d t o i n c r e as e

the s igna l - to - no ise r a t io in the u l t r a son ic inspec t ion of

m a te r ia l s wi th a coa r se - gr a ined an i so t r op ic s t r uc tur e .

eterm i nat i on o f s t ruc tura l no ise

Calcu la t ion of the m ean s t r uc tur a l no i se l eve l f o r the d i s tan t

f i e ld o f a p r obe has been done . 3 The ca lcu la t ion was pe r -

f o r m e d u s in g t h e m e t h o d o f d e t e r m i n i n g t h e v o l u m e r ev e r -

b e r a t i o n a t s e a . A u n i t a r y a p p r o a c h h a s b e e n p r o p o s e d 4 f o r

the de r iva t ion o f the s t r uc tur a l no i se equa t ion in the d i s tan t ,

nea r and in te r m edia te f i e lds o f a p r obe . I n deduc ing the

s t r uc tur a l no i se equa t ion , in bo th Ref e r ence 4 and in

R e f e r e n c e 3 , t h e f o l lo w i n g a s s u m p t i o n s w e r e m a d e : ( 1 ) t h e

dur a t ion of d i s s ipa t ion due to ind iv idua l d i s s ipa tor s ( c r ys -

ta l l it e s ) is equa l to tha t o f an em i t ted pu l se , ie d i s s ipa t ion

f r om an ind iv idua l d i s s ipa tor s t a r t s a t the ins tan t o f a r r iva l

the r e o f a p r ob in g pu lse and ends wi th the pu l se ; ( 2 ) d i ss ipa -

t ion i s i so t r op ic in al l d i r ec t ions ; ( 3 ) the in tens i ty o f the

o

x x x

x x

I

I I

O I 2 3

N / 2

F i g . 1 S t r u c t u r a l

n o i se l ev e l a s a f u n c t i o n o f t h e d i s t a n c e f r o m t h e

p r o b e . N o t a t i o n a s f o l l o w s : s o l i d l i n e re p re s e nt s t h e o r e t i c a l p r e d i c -

t i o n ; x x x x x x e x p e r i m e n t a l p e a r l i t i c s t e e l , f = 4 M H z , 2 a = 2 4 r a m ;

o o o o o o e x p e r i m e n t a l a u s t e n i t i c s t e e l , f = 2 . 5 M H z , 2 a = 2 4 r a m

sound d i s s ipa ted f r om an e lem enta r y vo lum e va r ie s d i r ec t ly

w i t h t h e v o l u m e i n q u e s t i o n , i n t e n s it y o f t h e i n c id e n t s o u n d

and d i s s ipa t ion f ac to r , the l a t t e r be ing dependent on ly on

t h e p r o p e r t i e s o f t h e m e d i u m . T h u s , i n t h e p r o p o s e d s o l u -

t i o n b e l o w , n o a c c o u n t i s t a k e n o f t h e s e c o n d a r y d i s s ip a t i o n

of u l t r a son ic waves which have a l r eady been d i s s ipa ted once

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

w a v e m o d e t r a n s f o r m a t i o n . S u c h a p p r o x i m a t i o n s a r e a c c e p t-

able on ly in the case of inspe ct ion o_f re la t ively small-grain

m ate r ia l s wi th an ave r age gr a in s ize D w hich i s m uc h le s s

than the u l t r a son ic wave leng th .

The exp r es s ion of in tens i ty o f s t r uc tur a l no i se a t an y d i s-

t ance r f r om the p r obe , de r ived in Ref e r ence 4 , has the

f o l lo w i n g f o r m :

C T

r

P o6sX2 q-

- ( e -46 r dr

In 47rSa 2 z

r

f l e i kr A B 4

a . . . . ~ d g t} dSB

r = c o I I s t

Sa

2 )

The expr es s ion in squa r e b r acke t s in Equa t ion ( 2 ) i s a d im en-

s ion les s quan t i ty cha r ac te r iz ing the son ic f i e ld o f the p r obe .

As is shown in R ef e r ences 5 and 26 , th i s quan t i ty i s a f unc -

t i o n o f t h e d i m e n s i o n l e ss p a r a m e t e r s r / N which is a ra t io

b e t w e e n t h e d i s t a n ce t o p o i n t B a lo n g t h e p r o b e a x i s a n d

t h e l e n g t h o f t h e n e a r fi e l d o f t h e p r o b e , a n d

p/a

which is a

r a t io b e t w e e n t h e d i s t a n c e f r o m t h e p r o b e a x i s t o p o i n t B

and the p r obe r ad ius .

S ince the ca lcu la t ion o f the s t r uc tur a l no i se l eve l wi th the

a id o f Equ a t ion ( 2 ) is d i f f icu l t , the pa r t i cu la r cases o f de te r -

m in ing the m agni tude of the s t r uc tur a l no i se in the d i s tan t

and n ea r f i e lds o f the p r o be wi ll be d i s cus sed .

T h e r o o t - m e a n - s q u a r e v a l u e o f t h e s t r u c t u r a l n o i s e a m p l i t u d e

in the dis tan t f ie ld (Pn) is given as :

p . P o , ~ / T ~ - ~ e_ 2~ ~

= 2 7 ~ / ~ ( 3)

and th i s conf or m s to the expr es s ion de r ived in Ref e r ence 3 .

I n t h e n e a r f i el d , in t h e i n t e r m e d i a t e p r o x i m i t y o f th e p r o b e ,

Pno Po X ,~ 8 ~ r e - 2~r

= 2 ~ / - ~ a ( 4)

I n t h e f o c a l p l an e o f t h e f o c u s i n g p r o b e ,

P n F e o ,t ~ s C ~ e - 2 8 F

= 2 - F ~ / - - ~ n 5 )

F ig . 1 shows the theor e t i ca l l eve l o f s t r uc tur a l no i se a s a

f u n c t i o n o f t h e d i s t a n c e f r o m t h e p r o b e r e la t iv e t o t h e

leng th o f the nea r zone of the p r obe . Also ind ica ted in F ig . 1

a r e e x p e r i m e n t a l d a t a o b t a i n e d f r o m m e a s u r e m e n t s o f t h e

s t r uc tur a l no i se l eve l , which cor r obor a te the theor e t i ca l

2 7 6 N D T I N T E R N A T I O N A L . D E C E M B E R 1 97 6

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c u r v e w i t h i n a c c e p t a b l e l i m i ts o f e x p e r i m e n t a l e r r o r . E x p e r i -

m e n t s h a v e a ls o s h o w n t h a t w h e n u l t r a so u n d i s e m i t t e d i n t o

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

t h e m e d i u m b e i n g i n v e s ti g a t e d , t h e s t r u c t u r a l n o i s e l ev e l di f-

f e rs f r o m t h e d e t e r m i n e d t h e o r e t i c a l r e la t i o n s h i p - E q u a t i o n

( 2 ) - a nd , i n t he d i s t a n t f i e l d , i t d i m i n i s he s w i t h d i s t a nc e r

p r o p o r t i o n a l l y w i t h

r - 1 / 3

t o

r - 2 : 3

a n d n o t r - t a s w o u l d

b e i n f e r r e d f r o m E q u a t i o n ( 3 ) . T h e s a m e e f f e c t i s p r o d u c e d

b y s e c o n d a r y r e v e r b e ra t io n , w h i c h b e c o m e s m o r e m a n i f e s t

a s t he r a t i o X / D de c r e a s e s .

S t r u c t u r a l n o i s e a n d f l a w s i g n a ls

T h e a n a l y t i c a l r e la t i o n s h i p b e t w e e n s t r u c t u r a l n o i s e a n d s i g-

n a l s p r o d u c e d b y v a r i o u s f l a w s , a c c o r d i n g t O t h e r e s u lt s

d i s c lo s e d i n R e f e r e n c e s 3 , 6 , 7 a n d 2 6 , c a n b e e x p r e s s e d a s

i n Ta b l e 1 . A s c a n be s e e n , i f a f l a w is in t he d i s t a n t f i e l d

t h e p r o b e a r e a s h o u l d b e i n c r e a s e d t o e n h a n c e t h e s i g n a l - t o -

no i s e r a t i o : i n t h i s w a y i t s d i r e c t i v i t y i s i m pr ove d ( s e e F i gs .

2 a a n d 2 b ) , b u t , w h e n a f l a w i s d e t e c t e d i n t h e n e a r z o n e ,

t h e p r o b e a r e a s h o u l d b e d e c r e a s e d ( F i g . 2 c ) . I n p r a c t i c a l

t e r m s t h i s m e a n s t h a t t h e d e t e c t i o n o f f l aw s a g a in s t a b a c k -

g r o u n d o f s tr u c t u r a l n o i s e i n c re a s e s w i t h t h e r a t i o o f t h e

r e f l e c ti n g s u r f a c e o f a f l a w t o t h e a r e a o f m e t a l c r y s t a l l it e s

w h i c h a r e e x p o s e d t o u l t r a s o u n d a n d a r e r e s p o n s i b l e f o r t h e

s t r uc t u r a l no i s e . Fu r t he r i nc r e a s e s i n t h i s r a t i o , i n t he ne a r

z o n e , a r e p o ss i b le i f th e u l t r a s o n i c b e a m is f o c u s e d b y m e a n s

o f f o c u s i n g p r o b e s ( F i g . 2 d ) 8 .

I m p r o v i n g t h e s i g n a l - t o - n o i s e

I t c a n a l so b e s e en f r o m T a b l e 1 t h a t t h e s h o r t e r t h e d u r a -

t i o n o f t h e p r o b i n g p u l s e , t h e b e t t e r t h e c o n d i t i o n s f o r d i s-

c r i m i n a t i n g t h e f l aw s i g n al a g a i n st t h e n o i s e b a c k g r o u n d ; ie

t he s i gna l - t o - no i s e r a t i o i s h i ghe r . A s c a n be i n f e r r e d f r om t he

a bov e t he s i gna l - to - no i s e r a t i o c a n be i nc r e a s e d i f t he vo l um e

o f t h e s p a c e c o n f i n i n g t h e u l t r a s o n i c p u l s e a t t h e s it e o f a

f l a w i s r e duc e d .

r f

o) S > r X

L

Fig. 2

e l a t i o n s h i p b e t w e e n a m p l i t u d e s o f f l a w si g n a l s

(Vf) versus

t hat o f s t ruc tura l no ise (Vn) : a = f law i n t h e d i s t a n t z o n e ;

b =

i m p r o v e m e n t i n t h e d i r e c t i v i tv

pa t t e rn t h rough

e n l a r g e m e n t o f

t h e p r o be s ; c = f l a w i n t h e n e a r z o n e ; d = f l a w i n t h e fo c a l p l a n e o f

a fo cu s in g p r o b e

T o d e t e r m i n e t h e e f f e c t o f f r e q u e n c y o n t h e s i g n a l- t o -n o i s e

r a t io , t h e f r e q u e n c y d e p e n d e n c e o f th e d i s s i p a t io n f a c t o r 6s

m u s t b e t a k e n i n t o a c c o u n t . A s is k n o w n , 9 1 6 s i s p r o p o r -

t i o n a l t o f n , w h e r e , d e p e n d i n g o n t h e r e l a ti o n s h i p

X / D n

m a y v a r y f r o m 2 t o 4 . T a b l e 1 s u g g e s t s t h a t d e p e n d i n g o n

t h e v a l u e o f n , t h e s i z e o f t h e r e f l e c t o r a n d p r o b e f ie l d in

w h i c h t he r e f l e c t o r i s l oc a t e d , t he s i gna l - t o - no i s e r a t i o m a y

i n c r ea s e o r d e c r e a s e a s t h e f r e q u e n c y i n c re a s e s. A c c o r d i n g t o

a w e l l - k n o w n p r a c t i c a l ru l e , t h e g r e a t e r t h e t h i c k n e s s o f t h e

i t e m b e i n g i n v e s ti g a t e d a n d t h e d e g r e e o f u l t r a s o u n d a t t e n u a -

t i o n , t h e l o w e r s h o u l d b e t h e o s c i l l a ti n g f r e q u e n c y s e l e c te d .

T h i s r u le , h o w e v e r , h o l d s t r u e i f t h e f o r m e r c o n d i t i o n i s m e t

r a t he r t ha n t he l a t t e r .

T o s u m m a r i z e, t h e f o l l o w i n g re c o m m e n d a t i o n s c a n b e g iv e n

a s t o u l t r a s o n i c i n s p e c t i o n o f c o a r s e - g ra i n e d m a t e r i a ls :

h i g h l y d i r e c t i o n a l p r o b e s s h o u l d b e u s e d ;

t he u l t r a s on i c pu l s e s e le c t e d s hou l d be as s ho r t a s pos s i b l e ;

d e p e n d i n g o n t h e s i z e o f c r y s ta l l it e s in t h e m a t e r ia l b e i n g

i n v e s t i g a t e d , t h e u l t r a s o n i c f r e q u e n c y s h o u l d b e s e l e c t e d

s u c h a s t o e n s u r e m a x i m u m s i g n a l- t o -n o i s e r a ti o .

T a b l e 1 . A n a l y t i c a l r e l a t i o n s h i p b e t w e e n s t r u c t u r a l n o i s e a n d f l a w s i g n al s s e e a l s o R e f e r e n c e s 3 , 6 , 7 a n d 2 6 )

T y p e o f r e f le c t o r

R a t i o o f f l a w s i g n a l a m p l i t u d e t o R M S l e ve l o f s t r u c t u r a l n o i s e

i n t h e n e a r f i e l d i n t h e d i s t a n t f i e l d

r < N r > 3 N

P f K 2S f , , / / r P s 2S f .

D i sk w i t h

area S f

= T v g s a p o - X 2 r

S p h e r e w i t h d i a m e t e r d

I n f i n i t e c y l i n d e r w i t h d i a m e t e r d

P n -

2 ~ / 8 , c - rrSa P n - 2 ~ / ~ a

P f 4 d P f 1 A 2 ~ S d

P n X S c P o X

N D T I N T E R N A T I O N A L . D E C E M B E R 1 97 6 2 77

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Stat is tica l app roach

~ n o t h e r m e t h o d o f e n h a n c i n g t h e s i g n a l -t o - n o is e r a t io i s t h e

us e o f t he d i f f e r e nc e i n t he s t a t i s t i c a l c ha r a c t e r i s t i c s o f f l a w

s i gna l a nd s t r uc t u r a l no i s e . The ne e d t o u s e p r oba b i l i s t i c -

s t a t is t i c a l m e t ho ds o f de t e c t i n g a s i gnal i n the p r e s e nc e o f

no i s e a r is e s be c a us e o f the f a c t t ha t s t r uc t u r a l no i s e i s, i n

m a ny r e ps e c t s , s i m i l a r t o f l a w s i gna l s , a s f a r a s i t s e f f e c t on

t he r e c e i ve r i s c on c e r n e d . D e v i c e s ba s e d o n t he a na l ys i s o f

s t a t is t i c a l c ha r a c t e r i s t i c s o f s i gna ls a nd no i s e m a ke i t pos s i b le

( w i t h t he s i gna l - t o - no i s e r a t i o be i ng i nva r i a b l e a t t he i npu t o f

t he r e c e i v i ng c ha nne l ) e i t he r t o i nc r e a s e t h i s r a t i o a t t he

d e v ic e o u t p u t o r t o r a i se t h e p r o b a b i l i t y o f d e t e r m i n i n g t h e

p r e s e n c e o r a b s e n c e o f a fl a w s ig n a l a g a i n s t t h e b a c k g r o u n d

of no i s e : t h i s la t t e r l e a ds t o m o r e r e l i a b l e r e s u l t s.

A r e q u i si t e c o n d i t i o n f o r c a r r y i n g o u t s t a ti s ti c a l m e t h o d s o f

de t e c t i n g a f l a w s igna l i n t he p r e s e nc e o f s t r uc t u r a l no i s e i s

t h e a l lo w a n c e f o r s u c h c h a n g e s i n t h e a c o u s t i c f i e ld o f t h e

p r obe w he r e t he no i s e s i gna l s a r e non - c o r r e l a t e d , w h i l e t he

f l a w s i gna ls r e m a i n l a r ge l y c o r r e l a t e d . G i ve n t h i s , i t is pos s ib l e

t o pe r f o r m p r oba b i l i s t i c - s t a t i s t i c a l , c o r r e l a t i ve p r oc e s s i ng o f

t he r e c e i ve d f l a w s i gna l no i s e c om bi na t i on a nd t o d i s c r i m -

i n a te t h e u s e f u l si g na l f r o m t h is c o m b i n a t i o n J ~

M o v i n g p r o b e a c c u m u l a t io n ) m e t h o d

A s h a s a lr e a d y b e e n m e n t i o n e d , s t r u c t u r a l n o i s e o c c u r s a s a

r e s u l t o f e m i t t i ng u l t r a s on i c v i b r a t i on i n t o a s o l i d in w h i c h

t h e m u t u a l a r r a n g e m e n t a n d o r i e n t a t i o n o f d i s si p a ti n g e le -

m e n t s r e m a i n s i n v a r ia b l e . U n d e r i n v a ri a b le c o n d i t i o n s o f

e m i s s io n a n d r e c e p t i o n o f e l a st ic w a v e s ( th e p r o b e is s ta t i o n -

a r y w i t h r e s p e c t t o t h e i te m b e i n g in s p e c t e d a n d t h e p a r a -

m e t e r s o f t h e e m i t t e d p u l s e r e m a i n i n v a ri a b le f r o m e m i s s io n

t o e m i s s i o n ) , n o i s e c a n b e c o n s i d e r e d t o b e r a n d o m w i t h i n a

p u l s e - to - p u l s e i n te r v a l a n d c o m p l e t e l y c o r r e l a t e d i n o t h e r

i n t e r va ls ; t h i s r u l e s ou t t he po s s i b i l i t y o f p r oc e s s i ng s i gna ls

b e t w e e n s u c h i n te r v a ls . I n o r d e r t o m a k e u s e , d u ri n g p r o -

c e s s ing o f s i gnal s , o f t e c hn i que s e l a b o r a t e d f o r a na l ys i s o f

r a n d o m p r o c e s s e s , a p p r o p r i a t e m e t h o d s o f e s ta b l i sh i n g a

t i m e d e p e n d e n c e o f e c h o s i g n a l s a t d i f f e r e n t p e r i o d s o f

e m i s s i o n a n d r e c e p t i o n s h o u l d b e c h o s e n .

- f o t h is e nd , i t ha s be e n p r opo s e d r2 t ha t t he p r o be s h ou l d

b e m o v e d i n a c o n t i n u o u s , u n i f o r m m a n n e r w i t h r e s p e c t t o

t he i t e m be i ng i n s pe c t e d . I n t h i s c a s e , s t r uc t u r a l no i s e

r e c o r d e d d u r i n g e a c h p u l s e - t o - p u ls e i n t e rv a l m a y b e r e g a r d e d

a s r a ndom i n t i m e .

Theo ret ica l considerations

T h e e s s e n ce o f t h e p r o p o s e d m e t h o d o f i n s p e c t in g h i g h - n o is e

m a t e r i a l s 1~ i s a s f o l low s . I n t he c a s e o f c on t i nu ou s u n i f o r m

m o t i o n o f th e p r o b e , e c h o s i g n al s a r e a c c u m u l a t e d a s t h e

p r ob e c ove r s e qua l d i s t a nc e s w i t h i n s e ve r a l e m i s s i on -

r e c e p t i on c yc l e s . S i nc e t he a m pl i t ude o f f l a w e c ho s i gna l s i s

d e t e r m i n e d b y t h e d i r e c t i o n o f t h e p r o b e a n d t h e f l a w i ts e lf ,

i t w i l l v a r y a c c o r d i n g t o t h e m o t i o n o f t h e p r o b e , a n d , i n

t h e p r o c e s s o f a c c u m u l a t i o n , i t w il l m a n i f e s t i t s e l f a s a

r e gu l a r ( h i gh l y c o r r e l a t e d ) s i gna l . S t r uc t u r a l no i s e s i gna l s

e x h i b i t a r b i t r a r y , r a n d o m v a l u es ( i n s ig n i f i c a n t ly c o r r e l a t e d

s ig n a ls ) d u r i n g t h e m o v e m e n t o f p r o b e . T h e r e f o r e , i n a c c o r d -

a n c e w i t h t h e p r o b a b i l i t y t h e o r y , i n t h e a c a s e o f a c c u m u l a -

t i on o f s i gna l s w he r e t he r e i s a f l a w s i gna l , t he a c c um ul a t e d

s i gna l i s g r e a t e r t ha n t ha t a r i s i ng w he r e on l y s t r uc t u r a l no i s e

is p r e s e n t .

The ga i n i n t he i nc r e a s i ng s i gna l - to - no i s e r a t i o a t t he p r obe

ou t pu t ( qou t ) w i t h r e s pe c t t o t he s i gna l - t o - no i s e r a t i o a t t he

i npu t ( q i n ) w a s c a l c u l a t e d f o r a po i n t d e f e c t , i e a fl a w ha v i ng

a m a x i m u m s i z e ( d ) m u c h l e s s t h a n t h e w i d t h ( A ) o f t h e

m a i n l o b e o f t h e d i r e c ti o n a l f u n c t i o n o f th e p r o b e . T h i s

ga i n c a n be e xp r e s s e d a s f o l l ow s :

r

qou t = a k l o ' f \ 2 r } ( 6 )

qin

w h e r e r is th e d i s t a n c e f r o m t h e p r o b e t o t h e z o n e b e i n g

c h e c k e d ; a is th e r a d i u s o f t h e p r o b e p i e z o e l e c t r ic e l e m e n t ;

k i s t he w a ve nu m b e r ; I i s t he a c c um ul a t i o n i n t e r va l ; l o is

t he s t r uc t u r a l no i s e c o r r e l a t i on i n t e r va l ; f ( a k l / 2 r ) i s a func-

t i o n d e t e r m i n e d b y t h e d i r e c t iv i t y p a t t e r n o f t h e p r o b e a n d ,

i n t h e c a s e o f a d is k p r o b e , t a k e s t h e f o r m ( s h o w n i n F i g . 3 ):

f ( a k l l ~ k ( a k t l

= 2 , \ 2 r J . d ( a k l t

\ 2 r J f a k l k 2 r ] ( 6 )

0

2 r

A s c an b e s e e n f r o m t h e a n a l y s is o f E q u a t i o n ( 6 ) , a n o p t i-

m u m a c c u m u l a t i o n i n t e r v a l ( / o p t ) e x i s t s a t w h i c h m a x i m u m

ga i n i s a c h i e ve d . Th e i n t e r va l va l ue f o r d ~ A c o r r e s pon ds

t o t h e w i d t h A o f th e p r o b e d i r e c t i v i ty p a t t e r n a n d i s g i v en

as

r

/ o p t = 3 . 8 2 a 7 7 )

E q u a t i o n ( 7 ) s u gg e s ts t h a t t h e o p t i m u m a c c u m u l a t i o n i n t er -

va l i nc r e a s e s w i t h t he d i s t a nc e f r om t he p r obe . I n t he c a s e

2 .0

15

~ i.o

4--

0 .5

O I

l

o I 3 4

o k AL

2 r

F i g. 3 D i r e c t i v i t y p a t t e r n i n t e g r a t i o n f u n c t i o n i n t h e ca s e o f a

m o v e a b l e p r o b e

278 NDT INTERNATIONAL DECEMBER 1976

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of an op t im um accum ula t ion in te r va l , the ga in in the s igna l -

t o - n o is e r a t io d u e t o a c c u m u l a t i o n i s e q u a l to

qout = 0.78 - //7 ~- t (8)

q n ~/ 1o

I t c a n b e s ee n f r o m E q u a t i o n ( 8 ) t h a t t h e g a i n i n a c c u m u l a -

t i o n i s d e t e r m i n e d b y t h e r a t io o f t h e a c c u m u l a t i o n i n t e rv a l

to the s t r uc tur a l no i se cor r e la t ion in te r va l , the e f f i c iency of

accu m u la t ion o f s igna ls inc r easing wi th the d ep th o f the

l a y e r b e i n g i n v e s ti g a t ed : i e t h e e f f i c ie n c y o f a c c u m u l a t i o n

inc r eases p r ec i se ly when the condi t ions o f de tec t ing a f l aw

a g a in s t th e b a c k g r o u n d o f n oi s e b y c o n v e n t i o n a l m e t h o d s

of s e lec t ion de te r io r a te .

P r a c t i c a l t e s t i n g

T o c h e c k t h e t h e o r e t i c a l r e su l t s o f t h e p r o p o s e d m e t h o d o f

im pr oving the s ens i t iv i ty , a t e s t f l aw de tec tor was des igned

and bu i l t . I t was deve loped f o r check ing the shr ink r ings o f

t u r b o g e n e r a t o r s m a n u f a c t u r e d f r o m a u s t e n i ti c s t e el o f c o m -

p l e x c o m p o s i t i o n w i t h a n i s o t r o p i c s t r u c t u r e , t h e a v e ra g e

s ize o f the c r ys ta l l i t e s in the s t r uc tur e be ing 0 . 35 to 0 . 17 r am .

T h e v a l u e o f l o a p p e a r e d t o b e e q u a l t o 2 m m a t a d e p t h o f

7 0 m m f r o m t h e s u r f a c e . L a b o r a t o r y a n d p r o d u c t i o n t e s t s

o f t h e f l aw d e t e c t o r h a v e p r o v e d t h e e f f i c i e n c y a n d f e a s i b il i ty

of accum ula t ing s ignal s in the p r oces s o f s cann ing dur ing

u l t r a son ic inspec t ion of coa r se - gr a ined m a te r ia l s .

The r e su l ts o f expe r im e nts and f u r the r theor e t i ca l s tud ies ~3

h a v e s h o w n a p a r t i c u la r l y h i g h e f f i c ie n c y o f t h e a c c u m u l a -

t io n m e t h o d i n d e te c t i n g e l o n g a t e d r a th e r t h a n p o i n t d e f e c t s

n a m e l y c r a c k s, p o r e c h a in s a n d o t h e r d e f e c t s e x t e n d i n g i n

t h e d i r e c t io n o f m o v e m e n t o f t h e p r o b e . W i th e l o n g a t e d

d e f e c t s , th e g a i n in s e n s i ti v i ty w i t h a n o p t i m u m a c c u m u l a t i o n

in te r va l inc reases wi th the l eng th o f a de f ec t .

I n o r d e r t o u s e t h e a c c u m u l a t i o n m e t h o d w i t h a m o v a b l e

p r o b e , a n u m b e r o f s o l u ti o n s h a v e b e e n p r o p o s e d ; i n p a rt i c -

u la r a f law d e tec to r w i th A- scan , ~4 a f l aw de te c to r w i th

B- scan i s and a f l aw de tec to r f o r d i f f e r en t ia l l ay e r - by- laye r

che cks . 16

th i s l aye r aga ins t the backgr ound of s t r uc tur a l no i se : the

do ts cor r e sponding to the f l aw a r e m uch wide r in the d i r ec -

t i o n o f m o v e m e n t o f th e p r o b e t h a n t h o s e c o r r e s p o n d i n g t o

s t r uc tur a l no i se ( s ee F ig . 4 ) . The ope r a to r com par es , on the

d i sp lay sc r een , the f l aw signa ls w i th no i se and , by w ay o f

visual cor rela t ion, discr iminates the f law s ignal . ( In this case ,

t h e o p e r a t o r ' s o w n m e m o r y p e r f o r m s th e f u n c t i o n o f a

s to r age dev ice . )

T e s t s i n d i c a te t h a t t h e m e t h o d o f s t at i st i c al a c c u m u l a t i o n o f

e c h o s i gn al s d u ri n g s c an n i n g b y t h e p r o b e a n d t h e m e t h o d o f

v i sua l de tec t io n o f fl aws aga ins t the backg r ound of no i se

h a v e p r a c ti c a l ly t h e s a m e s e n s it i v it y a n d c o m p l e m e n t e a c h

o t h e r w e ll . T h e a c c u m u l a t i o n m e t h o d p e r m i t s o n - t h e - s p o t

checks and lends i t s e l f eas i ly to au to m a t ion , whi le the v i sua l

d e t e c t i o n m e t h o d a l lo w s m o r e p r e ci s e d e t e r m i n a t i o n o f th e

loca t ion of the f l aw and , in som e cases, it s si ze and conf igu-

r a t ion .

F r e q u e n c y v a r i a t i o n

A n o t h e r p r o m i s i n g w a y t o i m p r o v e t h e s e n s it i v it y o f u l tr a -

son ic inspec t ion of h igh- no ise m a te r ia l s i s to va r y the

V i s u a l f l a w d e t e c t i o n

The m e tho d o f s t a t i s t i ca l accu m u la t ion o f s ignal s in the

pr oces s o f s cann ing has the d i sadva n tage tha t i t is im po ss ib le

to loca te a f l aw pr ec i se ly ; on ly the a r ea w her e the f l aw is

l o c a t e d c a n b e d e f i n e d . A n o t h e r d i s a d v an t a g e is t h a t w h e n

s ignal s a r e accum ula ted , the r e i s a los s o f in f o r m a t ion on

t h e m a x i m u m v a l u e o f t h e a m p l i t u d e o f t h e e c h o s i g na l a n d

i t s v a r i at i o n in t h e c o u r s e o f m o v e m e n t o n t h e p r o b e .

Never the le s s i t i s kno wn ~7 tha t the m agni tu de of the ec ho

s ignal can be used f o r de te r m in ing th e s ize o f the f l aw, and ,

by s tudy ing the way in which the echo s igna l va r ie s ( depen-

d i n g o n t h e p r o b e p o s i t i o n r e l at iv e t o t h e f l a w ) t h e t y p e o f

t h e f l a w c a n b e d e t e r m i n e d .

A m e t h o d o f v i su a l f l a w d e t e c t i o n i n t h e p r e s e n c e o f s t r u c -

tu r a l no i se has been pr op osed , 1~ ,19 w hich i s fr ee o f the

a b o v e d i s a d v a n ta g e s an d w h i c h h a s f o u n d a p p l i c a t i o n f o r

u l t r a son ic inspec t io n of co a r se - gr a in m a te r ia l s . 12

T h e p r o p o s e d m e t h o d c o n s i st s o f v i s u al a n a ly s i s o f e c h o s i g-

na l s f r om a l aye r s e lec ted f o r check . Th ese s igna ls a r e d i s-

p l a y e d o n t h e s c r e e n o f a l o n g -p e r s is t e n c e c a t h o d e - r a y t u b e .

T h e i m a g e o n t h e s c r e e n p e r m i t s e a s y d e t e c t i o n o f a f l a w in

Fig . 4 Osci llograms of echo signals from the layer being checked:

a = s t ru c tu r al n o ise f r o m a d ep th o f 130 m m f r eq u en cy o f 2 . 5 M H z ;

b = h o l e w i th a f l a t b o t to m 6 mm i n d i ameter a t a d ep th o f 7 0 r am

fr eq u en cy o f 1 . 8 M H z ; c = h o l e w i th a f l a t b o t to m 3 m m i n d i a -

meter a t a d ep th o f 130 r am f r eq u en cy o f 2 . 5 M H z ; d = n atu r a l

f issur e 4 m m l o ng a t a d ep th o f 75 r am; f r eq u en cy o f 2 . 5 M H z an gl e

probe 50 ; e = natural f issure 3.5 m m long at a depth o f 75 ram;

f r eq u en cy o f 2 . 5 M H z ; an g le p r o b e 50

N D T I N T E R N A T I O N A L D E C EM B E R 1 97 6 2 79

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f r e q u e n c y o f p r o b i n g p u ls e s w h e n t h e f r e q u e n c y o f u lt ra -

s o n i c v i b ra t i o n o f o n e e m i t t e d p u l s e d i f fe r s f r o m t h a t o f

a no t he r pu l s e b y a c e r t a i n va l ue . 2 Th i s t e c hn i que i s a l s o

ba s e d o n t he d i f f e r e n c e i n t he s t a t is t i c a l c ha r a c t e r i s t i c s o f a

f l a w a n d t h e s t r u c t u r a l n o i s e .

T h i s f r e q u e n c y v a r i a t i o n w i l l b r i n g a b o u t a c o n s i d e r a b l e

c h a n g e i n t h e s t r u c t u r a l n o i s e a m p l i t u d e . A t t h e s a m e t i m e ,

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

t i on t o a l e s s e r de g r e e , w h i c h m a ke s i t pos s i b l e s t a t i s t i c a l l y

t o d i s c e rn i t a g a i n s t t h e b a c k g r o u n d o f v a r y i n g s ig n a ls . U s i n g

t h e p r i n c i p l e s o f f r e q u e n c y v a r i a t i o n , a f l a w d e t e c t o r h a s

b e e n d e v e l o p e d w h i c h e m i ts f r e q u e n c y - m o d u l a t e d p u l s es

i n t o t h e i t e m b e i n g i n s p e c t e d a n d p r o c e s s e s t h e m u p o n

r e c e p t i o n i n a n o p t i m a l m a n n e r . 21

I n a l a t e r s t u d y 22 a t h e o r e t i c a l d e p e n d e n c e o f t h e s t r u c t u r a l

n o i s e c o r r e l a t i o n f u n c t i o n o n t h e e l e c t r o - a c o u s t i c c h a n n e l

p a r a m e t e r s w a s d e v i s e d ; i n p a r t i c u l a r , i t s d e p e n d e n c e o n t h e

f r e q u e n c y a n d d u r a t i o n o f u l t r a s o n i c p r o b i n g p u l se s . T h e

i nc r e a s e i n t he s i gna l - t o - no i s e r a t i o w a s e s t i m a t e d qua n t i -

t a t iv e l y i n t h e c a s e o f a c c u m u l a t i o n o f e c h o s i g n al s w h o s e

f r e q u e n c y c h a n g e s f r o m e m i s s i o n t o e m i s s i o n .

Mu lt i f requency test ing

P a r ti c u la r c a s e s o f f r e q u e n c y m o d u l a t i o n , a i m e d a t e n h a n c -

i n g t h e s i g n a l- t o -n o i s e r a t io i n u l t r a s o n i c i n s p e c t i o n o f

c o a r s e - g ra i n e d m a t e r ia l s w i t h o b v i o u s e l a s ti c a n i s o t r o p y a n d

l a m i n a t io n , a r e t w o - a n d t h r e e - f re q u e n c y 2 3 z 4 m e t h o d s o f

i n s p e c t i o n w i t h a m p l i t u d e s e l e c t i o n . T h e d e t e c t i o n o f a f l a w

is i n d i c a t e d b y t h e c o i n c i d e n c e o f t h e c o - o r d i n a t e s o f p u l s e

r e f l e c t o r s w i t h t w o o r t h r e e f r e q u e n c i e s b e i n g u s e d , r e s p e c -

t i v e l y . T h e t e s t i n R e f e r e n c e 2 4 i n d i c a t e d t h a t i m m u n i t y t o

n o i s e d u r i n g i n s p e c t i o n o f c o a r s e - g r a in e d m a t e r i a l s c a n b e

s u b s t a n t i a l l y i m p r o v e d ( p a r t i c u l a r l y s o f o r a u s t e n i t i c w e l d

j o i n t s ) p r o v i d e d t h e p r e s e n c e o f a f a u l t is a s c e r t a i n e d f r o m

t h e r e s u l t s o f i n s p e c t i o n o n s e v er a l f re q u e n c i e s .

T h e m u l t i f r e q u e n c y m e t h o d o f i n s p e c t io n d o e s n o t r e q u i r e

t h e u s e o f s p ec i a l e q u i p m e n t a n d c a n e a s i ly b e p e r f o r m e d

w i t h t h e a i d o f s t a n d a r d u l t r a s o n i c f l a w d e t e c t o r s . O n l y o n e

c o n d i t i o n s h o u l d b e m e t , n a m e l y t h a t o n a l l f r e q u e n c i e s t h e

d i r e c t iv i t y p a t t e r n s o f t h e p r o b e s m u s t b e o f t h e s a m e w i d t h .

V a r i a t i o n o f p r o b e p a t t e r n w i d t h

Y e t a n o t h e r p r o m i s in g m e t h o d o f o b v i a ti n g t h e e f f e c t o f

s t r u c t u r a l n o i s e i s th e o n e i n w h i c h u s e i s m a d e o f p e r i o d i c a l

v a r i a ti o n s o f t h e p r o b e d i r e c t i v i ty p a t t e r n w i d t h , t h e u l t ra -

s o n i c p o w e r b e i n g k e p t c o n s t a n t . 2 s A v a r i a t io n i n t h e d i r e c t -

i v i ty p a t t e r n i s a t t a i n e d b y v a r y i n g t h e p r o b e d i a m e t e r . T h i s

m e t h o d i s b a s e d o n t h e f o l l o w i n g th e o r e t i c a l c o n s i d e r a t i o n s .

A s i s w e l l k n o w n , t h e a v e r a g e in t e n s i t y o f s t r u c t u r a l n o i s e

( I n ) i n th e d i s t a n t f i e ld o f t h e p r o b e i s i n d e p e n d e n t o f t h e

w i d t h o f i ts d i r e c t iv i t y p a t t e r n i f t h e p o w e r o f t h e e m i t t e d

pu l s e s ( W) i s i nva r i a b l e . Thus

W6s cr rl e 46r ( 9 )

In - 47r r 2

w h e r e r l i s d e t e r m i n e d b y t h e s h a p e o f th e p r o b e a n d i n t h e

c a s e o f a s phe r i c a l p r o be ha s a va l ue o f . Th e s i gna l

p r o d u c e d b y a f l a w ( I f ) v a r i e s d i r e c t l y w i t h t h e p r o b e a r e a

S ~ ) :

WSaSf2 e -46r ( 1 0 )

If -- X4 r4

T h e r e f o r e , i f t h e p r o b e a r e a is p e r io d i c a l l y v a r i e d w i t h I h e

e m i s s i on pow e r ke p t c ons t a n t , t he a ve r a ge no i s e l e ve l w i l l

a l s o be c ons t a n t , a nd t he f l a w s i gna l w i l l be a m pl i t ude -

m o d u l a t e d w i t h t h e f r e q u e n c y o f p r o b e a r e a v a r ia t i o n . B y

pa s s i ng t he r e c e i ve d e c ho s i gna l s t h r ough a n a de qua t e f i l t e r ,

t h e f l a w s ig n a l c a n b e e a si ly d i s c r im i n a t e d f r o m a b a c k g r o u n d

o f s t ru c t u r a l n o i s e . C a l c u l a t io n s i n d i c a t e t h a t t h e m e t h o d o f

m o d u l a t i o n o f t h e d i r e c t i v i ty p a t t e r n p e r m i t s a s u b s t a n ti a l

i m p r o v e m e n t i n t h e s e n s it i v it y o f u l tr a s o n i c i n s p e c t i o n o f

c oa r s e - g r a i n m a t e r i a l s , e ns u r i ng a s e ve r a l - f o l d i nc r e a s e i n t he

s ignal - to-noise ra t io .

Conclus ions

F r o m t h e w o r k d e s c r i b ed a b o v e it a p p e a rs t h a t t h e m e t h o d

o f s e l ec t io n o f o p t i m u m p a r a m e t e r s o f t h e e l e c t ro - a c o u s ti c

c h a n n e l a n d m e t h o d s m a k i n g u s e o f t h e p r o b a b i li s t ic -

s t a t i s ti c a l c ha r a c t e r i s t i c s o f f l a w s igna l s a nd s t r uc t u r a l no i s e

c o n t r i b u t e t o a c o n s i d e ra b l e d e g r e e t o s o lv i n g t h e p r o b l e m

o f u l t r a s o n i c i n s p e c t i o n o f c o a r s e - g r a in e d a n i s o t r o p i c

m a t e r ia l s . T h i s p r o b l e m h a s i n f a c t a t tr a c t e d t h e a t t e n t i o n

o f m a n y i n v e s t i g a to r s , a m e a s u r e o f it s i m p o r t a n c e a n d

u r g e n c y . T h e p r a c t i c a l r e s u l t s o b t a i n e d s o f a r h o l d o u t a

h o p e t h a t t h e p r o b l e m w i ll b e s u c c e ss f u l ly s o l v e d .

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