From B. Harris—Maddox

LETTERS TO THE EDITOR

ULTRASONIC

ENDARTERECTOMY

From Mr. G. D. Smellie In the hope of receiving suggestions about technique and apparatus I should like to outline a series of tests recently undertaken here. The commonest cause of defective circulation in the extremities is arteriosclerosis of the arteries of the lower limbs. The arteries become progressively obstructed by the deposition of a t h e r o m a - - a fibro fatty substance--on their inner walls. The presence of the atheroma encourages clotting of the blood within the artery, thereby completing the obstruction of the vessel. In the larger arteries the atheroma and clot can be cored out (endarterectomy) or by-passed with a graft. If the smaller arteries are blocked, only palliative surgery or amputation can be offered to the patient. The flow through the blocked vessels cannot be restored. It was hoped that ultrasound would emulsify the atheromatus material and leave the strong fibrous coat of the artery intact. Ultrasound, being conducted well in fluid, might have proved a way of "re-boring" arteries too small to be treated by endarterectomy. There would of course be many problems to be overcome, such as the emulsification of blood with lysis of the cells, to mention but one. On the technical side, too, the available transducers are too large to negotiate small blood vessels and are, moreover, of rigid construction. To test the value of the project, post-mortem specimens of arteries affected by various degrees of atheroma were irradiated with ultrasound at frequencies of 20 kc/s and 1 Mc/s using piezoelectric crystals, and also at 13 kc/s using an industrial transducer employing magnetostriction. The electrical powers used at the three frequencies were 60 W, 50 W and up to 100 W respectively. Irradiation was carried out in all experiments for at least half an hour. With the two higher frequencies the only discernible macroscopic effect was one of coagulation, partly due to heat. With the lowest frequency used there was no obvious effect whatever. All irradiation was carried out in water. It is concluded that in the frequencies studied, which include those for industrial cleaning, ultrasound has no effect on atheroma as seen in the cadaver. l am indebted to Dr. J. M. A. Lenihan and his staff at the Regional

Physics Department, Glasgow, for their interest and co-operation and for providing the ultrasonic generators. G. D. SMELLIE Victoria Infirmary, Glasgow C.4., Scotland

TRANSMITTED

ECHO

AMPLITUDE

From Dr. J. Krautkramer In his paper "'The ultrasonic testing of boost motors" (Ultrasonics, April-June 1964, p. 62) Mr. Harris-Maddox calculates the amplitude of an echo penetrating from water into steel and back. The result is wrong because of an erroneous conclusion from Equation 1. If 0.94 of the incoming amplitude is being reflected, which is perfectly right, the penetrating amplitude is not 0'06, which is the difference between 1 and 0.94. The right value is 1.94) It seems a paradox that an amplitude of more than 100~o of the incoming one is penetrating into the steel, but it must be kept in mind that we are calculating here with amplitudes (sound pressure or particle shift) and not energies. In calculations with energy (intensity), of course the sum of the transmitted and reflected waves equals the incoming one. In this case the square of Equation 1 would have to be used. This approach is a bit clearer when dealing with media of different impedances, but because the echo amplitude on the flaw detector is proportional to the pulse amplitude and not the pulse energy, at the end of such a calculation we have to go back to the square root to get the echo height on the screen. Therefore, the amplitude in the water after reflection at the steel-topropellant boundary is not 0.87 × (0-06) ~ × A (which is only 0.3 ~o of A), but 0.87 × 1.94 × 0.06 A (about 10% of A). In the case of non-bonding we have 0.87 1 times more, i.e. 12.5%, as indicated. J. KRAUTKRAMER J. u. H. Krautkramer (5) Koln-Klettenberg, Germany 1. KRAUTKRAMER,J. and H., "Werkstoffprufung mit Ultraschall," Springer (1961) p.23.

From B. Harris-Maddox I would like to thank Dr. Krautkramer for drawing my attention to an arithmetical slip on p.62 of my paper. Also the correct value for the steel impedance

is 46 g/cm~/s and the ratio of reflected and incident amplitude for the propellant interface is 0.88. I agree that the pressure amplitude in the steel is 1.94 and not 0.06. However, the pressure amplitude is not the same as the particle velocity or particle displacement amplitudes as Dr. Krautkramer implies. In fact the particle velocity amplitude in the steel is 0.06. The argument is best resolved by considering the essential boundary conditions that must be satisfied. For simplicity we take a plane progressive wave incident normally on the interface between two fluids of densities Pl, P2 and velocities Cl, c 2. The boundary conditions are: 1. The pressure variation 8P must be the same on both sides of the boundary. If the subscripts i, r and t refer to the incident, reflected and transmitted waves then : ~Pi + ~Pr = 8P . . . . . . . . . . . . . (1) dy

2. The particle velocity dt- must also be continuous:

dy,. dt

dy~ dy t dt - dt . . . . . . . . . . . .

(2)

The minus sign is inserted for the reversed direction of the reflected wave. The pressure variation may be expressed in terms of the particle velocity by considering a tube of unit cross-section in a fluid medium through which plane progressive waves are travelling. The particle displacement y is given by y = a sin n (t -- x/c) in which a is the maximum amplitude, t is the time and x is the position along the x-axis. At a fixed instant t the displacement of planes originally at x and x + &~ will be y and

The volume of the fluid between these planes is therefore changed from ~x to

('x

~ dY dx " r )

The ratio of the increment in volume to the original volume is therefore dy dx" The bulk modulus k is defined as

~p / dy • ~ - and so ~P = / dx

k dy" dx dy = _ PCdx

Since

c=~/k,sp p

But

dt = na cos n (t

and

-

dy

dy

a

dx

e

x/c)

.

n (t

sm

--

x/c).

Therefore

dy dt

and thus

dy 8P = pc dt . . . . . . . . . . . .

--

£

dy dx

ULTRASONICS~July-September 1964

(3)

161

dy

By s u b s t i t u t i o n for dt in E q u a t i o n 2 8P~

8P,

~,P,

PlCI

PIC1

P2C2

..........

(4)

From Equations I and 4

8P,.

p2C2

SP,

P2c,, + P~C'l ..

.(5)

p,zc,z

..

.(6)

.

.(7)

5P,

2

6P,

p2C2

plCl

i plCl

Solving for the particle velocities:

dy, / d y i

p2c,z

plc,

dt / d t

p2C2

i pl('l

"

2 Ptq p.,c., ptcl

..

( (~pi)2

i

dy,/dy, dt / dt

.(8)

If a wave of unit a m p l i t u d e is i n c i d e n t in the water, the reflected pressure a n d particle velocity a m p l i t u d e s are n u m e r i cally identical b u t in the steel the pressure a m p l i t u d e , with the i m p e d a n c e of w a t e r t a k e n as 1.4 10 s g/cruZ/s, is 1.94 a n d the particle velocity a m p l i t u d e is 0.06. It is the pressure anaplitude t h a t we m e a s u r e since the piezoelectric crystal is a pressure receiver. If the i m p e d a n c e o f the plastics p r o p e l l a n t is 3 l0 s g/cruZ/s, then f r o m E q u a t i o n 5 the reflected a m p l i t u d e is ( I .94) (0-88). At the s t e e l - t o - w a t e r interface E q u a tion 6 m u s t be used but it m u s t n o w be written as E q u a t i o n 8 since t r a n s m i s s i o n is f r o m m e d i u m I to m e d i u m 2. T h e pressure a m p l i t u d e in the w a t e r is (I.94) (0.88) (0.66) a n d this value is also o b t a i n e d for the particle velocity. If the p r o p e l l a n t is s e p a r a t e d , the reflection is total a n d the a m p l i t u d e b e c o m e s (1'94) (0-66), which is 0.88 1 times greater. I n d e e d this result is o b t a i n e d quite irrespective o f a n y a s s u m p t i o n s m a d e for t h e water-to-steel interface since the t e r m s for this b o u n d a r y cancel o u t on division. Dr. K r a u t k r a m e r suggests t h a t calculation with energies is s i m p l e r : this m e t h o d c o u l d be used, since the s o u n d is l a u n c h e d a n d detected in the one m e d i u m , i.e. water. U n f o r t u n a t e l y in a n u m b e r of i m p o r t a n t t r a n s m i s s i o n system a p p l i c a t i o n s the s o u n d is t r a n s m i t t e d a n d received in m e d i a o f different a c o u s t i c i m p e d a n c e . A typical e x a m p l e m i g h t consist of a pair of crystals c e m e n t e d to o p p o s i t e sides of a steel-andp r o p e l l a n t slab. By c o n s i d e r i n g the p o t e n t i a l a n d kinetic energies of a small layer, i n t e g r a t i n g a n d t a k i n g m e a n values, the flow of energy per s e c o n d per unit area of the w a v e f r o n t can be s h o w n to be ½ pc a2ll 2 for p l a n e waves. This m e a n s t h a t we can s q u a r e a n d a d d a m p l i t u d e s only in m e d i a of t h e same acoustic i m p e d a n c e . If we tried to calculate the t r a n s m i t t e d a m p l i t u d e in the p r o p e l l a n t by s q u a r i n g E q u a t i o n 5, s u b t r a c t i n g f r o m unity a n d t a k i n g the s q u a r e root the result w o u l d be

162

2 \ p,,c,, Ptq p,)c 2 : p,~c,, which is clearly incorrect. T h e crucial p o i n t is t h a t we m u s t s u m the instant a n e o u s values of the energies on b o t h sides o f t h e b o u n d a r y . T h e energy in a s o u n d wave is p r o p o r t i o n a l to the rate at which the s o u r c e is w o r k i n g . T h e rate at which work is d o n e is m e a s u r e d by the p r o d u c t of force a n d velocity a n d for the s o u r c e these are the pressure ratio a n d particle velocity. The instantaneous p o w e r per unit area of the w a v e f r o n t is t h e r e f o r e 8P dy/'dt a n d since 8P pc' dy/dt the energy r e l a t i o n s h i p is:

tqTlRANONl(S/Jldy-Seplemher

( (~p,)2

((~p¢)2

. . . . (9) ptc~ pff'] p2c., Division by (~P,)'-/plcl a n d r e a r r a n g e m e n t gives:

p,c, f ~p,~ "

I

/.,),c.,_ \~SP,/.

/ (~p,"]" \ . gP,/ 4 P2Cl p l c 2

.(10) (p2c., ! piQ) 2 " This is the r a t i o of t r a n s m i t t e d to incident energy but the s q u a r e root is not the t r a n s m i t t e d a m p l i t u d e . I-Iov,ever, solving for 6P,/SP~ leads to

2p.,c., p2ce

plcl

as before. T h e best m e t h o d is t h e r e f o r e to use E q u a t i o n s 5 a n d 6 since, as Dr. K r a u t k r a m e r states, the echo height is p r o p o r t i o n a l to a m p l i t u d e a n d not energy. T h e a b o v e discussion is on a very e l e m e n t a r y level a n d a full analysis of reflection a n d refraction at fluid-tosolid a n d solid-to-solid b o u n d a r i e s can be f o u n d in reference I. B. HARRIS- MADDOX

The Ultrasonoscope Co. (l.ondon), Ltd. Sudbourne Road, London, S.W.2. I. EWlNG, "'Elastic waves in layered media," M c G r a w - H i l l (1957}.

PULSE-ECHO

TESTING

From Sperry Products Inc. As p o i n t e d o u t by Dr. K r a u t k r a m e r in his letter in y o u r A p r i l - J u n e , 1964 issue, the basic F i r e s t o n e p a t e n t , No. 2280226, a n d its s t a n d i n g in the light of prior art was t h o r o u g h l y e x p l o r e d in C.A. No. 31.352, U.S. District C o u r t , N o r t h e r n District of O h i o , Eastern Division, Sperry P r o d u c t s Inc., et a/ versus A l u m i n i u m C o m p a n y of A m e r i c a , et al. T h e validity of the p a t e n t was affirmed a n d the rights of Dr. F i r e s t o n e a n d Sperry P r o d u c t s Inc. were established. O n e of the best s t a t e m e n t s of the c h r o n o l o g i c a l d e v e l o p m e n t of ultrasonic testing is q u o t e d f r o m the N o n d e s t r u c t i v e T e s t i n g H a n d b o o k by R. C. M c M a s t e r , 1959, Vol. 11, Section 43, page 43.3 : " ' D e v e l o p m e n t of Tests. T h e possibility of utilizing u l t r a s o n i c waves for n o n d e s t r u c t i v e testing was recognized in the 1930s in G e r m a n y by M u h l a u s e r , Trost,

1964

P o h l m a n a n d in R u s s i a by S o k o l o v , all o f w h o m i n v e s t i g a t e d v a r i o u s cont i n u o u s wave t e c h n i q u e s . Flaw d e t e c t i o n e q u i p m e n t was e v e n t u a l l y developed, based on the principle of u l t r a s o n i c energy i n t e r c e p t i o n by a gross flaw in the p a t h of the beam. This t e c h n i q u e later b e c a m e k n o w n as the t h r o u g h transmission method. An i n g e n i o u s transmission system developed by P o h l m a n p r o d u c e d s h a d o w - l i k e images of internal flaws. Later, several t r a n s mission flaw d e t e c t o r s were m a r k e t e d . " D u r i n g this early period, efforts were also m a d e to e m p l o y reflected as well as t r a n s m i t t e d u l t r a s o n i c waves. These were i n t e n d e d to o v e r c o m e certain l i m i t a t i o n s of the earlier m e t h o d s , especially the necessity of r e q u i r i n g access to b o t h s p e c i m e n surfaces. No practical m e t h o d was f o u n d , however, until Firestone in~ented apparatus utilizing pulsed u l t r a s o n i c w a v e t r a i n s to o b t a i n reflections f r o m m i n u t e defects. This d e v e l o p m e n t , which he called the "Supersonic Reflectoscope', was aided by the r a p i d g r o w t h of e l e c t r o n i c instrumentation techniques. It led d u r i n g the 1940s to the m a r k e t i n g of practical u l t r a s o n i c flaw d e t e c t o r s in the U n i t e d States a n d elsewhere. In the s a m e period, u l t r a s o n i c test e q u i p m e n t \~as developed independently b~ S p r o u l e in E n g l a n d (see the section on D o u b l e - T r a n s d u c e r U l t r a s o n i c Tests). As with early industrial X-ray e q u i p m e n t , the first i n s t r u m e n t s were for the m o s t part c o n s i d e r e d to be l a b o r a t o r 3 tools a n d were installed in metallurgical research d e p a r t m e n t s . " W e h o p e t h a t this i n f o r m a t i o n ma> help to clarify an area which has been \ e r y c l o u d y in the m i n d s of many w o r k e r s in o u r field a n d y o u r part in p r e s e n t i n g the record is very m u c h appreciated. Very truly yours, PHILU" R. N t n t Sperry Products Danbury, Connecticut II.S.~\. l. MUItI.HAUSI:R, O., "'Verfahrcn zur Zuslalld~, bestimmung yon Werkstoffen, besonders zur Ermittlung ,,'oll Fehlern darin.'" German Patent No. %9,498 (1931).

2. TROSI, A.. "'Nachwcis yon Werkstofftrcnningen in Blechen mit Ultraschall Zeitshril? /fir Deutsche hL~,eltieur, ,'¢7, 352 (1943). 3. POHLM,X',. R., "'Uebcr die Mocglichkcit einer akustischcn A b b i l d u n g in Analgoie zur Optischen,'" Zeitschri/t fiir Phv~ik, ll3, 697 (1939L 4. S()KOLOFF, S., "'Zur Fragc dcr Fortpflanzung Ultraakustischcr Schwingungen in Verschiedenen Koerpcrn,'" Eh'ktris~/tc Nachrichten-TekJfik, 6, 454 (1929). 5. VAN VALKINBFRO, H. E., HARDIt, F. g., and (]OOI)MAN, R. C., "'Acoustic image

inspection," Final Report, U.S. Nay,., BuAer, Contract No. NOa(s) 8868 (1950). 6. hRES[ONF, F. A., - F l a w detecting device and measuring i n s t r u m e n t " , U.S. Patent No. 2,280226 (April 21, 1942L 7. FIRFSIONt, F. A., "The supersonic reflcctoscope for interior inspection," MetaIProgre~, 505, 48 (1945). 8. DFSCII, C. H., DAV~ SON. W. J., and SPr
means of supersonic ~avcs,'" The Eii t,,illecr, lXl, 467 (19461.