Kutz M. Handbook of materials selection

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658 NONDESTRUCTIVE INSPECTION

the returning echoes, also gates the echoes that return between the front surface

and rear surfaces of the component. Thus, any unusually occurring echo can

either be displayed separately or used to set off an alarm.

A schematic diagram of a typical ultrasonic pulse echo setup is shown in Fig.

6. This method of displaying of voltage amplitude of the returning pulse versus

time or depth (if acoustic velocity is known) at a single point of the specimen

is known as an A-scan. In this ﬁgure, the ﬁrst signal corresponds to a reﬂection

from the front surface (FS) of the part and the last signal corresponds to the

reﬂection from its back surface (BS). The signal or echo between FS and BS is

from the defect in the middle of the part.

The portion of sound energy reﬂected from or transmitted through each in-

terface is a function of the impedances of media on each side of that interface.

The reﬂection coefﬁcient R (ratio of the sound pressures or intensities of the

reﬂected and incident waves) and transmission coefﬁcient T (ratio of the sound

pressures or intensities of the transmitted and incident waves) for an acoustic

wave normally incident on to an interface are

⫺ Z

t 12

R ⫽⫽

pZ⫹ Z

i 12

IZ⫺ Z

r 12

R ⫽⫽

冉冊

pwr

IZ⫹ Z

i 12

Likewise, the transmission coefﬁcients, T and T

pwr

, are deﬁned as

p 2

⫻ Z

t 2

T ⫽⫽

pZ⫹ Z

i 12

4 ⫻

冉冊

T ⫽⫽

␳

1 ⫹

冋冉冊册

where I

, I

, and I

are the incident, reﬂected, and transmitted acoustic ﬁeld

intensities, respectively. Z

is the acoustic impedance of the media from which

the sound wave is incident and Z

is impedance into which the wave is trans-

mitted. From these equations one can calculate the reﬂection and transmission

coefﬁcients for a planar ﬂaw containing air, Z

⫽ 450 kg/cm

s, located in a

steel part, Z

⫽ 45.4 ⫻ 10

kg/m

s. In this case, the reﬂection coefﬁcient for

the ﬂaw is practically

⫺1.0. The minus sign indicates a phase change of 180⬚

for the reﬂected pulse (note that the defect signal in Fig. 6 is inverted or phase

shifted by 180

⬚ from the front surface signal).

Effectively no acoustic energy is transmitted across an air gap, necessitating

the use of water as a coupling media in ultrasonic testing. The acoustic properties

of several common materials are shown in Appendix A. These data are useful

for a number of simple, yet informative, calculations.

3 ULTRASONIC METHODS 659

Voltage

time

Sweep Generator

Pulser

Time Base

Receiver

Ultrasonic Transducer

Couplant

Front Surface (FS)

Back Surface (BS)

Voltage

time

Sound

Field

x axis

y axis

Ultrasonic

Signal

Defect (D)

Fig. 6 A schematic representation of ultrasonic data collection and display

in the A-scan mode.

Thus far our discussion has involved only longitudinal waves. This is the only

wave type that travels through ﬂuids such as air and water. The particle motion

in this wave, if it were observed, is similar to the motion one would observe in

a spring, or a Slinky toy, where the displacement and wave motion are collinear

(the oscillations occur along the direction of propagation). The wave is referred

to as compressional or dilatational since both compressional and dilatational

forces are active in it. Audible sound waves are compressional waves. This wave

type is observed in liquids and gases as well as in solids. However, a solid

medium can also support additional types of waves such as shear and Rayleigh

or surface waves. Shear or transverse waves have a particle motion that is anal-

ogous to what one sees in a rope that has been snapped. That is, the displacement

of the rope is perpendicular to the direction of wave propagation. The velocity

of this wave is about half that of compressional waves and is only found in solid

media as indicated in the acoustic velocity appendix, i.e., Appendix A. Shear

waves are often generated when a longitudinal wave is incident on a ﬂuid/solid

interface at angles of incidence other than 90

⬚. Rayleigh or surface waves have

elliptical wave motion, as shown in Fig. 7, and penetrate the surface for about

one wavelength; therefore, they are used to detect surface and very near surface

ﬂaws. The velocity of Rayleigh waves is about 90% of the shear wave velocity.

Their generation requires the special device shown in Fig. 8, which enables an

660 NONDESTRUCTIVE INSPECTION

Transducer

Couplant

Conversion

Wedge

Direction of

Pro

ation

Wavelength

Air

Solid

Particle

displacement as

surface wave

propagates on a

material surface

Fig. 7 Generation and propagation of surface waves in a material.

Incident

Longitudinal

Wave

Reflected

Longitudinal

Wave

Refracted

Longitudinal

Wave

Refracted

Shear Wave

(Vertically

Polarized)

Reflected

Shear

Wave

Medium I

c , b , ␳

Medium II

c , b , ␳

Direction of

particle

displacement

Direction of

particle

displacement

Fig. 8 Schematic representation of Snell’s law and the mode conversion of a longitudinal wave

incident on a solid / solid interface.

incident ultrasonic wave on the sample at a speciﬁc angle that is characteristic

of the material (Rayleigh angle). The reader can ﬁnd more details in Ref. 63.

3.3 Refraction of Sound

The direction of propagation of acoustic waves is described by the acoustic

equivalent of Snell’s law. Referring to Fig. 8, the directions of propagation are

determined with the following equation:

sin

␪

sin

␪

sin

␥

sin

␪

sin

␥

irrtt

⫽⫽⫽⫽

ccbcb

II IIIII

where c

is the velocity of the incident longitudinal wave, c

and b

are the

velocities of the longitudinal and shear reﬂected waves, and c

and b

are the

velocities of the longitudinal and shear transmitted waves in solid II. The angles

of incidence and transmission are shown in Fig. 8. In the case of the water/steel

3 ULTRASONIC METHODS 661

Fig. 9 The amplitude (energy ﬂux) and phase of the reﬂected coefﬁcient and transmitted ampli-

tude versus angle of incidence for a longitudinal wave incident on a water –steel interface.

The arrows indicate the critical angles for the interface.

interface, there are no shear waves reﬂected because these waves do not prop-

agate in ﬂuids such as water. In this case, the above relationship is simpliﬁed.

Since the water has a lower wave speed than either the compressional or shear

wave speeds of the steel, the acoustic waves in the metal are refracted away

from the normal. There will be a critical angle at which the refracted wave travels

along the interface and does not enter the steel. Above this angle the acoustic

wave will not be generated in the metal. A computer-generated curve is shown

in Fig. 9 in which the normalized acoustic energy reﬂected and refracted at a

water/steel interface are plotted as a function of angle of incidence. Note that

the longitudinal or ﬁrst critical angle for steel occurs at 14.5

⬚. Likewise the shear

or second critical angle occurs at 50

⬚. If the angle of incidence is increased,

above the ﬁrst critical angle, only the shear wave is generated in steel and travels

at an angle of refraction determined by Snell’s law. Angles of incidence above

the second critical angle produce a complete reﬂection of the incident acoustic

wave; that is, no acoustic energy enters the solid. At a speciﬁc angle of incidence

(Rayleigh angle) surface acoustic waves are generating on the material. The

Rayleigh angle can be easily calculated from Snell’s law by assuming that the

refracted angle is 90

⬚. The Rayleigh angle for steel is 29.5⬚. In the region be-

tween the two critical angles only the shear wave is generated and is referred

to as ‘‘shear wave testing.’’ There are two distinct advantages to inspecting parts

with this type of shear wave. First, with only one type of wave present, the

ambiguity that would exist concerning which type of wave is reﬂected from a

defect does not occur. Second, the lower wave speed of the shear wave means

that it is easier to resolve distances within the part. For these reasons, shear wave

662 NONDESTRUCTIVE INSPECTION

inspection is often chosen for inspection of thin metallic structures such as those

in aircraft.

Using the relationships for the reﬂection and transmission coefﬁcients, a great

deal of information can be deduced about any ultrasonic inspection situation

with the acoustic wave incident at 90

⬚ to the surface. For other angles of inci-

dence, computer software is often used to analyze the acoustic interactions. For

more complicated materials or structures such as ﬁber-reinforced composites

analytical predictions require the use of a rather complex analysis. In some cases,

more complicated modes of wave propagation can occur. Examples of these

include Lamb waves (plate waves), Stoneley waves (interface waves), Love

waves (guided waves in the layer on a coated material), and others.

3.4 Inspection Process

Once the type of ultrasonic inspection has been chosen and the optimum ex-

perimental parameters determined, then one must choose the mode of presen-

tation of the data. If the principle dimension of the ﬂaw is less than the diameter

of the transducer, then the A-scan method may be chosen, as shown in Fig. 6.

The acquisition of a series of A-scans obtained by scanning the transducer in

one direction across the specimen and displaying the data as distance versus

depth is referred to as B-scan. This is the mode most often used by medial

ultrasound instrumentation. In the A-scan mode, the size of the ﬂaw may be

inferred by comparing the amplitude of the defect signal to a set of standard

calibration blocks. Each block has a ﬂat bottom hole (FBH) drilled from one

end. Calibration blocks have FBH diameters that vary in -in. increments.

––

Therefore, a number 5 block has a -in. FBH. By comparing the amplitude of

––

the signal from a calibration block with one from a defect, the inspector may

specify a defect size as equivalent to a certain size FBH. The equivalent size is

meaningful only for approximately smooth ﬂaws that are nearly perpendicular

to the path of the ultrasonic beam.

If the ﬂaw size is larger than the transducer diameter, then the C-scan mode

is usually selected. In this mode, shown in Fig. 10, the transducer is rastered

back and forth in two directions across the part. In normal operation a line is

traced on a monitor or piece of paper. When a ﬂaw signal is detected between

the front and back surface, a line with much increased darkness appears on the

paper or monitor. Using this mode of presentation, a planar projection of each

ﬂaw is presented to the viewer and its positional relationship to other ﬂaws and

to the component boundaries is easily ascertained. Unfortunately, the C-scan

mode does not show depth information, unless an electronic gate is set to capture

only information from within a speciﬁed time window or time gate in the part.

With current computer capability it is a rather simple matter to store all of the

returning A-scan data and display only the data in a C-scan mode for speciﬁc

depth. The C-scan mode provides a visual representation of a slice of the ma-

terial at a certain depth and is very useful for inspection purposes.

Depending on the structural complexity and the attenuation of the signal by

the material, ﬂaws as small as 0.015 in. can be reliably detected and quantiﬁed

using this inspection method. An example of a typical C-scan printout of an

adhesively bonded test panel is shown in Fig. 11. While the panel was fabricated

with a Teﬂon void-simulating implant in the center, the numerous additional

white areas indicate the presence of a great deal of porosity in the part.

50,58

4 RADIOGRAPHY 663

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

Pulser-Receiver

Recording

of C-scan

Time

Gate

Out

Transducer

Fig. 10 Schematic representation of ultrasonic data collection. The data are displayed using

the C-scan mode. The image shows a defect located at a certain depth in the material.

Delaminations

Fig. 11 Typical C-scan image of a composite specimen showing delaminations and porosity.

Black and white are reversed.

4 RADIOGRAPHY

In classical NDE radiography the projected X-ray attenuation for a multitude of

paths through a specimen are recorded as a two-dimensional image on some

type of recording media. In computed tomography (CT), the attenuation values

are used to calculate a cross-sectional image of the component being inspected.

A detailed description of radiography testing (RT) may be found in the Non-

destructive Testing Handbooks.

The classic RT process is shown schematically in Fig. 12. Note that RT re-

cords visually any feature that changes the attenuation of the X-ray beam as it

transverses a path through the component. This local change in attenuation pro-

duces a change in the intensity of the X-ray beam, which translates to a change

in the density or darkness on a ﬁlm or electronic recording device. The inspector

uses this change in brightness to detect internal anomalies, which sometimes

appear as a mere shadow on the radiograph. The inspector is greatly aided in

detecting and quantifying ﬂaws by knowing the geometry of the part and how

this relates to the image. It should be noted in Fig. 12 that only ﬂaws that change

the attenuation of the X-ray beam on passage through the part are recorded. For

example, a delamination in the laminated specimen is not visible because there

is no change in attenuation of the X-ray beam. Flaws that are oriented parallel

664 NONDESTRUCTIVE INSPECTION

Lead Diaphram

Collimated Beam

X-Ray Film

Crack

Large Pore

Delamination

Fig. 12 Schematic radiograph of a typical composite with typical ﬂaws.

Fig. 13 Radiograph of a crack in the end of an aluminum tubing.

to the X-ray path do not attenuate the X-ray beam and thus allow more radiation

to expose the ﬁlm and thus appear darker than the surrounding image. An ex-

ample of a crack in the correct orientation to be visible on a radiograph of a

piece of tubing is shown in Fig. 13.

4.1 Generation and Absorption of X-Radiation

X-radiation can be produced from a number of processes. The most common

form of producing X-rays is with an electron tube in which a beam of energetic

electrons impacts a metal target. As the electrons are rapidly decelerated in this

collision, a wide band of X-radiation is produced, analogous to white light. This

band of radiation is referred to as Bremsstrahlung or breaking radiation. Higher-

energy electrons produce shorter-wavelength or more energetic X-rays. The re-

lationship between the shortest-wavelength radiation and the highest voltage

applied to the tube is given by

12,336

␭

⫽

voltage

where

␭

,inA

ngstroms, is the shortest wavelength of the X-radiation produced.

4 RADIOGRAPHY 665

0.01 0.1 1.0 5.0

1000

100

Specimen Thickness, inches

X-Ray Potential, Kilovolts

Cooper & Nickel Alloys

Steel & Stainless Steel

Titanium Alloys

Aluminum &

Borsic/Aluminum

Boron/Epoxy

Fiberglass/

Epoxy

Graphite/Epoxy

& Adhesives

Fig. 14 Plot of the X-ray tube voltage versus thickness of several important

industrial materials.

Table 2 Approximate Radiographic Equivalence Factors

100 kV 150 kV 220 kV 250 kV 400 kV 1 MeV 2 MeV 4–25 MeV 192Ir 60Co

Metal

Magnesium 0.05 0.05 0.08

Aluminum 0.08 0.12 0.18 0.35 0.35

Aluminum alloy 0.10 0.14 0.18 0.35 0.35

Titanium 0.54 0 54 0.71 0.9 0.9 0.9 0.9 0.9

Iron / all steels 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Copper 1.5 1.6 1.4 1.4 1.4 1.1 1.1 1.2 1.1 1.1

Zinc 1.4 1.3 1.3 1.2 1.1 1.0

Brass 1.4 1.3 1.3 1.2 1.1 1.0 1.1 1.0

Inconel X 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1 3

Monel 1.7 1.2

Zirconium 2.4 2.3 2.0 1.7 1.5 1.0 1.0 1.0 1.2 1.0

Lead 14.0 14.0 12.0 5.0 2.5 2.7 4.0 2.3

Halfnium 14.0 12.0 9.0 3.0

Uranium 20.0 16.0 12.0 4.0 3.9 12.6 3.4

The more energetic the radiation, the more penetrating power it has. Therefore,

higher energy radiation is used on dense materials such as metals. While it is

possible to analytically predict what X-ray energy would provide the best image

for a speciﬁc material and geometry, a simpler method of determining the op-

timum X-ray energy is shown by Fig. 14. Note that higher energies are used for

dense materials, e.g., steels, or for thick light materials, e.g., large plastic parts.

An alternative method to using this ﬁgure is to use radiographic equivalence

factors shown in Table 2.

Aluminum is the standard material for voltages below

100 KeV, while steel is the standard above this voltage. When radiographing

any other material, its thickness is multiplied by the factor to obtain the equiv-

alent thickness of the standard material. The radiographic parameters are set for

this thickness of aluminum or steel. In this manner a good-quality radiograph is

666 NONDESTRUCTIVE INSPECTION

Log(mass absorption coefficient)

Atomic Number

•

• B

• H

• Li

•

N •

•

Ni •

O •

S •

Al •

•

Pb •

Sn •

•

• Fe

•

Fig. 15 Plot of mass absorption coefﬁcient versus atomic number.

obtained for the part in question. For example, assume that one must radiograph

a 0.75-in.-thick piece of brass with a 400 KeV X-ray source; then the inspector

should multiply 0.75 by the factor of 1.3 to obtain 0.98. This means that an

acceptable radiograph of the brass plates would be obtained with the same ex-

posure parameters as would be used for 0.98 in. (approximately 1 in.) of steel.

Radiation for RT can also be obtained from the decay of radioactive sources.

In this case, the process is usually referred to as gamma radiography. These

radiation sources have several different characteristics from X-ray tubes. First,

the gamma radiation is very nearly monochromatic; that is, the spectrum of

radiation contains only one or two dominant energies. Second, the energies of

most sources is in the million-volt range, making this source ideal for inspecting

highly attenuating materials and structures. Third, the small size of these sources

permits them to be used in tight locations where an X-ray tube could not ﬁt.

Fourth, since the gamma-ray source is continually decaying, adjustments to the

exposure time must be made to achieve consistent results over time. Finally, the

operator must always remember that the source is continually on and is therefore

a persistent safety hazard. Aside from these differences, gamma radiography

differs little from standard practice, so no further distinction between the two

will be given.

4.2 Neutron Radiography

Neutron radiography

may be useful in inspecting materials and structures in

some circumstances. Because the attenuation of neutrons is not related to atomic

number in a regular manner, some elements can be more easily detected that

others. While X-rays are most heavily absorbed by high-atomic-number ele-

ments, this is not true of neutrons, as shown in Fig. 15. The reader can discern

that hydrogen adsorbs neutrons more strongly than do most metals. This means

that any hydrogen-containing materials would be easily detected within a heavy

metal container. Neutron radiography has been used to detect porosity in the

4 RADIOGRAPHY 667

Missing Adhesive

Porosity

Fig. 16 Neutron radiograph of specimen showing bond line ﬂaws.

adhesive used to join metal structures. In this case, the hydrogen of the adhesive

is preferentially absorbed compared to the metal—see the schematic represen-

tation of a neutron radiograph of an adhesively bonded specimen with various

ﬂaws shown in Fig. 16.

Neutron radiography, however, does have several constraints. First, neutrons

do not expose radiographic ﬁlm and therefore ﬂuorescing must be used to pro-

duce an image with light. The image produced in this manner is not as sharp

and well deﬁned as that from X-rays. Second, there does not exist a high-ﬂux,

portable source of neutrons. This means that a nuclear reactor is most often used

to supply the penetrating radiation. Given these restrictions, there are times when

there is no other alternative to neutron radiography, and utility of the method

outweighs its expense and difﬁculty.

4.3 Attenuation of X-Radiation

An appreciation of how radiographs are interpreted requires a fundamental un-

derstanding of the X-ray absorption. The basic relationship governing this phe-

nomenon is de Beer’s law.

⫺

␮

I ⫽ Ie

where I and I

are the transmitted and incident X-ray beam intensities, respec-

tively,

␮

is the attenuation coefﬁcient of the material in reciprocal centimeters

(cm

⫺

), and x is the thickness of the specimen, in centimeters. Since the atten-

uation coefﬁcient is a function of both the composition of the specimen and the

wavelength of the X-rays, it would be necessary to calculate or measure it for

each wavelength used in radiographs testing (RT). However, it is possible to

calculate the attenuation coefﬁcient of a material for a speciﬁc X-ray energy

using the mass absorption coefﬁcient,

␮

, as deﬁned below. The mass absorption

coefﬁcients for most elements are readily available for a variety of X-ray ener-

gies

␮

⫽

␳

where

␮

is the attenuation coefﬁcient of one element of the material, in recip-

rocal cm, and

␳

its density in g/cm

. The mass absorption coefﬁcient for the

material is obtained, at a speciﬁc X-ray energy, by multiplying

␮

of each ele-