u2-ch2

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2-1

2. TERMINOLOGY, PHYSICAL PRINCIPLES AND FUNDAMENTALS OF

ULTRASONICS

2.1 THE NATURE OF ULTRASONIC WAVES

Ultrasonics is the study of sound propagated at frequencies beyond the range audible to

people (20 kHz). t !as first disco"ered by #alton in 1$$%. &apid de"elop'ent of the

subect ho!e"er took place during the t!o !orld !ars. *he use of pulse 'ethods deri"ed

fro' radar techniques enhanced the scope of ultrasonics considerably and it beca'e !idely

applied in non-destructi"e testing of 'aterials besides 'any other areas of applications such

as 'edical diagnosis instru'entation and control cleaning e'ulsification drilling and

"arious 'ethods of processing 'aterials. Ultrasonic is used in preference to audible sound in

'any applications for one or 'ore of the follo!ing reasons+

(i) t has directional properties − the higher the frequency the greater the directi"ity.

*his is the 'ain consideration in for e,a'ple fla! detection and under-!ater signalling.

(ii) t the higher frequencies the !a"elengths beco'e correspondingly shorter and are

co'parable !ith or e"en 'uch less than the di'ensions of the sa'ples of the

'aterial through !hich propagation takes place. *his is i'portant for the

'easure'ent of s'all thicknesses or for high-resolution fla! detection.

(iii) t is silent !hich is ad"antageous for high intensity applications. *hese applications

can often be carried out 'ore efficiently at audible frequencies but the resulting

noise 'ay be intolerable and possibly inurious.

Utrasound as !e kno! is a for' of 'echanical "ibration. *o understand ho! ultrasonic

'otion occurs in a 'ediu' it is necessary to understand the 'echanis' !hich transfers the

energy bet!een t!o points in a 'ediu'. *his can be understood by studying the "ibration of

a !eight attached to a spring (igure 2.1a).

(a) (b)

igure 2.1 + (a) /eight attached to a spring (b) lot of displace'ent of / !ith ti'e

!.r.t. position .

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2-2

*he t!o forces acting on / !hile it is at rest are force of gra"ity # and tension * in the

spring. o! if / is 'o"ed fro' its equilibriu' position to position tension *

increases. f it is no! released at position / !ould accelerate to!ards position under

the influence of this increase in tension. t the gra"ity # and tension * !ill again be

equal but as no! / is 'o"ing !ith a certain "elocity it !ill o"ershoot . s it 'o"es

to!ards position 3 tension * decreases and the relati"e increase in gra"ity # tends todecelerate / until it has used up all its kinetic energy and stops at 3. t 3 # is greater than

* and so / falls to!ards again. t it possesses kinetic energy and once 'ore

o"ershoots. s / tra"els bet!een and * gradually increases and slo!s do!n / until it

co'es to rest at . t * is greater than # and the !hole thing starts again. *he sequence

of displace'ents of / fro' position to to to 3 and 3 to is ter'ed a cycle.

*he nu'ber of such cycles per second is defined as the frequency of "ibration. *he ti'e

taken to co'plete one cycle is kno!n as the ti'e period * of the "ibration !here * 4 15f.

*he 'a,i'u' displace'ent of / fro' to or to 3 is called the a'plitude of "ibration.

ll these concepts are illustrated in igure 2.1(b).

ll 'aterials are 'ade of ato's (or 'olecules) !hich are connected to each other by

interato'ic forces. *hese ato'ic forces are elastic i.e. the ato's can be considered to be

connected to each other as if by 'eans of springs. si'plified 'odel of such a 'aterial is

sho!n in igure 2.2.

igure 2.2+ 6odel of an elastic body.

o! if an ato' of the 'aterial is displaced fro' its original position by an applied stress it

!ould start to "ibrate like the !eight / of igure 2.1(a). ecause of the interato'ic

coupling "ibration of this ato' !ill also cause the adacent ato's to "ibrate. /hen the

adacent ato's ha"e started to "ibrate the "ibratory 'o"e'ent is trans'itted to their

neighbouring ato's and so forth. f all the ato's !ere interconnected rigidly they !ould all

start their 'o"e'ent si'ultaneously and re'ain constantly in the sa'e state of 'otion i.e.

in the sa'e phase. ut since the ato's of a 'aterial are connected to each other by elastic

forces instead the "ibration requires a certain ti'e to be trans'itted and the ato's reached

later lag in phase behind those first e,cited.

/hen a 'echanical !a"e tra"erses a 'ediu' the displace'ent of a particle of the 'ediu'

fro' its equilibriu' position at any ti'e 7t8 is gi"en by+

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2-%

a 4 ao sin 2 π ft ------------------------------------------------- (2.1)

!here

a 4 displace'ent of the particle at ti'e 7t8

ao 4 a'plitude of "ibration of the particle 9f 4 frequency of "ibration of the particle.

graphical representation of :quation 2.1 is gi"en in igure 2.%.

igure 2.%+ #raphical representation of :quation 2.1 sho!ing "ariation of particle

displace'ent !ith ti'e.

:quation 2.2 is the equation of 'otion of a 'echanical !a"e through a 'ediu'. t gi"es thestate of the particles (i.e. the phase) at "arious distances fro' the particle first e,cited at a

certain ti'e 7t8.

a 4 ao sin2π f (t - , 5") ---------------------------------------- (2.2)

!here

a 4 displace'ent (at a ti'e 7t8 and distance 7,8 fro' the first e,cited

particle) of a particle of the 'ediu' in !hich 'echanical !a"e is

tra"elling

ao 4 a'plitude of the !a"e !hich is the sa'e as that of the a'plitude of

"ibration of the particles of the 'ediu'

" 4 "elocity of propagation of the !a"e 9

f 4 frequency of the !a"e.

, 4 distance of the particle fro' the first e,cited particle

igure 2.; gi"es the graphical representation of :quation 2.2.

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2-;

igure 2.; + #raphical representation of :quation 2.2.

<ince in the ti'e period * a 'echanical !a"e of "elocity 7"8 tra"els a distance 7 λ8 in a

'ediu' therefore !e ha"e+

λ 4 "*

or " 4 λ5* --------------------------------------------------------------- (2.%)

ut the ti'e period 7*8 is related to the frequency 7f 8 by+

f 4 1 5 * ----------------------------------------------------------------- (2.;)

3o'bining :quations 2.% and 2.; !e ha"e the funda'ental equation of all !a"e 'otion i.e.

" 4 λ f ------------------------------------------------------------------ (2.=)

n :quation 2.= if 7f8 is in Hz 7λ8 in '' then 7"8 is in ''5sec. lternati"ely if 7f8 is in 6Hz

7λ8 in '' then 7"8 is in k's-1 .

2.2 CHARACTERISTICS OF WAVE PROPAGATION

2.2.1 Frequenc

*he frequency of a !a"e is the sa'e as that of the "ibration or oscillation of the ato's of the

'ediu' in !hich the !a"e is tra"elling. t is usually denoted by the letter 7f 8 and until

recently !as e,pressed as the nu'ber of cycles per second. *he international ter' for a

cycle per second is na'ed after the physicist H. Hertz and is abbre"iated as Hz.

1 Hz 4 1 cycle per second

1 kHz 4 1000 Hz 4 1000 cycles per second

1 6Hz 4 1000000 Hz 4 1000000 cycles per second

1 #Hz 4 1000000000 Hz 4 1000000000 cycles per second

/ith the 'odern equip'ent frequencies in the range of #Hz can be generated. Ho!e"er in

general ultrasonic !a"es of frequency range 0.= 6Hz to 20 6Hz are used for the testing of

'aterials. *he 'ost co''on range for testing 'etals is fro' 2 6Hz to 20 6Hz. requency

plays an i'portant role in the detection and e"aluation of defects.

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2-=

2.2.2 A!"#$%u&e

*he displace'ent of the !eight fro' its position of rest in igure 2.1 and that of the

particles of a 'ediu' in igures 2.% and 2.; is called the a'plitude. n :quation 2.2 7a8 is

the a'plitude at any ti'e 7t8 !hile 7ao8 is the 'a,i'u' a'plitude. (lso see <ection ;.%.1)

2.2.' W()e#en*%+

>uring the ti'e period of "ibration * a !a"e tra"els a certain distance in the 'ediu'. *his

distance is defined as the !a"elength of the !a"e and is denoted by the #reek letter λ.

to's in a 'ediu' separated by distance 7λ8 !ill be in the sa'e sate of 'otion (i.e. in the

sa'e phase) !hen a !a"e passes through the 'ediu'.

*he relationship bet!een 7λ8 7f 8 and 7"8 is gi"en in :quation 2.= !hich sho!s that in a

particular 'ediu' the !a"elength is the reciprocal of frequency. *herefore higher the

frequency shorter the !a"elength and "ice "ersa. n practical testing usually fla!s of the

order of λ52 or λ5% can be detected. *herefore s'aller the !a"elength s'aller are thedetectable defects. *hus s'aller !a"elength or higher frequency ultrasound !a"es pro"ide a

better fla! sensiti"ity. *his is further elaborated by the follo!ing e,a'ple.

:,a'ple + 3o'pare the fla! sensiti"ities for probes of frequencies 1 6Hz and ? 6Hz in

steel.

@et us assu'e that fla! sensiti"ity is of the order of λ5%. *hen for a 1 6Hz frequency !e

ha"e

λ 4 "5f4 =A;0 (for steel) x 100051 x 1000000 ''

4 =.A; ''

la! sensiti"ity 4 λ5%

4 1.A$ ''

or the ? 6Hz frequency !e ha"e

λ 4 =A;0 , 1000 5 ? , 1000000 ''

4 0.AA ''

la! sensiti"ity 4 λ5%

4 0.%% ''

2.2. Ve#-c$%

*he speed !ith !hich energy is transported bet!een t!o points in a 'ediu' by the 'otion

of !a"es is kno!n as the "elocity of the !a"es. t is usually denoted by the letter 7"8.

*he "elocity of propagation of longitudinal trans"erse and surface !a"es (<ection 2.%)

depends on the elastic 'odulus and the density of the 'aterial and in the sa'e 'aterial it is

independent of the frequency of the !a"es and the 'aterial di'ensions.

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2-?

Belocities of longitudinal trans"erse and surface !a"es are gi"en by the follo!ing

equations.

":

l =

ρ ----------------------------------------------------------- (2.?)

"#

t =

ρ ------------------------------------------------------------ (2.C)

"s 4 0.A x "t ------------------------------------------------------ (2.$)

!here

"l 4 "elocity of longitudinal !a"es

"t 4 "elocity of trans"erse !a"es

"s 4 "elocity of surface !a"es: 4 DoungEs 'odulus of elasticity

# 4 'odulus of rigidity

ρ 4 density of the 'aterial

or steel

"t 5 "l 4 0.== ------------------------------------------------- (2.A)

*he "elocity of propagation of @a'b !a"es depends not only on the 'aterial density but

also on the type of !a"e itself and on the frequency of the !a"e.

:quation 2.? also e,plains !hy the "elocity is lesser in !ater than in steel because although

the density for steel is higher than that of !ater the elasticity of steel is 'uch higher than

that of !ater and this outclasses the density factor.

*able 2.1 gi"es the "elocities of longitudinal and trans"erse !a"es in so'e co''on

'aterials.

2.2. Ac-u/%$c $!"e&(nce

*he resistance offered to the propagation of an ultrasonic !a"e by a 'aterial is kno!n as the

acoustic i'pedance. t is denoted by the letter F and is deter'ined by 'ultiplying thedensity of the 'aterial by the "elocity 7"8 of the ultrasonic !a"e in the 'aterial i.e.

F 4 ρ" -------------------------------------------------------- (2.10)

*he "alue of the acoustic i'pedance for a gi"en 'aterial can be seen to depend only on its

physical properties and thus to be independent of the !a"e characteristics and the frequency.

Balues of acoustic i'pedances for a nu'ber of fa'iliar 'aterials are gi"en in *able 2.1.

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2-C

*able 2.1 + >ensities sound "elocities and acoustic i'pedances of so'e co''on 'aterials

M(%er$(#

Den/$%

0*!'

)%

!/

)#

!/

3 14' 0* !52 /51

air 1.% - %%0 0.;%0

alu'iniu' 2C00 %1%0 ?%20 1C0?;

alu'iniu' o,ide %?00 ==00 A000 %2;00

bariu' titanate =;00 - =000 2C000

brass $100 2120 ;;%0 %=$$%

cast iron ?A00 2200 =%00 2;1=0

concrete 2000 - ;?00 A200

copper $A00 22?0 ;C00 ;1$%0epo,y resin 11C0 1100 2?=0 %1=0

glass %?00 2=?0 ;2?0 1=%%?

glycerine 1%00 - 1A20 2;A?

grey casting C200 2?=0 ;?00 %%120

lead 11;00 C00 2??0 2;?2;

'agnesiu' 1C00 %0=0 =CC0 A$0A

'otor oil $C0 - 1C;0 1=1;

nickel $$00 2A?0 =?%0 ;A=;;

nylon 11;0 - 2C00 %000oli"e oil A00 - 1;00 1%00

teflon 2200 ==0 1%=0 %000

perspe, 11$0 1;%0 2C%0 %221

polya'ide (nylon) 1100 10$0 2?20 2$$2

polyethylene A;0 A2= 2%;0 2200

polystyrol 10?0 11=0 2%$0 2=2%

poly"inylchloride (p"c

hard)

1;00 10?0 2%A= %%=%

quartz 2?=0 - =C?0 1=2?;quartz glass 2?00 %=1= ==C0 1;;$2

rubber "ulcanized 1200 - 2%00 2$00

sil"er 10=00 1=A0 %?00 %C$00

steel (lo! alloy) C$=0 %2=0 =A;0 ;??20

steel (calibration block) C$=0 %2=0 =A20 ;?;C2

steel (stainless) C$00 %1%0 =C;0 ;;$00

titaniu' ;=00 %120 =AA0 2C000

tungsten 1A%00 2$$0 =1C0 100000

tungsten a"aldite 10=00 - 20?0 21?=0uraniu' 1$C00 2020 %%C0 ?%000

!ater 1000 - 1;$0 1;$0

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2-$

zirconiu' ?;00 2%00 ;?=0 2A$00

2.' TYPES OF ULTRASONIC WAVE S AND THEIR APPLICATIONS

Ultrasonic !a"es are classified on the basis of the 'ode of "ibration of the particles of the

'ediu' !ith respect to the direction of propagation of the !a"es na'ely longitudinal

trans"erse surface and @a'b !a"es. *he 'aor differences of these four types of !a"es are

discussed belo!+

2.'.1 L-n*$%u&$n(# -r c-!"re//$-n(# 6()e/

n this type of ultrasonic !a"e alternate co'pression and rarefaction zones are produced by

the "ibration of the particles parallel to the direction of propagation of the !a"e. igure 2.=

represents sche'atically a longitudinal ultrasonic !a"e.

igure 2.= + @ongitudinal !a"e consisting of alternate rarefactions and co'pressions along

the direction of propagation.

or a longitudinal ultrasonic !a"e the plot of particle displace'ent "ersus distance of !a"e

tra"el along !ith the resultant co'pression crest and rarefaction trough is sho!n in

igure 2.?.

igure 2.? + lot of particle displace'ent "ersus distance of !a"e tra"el.

ecause of its easy generation and detection this type of ultrasonic !a"e is 'ost !idely

used in ultrasonic testing. l'ost all of the ultrasonic energy used for the testing of 'aterials

originates in this 'ode and is then con"erted to other 'odes for special test applications.

*his type of !a"e can propagate in solids liquids and gases.

2.'.2 Tr(n/)er/e -r /+e(r 6()e/

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2-A

*his type of ultrasonic !a"e is called a trans"erse or shear !a"e because the direction of

particle displace'ent is at right angles or trans"erse to the direction of propagation. t is

sche'atically represented in igure 2.C.

igure 2.C + <che'atic representation of a trans"erse !a"e.

or such a !a"e to tra"el through a 'aterial it is necessary that each particle of 'aterial is

strongly bound to its neighbours so that as one particle 'o"es it pulls its neighbour !ith it

thus causing the ultrasound energy to propagate through the 'aterial !ith a "elocity !hichis about =0 percent that of the longitudinal "elocity.

or all practical purposes trans"erse !a"es can only propagate in solids. *his is because the

distance bet!een 'olecules or ato's the 'ean free path is so great in liquids and gases

that the attraction bet!een the' is not sufficient to allo! one of the' to 'o"e the other

'ore than a fraction of its o!n 'o"e'ent and so the !a"es are rapidly attenuated.

*he trans'ission of this !a"e type through a 'aterial is 'ost easily illustrated by the

'otion of a rope as it is shaken. :ach particle of the rope 'o"es only up and do!n yet the

!a"e 'o"es along the rope fro' the e,citation point.

2.'.' Sur7(ce -r R(#e$*+ 6()e/

<urface !a"es !ere first described by @ord &ayleigh and that is !hy they are also called

&ayleigh !a"es. *hese type of !a"es can only tra"el along a surface bounded on one side

by the strong elastic forces of the solid and on the other side by the nearly non-e,istent

elastic forces bet!een gas 'olecules. <urface !a"es therefore are essentially non-e,istent

in a solid i''ersed in a liquid unless the liquid co"ers the solid surface only as a "ery thin

layer. *he !a"es ha"e a "elocity of appro,i'ately A0 percent that of an equi"alent shear

!a"e in the sa'e 'aterial and they can only propagate in a region no thicker than about one

!a"elength beneath the surface of the 'aterial. t this depth the !a"e energy is about ;

percent of the energy at the surface and the a'plitude of "ibration decreases sharply to a

negligible "alue at greater depths.

n surface !a"es particle "ibrations generally follo! an elliptical orbit as sho!n

sche'atically in igure 2.$.

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2-10

igure 2.$ + >iagra' of surface !a"e propagating at the surface of a 'etal along a 'etal-air

interface. <'all arro!s indicate directions of particle displace'ent.

*he 'aor a,is of the ellipse is perpendicular to the surface along !hich the !a"es are

tra"elling. *he 'inor a,is is parallel to the direction of propagation. practical 'ethod of

generating surface !a"es is gi"en in <ection 2.;.2.%.

<urface !a"es are useful for testing purposes because the attenuation they suffer for a gi"en

'aterial is lo!er than for an equi"alent shear or longitudinal !a"es and because they can

tra"el around corners and thus be used for testing quite co'plicated shapes. Gnly surface or

near surface cracks or defects can be detected of course.

2.'. L(!8 -r "#(%e 6()e/

f a surface !a"e is introduced into a 'aterial that has a thickness equal to three

!a"elengths or less of the !a"e then a different kind of !a"e kno!n as a plate !a"e

results. *he 'aterial begins to "ibrate as a plate i.e. the !a"e enco'passes the entire

thickness of the 'aterial. *hese !a"es are also called @a'b !a"es because the theory

describing the' !as de"eloped by Horace @a'b in 1A1?. Unlike longitudinal shear or

surface !a"es the "elocities of these !a"es through a 'aterial are dependent not only on

the type of 'aterial but also on the 'aterial thickness the frequency and the type of !a"e.

late or @a'b !a"es e,ist in 'any co'ple, 'odes of particle 'o"e'ent. *he t!o basic

for's of @a'b !a"es are (a) sy''etrical or dilatational and (b) asy''etrical or bending.

*he for' of the !a"e is deter'ined by !hether the particle 'otion is sy''etrical or

asy''etrical !ith respect to the neutral a,is of the test piece. n sy''etrical @a'b

(dilatational) !a"es there is a longitudinal particle displace'ent along neutral a,is of the

plate and an elliptical particle displace'ent on each surface (igure 2.A a).

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2-11

igure 2.A + >iagra's of the basic patterns of (a) sy''etrical (dilatational) and

(b) asy''etrical (bending) @a'b !a"es.

*his 'ode consists of the successi"e thickening and thinning in the plate itself as !ould be

noted in a soft rubber hose if steel balls larger than its dia'eter !ere forced through it. n

asy''etrical (bending) @a'b !a"es there is a shear particle displace'ent along the neutral

a,is of the plate and an elliptical particle displace'ent on each surface

(igure 2.A b). *he ratio of the 'aor to 'inor a,es of the ellipse is a function of the 'aterial

in !hich the !a"e is being propagated. *he asy''etrical 'ode of @a'b !a"es can be

"isualized by relating the action to a rug being !hipped up and do!n so that a ripple

progresses across it.

2. 9EHAVIOUR OF ULTRASONIC WAVES

2..1 Re7#ec%$-n (n& %r(n/!$//$-n (% n-r!(# $nc$&ence

2.4.1.1 Reflected and transmitted intensities

/hen ultrasonic !a"es are incident at right angles to the boundary (i.e. nor'al incidence) of

t!o 'edia of different acoustic i'pedances then so'e of the !a"es are reflected and so'e

are trans'itted across the boundary. *he surface at !hich this reflection occurs is also calledan interface. *he a'ount of ultrasonic energy that is reflected or trans'itted depends on the

difference bet!een the acoustic i'pedances of the t!o 'edia. f this difference is large then

'ost of the energy is reflected and only a s'all portion is trans'itted across the boundary.

/hile for a s'all difference in the acoustic i'pedances 'ost of the ultrasonic energy is

trans'itted and only a s'all portion is reflected back.

uantitati"ely the a'ount of ultrasonic energy !hich is reflected !hen ultrasonic !a"es are

incident at the boundary of t!o 'edia of different acoustic i'pedances (igure 2.10) is

gi"en by+

ntensity of reflected !a"es at the boundary&eflection coefficient 4

ntensity of incident !a"es at the boundary

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2-12

or & 4 r 5i 4 (F2-F1)2 5 (F1IF2)

2 ---------------- (2.11)

!here

& 4 reflection coefficient

F1 4 acoustic i'pedance of 'ediu' 1


r 4 reflected ultrasonic intensity

i 4 incident ultrasonic intensity

igure 2.10 + &eflection and trans'ission at nor'al incidence.

*he a'ount of energy that is trans'itted across the boundary is gi"en by the relation+

ntensity of trans'itted !a"es at the boundary

*rans'ission coefficient 4

ntensity of incident !a"es at the boundary

or * 4 t5i 4 ;F1F25(F1IF2)2 ----------- (2.12)

!here

* 4 trans'ission coefficient



t 4 trans'itted ultrasonic intensity

i 4 incident ultrasonic intensity.

*he trans'ission coefficient * can also be deter'ined fro' the relation+

* 4 1 - & -------------------------------------------------- (2.1%)

!here

* 4 trans'ission coefficient

& 4 reflection coefficient

Using the "alues of the characteristic i'pedances gi"en in *able 2.1 reflection andtrans'ission coefficients can be calculated for pairs of different 'aterials. *he equations

sho! that the trans'ission coefficient approaches unity and the reflection coefficient tends

to zero !hen F1 and F2 ha"e appro,i'ately si'ilar "alues. *he 'aterials are then said to be

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2-1%

!ell 'atched or coupled. Gn the other hand !hen the t!o 'aterials ha"e substantially

dissi'ilar characteristic i'pedances e.g. for a solid or liquid in contact !ith a gas the

trans'ission and reflection coefficients tend to zero and 100 percent respecti"ely. *he

'aterials are then said to be 'is'atched or poorly coupled. difficulty 'ay arise !hen

both the 'aterials are solids. Unless their surfaces are ground flat to optical precision

contact occurs only in a fe! places and there is effecti"ely a thin layer of fluid bet!eenthe'. f the fluid is a liquid for !hich the characteristic i'pedance is not too far re'o"ed

fro' those of the solids and the thickness of the layer is 'uch less than a !a"elength the

"alue of the trans'ission coefficient is the sa'e as if the t!o solids !ere in perfect contact.

Gn the other hand if the layer of fluid !ere a gas as !ould be the case if the t!o 'aterials

!ere in air the trans'ission coefficient is reduced al'ost to zero. <ubstitution of "alues of

acoustic i'pedances sho!n in *able 2.1 into :quation 2.12 gi"es C= percent for the

trans'ission coefficient !hen a quartz crystal is placed in perfect contact !ith a steel block.

n practice ho!e"er there is a gap of an effecti"e !idth of 1 µ' !hen the surface of steel is

'achined to a tolerance of this 'agnitude. t a frequency of 1 6Hz there is a reduction of

trans'ission coefficient by only one or t!o per cent !hen the gap is filled !ith a liquid. Gn

the other hand if the gap !ere to contain air the trans'ission coefficient !ould be reduced

to about ;,10-A a decrease of 'ore than $0 d. *his illustrates the i'portance of the use of a

coupling fluid !hen trans'itting or recei"ing sound !a"es in solids.

:,a'ple + !hat !ould be the percentage of acoustic energy reflected and trans'itted at the

interface bet!een !ater and steelJ

ro' *able 2.1 !e ha"e the follo!ing data+

F !ater 4 F1 4 1;$0,10% kg '-2s-1

F steel 4 F2 4 ;??2A,10% kg '-2 s-1

&eflection coefficient (&) 4 (F2-F1)2 5 (F1IF2)

2

4 (;??2A-1;$0)2 5 (1;$0 I ;??2A)2

4 (;=1;A)2 5 (;$10A)2

4 2.0%$;%2252.%1;;C=A

4 0.$$

K reflection 4 0.$$ , 100

4 $$K

*rans'ission coefficient (*) 4 (;F1 F2) 5 (F1 I F2)2

4 ; , 1;$0 , ;??2A 5 (;$10A)2

4 2.C?0;%?$ , 10$ 5 2%.1;;C=A , 10$

4 0.11A 4 0.12

K trans'ission 4 0.12 , 100

4 12K

:,a'ple + /hat percentages of the original sound energy !ill be reflected and trans'itted at

the !ater to alu'iniu' interface as sho!n in the diagra' (igure 2.11). lso

calculate the percentage of the original sound energy that !ill finally enter the

!ater on its !ay back to the transducer fro' the back surface of the alu'iniu'

part.

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2-1;

igure 2.11 + rrange'ent of probe and alu'iniu' block.

Using *able 2.1 !e ha"e the follo!ing data+

F !ater 4 F1 4 1;$0 , 10% kg '-2 s-1

F alu'iniu' 4 F2 4 1C0?;,10% kg '-2 s-1

&eflection coefficient (&) 4 (1.;$ - 1C.0?)2 5 (1.;$ I 1C.0?)2

4 2;2.C% 5 %;%.C%

4 0.C1

K reflection 4 C1K

*rans'ission coefficient (*) 4 (;F1 F2) 5 F1IF2)

2

4 (; , 1.;$ , 1C.0?) 5 (1.;$I1C.0?)2

4 (100.AA) 5 (%;%.C%)

4 0.2A

K trans'ission 4 2AK

*herefore 2AK of the energy is trans'itted into the alu'iniu' test piece. t the back it

faces an alu'iniu' !ater interface. C1K of this 2AK is reflected back fro' the back !all.

*his co'es to 20.?K !hich co'es up and encounters the alu'iniu' !ater boundary once

again. t this C1K of 20.?K is reflected back into the test speci'en. *his co'es out to

1;.?K. *he re'aining (20.? - 1;.?) !hich co'es to about ?K finally enters the !ater.

:,a'ple + clad 'aterial is to be tested for bond defects. Gne 'aterial has a thickness of

C.= '' and an acoustic i'pedance of =.0 , 10% kg '-2 s-1 and the other 'aterial

is 100 '' thick and has an acoustic i'pedance of ;.= , 10 % kg '-2 s-1. f the

bond is perfect and acceptable !hat percentage of sound is e,pected to be

reflected fro' the interface.

*he bond being perfect the reflection !ill be only as a consequence of differences in the

acoustic i'pedances. t 'ay be 'entioned that because of the near zone proble's the

testing !ill be done fro' the side of the larger thickness.

&eflection coefficient (&) 4 (F1 - F2)

2

5 (F1 I F2)

2

4 (= - ;.=)2 5 (= I ;.=)2

4 (0.2=) 5 (A0.2=)

4 0.002C

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2-1=

K reflection 4 0.002C , 100

4 0.2C K

2..2 Re7#ec%$-n (n& %r(n/!$//$-n (% -8#$que $nc$&ence

2.4.2.1 Refraction and mode conversion

f ultrasonic !a"es strike a boundary at an oblique angle then the reflection and

trans'ission of the !a"es beco'e 'ore co'plicated than that !ith nor'al incidence. t

oblique incidence the pheno'ena of 'ode con"ersion (i.e. a change in the nature of the

!a"e 'otion) and refraction (a change in the direction of !a"e propagation) occur.

igure 2.12 sho!s !hat happens !hen a longitudinal !a"e strikes obliquely a boundary

bet!een t!o 'edia. *he incident longitudinal !a"e splits up into t!o co'ponents one

longitudinal and the other trans"erse and this happens for both the reflected as !ell as

refracted parts. @1 and <1 denote respecti"ely longitudinal and shear !a"es in 'ediu' 1

!hile @2 and <2 denote these !a"es in 'ediu' 2. Gf course there !ill be no reflected

trans"erse co'ponent or refracted trans"erse co'ponent if either 'ediu' 1 or 'ediu' 2 isnot solid. igure 2.12 gi"es all the reflected and trans'itted !a"es !hen a longitudinal

ultrasonic !a"e strikes a boundary bet!een t!o 'edia. *he refracted trans"erse co'ponent

in 'ediu' 2 !ill disappear if 'ediu' 2 is not a solid.

αl 4 angle of incidence of longitudinal !a"e

αt 4 angle of reflection of trans"erse !a"e

βl 4 angle of refraction of longitudinal !a"e

βt 4 angle of refraction of trans"erse !a"e

igure 2.12 + &efraction and 'ode con"ersion for an incident longitudinal !a"e.

2.4.2.2 Snell's law

*he general la! that for a certain incident ultrasonic !a"e on a boundary deter'ines the

directions of the reflected and refracted !a"es is kno!n as <nellEs @a!. ccording to this

la! the ratio of the sine of the angle of incidence to the sine of the angle of reflection or refraction equals the ratio of the corresponding "elocities of the incident and reflected or

refracted !a"es. 6athe'atically <nellEs @a! is e,pressed as+

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2-1?

<in α 5 <in β 4 "15"2 ---------------------------------------------- (2.1;)

!here

α 4 the angle of incidence

β 4 the angle of reflection or refraction"1 4 "elocity of incident !a"e

"2 4 "elocity of reflected or refracted !a"es

oth α and β are 'easured fro' a line nor'al to the boundary.

2.4.2.3 First and second critical angles

pplying <nellEs @a! to igure 2.12 !e can !rite

<in αl 5 <in βt 4 "l1 5 "t2

<in βl 5 <in βt 4 "l2 5 "t2

<in αt 5 <in βl 4 "t1 5 "l2

<in βt 5 <in βl 4 "t2 5 "l2

*hese equations can be co'bined to gi"e

<in αl 5 "l1 4 <in βl 5 "l2 4 <in βt 5 "t2 4 <in αt 5"t1 ----------- (2.1=)

!here αl αt βl and βt ha"e already been defined and

"l1 4 "elocity of longitudinal !a"es in 'ediu' 1"l2 4 "elocity of longitudinal !a"es in 'ediu' 2

"t1 4 "elocity of trans"erse !a"es in 'ediu' 1

"t2 4 "elocity of trans"erse !a"es in 'ediu' 2

3onsider no! the relation <in αl 5 <in βl 4 "l1 5 "l2. f the angle of incidence αl is s'all

ultrasonic !a"es tra"elling in a 'ediu' undergo the pheno'ena of 'ode con"ersion and

refraction upon encountering a boundary !ith another 'ediu'. *his results in the

si'ultaneous propagation of longitudinal and trans"erse !a"es at different angles of

refraction in the second 'ediu'. s the "elocity of trans"erse !a"es for a gi"en solid is

al!ays less than that of longitudinal !a"es the angle of refraction βl for longitudinal !a"es

is al!ays greater than the angle of refraction βt for trans"erse !a"es. s the angle of

incidence is increased the angle of refraction also increases. or a certain "alue of the angle

of incidence αl the refraction angle βl reaches A0L. *he longitudinal !a"e then e'erges fro'

the second 'ediu' and tra"els parallel to the boundary. *he angle of incidence at !hich the

refracted longitudinal !a"e e'erges is called the first critical angle. t is gi"en by αl 4 <in-

1 ("l1 5 "l2) (igure 2.1% a).

o! consider the relationship <in αl 5 <in βt 4 "l1 5 "t2. f the angle of incidence αl is further

increased the angle of refraction for trans"erse !a"e βt also approaches A0L. *his "alue of

αl for !hich the angle of refraction of the trans"erse !a"e is e,actly A0L is called the second

critical angle. t the second critical angle the refracted trans"erse !a"e e'erges fro' the'ediu' and tra"els parallel to the boundary. *he trans"erse !a"e has beco'e a surface or

&ayleigh !a"e. *he "alue of second critical angle is gi"en by αl 4 <in-1 ("l15"t2).

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2-1C

<che'atically the critical angles are sho!n in igure 2.1% b. or propagation fro' !ater to

steel the "alues of first and second critical angles co'e out to be 1;L and %0L respecti"ely.

/ith plastic to steel boundary these angles ha"e "alues of 2$L and =$L.

(a) (b)

igure 2.1% + (a) irst critical angle (b) <econd critical angle.

2.4.2.4 Reflected acoustic pressure at angular incidence

igure 2.1; gi"es the acoustic pressure reflection factors for reflected trans"erse and

longitudinal !a"es at a steel - air boundary.

igure 2.1; + coustic pressure of reflected !a"es "s. angle of incidence.

ngle of incidence of trans"erse !a"es

ngle of incidence of longitudinal !a"es

K&eflectedenergy

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2-1$

*he angle of incidence of longitudinal !a"es is sho!n by lo!er horizontal scale and the

angle of incidence of shear !a"es by the upper horizontal scale. *he "ertical scale sho!s the

reflection factor in percentages. t can be noted fro' igure 2.1; that+

() *he reflected acoustic pressure of longitudinal !a"es is at a 'ini'u' of 1%K at ?$L

angle of incidence. *his 'eans the other portion of the !a"es is 'ode con"erted totrans"erse !a"es.

(ii) or an angle of incidence of about %0L for incident trans"erse !a"es only 1%K of

the reflected acoustic pressure is in the trans"erse 'ode. *he re'ainder is 'ode

con"erted into longitudinal !a"es.

(iii) or incident shear !a"es if the angle of incidence is larger than %%.2L the shear

!a"es are totally reflected and no 'ode con"ersion occurs.

:,a'ple + f it is desired that a shear !a"e tra"els into steel at ?0 degrees !hat !ould bethe incident angle on the @ucite (erspe,) !edgeJ

t is required to find the angle αl in the follo!ing sketch (igure 2.1=) !hile the angle βt is

gi"en to be ?0 degrees.

ro' *able 2.1 the "elocity of longitudinal !a"es in erspe, is " l1 4 2C%0 's-1 and "elocity

of shear !a"es in steel is " t2 4%2=0 's-1. pplying <nellEs @a!+ <in αl 5 <in βt2 4 "l15"t2

!e kno! βt2 4 ?0L and fro' the *able 2.2 <in ?0 4 0.$??0. utting this "alue

!e get

sin αl1 4 0.$??0,2C%05%2=0 4 0.C2C;. *herefore αl1 4 <in-1

(.C2C;) 4 ;C degrees.

igure 2.1=

:,a'ple + /hat !ould be the refracted longitudinal !a"e if the angle of incidence through

a !ater to steel interface is 12 degrees.

t is required to find the angle βl2 in the follo!ing sketch (igure 2.1?) !hile the angle of

incidence αl1 is gi"en to be 12 degrees.

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2-1A

igure 2.1?

Using *able 2.1 and applying <nellEs @a! !e get+

<in αl1 5 <in βl2 4 "l1 5 "l2 or

<in βl2 4 <in αl2 , "l2 5 "l1

4 0.20CA , =A;0 51;$0

4 0.$%;; or

βl2 4 <in-1 (0.$%;;)

4 =C degrees

:,a'ple+ f the angle of incidence through erspe, is %?° is it possible to ha"e a refracted

longitudinal !a"eJ f yes !hat is it J f no !hy notJ

t is required to find the "alue of angle βl2 in the igure 2.1? !hile the "alue of αl1 is gi"en to

be %?°.

Using *able 2.1 and applying <nellEs @a! !e get+

<in βl2 4 <in %? , "l2 (steel) 5 "l1 (erspe,)

4 0.=$C$ , =A;052C%0

4 1.2C$A

*his indicates that angle βl2 i.e. refracted angle for longitudinal !a"es is greater than A0°.

*herefore there !ill be no refracted longitudinal !a"e in steel in this case.

:,a'ple + n angle probe gi"es a bea' angle of ==° in steel. /hat is its bea' angle !hen

used to inspect alu'iniu'J

*ake "elocities + shear !a"es steel 4 %2=0 '5s

shear !a"es 1 4 %1%0 '5s

co'pressional !a"es steel 4 =A;0 '5s

co'pressional !a"es 1 4 ?%20 '5s

7/23/2019 U2-Ch2


2-20

s !e are considering angle probes !e are generating shear !a"es so !e use <nell8s @a!.

<inα 5 <inβ 4 "1 5 "2

!here "2 is the shear !a"e "elocity

α is the incident bea' angle

β is the refracted bea' angle

and !e !ish to calculate angle α in the angle probe kno!ing that in steel βsteel 4 ==°

<inα 5 "1 4 <inβsteel 5 "2 (steel) 4 <in== 5 %2=0

!here "1 is the co'pressional !a"e "elocity in the 'aterial of the probe shoe. n the

alu'iniu' case

lso <inβl 5 "2 (l) 4 <inα 5 "1 or <inβl 4 "2 (l) , <inα 5 "1

ut fro' pre"ious equation !e ha"e

<inα 5 "1 4 <in== 5 %2=0 and therefore

<inβl 4 %1%0 , <in== 5 %2=0 4 %1%0 , 0.$1A2 5 %2=0

Using log tables or a calculator

sin βl 4 0.C$A2 so βl 4 =2 degrees appro,. !hich is the bea' angle in alu'iniu'.

2. TRANSFER OF ENERGY FROM ONE MEDIUM TO ANOTHER

2..1 Gener(%$-n -7 u#%r(/-n$c 6()e/

#eneration of sound is a pheno'enon !herein different for's of energy are con"erted into

sound energy !hich in turn is the energy of 'echanical "ibrations. or e,a'ple in the case

of piezoelectric transducers electrical energy is con"erted to sound energy (section 2.?.1). n

'agnetostricti"e transducers it is the effect of 'agnetic field !hich is utilized to induce

'echanical "ibrations in so'e special 'aterials. n 'echanical transducers it is the shock or

friction !hich generates ultrasound. *he electro'agnetic generation of sound is by the useof the fact that if a 'agnetic alternating field acts upon an electrically conducti"e body eddy

currents are induced in it. >ue to the interaction bet!een eddy currents and the e,ternal

'agnetic field a force called @oretz force is produced in the test piece !hich generates the

sound. n the electrostatic process a force acts bet!een the plates of a capacitor. f one plate

of the capacitor is 'o"able then sound can be generated by an alternating "oltage. Use can

also be 'ade to con"ert ther'al energy into sound energy. sudden heating up of a solid

surface causes a sudden local e,tension of the 'aterial. *he 'echanical tensions produced

by this process e,cite sound !a"es !ith a !ide frequency spectru'. @aser lights and

electron bea's are usually used for "ery rapid and strong heating.

2..2 Ener* #-//e/ $n )(r$-u/ !e&$(

n sections 2.2.; and 2.2.= it has been said that the "elocities of sound are different in

different 'edia and therefore different 'edia ha"e different acoustic i'pedances i.e. they

7/23/2019 U2-Ch2


2-21

offer differing degrees of resistance to the passage of sound energy through the'. *his

indicates that so'e part of the sound energy 'ust be lost during its passage through

'aterials such as air !ater oil steel erspe, etc.

n section 2.; it has been sho!n ho! the ultrasound beha"es at the interfaces of different

'edia. n case of nor'al incidence a portion of the sound energy is reflected back into thefirst 'ediu' !hile the re'aining portion is trans'itted into the second 'ediu'. *he

percentage of these portions of sound energy depends upon the differences or 'is'atch

bet!een the acoustic i'pedances of the t!o 'edia. t oblique incidence apart fro' the

usual reflection and trans'ission the pheno'enon of 'ode con"ersion is encountered

!hich con"erts a part of the longitudinal sound !a"es into trans"erse 'ode. *he latter ha"e

'uch lo!er "elocity of propagation into the second 'ediu'.

*he ultrasonic bea' fro' the probe is di"ergent (<ection 2.C.2). /ith increase of distance

fro' the transducer the bea' intensity is distributed o"er an increasing cross section and is

consequently decreased throughout space.

*he ultrasonic energy undergoes interaction !ith the 'ediu' through !hich it tra"els and is

consequently attenuated (<ection 2.$). <uch attenuation or decrease falls under t!o

headings.

(i) *he true absorption !hich occurs in e"ery 'ediu' and by !hich is 'eant the

con"ersion into other for's of energy notably into heat.

(ii) *he scatter of ultrasonic energy !hich occurs 'ainly in inho'ogeneous poly-

crystalline 'edia (i.e. notably in 'etals). *his co'prises the deflection of a part of

the energy fro' the original bea' direction o!ing to diffraction reflection and

refraction at anisotropic single crystallites.Barious other factors !hich contribute to the loss of sound energy in a bea' are gi"en in

<ection 2.C.%.

2.: PIEOELECTRIC EFFECT ON THE CRYSTAL

2.:.1 P$e;-e#ec%r$c e77ec%

transducer is a de"ice !hich con"erts one for' of energy into another. Ultrasonic

transducers con"ert electrical energy into ultrasonic energy and "ice "ersa by utilizing a

pheno'enon kno!n as the piezoelectric effect. *he 'aterials !hich e,hibit this property are

kno!n as piezoelectric 'aterials.

n the direct piezoelectric effect first disco"ered by the 3urie brothers in 1$$0 a

piezoelectric 'aterial !hen subected to 'echanical pressure !ill de"elop an electrical

potential across it (igure 2.1C a). n the in"erse piezoelectric effect first predicted by

@ipp'ann in 1$$1 and later confir'ed e,peri'entally by the 3urie brothers in the sa'e

year 'echanical defor'ation and thus "ibration in piezoelectric 'aterials is produced

!hene"er an electrical potential is applied to the' (igure 2.1C b). *he direct piezoelectric

effect is used in detecting and the in"erse piezoelectric effect in the generation of ultrasonic

!a"es.

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2-22

igure 2.1C (a) + >irect piezoelectric effect.

igure 2.1C (b) + n"erse piezoelectric effect.

2.6.1.1 Types of pieoelectric transducers

iezoelectric transducers can be classified into t!o groups. *he classification is 'ade based

on the type of piezoelectric 'aterial !hich is used in the 'anufacture of the transducer. f

the transducers are 'ade fro' single crystal 'aterials in !hich the piezoelectric effect

occurs naturally they are classified as piezoelectric crystal transducers. Gn the other hand

the transducers !hich are 'ade fro' polycrystalline 'aterials in !hich the piezoelectric

effect has to be induced by polarization are ter'ed as electrostricti"e 'aterials or polarized

cera'ic transducers. erroelectric 'aterials are those 'aterials !hich e,hibit electrostricti"eeffect to a larger degree.

2.?.1.1.1 iezoelectric crystal transducers

<o'e of the single crystal 'aterials in !hich the piezoelectric effect occurs naturally are

quartz tour'aline lithiu' sulphate cad'iu' sulphide and zinc o,ide. 'ong these quartz

and lithiu' sulphate are the 'ost co''only used in the 'anufacture of ultrasonic

transducers.

(a) uartz

aturally or artificially gro!n quartz crystals ha"e a certain definite shape !hich is

described by crystallographic a,es consisting of an M- D- and F-a,is.

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2-2%

igure 2.1$ + <yste' co-ordinates in a quartz crystal (si'plified) and positions at M and D-

cut crystals.

*he piezoelectric effect in quartz can only be achie"ed !hen s'all plates perpendicular either to the M-a,is or D- a,is are cut out of the quartz crystal. *hese are called M-cut or D-

cut quartz crystals or transducers. M-cut crystals are used for the production and detection of

longitudinal ultrasonic !a"es (igure 2.1A) !hile D-cut crystals are used for the generation

and reception of trans"erse ultrasonic !a"es (igure 2.20). *rans"erse and surface !a"es

can be produced fro' an M-cut crystal by taking ad"antage of the pheno'enon of 'ode

con"ersion !hich occurs at an interface of t!o 'edia of different acoustic i'pedances !hen

a longitudinal ultrasonic !a"e strikes the interface at an angle. /hen an alternating "oltage

is applied across its electrodes a piezoelectric transducer oscillates at the applied frequency

!ith an a'plitude of the order of 10 ti'es its thickness. f ho!e"er the transducer is

e,cited at one of its resonance frequencies the a'plitude is considerably increased e.g. to

about 10 ti'es the thickness at the funda'ental frequency.

igure 2.1A + *he piezoelectric effect of quartz (M-cut sche'atic).

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2-2;

igure 2.20 + *he piezoelectric effect of quartz (D-cut sche'atic).

<o'e of the ad"antages and li'itations of quartz !hen used as an ultrasonic transducer aregi"en belo! +

d"antages

(i) t is highly resistant to !ear.

(ii) t is insoluble in !ater.

(iii) t has high 'echanical and electrical stability.

(i") t can be operated at high te'peratures.

@i'itations

(i) t is co'parati"ely e,pensi"e.

(ii) t is the least efficient generator of ultrasonic energy.

(iii) t suffers fro' 'ode con"ersion − !hen an M-cut quartz is used besides generating

longitudinal !a"es it also generates trans"erse !a"es. *rans"erse !a"es are

generated because an M-cut crystal !hen co'pressed elongates in the D-direction

also. roduction of trans"erse !a"es gi"es rise to spurious signals after the 'ain pulse.

(i") t requires an high "oltage for its operation.

(b) @ithiu' sulphate

@ithiu' sulphate is another piezoelectric crystal !hich is co''only used for the

'anufacture of ultrasonic transducers. <o'e of the ad"antages and li'itations of a lithiu'

sulphate transducer are as follo!s +

d"antages

(i) t is the 'ost efficient recei"er of ultrasonic energy.

(ii) t can be easily da'ped because of its lo! acoustic i'pedance.

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2-2=

(iii) t does not age.

(i") t is affected "ery little fro' 'ode con"ersion.

@i'itations

(i) t is "ery fragile.

(ii) t is soluble in !ater.

(iii) t is li'ited in use to te'peratures belo! C=°3.

2.?.1.1.2 olarized cera'ic transducers

olarized cera'ic transducers ha"e nearly co'pletely replaced quartz and are on their !ay

to replacing artificially gro!n crystals as transducer ele'ents. olarized cera'ic transducer

'aterials are ferroelectric in nature. erroelectric 'aterials consist of 'any Ndo'ainsN each

of !hich includes large nu'ber of 'olecules and each of !hich has a net electric charge.

/hen no "oltage gradient e,ists in the 'aterial these do'ains are rando'ly oriented

(igure 2.21). f a "oltage is applied the do'ains tend to line up in the direction of the field.

<ince a do'ainEs shape is longer in its direction of polarization than in its thickness the

'aterial as a !hole e,pands. f the "oltage is re"ersed in direction the do'ains also re"erse

direction and the 'aterial again e,pands. *his is in contrast to the piezoelectric crystal

'aterials !hich contract for a "oltage in one direction and e,pand for a "oltage in the

opposite direction.

*he ferroelectric 'ode (i.e. e,pansion for both positi"e and negati"e "oltage) can be easily

changed to piezoelectric 'ode by heating the ferroelectric 'aterial to its 3urie point (thete'perature abo"e !hich a ferroelectric 'aterial loses its ferroelectric properties) and then

cooling it under the influence of a bias "oltage of appro,i'ately 1000 B per '' thickness.

n this !ay the ferroelectric do'ains are effecti"ely frozen in their bias field orientations and

the polarized 'aterial 'ay then be treated as piezoelectric.

olarized cera'ic transducers as the na'e i'plies are produced like cera'ic dishes etc.

*hey are 'ade fro' po!ders 'i,ed together and then fired or heated to a solid. *he

characteristic properties required of a transducer for certain applications are controlled by

adding "arious che'ical co'pounds in different proportions. ecause prior to polarization

these cera'ic transducers are isotropic they do not require to be cut !ith reference to any

particular a,is. *hus it is possible to shape the' in any con"enient for' e.g. a conca"etransducer capable of focusing ultrasound can be produced !ithout difficulty. <o'e of the

ad"antages and li'itations of cera'ic transducers are+

d"antages

(i) *hey are efficient generators of ultrasonic energy.

(ii) *hey operate at lo! "oltages.

(iii) <o'e can be used for high te'perature applications e.g. lead 'etaniobate 3urie

point is ==0°3.

@i'itations

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2-2?

(i) iezoelectric property 'ay decrease !ith age.

(ii) *hey ha"e lo! resistance to !ear.

(iii) *hey suffer fro' 'ode con"ersion.

o potential applied

otential applied

igure 2.21 + >o'ains in ferroelectric 'aterial.

2.?.1.1.% 3o'parison of piezoelectric transducers

*he piezoelectric defor'ation constant EHE is a 'easure of the ability of a transducer to act

as an ultrasonic recei"er. High H "alues sho! the greater ability of the transducer as a

recei"er. ro' *able 2.2 it is e"ident that lithiu' sulphate is the best recei"er of ultrasonic

energy. *he electro'echanical coupling factor OPE sho!s the efficiency of a transducer for

the con"ersion of electric "oltage into 'echanical displace'ent and "ice "ersa. *his "alue is

i'portant for pulse echo operation as the transducer acts both as a trans'itter and recei"er.

Higher "alues of P 'ean that the o"erall efficiency of the transducer as a trans'itter and

recei"er is better. *he "alues for lead 'etaniobate lead zirconate-titanate and bariu'-

titanate lie in a co'parable order. satisfactory resolution po!er requires that the coupling

factor for radial oscillation P p is as lo! as possible. P p is a 'easure for the appearance of

disturbing radial oscillations !hich !iden the signals. *hese radial oscillations are becauseof the 'ode con"ersion disturbances of the transducers. ro' this point of "ie! lithiu'

sulphate and lead 'etaniobate are the best transducer 'aterials. <ince in the case of contact

as !ell as i''ersion testing a liquid couplant !ith a lo! acoustic i'pedance F is required

the transducer 'aterial should ha"e an acoustic i'pedance of the sa'e order to gi"e a better

trans'ission of ultrasonic energy into the test obect. n this respect the best choices are

lithiu' sulphate or lead 'etaniobate or quartz as all of the' ha"e lo! acoustic i'pedances.

*able 2.2 + <o'e characteristics of co''on piezoelectric transducers

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2-2C

@ead zirconatetitanate

ariu'titanate

@ead'etaniobate

@ithiu'sulphate

uartz @ithiu'niobate

<ound "elocity 7"8 '5s ;000 =100 %%00 =;?0 =C;0 C%20

coustic i'pedance 7F8 10?

kg5'2s%0 2C 20.= 11.2 1=.2 %;

:lectro'echanical couplingfactor 7P8

0.? - 0.C 0.;= 0.; 0.%$ 0.1 0.2

iezoelectric 'odulus 7d8 1=0 - =A1 12= -1A0

$= 1= 2.% ?

iezoelectric defor'ationconstant 7H8

1.$ - ;.? 1.1 -1.?

1.A $.2 ;.A ?.C

3oupling factor for radialoscillations 7P p8

0.= - 0.? 0.$ 0.0C 0 0.1 -

2.< THE CHARACTERISTICS OF THE ULTRASONIC 9EAM

2.<.1 T+e u#%r(/-n$c 8e(!

*he region in !hich ultrasonic !a"es are propagated fro' an ultrasonic transducer is kno!n

as the ultrasonic bea'. or the purpose of ultrasonic testing of 'aterials the greatly

si'plified shape of an ultrasonic bea' for a circular transducer is as sho!n in igure 2.22.

*his could be i'agined like a cone as is the light co'ing out of a torch. *!o distinct regions

of the bea' e,ist and are classified as near field (resnel zone) and far field (raunhofer

zone).

igure 2.22 + <hape of a typical sound bea' fro' a circular transducer.

*he intensity "ariation along the a,ial distance for a typical transducer is sho!n in

igure 2.2%. *he intensity passes through a nu'ber of 'a,i'a and 'ini'a. *he last 'ini'a

occurs at 52 !hile the last 'a,i'a occurs at !here denotes the near field length. fter

one near field length the intensity decreases continuously. ro' a distance of appro,i'ately

three near field lengths the sound pressure on the central a,is of the bea' is reduced

proportional to the in"erse distance and the sound bea' di"erges !ith a constant angle of

di"ergence. /e call this area the far field or the raunhofer zone. *he area fro' 1 to

appro,i'ately % is referred to as the transition zone !here the di"ergence angle still

changes and is not constant and the decrease of the sound pressure is not yet proportional tothe in"erse distance.

θ52

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2-2$

igure 2.2%+ >istribution of intensity along the a,ial distance.

igure 2.2; sho!s the radial distribution of acoustic intensity fro' a typical disc type

circular transducer. <uch a diagra' in practice can be dra!n using reflections fro' a s'all

round ball in !ater or a s'all flat botto' or side drilled hole. *he ball or holes are scanned

at a distance. *he echo is 'a,i'ized !hich sho!s the position of the central bea' a,is.

*hen the reflector is 'o"ed perpendicularly to the a,is and the positions are noted !hen theecho a'plitude falls to =0K and 10K of its 'a,i'u'. <uch points no doubt e,ist on both

the sides of the central bea' a,is. *his is sche'atically presented in igure 2.2; (also see

<ection 2.C.1.%).

igure 2.2; + <che'atic presentation of the radial distribution of intensity in a sound bea'.

*he quantities describing the shape of the sound field in a useful practical appro,i'ation are

the near field length and the half di"ergence angle θ52. *hese t!o "alues are functions of

the crystal dia'eter 7>8 the frequency 7f 8and the sound "elocity 7"8 in the 'ediu' in !hich

the sound bea' de"elops. <o'e for'ulae that apply are e,plained in the follo!ing sections.

<u''arising the results concerning the sound field !e can say that+

(i) *he character of sound field is deter'ined by the ratio of the di'ensions of the

crystal to the !a"elength. large "alue furnishes a sharp far-reaching bea' !ith a

long near zone.

(ii) *he intensity of the sound pressure at a gi"en distance is deter'ined by the ratio of

surface area to !a"elength.

(iii) t sufficient distance a sound field follo!s the la! that the sound pressure

decreases in"ersely !ith the distance

2.!.1.1 "ear field

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2-2A

piezoelectric transducer can be considered to be a collection of point sources each of

!hich is e'itting spherical ultrasonic !a"es to the surrounding 'ediu' (igure 2.2=).

igure 2.2= + <hape of the !a"e front in the near field.

*he spherical !a"es interfere !ith each other and result in a syste' of 'a,i'a and 'ini'a

in intensity in the region close to the transducer. *his region is kno!n as the near field

region or reznel zone. *he near field sho!s a bea' ha"ing a !idth appro,i'ating the

dia'eter of the crystal. Ho!e"er it is reduced up to the end of the near field !hich is called

the focus.

la!s appearing in the near field 'ust be carefully interpreted because a fla! occurring in

this region can produce 'ultiple indications and the a'plitude of the reflected signal fro'the fla! can "ary considerably if the effecti"e distance fro' the probe "aries. *his is

specially true in the case of s'aller defects !ith !hich there are greater difficulties of

interpretation in the near zone as co'pared to larger defects (co'parable !ith crystal

dia'eter). *he near field proble' can be reduced or e"en co'pletely o"erco'e by the use

of plastic shoes in front of the crystals generating ultrasound.

2.!.1.2 #alculation of near field lengt$

*he length of the near field depends upon the dia'eter of the transducer and the

!a"elength of the ultrasonic !a"es in the particular 'ediu'. *he near field length for a

probe increases !ith increase in its dia'eter and frequency and can be calculatedappro,i'ately fro'+

4 >2 5; λ --------------------------------- (2.1? a)

4 >2 f 5;" --------------------------------- (2.1? b)

!here

4 near field length

> 4 dia'eter of transducer

" 4 "elocity of sound in 'aterial

f 4 frequency

2.!.1.3 Far field

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*he region beyond the near field is kno!n as the far field. *he !a"e front of ultrasonic

!a"es in the far field beyond a distance of three near field lengths fro' the transducer is

spherical as co'pared to the !a"e front in the near field !hich is planar. *he region in the

far field bet!een one near field length and three near field lengths is kno!n as the transition

region because transition in shape of the !a"e front fro' planar to spherical occurs in this

region.

*he intensity in the far field along the a,ial distance fro' the transducer beyond three near

field lengths falls off !ith distance in accordance !ith the in"erse square la! i.e. the

intensity decreases in"ersely !ith the square of the distance (igure 2.22). *he intensity in

the transition region of the far field "aries e,ponentially !ith distance !ith an e,ponent of

distance bet!een 1 and 2.

*he reflected intensity of ultrasonic !a"es fro' fla!s occurring in the far field depends

upon the size of the fla! !ith respect to the bea' di'ensions. f the fla! is larger than the

bea' then the reflected intensity follo!s the in"erse proportional la! i.e. intensity of

reflection α 15distance. Gn the other hand if the size of the fla! is s'aller than the bea'di'ensions then the reflected intensity "aries in"ersely as the square of the distance i.e.

ntensity α 15(distance)2.

2.<.2 F$e#& &$)er*ence -r 8e(! /"re(&

t has already been 'entioned in <ection 2.C.1 that there is al!ays so'e spreading of the

ultrasonic bea' in the far field as the !a"es tra"el fro' the transducer. t is i'portant to

understand the bea' spread as it helps to point out the i'portance of selecting the proper

frequency and size of the transducer. *he length of the ultrasonic !a"e and the dia'eter of

the transducer are often critical in the deter'ination of fla! size and location. *he intensity

of the bea' is 'a,i'u' on the central a,is and decreases in proportion to the distance fro'the centre. *he angle of bea' spread or di"ergence angle θ52 can be calculated fro' the

follo!ing equation+

θn52 4 <in-1 P n λ 5> 4 <in-1 (P n"5>f) ---------------------------- (2.1C)

!here λ is the !a"elength of the ultrasonic !a"es > is the dia'eter in case of a circular

transducer and P is a constant !hich depends +

(i) Gn the edge of the bea' !hich is considered. Usually the "alue of P is deter'ined

!ith respect to the reduction of the bea' intensity to =0K (? d) 10K (20 d) and

0K (e,tre'e edge) of the 'a,i'u' a'plitude. *he subscript NnN in θn and P n

denotes the respecti"e edge e.g. θ? is the di"ergence angle for ? d edge and θ20 is

the di"ergence angle for 20 d edge.

(ii) *he 'ethod !hich is used to deter'ine bea' spread. n one 'ethod the through

trans'ission technique is used. n this case a "ery s'all dia'eter probe is 'o"ed

o"er the back!all surface of se"eral plane parallel speci'ens of different thicknesses

and a record is 'ade of the a'plitudes of the 3&* screen indications. *he bea'

spread is then plotted by oining together those points !hich ha"e the sa'e

indications a'plitude. *he sound bea' thus obtained is also referred to as the free

field.

n the second 'ethod the bea' spread is 'easured by 'aking use of the pulse echo

technique. n this 'ethod s'all reflectors of constant size at different depths are

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used to plot the bea'. *he plot of the bea' 'ade by this 'ethod is kno!n as the

Necho field″.

(iii) *he shape of the transducer i.e. !hether circular or rectangular.

Balues of P for circular and rectangular transducers deter'ined by the first 'ethodare gi"en in *able 2.% !hile *able 2.;. gi"es different "alues of P deter'ined by the

second 'ethod for both circular and rectangular transducers.

*able 2.% + Balues of k for circular and rectangular transducers as deter'ined by through

trans'ission technique

:dge P P

K (d) circular rectangular

0 K 1.22 1.00

10 K (20 d) 1.0$ 0.?0

=0 K (? d) 0.=; 0.A1

*able 2.; + Balues of k for circular and rectangular transducers as deter'ined by pulse

echo technique

:dge P P

K (d) circular rectangular

0 K 1.22 1.00

10 K (20 d) 0.$C 0.C;

=0 K (? d) 0.=1 0.;;

2.<.' In7#uence -7 /-un& )e#-c$% (n& %r(n/&ucer /$;e.

*he near field length of an ultrasonic field is gi"en by > 25;λ or >2f5;". @arger "alues of this

factor furnish a sharp far-reaching bea' !ith a long near zone. *hese large "alues 'ean

that larger the transducer size longer the near field length in a gi"en 'aterial for a gi"en

frequency. @arger dia'eter gi"es greater output of sound energy !hich acts like a big bang

and pushes 'ore and further in front of it. *his results in longer near field length on the one

hand and greater depth of penetration into 'aterial under test on the other. *herefore if for e,a'ple !e are testing steel !ith a ; 6Hz probe the near field length !ill be about 1C ''

for a 1 c' dia'eter probe !hile it !ill be ;21 '' for a = c' dia'eter probe. <i'ilarly if

!e are testing steel !ith a ; 6Hz probe ha"ing crystal dia'eter of 1 c' then the near field

length !ill be 1C '' as before. o! if the sa'e probe is used for testing of perspe, then

the near field length !ill be about %? ''. *his difference is because of the difference in

sound "elocities in steel and perspe,. e,t let us see the effect of sound "elocity and the

transducer size on the bea' di"ergence. :quation 2.1C gi"es the half bea' di"ergence angle

θ to be <in-1(P λ5>) or <in-1(P"5>f) !hich sho!s that the transducer dia'eter has a definite

influence on the sound bea' for a gi"en frequency a s'aller transducer has a greater bea'

spread angle than a larger dia'eter transducer as sho!n in igure 2.2?.

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igure 2.2? + nfluence of transducer size on the bea' di"ergence.

3hanging the transducerEs "ibrating frequency !ill also change the bea' spread. ea'

di"ergence is in"ersely proportional to frequency. *herefore a high frequency transducer has

a 'ore constant (less di"ergent) sound bea' than a lo! frequency transducer.

:,a'ple + /hat !ould be the half bea' spread (di"ergence angle) !hen testing steel using

a = 6Hz transducer ha"ing a dia'eter of 2= ''.

θ52 4 <in-1(P λ5>) 4 <in-1 1.22 λ 5>

λ 4 "5f 4 =A;0,1000 5 = , 1000000 4 1.1$ ''.

*hen

θ52 4 <in-1 (1.22 , 1.1$52=) 4 <in-1 (0.0=C=) 4 % degrees

:,a'ple+ /hat !ould be the bea' spread using a 2=.; '' dia'eter 2.2= 6Hz transducer

on an alu'iniu' test piece.

λ 4 "5f 4 ?%20,100052.2=,1000000 4 2.$ ''

θ52 4 <in-1 1.22 λ 5> 4 <in-1 (1.22 , 2.$ 5 2=.;)

4 <in-1 (0.1%;;) 4 $ degrees

2.= ATTENUATION OF SOUND

2.=.1 C(u/e (n& e77ec%

*he intensity of an ultrasonic bea' that is sensed by a recei"ing transducer is considerably

less than the intensity of the initial trans'ission. ttenuation is the ter' used to describe this

condition of energy loss. ttenuation 'eans the process of lessening the a'ount. /ith

sound attenuation the echo a'plitudes of any reflectors are additionally reduced

proportional to their distance. *his additional reduction per unit distance is called the sound

attenuation coefficient. ssu'ing that there are no 'aor discontinuities producing regular

reflections for e,a'ple cracks etc. "arious causes of attenuation e,ist na'ely scattering

absorption surface roughness and diffraction etc. *hese causes !ill be described in the

follo!ing sections.

2.%.1.1 Scattering of ultrasonic waves

*he scattering of ultrasonic !a"es is due to the fact that the 'aterial in !hich the ultrasonic

!a"e is tra"elling is not absolutely ho'ogeneous. *he inho'ogeneities can be anything that

!ill present a boundary bet!een t!o 'aterials of different acoustic i'pedance such as an

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inclusion or pores and possibly grain boundaries containing conta'inants. 3ertain 'aterials

are inherently inho'ogeneous such as cast iron !hich is co'posed of a 'atri, of grains

and graphite particles !hich differ greatly in density and elasticity. :ach grain in the

agglo'eration produces se"ere scattering. t is possible to encounter scattering in a 'aterial

of ust one crystal type if the crystals e,hibit "elocities of different "alues !hen 'easured

along a,es in different directions. 'aterial of this type is said to be anisotropic. f indi"idual grains are rando'ly oriented throughout a 'aterial scattering !ill occur as if the

'aterial is co'posed of different types of crystals or phases. 6aterials e,hibiting these

qualities not only decrease the returned ultrasonic signal because of scattering but also often

produce nu'erous s'all echoes !hich 'ay 'ask or Nca'ouflageN real indications.

condition for scattering not to occur is that the di'ensions of the particles 'ust be s'all

co'pared !ith !a"elength i.e. the particle di'ensions 'ust be less than 0.1 ti'es the

!a"elength.

2.%.1.2 &sorption of ultrasonic waves

bsorption of ultrasonic !a"es is the result of the con"ersion of a portion of the sound

energy into heat. n any 'aterial not at absolute zero te'perature the particles are in rando'

'otion as a result of the heat content of the 'aterial. s the te'perature increases there !ill

be an increase in particle acti"ity. s an ultrasound !a"e propagates through the 'aterial it

e,cites the particles. /hen these particles collide !ith une,cited particles energy is

trans'itted causing the' to oscillate faster and through larger distances. *his 'otion

persists after the sound !a"e has passed on so energy of the passing !a"e has been

con"erted to heat in the 'aterial. bsorption can roughly be "isualized as a sort of braking

effect of the oscillations of the particles !hich also 'ake it clear !hy a rapid oscillation

loses 'ore energy than a slo! oscillation. *he absorption usually increases proportional to

frequency at a rate 'uch slo!er than the scattering.

2.%.1.3 (oss due to coupling and surface roug$ness

third cause of attenuation is trans'ission loss due to the coupling 'ediu' and the surface

roughness. /hen a transducer is placed on a "ery s'ooth surface of a speci'en using a

couplant the a'plitude of signal fro' the back surface "aries !ith the thickness as !ell as

the type of the couplant.

2.%.1.4 )iffraction

n i'portant property of ultrasonic !a"es is their ability or tendency to bend around and pass obstacles !hich are co'parable in size to their !a"e length. *his !a"e interference or

diffraction occurs if the !a"e i'pinges upon a s'all inclusion or pore in the 'etal.

portion of the energy bends around the defect and reflection is 'uch reduced

(igure 2.2C a). second e,a'ple of this pheno'enon is the bending of ultrasonic !a"es

near the edge of a speci'en (igure 2.2C b). *his bending 'ay di"ert the ultrasonic !a"e

fro' !here it !ould nor'ally be recei"ed to so'e other point.

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(a) (b)

igure. 2.2C + >iffraction of ultrasound in solidsQ (a) round the defect (b) ear the

irregular edge.

2.%.1.* +verall effect of attenuation

n addition to the a'ount of sound lost due to the abo"e causes there are other factors to

consider such as losses in scattering due to surface roughness of a reflector and spreading of

the sound bea'. n this instance attenuation is considered as the su' of all these factors

since they all affect the a'ount of sound trans'itted to and returned fro' an area of interest

in the test 'aterial. *he attenuation losses during propagation in a 'aterial are sho!n in

igure 2.2$.

igure 2.2$ + ttenuation losses during trans'ission.

<cattering increases rapidly !ith increasing grain size of the 'aterial. bsorption is reduced

!ith decreasing frequency. /hen absorption and scattering act together one has to

co'pro'ise in order to find the ideal test frequency. s long as the 'ini'u' equi"alent

reflector size to be recorded is large co'pared to the a"erage grain size a frequency

reduction 'ay lead to an i'pro"ed fla! detectability. s a thu'b rule a fla! can be

regarded as being detectable if its size is bigger or equal to 15= of the !a"elength in a finegrain 'aterial.

/ith 'ost frequencies up to = 6Hz and !ith longitudinal !a"es (straight bea' probes and

longitudinal angle bea' probes) sound attenuation can nor'ally be neglected in all lo!

alloy forged steel in lo! alloy cast alu'iniu' and 'agnesiu' !orked steel nickel etc.

*hese are ter'ed as 'aterials of lo! attenuation. *he attenuation coefficient for these stays

belo! 10 d5'. *he 'aterials of 'ediu' attenuation include cast steel defor'ed copper

zinc brass bronze lead hard 'etals and sintered 'etals. ttenuation coefficients of up to

100 d5' occur in these 'aterials. @astly attenuation coefficients greater than 100 d5'

occur in 'aterials !ith high attenuation. *o this category belong 'aterials such as all kinds

of plastics rubber concrete and !ood as !ell as high alloy cast steel high alloy castalu'iniu' and 'agnesiu' cast copper zinc brass bronze porous cera'ics and rocks etc.

Ultrasonic testing of these 'aterials turns out to be "ery difficult although in practical

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applications 'any proble's ha"e already been sol"ed. f testing is possible then due to the

high loss of sound energy this !ould only be for quite thin !orkpieces. f the pulse echo

technique fails in these cases the through trans'ission technique 'ay still be applicable.

*he discussion of attenuation 'ade so far is applicable to the longitudinal !a"es. or

trans"erse !a"es the attenuation is generally 'uch stronger particularly in plastics.<i'ilarly attenuation usually increases !ith the te'perature of the test speci'en. or steel a

'a,i'u' of the attenuation of sound appears at the transition point fro' body-centred to

face-centred iron (appro, C21°3).

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