2
CHAPTER
Fundamentals of Magnetic
Testing1,2
Roderic K. Stanley, NDE Information Consultants,
Houston, Texas
Satish S. Udpa, Michigan State University, East Lansing,
Michigan (Parts 1, 9, 10 and 11)
Rusty G. Waldrop, United States Coast Guard,
Elizabeth City, North Carolina
PART 1. Introduction to Magnetic Tests
Magnetic testing is part of the widely used independent testing companies or the end
family of electromagnetic nondestructive user’s quality assurance department. Oil
testing. The theory and practice of field tubular goods are often tested at this
electromagnetic techniques are discussed stage.
elsewhere in the NDT Handbook.1 When
used with other methods, magnetic tests Inservice Testing
can provide a quick and relatively
inexpensive assessment of the integrity of Good examples of inservice applications
ferromagnetic materials. are the testing of used wire rope, installed
tubing, or retrieved oil field tubular goods
Magnetic particle testing is in fact a by independent facilities. Many
variation of flux leakage testing that uses laboratories also use magnetic techniques
particles to produce indications. Because (along with metallurgical sectioning and
of the prevalence of tests specifically using other techniques) for the assessment of
particles, magnetic particle testing is steel products and prediction of failure
usually treated as a separate method by modes.
industry and in the literature. The term
flux leakage testing, also called diverted flux Steps in Magnetic Testing
testing, is then meant to exclude tests with
particles. There are four steps in magnetic testing:
(1) magnetize the test object so that
The magnetic circuit and the means for discontinuities perturb the flux, (2) scan
producing the magnetizing force that the surface of the test object with a
causes magnetic flux leakage are described magnetic flux sensitive detector,
below. Theories developed for surface and (3) process the raw data from these
subsurface discontinuities are outlined detectors in a manner that best
along with some results that can be accentuates discontinuity signals and
expected. (4) present the test results clearly for
interpretation. The following discussion
Industrial Uses3 deals with the first step, producing the
magnetizing force.
Magnetic testing is used in many
industries to find a wide variety of Magnetic Particle Testing
discontinuities. Much of the world’s
production of ferromagnetic steel is tested Principles
by magnetic or electromagnetic
techniques. Steel is tested many times Magnetic particle testing is a
before it is used and some steel products nondestructive method of revealing
are tested during use for safety and surface and subsurface discontinuities in
reliability and to maximize their length of magnetizable materials. It may be applied
service. to raw materials such as billets, bars and
shapes; during processes such as forming,
Production Testing machining, heat treating and
electroplating; and in testing for service
Typical applications of magnetic flux related discontinuities.
leakage testing are by the steel producer,
where blooms, billets, rods, bars, tubes The testing method is based on the
and ropes are tested to establish the principle that magnetic flux in a
integrity of the final product. In many magnetized object is locally distorted by
instances, the end user will not accept the presence of a discontinuity. This
delivery of steel product without testing distortion causes some of the magnetic
by the mill and independent agencies. field to exit and reenter the test object at
the discontinuity. This phenomenon is
Receiving Testing called magnetic flux leakage (MFL). Flux
leakage is capable of attracting finely
The end user often uses magnetic flux divided particles of magnetic materials
leakage tests before fabrication. This test that in turn form an outline or indication
ensures the manufacturer’s claim that the of the discontinuity. The intensity or
product is within agreed specifications.
Such tests are frequently performed by
42 Magnetic Testing
curvature of magnetic flux leakage fields is Capabilities and Limitations
critical in causing particles to remain held
at an indication. Magnetic particle testing can reveal
surface discontinuities, including those
One of the objectives of magnetic too small or too tight to be seen with the
particle testing is to detect discontinuities unaided eye. Magnetic particle indications
as early as possible in the processing form on an object’s surface above a
sequence, thus avoiding the expenditure discontinuity and show the location and
of effort on materials that will later be approximate size of the discontinuity.
rejected. Practically every process, from Magnetic particle tests can also reveal
the original production of metal from its discontinuities that are slightly below the
ore to the last finishing operation, may surface, depending on their size.
introduce discontinuities. Magnetic
particle testing can reveal many of these, There are limits on this ability to locate
preventing flawed components from subsurface discontinuities. These limits are
entering service. Even though magnetic determined by the intensity of the applied
particle testing may be applied during and field and by the discontinuity’s depth,
between processing operations, a final test size, type and shape. In some cases,
is usually performed to ensure that all special techniques or equipment can
detrimental discontinuities have been improve the test’s ability to detect
detected. In welds with a tendency toward subsurface discontinuities.
delayed cracking, there may be a specified
time delay between the completion of Magnetic particle testing is for
welding and the final test. ferromagnetic materials only: it cannot be
used on nonmagnetic materials, including
The test itself consists of three basic glass, ceramics, plastics or such common
operations: (1) establish a suitable metals as aluminum, magnesium, copper
magnetic flux in the test object; (2) apply and austenitic stainless steel alloys.
magnetic particles in a dry powder or a
liquid suspension; and (3) examine the In addition, there are certain positional
test object under suitable lighting limitations: a magnetic field is directional
conditions, interpreting and evaluating and for best results must be perpendicular
the test indications (as in Fig. 1). to the discontinuity. This generally
FIGURE 1. Forging laps in piston rods. requires magnetizing operations in
different directions to detect
discontinuities. Objects with large cross
sections may require a very high current
to generate a magnetic field adequate for
magnetic particle tests. A final limitation
is that a demagnetization procedure is
usually required following the magnetic
particle process.
Knowledge of limitations can be
helpful to managers, supervisors and
personnel outside nondestructive testing
who require general information on the
magnetic particle testing process. It may
also be helpful for introductory studies by
individuals already using magnetic
particle testing or those preparing for
advanced training in the technique.
Fundamentals of Magnetic Testing 43
PART 2. Magnetic Field Theory
Magnetic Domains 5. They seek the path of least magnetic
resistance or reluctance in completing
Materials that can be magnetized possess their loops.
atoms that group into magnetically When a bar magnet is broken into two
saturated regions called magnetic domains.
These domains have a positive and or more pieces, new magnetic poles are
negative polarity at opposite ends. In formed. The opposing poles attract one
macroscopically unmagnetized material, another as shown in Fig. 4.
the domains are randomly oriented,
usually parallel with the crystalline axes If the center piece in Fig. 4 is reversed
of the material, resulting in zero net so that similar poles are adjacent, the
magnetization. lines of force repel one magnet from the
other. If one of the bars is small enough,
When the material is subjected to a the lines of force can cause it to rotate so
magnetic field, the domains attempt to that unlike poles are again adjacent. This
align themselves parallel with the external illustrates the most basic rule of
magnetic field. The material then acts as a magnetism: unlike poles attract and like
magnet. Figure 2 illustrates the domain poles repel.
alignment in nonmagnetized and FIGURE 2. Orientation of magnetic domains:
magnetized material. (a) in nonmagnetized material; (b) in
magnetized material.
Magnetic Poles (a)
A magnet has the property of attracting (b)
ferromagnetic materials. The ability to
attract (or repel) is not uniform over the FIGURE 3. Magnetic field surrounding bar
surface of a magnet but is concentrated at magnet.
localized areas called poles. In every
magnet, there are two or more poles with
opposite polarities. These poles are
attracted to the Earth’s magnetic poles
and therefore are called north and south
poles.
Figure 3 can be duplicated by placing a
sheet of paper over a bar magnet and
sprinkling iron particles on the paper. It
shows the magnetic field leaving and
entering the ends or poles of the magnet.
This characteristic pattern illustrates the
term lines of force used to describe a
magnetic flux field. There are a number of
important properties associated with lines
of force.
1. They form continuous loops that are
never broken but must complete
themselves through some path.
2. They do not cross one another.
3. They are considered to have direction,
leaving from the north pole and
traveling through air to the south
pole, where they reenter the magnet
and return through the magnet to the
north pole.
4. Their density decreases with increasing
distance from the poles.
44 Magnetic Testing
Types of Magnetic Sources of Magnetism
Materials
Permanent Magnets
All materials are affected to some degree
by magnetic fields. Matter is made up of Permanent magnets are produced by heat
atoms with a positively charged nucleus treating specially formulated alloys in an
surrounded by a field or cloud of intense magnetic field. During heat
negatively charged electrons. The electron treatment, the magnetic domains become
field is in continual motion, spinning aligned and remain aligned after removal
around the nucleus. When the material is of the external field. Permanent magnets
subjected to a magnetic field, the electron are essential to modern technology; their
orbits are distorted to some degree. The applications include magnetos, direct
amount of this distortion (or the current motors, telephones, loud speakers
corresponding change in magnetic and many electric instruments.
characteristics) when subjected to an
external magnetic field provides a means Common examples of permanent
of classifying materials into three main magnetic materials include alloys of
groups: diamagnetic, paramagnetic or aluminum, nickel and cobalt (alnico);
ferromagnetic. copper, nickel and cobalt (cunico); copper,
nickel and iron (cunife); and cobalt and
Diamagnetic Materials molybdenum (comol). Supermagnet
materials such as neodymium-iron-boron
The term diamagnetic refers to a substance and samarium-cobalt are now common.
whose magnetic permeability is slightly
less than that of air. When a dimagnetic Magnetic Field of the Earth
object is placed in an intense magnetic
field, the induced magnetism is in a The planet Earth is itself a huge magnet,
direction opposite to that of iron. with north and south poles slightly
Diamagnetic materials include mercury, displaced from the Earth’s axis. This
gold, bismuth and zinc. displacement results in a slight deviation
between geographic north and magnetic
Paramagnetic Materials north.
Paramagnetic describes a substance whose As a magnet, the Earth is surrounded
permeability is slightly greater than that by magnetic lines of force as shown in
of air or unity. When such materials are Fig. 5. These lines of force make up what
placed in an intense magnetic field, there is sometimes called the earth field and
is a slight alignment of the electron spin they can cause problems in both
in the direction of the magnetic flux flow. magnetizing and demagnetizing of
This alignment exists only as long as the ferromagnetic test objects. The earth field
paramagnetic material is in the external is weak, on the order of 0.03 mT (0.3 G).
magnetic field.
Movement of ferromagnetic objects
Aluminum, platinum, copper and through the earth field can induce slight
wood are paramagnetic materials magnetization. This is a problem in
aircraft where magnetized components
Ferromagnetic Materials can affect the compasses used in
navigation. Similarly, demagnetizing can
Ferromagnetic substances have a be difficult if certain objects, usually long
permeability that is much greater than shafts, are not oriented from east to west
that of air. When placed in an external during the demagnetization process.
magnetic field, the magnetic domains
align parallel with the external field and Mechanically Induced Magnetism
remain aligned for some period of time
after removal from the field. Cold working of some ferromagnetic
Ferromagnetism can only be explained via materials, either by forming operations or
the domain theory. Paramagnetic and during service, can magnetize the objects.
diamagnetic materials do not contain
such domains. FIGURE 4. Broken bar magnet illustrating
locations of newly formed magnetic poles.
This continued alignment after
removal from the external field is called NS NS
retentivity and can be an important
property in some magnetic particle testing S NS NS N
procedures.
Legend
Some examples of ferromagnetic N = north
materials are iron, cobalt, nickel and S = south
gadolinium.
Fundamentals of Magnetic Testing 45
When mechanically induced FIGURE 5. Magnetic field of Earth.
magnetization occurs as a result of
forming operations, it can be removed by
subjecting the magnetized object to a
routine demagnetization process.
It can be difficult to remove
mechanically induced magnetization
resulting from cold working. Disassembly
is usually impractical and
demagnetization must be accomplished
using portable yokes or cable coils. The
operation is complicated when other
ferromagnetic components are near the
magnetized object: the demagnetizing
operation can magnetize adjacent objects
and a sequence of demagnetizing
operations must then be performed.
46 Magnetic Testing
PART 3. Magnetic Flux and Flux Leakage
Circular Magnetic Fields the poles. Magnetic poles can be thought
of as occurring wherever field lines enter
The most familiar type of magnet is the and leave a magnetized object.
horseshoe shape shown in Fig. 6a. It Ferromagnetic materials are attracted only
contains both a north and south pole to the poles and such an object is said to
with the lines of magnetic flux leaving have a longitudinal field or to be
the north pole and traveling through air longitudinally magnetized.
to reenter the magnet at the south pole.
Ferromagnetic materials are only attracted If these magnetic flux lines are
and held at or between the poles of a interrupted by a discontinuity, additional
horseshoe magnet. north and south poles are formed on
either side of the interruption (Fig. 7b).
If the ends of such a magnet are bent FIGURE 6. Horseshoe magnet illustrating
so that they are closer together (Fig. 6b), fundamental properties of magnetism:
the poles still exist and the magnetic flux (a) direction of magnetic flux; (b) magnetic
still leaves and reenters at the poles. In flux in air around poles (moving poles close
such a case, however, the lines of force are together raises magnetic flux density);
closer and more dense. The number of (c) fusing poles, forming a circularly
lines of flux per unit area is called magnetized object; (d) discontinuity in
magnetic flux density and is measured in circularly magnetized object and its resulting
tesla or gauss. flux leakage field.
(a)
If the magnetic flux density is high
enough, ferromagnetic particles are NS
strongly attracted and can even bridge the
physical gap between poles that are close (b)
enough together. The area where the flux
lines leave the pole, travel through air and NS
reenter the magnet is called a magnetic Magnetic particles
flux leakage field.
(c)
When the ends of a magnet are bent
together and the poles are fused to form a Magnetic particles
ring (Fig. 6c), the magnet no longer
attracts or holds ferromagnetic materials (d)
(there are no magnetic poles and no flux
leakage field). The magnetic flux lines still SN
exist but they are completely contained
within the magnet. In this condition, the
magnet is said to contain a circular
magnetic field or to be circularly
magnetized.
If a crack crosses the magnetic flux
lines in a circularly magnetized object,
north and south poles are immediately
created on either side of the discontinuity.
This forces a portion of the magnetic flux
into the surrounding air, creating a flux
leakage field that attracts magnetic
particles (Fig. 6d) and forms a crack
indication.
Longitudinal
Magnetization
If a horseshoe magnet is straightened, a
bar magnet is formed with north and
south poles (Fig. 7a). Magnetic flux flows
through the magnet and exits or enters at
Fundamentals of Magnetic Testing 47
Such secondary poles and their associated Subsurface Discontinuities
flux leakage fields can attract magnetic
particles. Even if the discontinuity is a A slot such as a keyway on the backside of
very narrow crack, it will still create an object creates new magnetic poles that
magnetic poles (Fig. 7c) that hold distort the internal flux flow. If the slot is
magnetic materials (the magnetic flux close enough to the surface, some
leakage field is still finite). magnetic flux lines may be forced to exit
and reenter the magnetized object at the
Magnetic Field Intensity surface. The resulting leakage field can
form a magnetic particle test indication.
The intensity of a flux leakage field from a
discontinuity depends on several factors: Size and intensity of the indication
(1) the number of magnetic flux lines, depends on: (1) the proximity of the slot
(2) the depth of the discontinuity and to the top surface; (2) the size and
(3) the width of the discontinuity’s air gap orientation of the slot; and (3) the
at the surface (the distance between the intensity and distribution of the magnetic
magnetic poles). flux field. A similar effect occurs if the
discontinuity is completely internal to the
The intensity and curvature of the object. Figure 8 is an illustration of a
leakage field determines the number of keyway on the far side of a bar and Fig. 9
magnetic particles that can be attracted to illustrates a midwall discontinuity.
form a test indication. The greater the
leakage field intensity, the denser the Effect of Discontinuity
indication, so long as the magnetic flux Orientation
leakage field is highly curved.
The orientation of a discontinuity in a
FIGURE 7. Bar magnet illustrating magnetized object is a major factor in the
longitudinal magnetization: (a) horseshoe intensity of the magnetic flux leakage
magnet straightened into bar magnet with field that is formed. This applies to both
north and south poles; (b) bar magnet surface and internal discontinuities. The
containing machined slot and most intense magnetic flux leakage field is
corresponding flux leakage field; (c) crack in formed when the discontinuity is
longitudinally magnetized object, producing perpendicular to the magnetic flux flow. If
poles that attract and hold magnetic the discontinuity is not perpendicular, the
particles. intensity of the magnetic flux leakage
field is reduced and disappears entirely
(a) S when the discontinuity is parallel to the
magnetic flux flow.
N
NS FIGURE 8. Slot or keyway on reverse side of
magnetized bar.
(b) Magnetic
S
particles
SN
N
(c) Magnetic FIGURE 9. Internal or midwall discontinuity
in magnetized test object. There may or
particles may not be magnetic flux leakage,
depending on value of flux in object.
SN
N S
Crack
48 Magnetic Testing
Figure 10 illustrates the effect of FIGURE 10. Flux leakage fields from
discontinuity orientation on the intensity discontinuities with different orientations:
of the magnetic flux leakage field. (a) perpendicular to magnetic flux; (b) at
45 degree angle to magnetic flux;
Formation of Indications (c) parallel to magnetic flux.
(a)
When magnetic particles collect at a flux
leakage site, they produce an indication (b)
visible to the unaided eye under the
proper lighting conditions. Tighter
magnetic flux leakage fields create the
ideal conditions for particle attraction, the
force on an individual particle being given
by the product of terms involving the
particle shape, the local value of the field
intensity and a term involving the local
curvature of the magnetic flux leakage
field. Particles then tend to align end to
end in this field. The stronger the ability
to hold particles, the larger the indication.
(c)
Fundamentals of Magnetic Testing 49
PART 4. Electrically Induced Magnetism
Circular Magnetization Inducing Circular Magnetization
in a Test Object
When an electric current flows through a
conductor such as a copper bar or wire, a Figure 12 illustrates a method for
magnetic field is formed around the inducing a circular field using a magnetic
conductor (Fig. 11a). The direction of the particle testing unit. The test object is
magnetic lines of force is always clamped between the contact plates so
90 degrees from the direction of current that electric current passes through it.
flow. When the conductor has a uniform
shape, the flux density or number of lines When tubes are tested by passing a
of force per unit area is uniform along the current through them, the magnetic flux
length of the conductor and uniformly is zero at the inner surface or axis and is
decreases as the distance from the its maximum at the outside surface. The
conductor increases. inside surface is often equally important
when testing for discontinuities. Because a
Because a ferromagnetized object is a magnetic field surrounds a conductor, it is
large conductor, electric current flowing possible to induce a satisfactory field in
through the object forms a circular the tube by inserting a copper bar or some
magnetic field. This magnetic field is other conductor through the tube and
known as circumferential magnetization passing the current through the bar.
because the magnetic flux lines form
complete loops in the object (Fig. 11b). This method is called internal conductor
magnetization. Figure 13 indicates a
A characteristic of circumferential method employed for circular field
magnetic fields is that the magnetic flux inspection of short parts. For longer parts
lines form complete loops without such as steel tubes, an insulated metal rod
magnetic poles. Because magnetic is run along the bore of the tube, exciting
particles are only attracted to and held it with a high current. The rod should not
where flux lines exit and enter the object touch the inside of the tube and the tube
surface, indications do not occur unless a should be placed on wooden planks to
discontinuity crosses the flux lines. isolate it from the ground. These measures
should eliminate arc burns from
FIGURE 11. Magnetic field generated: magnetizing current grounding.
(a) around conductor carrying electric
current; (b) around ferromagnetic test Magnetic Field Direction
object used as conductor.
(a) The magnetic lines of force are always at
right angles to the direction of the
Magnetic field magnetizing current. One way to visualize
the direction of the magnetic flux is to
Magnetizing Conductor imagine the conductor held in your right
current hand with the thumb extended in the
direction of the electric current flow. Your
(b) Magnetic field curved fingers then point in the direction
of the magnetic flux flow. This is known
as the right hand rule (Fig. 14).
FIGURE 12. Inducing circumferential
magnetic field in object used as conductor.
Magnetizing Test object Electric Magnetic field
current current
50 Magnetic Testing
Longitudinal coil found on magnetic particle test
Magnetization systems used to locate transverse
discontinuities.
Electric current can induce longitudinal
fields in ferromagnetic materials. The Multidirectional
magnetic field around a conductor is Magnetization
oriented lengthwise direction by forming
the conductor into a coil (Fig. 15). The When testing for discontinuities in
right hand rule shows that the magnetic different directions, it is standard practice
field at any point within the coil is in a to perform two tests, one with circular
lengthwise direction. magnetization and the one with
longitudinal. Two or more fields in
When a ferromagnetic object is placed different directions can be imposed on an
inside a coil carrying an electric current object in rapid succession.
(Fig. 16), the magnetic flux lines
concentrate themselves in a longitudinal When this is done, magnetic particle
direction. An object that has been indications are formed when
longitudinally magnetized is characterized discontinuities are favorably oriented to
by poles close to each end where the field the direction of any field. Such
lines leave and enter the test object to indications persist as long as the rapid
form continuous loops around the alternations of current continue.
associated current.
FIGURE 15. Formation of longitudinal
When a longitudinally magnetized magnetic field using coiled conductor.
object contains a transverse discontinuity,
a leakage field is produced that attracts
magnetic particles and forms an
indication. Figure 17 illustrates a typical
FIGURE 13. Inducing circumferential Magnetic
magnetic field using internal conductor: field
(a) for tube with inside and outside surface
discontinuities; (b) for multiple ring shapes Current
with cracking on inside and outside surfaces.
(a) Conductor
Magnetic
field
Magnetizing FIGURE 16. Test object containing
longitudinal magnetic field induced by coil.
current Cracks Path of
magnetizing
Permanent or Magnetic lines
current flexible cable of force
(b) Cracks
Magnetic field Longitudinal crack Transverse
Magnetizing (not detected) crack
Forty-five degree (detected)
current crack (detected)
FIGURE 14. Right hand rule indicates direction of magnetic FIGURE 17. Formation of transverse
flux flow based on direction of magnetizing current. discontinuity indication during longitudinal
magnetization.
Current
– Current Bath
Magnetic field + Transverse
cracks
Magnetic field
Fundamentals of Magnetic Testing 51
PART 5. Magnetic Particle Test Systems
Stationary Magnetic A common cause of missed
Particle Test Systems discontinuities is the misuse of the system
parameters. The magnetic particle system
Wet method horizontal magnetic particle requires an array of process controls and
test systems typically consist of (1) a high maintenance. An organization using a
current, low voltage magnetizing source; magnetic particle system should
(2) head stock and tail stock for holding incorporate an intensive maintenance
test objects and providing electrical plan with a demanding training,
contact for circumferential magnetization; qualification and certification program for
(3) a movable coil for longitudinal individuals using the magnetic particle
magnetization; and (4) a particle system. The maintenance plan should
suspension tank with an agitation system. include daily process validation checks.
The basic components, along with Power Packs
magnetizing control indicators and
ampere meters, are enclosed within a Power packs are the electrical sources
tabletop structural frame. Systems are needed to produce high amperage, low
available in a large number of sizes from a voltage magnetizing current. They are
25 mm (1 in.) contact plate opening up to used to magnetize test objects such as
systems that are 6 m (20 ft) long. The castings and forgings that are too large to
systems provide alternating current, direct be placed in a stationary testing unit. The
current or a combination of the two, with size and weight of power packs prevent
maximum magnetizing current output moving them and test objects are
from 1 to 10 kA. Figure 18 shows a typical accordingly transported to the test site.
stationary or wet horizontal unit. The rating or current output of
commercial power packs varies widely but
Stationary magnetic particle systems is typically from 6 to 20 kA of
include structures designed to be magnetizing current.
ergonomically healthful for the user.
Control functions are positioned The current is applied by cable wraps,
conveniently for the human body. formed coils, clamps and prods. Most
Instrumentation includes liquid crystal power pack units incorporate an
displays for digital readouts of amperes adjustable current control, one or two
achieved and smart knobs for fine tuning ammeters and an automatic shot duration
of settings. Magnetic particle stationary timer.
systems are designed for rugged durability
and require practice to operate efficiently. Mobile and Portable
Testing Units
FIGURE 18. Typical wet horizontal magnetic
particle test system. There are many applications where it is
not possible to bring the test object to the
magnetic particle system. Mobile units are
one type of equipment that can be
transported to the test site and still
provide relatively high magnetizing
currents. Traditional mobile units may be
considered small versions of the power
pack systems. Some mobile units have a
magnetizing current output of 6 kA but
most are limited by size considerations to
between 3 and 4 kA. Transportability is
also improved by restricting the types of
magnetizing current to alternating current
and half-wave direct current. Magnetizing
current is applied to the test object by
cable wraps, formed coils, prods and
clamps. Oil field portable magnetizing
52 Magnetic Testing
units can reach 15 kA by capacitor either be fixed or articulated. When
discharge through internal conductors or magnetizing current is applied to the coil,
cable wraps. a longitudinal magnetic field is created in
the core and transmitted to the legs.
The term portable equipment refers to When coupled to a test object, a
compact, lightweight units that can be longitudinal magnetic field is generated
hand carried to the test site. Some between the poles as shown in Fig. 20.
portable units are mounted on wheeled
carts to facilitate portability. Like Yokes are often specified by their lifting
stationary and mobile equipment, ability or the surface field they create
portable units come in a variety of sizes, midway between their poles, as measured
shapes, weights and amperage outputs. with a tesla meter.
The most common method of applying FIGURE 19. Circular magnetic field generated
current with a portable unit is with prods around magnetizing prods.
or clamps. However, cable wraps and
formed coils are also used in many
applications. Reduced weight and size are
achieved by omitting the step down
transformer needed for demagnetization.
Prods and Yokes Weld Lines of force
Prods are magnetization accessories that FIGURE 20. Longitudinal magnetic field
may be used with stationary, power pack, generated by yoke.
mobile and portable units. They typically
consist of a pair of copper bars 12 to Current – Yoke
20 mm (0.5 to 0.75 in.) in diameter with +
handles and connecting cables. One of
the prod handles has a trigger to remotely Weld
activate the magnetizing current from the
unit’s mainframe. Prods set up a circular Magnetic
magnetic field that diminishes in lines of force
intensity as the distance between prods Test object
increases (Fig. 19). Prods are avoided with
components that can be damaged by
arcing.
Yokes are often cable connected to a
mobile or portable unit that provides the
magnetizing current. A yoke designed
with a self-contained magnetizing source
is often called a hand probe. Hand probes
contain small transformers that generate
low voltage and high current. Yokes
usually contain a magnetizing coil with a
core of laminated transformer iron.
Attached to the core are legs that may
Fundamentals of Magnetic Testing 53
PART 6. Ferromagnetic Material Characteristics
Magnetic Flux and Units of specific change in H may produce a
Measure smaller or larger change in B as shown in
Fig. 21, the initial curve for an
A magnetic field is made up of flux lines unmagnetized piece of steel. Starting at
within and surrounding a magnetized point O (zero magnetic field intensity and
object or a conductor carrying an electric zero magnetic flux) and increasing H in
current. The term magnetic flux is used small increments, the flux density in the
when referring to all of the lines of flux in material increases quite rapidly at first,
a given area. Flux per unit area is called then gradually slows until point P1 is
magnetic flux density (the number of lines reached. At point P1, the material
of flux passing transversely through a unit becomes magnetically saturated. Beyond
area). Flux density in a magnetized object the saturation point, increases in magnetic
will decrease with distance. Flux density is field intensity do not increase the flux
greatest at the poles. density in the material. In diagrams of full
hysteresis loops, the curve OP1 is often
There can be some confusion about the drawn as a dashed line because it occurs
units of measure used to define these only during the initial magnetization of
magnetic quantities. The unit of magnetic an unmagnetized material. It is referred to
flux was originally called a maxwell with as the virgin curve of the material
one maxwell being one line of flux. The (Fig. 21a).
unit of flux density was the gauss with
one gauss equal to one maxwell per When the magnetic field intensity is
square centimeter. In 1930, the reduced to zero (Br in Fig. 21b), the flux
International Electrotechnical density slowly decreases. It lags the field
Commission redefined and renamed the intensity and does not reach zero. The
gauss as an oersted, or the intensity of a amount of flux density remaining in the
magnetic field in which a unit magnetic material (line B1O) is called residual
pole experiences a force of one dyne.3 magnetism or remanence. The ability of
ferromagnetic materials to retain a certain
In 1960, the International amount of magnetism is called retentivity.
Organization for Standardization released
ISO 1000: The International System of Units Removal of residual magnetism
(SI). This document standardizes the requires the application of a magnetic
metric units for magnetic flux. Flux field intensity in an opposite or negative
intensity is measured using the weber direction, of force equal or greater than
(Wb) with one weber equal to 108 lines of used to saturate the test object (Fig. 21c).
flux. The flux density unit is the tesla (T) When the magnetic field intensity is first
or one weber per square meter (Wb·m–2); reversed and only a small amount is
1 Wb·m–2 = 1 T = 10 000 gauss (10 kG). applied, the flux density slowly decreases.
As additional reverse field intensity is
Magnetic Hysteresis applied, the rate of reduction in flux
density (line –HcO) increases until it is
All ferromagnetic materials have certain almost a straight line (point –Hc) where B
magnetic properties specific to that equals zero.
material. Most of these properties are
described by a magnetic hysteresis curve. The amount of magnetic field intensity
The data for the hysteresis curve are necessary to reduce the flux density to
collected by placing a bar of zero is called coercive force. Coercive force
ferromagnetic material in a coil and is a factor in demagnetization and is also
applying an alternating current. By very important in eddy current testing of
increasing the magnetizing field intensity ferromagnetic materials.
H in small increments and measuring the
flux density B at each increment, the As the reversed magnetic field intensity
relationship between magnetic field is increased beyond point –Hc, the
intensity and flux density can be plotted. magnetic flux changes its polarity and
initially increases quite rapidly. It then
The relationship between magnetic gradually slows until point P2 is reached
field intensity and flux density is not (Fig. 21). This is the reverse polarity
linear for ferromagnetic materials. A saturation point and additional magnetic
field intensity will not produce an
increase in flux density.
54 Magnetic Testing
When the reversed magnetic field acceptable. An initial cycle illustrates the
intensity is reduced to zero (point –Br in physical characteristics of permeability.
Fig. 21), the flux density again lags the
magnetic field intensity, leaving residual Magnetic Domains
magnetism in the material (line –BrO).
The flux densities of the residual When saturation is achieved, the
magnetism from the straight and reversed magnetic domains are all aligned. When
polarities are equal (line B1O is equal to the magnetizing force is removed and the
line B1O). ferromagnetic component is at its
remanent field state, some of the
Removal of the reversed polarity domains stay aligned while some return
residual magnetism requires application of to random positioning. When coercive
magnetic field intensity in the original force is applied and the remanent field is
direction. Flux density drops to zero at at B (Fig. 21b) and the magnetizing force
point Hc in Fig. 21 with the application of is at negative, the oriented domains rotate
coercive force HcO. Continuing to increase 90 degrees from initial orientation. When
the field intensity results in the magnetic negative saturation is accomplished, the
polarity changing back to its original magnetic domains are 180 degrees out of
direction. This completes the hysteresis original alignment. This effect continues
loop (note that the lower curve is a mirror as long as demagnetization continues
image of the upper curve). using a reversing polarity.
The hysteresis cycle repeats in this loop
until the level of demagnetization is
FIGURE 21. Hysteresis data for unmagnetized steel: (a) virgin curve of hysteresis loop;
(b) hysteresis loop showing residual magnetism; (c) hysteresis loop showing coercive force;
(d) hysteresis loop showing reverse saturation point; (e) hysteresis loop showing reverse
residual magnetism; (f) complete hysteresis loop.
(a) (d) B P1
Br H
B P1
Zero flux density and
H Reverse –Hc
zero magnetic magnetization O
strength
O
saturation point
(b) B P2 B
Residual Br P1 (e) P1
magnetism H Br
Reverse
O P1 magnetization –Hc H
H O
point
P2 –Br Residual
magnetism
(f)
(c) B
Reverse
B residual
Br point Br P1
P2 H
–Hc O –Hc HC
Coercive O
force –Br
Legend
B = magnetic flux density
H = magnetic field intensity
O = origin before magnetization
P = saturation point
Fundamentals of Magnetic Testing 55
Magnetic Permeability Magnetic properties and hysteresis
loops vary widely between materials and
One of the most important properties of material conditions. They are affected by
magnetic materials is permeability. temperature, chemical composition,
Permeability can be thought of as the ease microstructure and grain size. Figure 23a
with which materials can be magnetized. is a hysteresis loop for hardened steel and
More specifically, permeability is the ratio the loop is typical of a material with low
of the flux density to the magnetic field permeability, high reluctance, high
intensity (B divided by H). Figure 22a is retentivity and high residual magnetism
the virgin curve of a high permeability that requires high coercive force for
material and Fig. 22b is the curve of a low removal. Figure 23b is the hysteresis loop
permeability material. for an annealed low carbon steel. It is
typical of a material with high
The reciprocal of permeability is permeability, low reluctance, low
reluctance, defined as the resistance of a retentivity and low residual magnetism
material to changes in magnetic field that requires a low coercive force for
intensity. removal.
FIGURE 22. Magnetic permeability curves: FIGURE 23. Hysteresis loops: (a) hardened
(a) high permeability virgin curve; (b) low steel hysteresis loop; (b) annealed low
permeability virgin curve. carbon steel hysteresis loop.
(a) (a)
Saturation point Residual
magnetism
Flux density B Flux density B
Positive magnetic field intensity H Coercive force
(b) Saturation point Positive magnetic field intensity H
(b)
Residual
magnetism
Flux density B Flux density B
Positive magnetic field intensity H Coercive force
Positive magnetic field intensity H
56 Magnetic Testing
PART 7. Types of Magnetizing Current
Flux densityIn the early days of magnetic particle There are three primary advantages to
testing, it was believed that the best using alternating current as a magnetizing
current for magnetization was direct source. First, the current reversal causes an
current from storage batteries. As inductive effect that concentrates the
knowledge of the magnetic particle magnetizing flux at the object surface
process expanded and electrical circuitry (called the skin effect) and provides
continued to advance, many types of enhanced indications of surface
magnetizing currents became available: discontinuities. This is especially
alternating current, half-wave direct important for inspection of irregularly
current and full-wave direct current. The shaped components, such as crankshafts.
terms half-wave rectified direct current and Magnetic fields produced by alternating
full-wave rectified direct current are used for current are also much easier to remove
alternating current rectified to produce during demagnetization. A third
half-wave and full-wave direct current. advantage is that the pulsing effect of the
flux caused by the current reversals
Alternating Current agitates the particles applied to the test
object surface. By increasing particle
Alternating current is useful in many mobility, this agitation allows more
applications because it is commercially particles to collect at flux leakage points
available in voltages ranging from 120 to and so increases the size and visibility of
440 V. Electrical circuitry to produce discontinuity indications.
alternating magnetizing current is simple
and relatively inexpensive because it only Concentration of the flux at the test
requires transforming commercial power object surface can be a disadvantage also
into low voltage, high amperage because most subsurface discontinuities
magnetizing current. are not detected. Another disadvantage is
that some specifications do not allow
In the United States and some other alternating current on plated components
countries, alternating current alternates when the coating is thicker than 0.08 mm
sixty times in a second. Many other (0.003 in.). It is hard to determine when
countries have standardized fifty the flux in a test object is at peak; it
alternations per second. The alternations depends on when in the magnetizing
are called cycles. One hertz (Hz) equals cycle the current is turned off.
one cycle per second and 60 Hz is sixty
cycles per second. Figure 24 shows the Alternating current is more effective
waveform of alternating current. In one than direct current on objects with thick
cycle, the current flows from zero to a nonmetallic coatings.
maximum positive value and then drops
back to zero. At zero, it reverses direction Half-Wave Direct Current
and goes to a maximum negative peak
and returns to zero. The curve is When single-phase alternating current is
symmetrical with the positive and passed through a simple rectifier, the
negative lobes being mirror images. reversed flow of current is blocked or
clipped. This produces a series of current
FIGURE 24. Waveform of alternating current. pulses that start at zero, reach a maximum
point, drop back to zero and then pause
1 cycle until the next positive cycle begins. The
+ result is a varying current that flows only
0 in one direction. Figure 25 shows the
– waveform for half-wave direct current.
Time Half-wave direct current has
penetrating power comparable to
single-phase full-wave direct current.
Half-wave current has a flux density of
zero at the center of a test object and the
density increases until it reaches a
maximum at the object surface. The
pulsing effect of the rectified wave
produces maximum mobility for the
Fundamentals of Magnetic Testing 57
magnetic particles; dry method tests are in the circuit that reverse the current flow.
enhanced by this effect. Another distinct This permits built-in reversing direct
advantage of half-wave direct current is current demagnetization. Because of its
the simplicity of its electrical components. simpler components, the initial cost of
It can be easily combined with portable single-phase full-wave direct current
and mobile alternating current equipment equipment is much less than that of
for weld, construction and casting tests. three-phase full-wave equipment.
One of the disadvantages of half-wave One disadvantage of single-phase units
magnetization is the problem in is the input power requirement. Single
demagnetization: the current does not phase equipment requires 1.73 times
reverse so it cannot be used for more input current than three-phase
demagnetizing. Alternating current can be units. This becomes very significant at
used to remove some residual magnetism higher magnetizing currents where input
but the skin effect of alternating current values can exceed 600 A.
and the deeper penetration of half-wave
direct current cause incomplete Three-Phase Full-Wave
demagnetization. Direct Current
Full-Wave Direct Current Commercial electric power, especially at
220 and 440 V, is provided as three-phase
Electrical circuits can rectify and invert so alternating current with each phase
that so that the number of positive pulses providing part of the total current.
is doubled. Figure 26 shows the waveform Figure 27 shows the time relation of
of single-phase full-wave rectified three-phase alternating current.
alternating current. The resulting current Three-phase full-wave magnetic particle
is called single-phase full-wave direct current. equipment rectifies all three alternating
current phases and inverts the negative
Single-phase full-wave direct current flow to a positive direction, producing a
has essentially the same penetrating nearly flat line direct current magnetizing
ability as three-phase full-wave direct current. Figure 28 shows the waveform of
current. The current fluctuation causes a three-phase full-wave direct current.
skin effect that is not significant. It is also
possible to incorporate switching devices Three-phase full-wave direct current
has all of the advantages of single-phase
FIGURE 25. Half-wave direct current full-wave direct current plus some
waveform. additional benefits. The current draw on
the power line is spread over three phases,
+ reducing the demand by nearly half. The
0 demand on the line is also balanced, with
–
FIGURE 27. Waveform of three-phase
Alternating current input alternating current.
+ Current +
0
– Half-wave 0
direct current output 1/60 2/60
Seconds
FIGURE 26. Single-phase full-wave directCurrent CurrentFIGURE 28. Three-phase full-wave direct
current waveform. current waveform.
+ +
0 0
Time Time
58 Magnetic Testing
each leg providing part of the current hardened alloy steels retain intense
(single-phase pulls all of the current from magnetic fields for long periods of time.
one leg, resulting in an unbalanced line).
Many power companies charge a higher A metal may be demagnetized either by
rate to customers with unbalanced, high heating it to the curie temperature or by
current requirements. The three-phase reverse electromagnetization. Reverse
design also permits incorporating a quick electromagnetization subjects a
break circuit that improves the formation magnetized object to a magnetic force
of indications at the ends of that is continually reversing its direction
longitudinally magnetized test objects. and gradually decreasing in intensity.
Demagnetization A common method of demagnetizing
small objects is to pass them through a
Objects that have been magnetic particle coil carrying alternating current or to
tested retain some magnetism. The place the object in the coil and gradually
amount of residual magnetism depends reduce the current to zero. The principle
on the material and its condition. Low of demagnetizing with direct current is
carbon steel in the annealed condition the same with alternating current. The
retains little or no magnetism while magnetic field intensity or current must
reverse serially and reduce gradually.
Demagnetization is discussed in detail
elsewhere in this volume.
Fundamentals of Magnetic Testing 59
PART 8. Media and Processes in Magnetic Particle
Testing
The formation of reliably visible Magnetic Permeability
discontinuity indications is essential to
the magnetic particle testing method. An Magnetic particles should have the
important factor in the formation and highest possible permeability and the
visibility of indications is the use of the lowest possible retentivity. This allows
proper magnetic particles to obtain the their attraction only to low level leakage
best indication from a particular fields emanating from discontinuities. As
discontinuity under the given conditions. the particles become magnetized, they
Selection of the wrong particles can result then attract additional particles to bridge
in (1) failure to form indications, (2) the and outline the discontinuity, thus
formation of indications too faint for forming a visible indication.
detection or (3) a distorted pattern over
the discontinuity and the resulting Magnetic permeability alone does not
misinterpretations. produce a highly sensitive particle
material. For example, iron based dry
In magnetic particle tests, there are two powders have a higher permeability than
classes of media that define the method: the oxides used in wet method
dry and wet. Dry method particles are suspensions. Yet a typical dry powder does
applied without the addition of a carrier not produce indications of extremely fine
vehicle. Wet method particles are surface fatigue cracks that are easily
suspended in a liquid vehicle. The liquid detected with wet method suspensions.
vehicle may be water or a light petroleum High permeability is desirable but is no
distillate similar to kerosene. more important than size, shape or the
other critical properties. All of these
Magnetic particles are also categorized characteristics are interrelated and must
by the type of pigment bonded to them occur in appropriate ranges in order for
to improve visibility. Visible particles are high permeability to be of value.
colored to produce a good contrast with
the test surface under white or visible Magnetic Retentivity
light. Fluorescent particles are coated with
pigments that fluoresce when exposed to Materials used in dry method powders
ultraviolet light. A third pigment category and wet method suspensions should have
includes particles coated with a material a low coercive force and low retentivity. If
that is both color contrasting under these properties were high in dry powders,
visible light and fluorescent when the particles would become magnetized
exposed to ultraviolet light. during manufacture or during their first
use, reducing contrast and masking
Magnetic Particle relevant discontinuity indications.
Properties
When wet method particles have a
The media used in magnetic particle high coercive force, they are also easily
testing consist of finely divided iron magnetized, producing the same high
powder ferromagnetic oxides. The level of background. Magnetized particles
particles can be irregularly shaped, are attracted to any ferromagnetic
spheroidal, flakes or rod shaped material in the testing system (bath tank,
(elongated). The properties of different plumbing system or rails) and this causes
materials, shapes and types vary widely an extensive loss of particles from the
and some are discussed below. suspension. Particle depletion creates
process control problems and requires
The level of particles in suspension frequent additions of new particles to the
should be maintained consistently, from bath.
0.1 to 0.4 mL in a 100 mL settling test.
For consistent results, the suspension Another disadvantage of magnetically
vehicle must be changed frequently retentive wet method particles is their
because of foreign material tendency to clump, forming large clusters
contamination. on the test object surface if warmth makes
the pigment sticky.
Strongly magnetized particles form
clusters and adhere to the test object
surface as soon as bath agitation stops.
Particles with low magnetic field intensity
cluster more slowly while indications are
60 Magnetic Testing
forming. The leakage field at the particles may line up in drainage lines
discontinuity draws the particles toward it that could be confused with discontinuity
and the clusters are constantly enlarging indications.
due to agglomeration. At the same time,
the clusters sweep up nearby fine particles Wet Method Fluorescent Particles
as they move toward the discontinuity.
Particles treated with a fluorescent
Effects of Particle Size pigment or some of the visible pigments
differ in size and behavior from black or
The size and shape of magnetic particles red (uncoated) visible particles.
play an important role in how they Fluorescent particles must be
behave when subjected to a weak compounded and structured to prevent
magnetic field such as that from a separation of the pigment and magnetic
discontinuity. Large, heavy particles are material during use. A mixture of loose
not likely to be attracted and held by a pigment and unpigmented magnetic
weak leakage field as they move over the material produces a dense background
object surface. However, very small and dim indications. In addition, the
particles may adhere to the surface where unpigmented magnetic particles may be
there is no leakage field and thus form an attracted and held at leakage fields but
objectionable background. their lack of contrasting color makes them
difficult to see.
Dry Powder Particles
Producing fluorescent magnetic
Within limits, sensitivity to very fine particles involves bonding pigment
discontinuities typically increases as around each magnetic particle. The
particle size decreases. Extremely small bonding must resist the solvent action of
particles, on the order of a few petroleum vehicles and surfactants and
micrometers, behave like dust. They settle the abrasive action occurring in pumping
and adhere to the object surface even and agitation systems. Some
though it may be very smooth. Extremely manufacturers encapsulate the bonded
fine particles are very sensitive to low dye particle in a layer of resin. As a result
level leakage fields but are not desirable of their processing, fluorescent particles
for production tests because of intense have a definite size range that is
backgrounds that obscure or mask maintained throughout the suspension’s
relevant indications. service cycle.
Large particles are not as sensitive to Effect of Particle Shape
fine discontinuities. However, in
applications where it is desired to detect Magnetic particles are available in a
large discontinuities, powders containing variety of shapes: spheres, elongated
only large particles may be used. needles (or rods) and flakes. The shape of
the particles affects how they form
Many commercial dry powders are a indications. When exposed to an external
carefully controlled mixture of particles magnetic field, all particles tend to align
containing a range of sizes. The smaller along the flux lines. This tendency is
particles provide sensitivity and mobility much stronger with elongated particles
while larger particles serve two purposes. such as the needle or rod shapes.
They assist in building up indications at Elongated shapes develop internal north
larger discontinuities and help reduce and south poles more reliably than
background by a sort of sweeping action, spheroid or globe shaped particles,
brushing finer particles from the test because they have a smaller internal
object surface. A balanced mixture demagnetization field.
containing a range of sizes provides
sensitivity for both fine and large Because of the attraction of opposite
discontinuities, without disruptive poles, the north and south poles of these
backgrounds. small magnets arrange the particles into
strings. The result is the formation of
Wet Method Visible Particles more intense patterns in weaker flux
leakage fields, as these magnetically
Particles used in a liquid suspension are formed strings of particles bridge the
usually much smaller than those used in discontinuity. The superior effectiveness
dry powders. The smaller the of elongated shapes over globular shapes
discontinuity, the smaller the particles is particularly noticeable in the detection
should be. of wide, shallow discontinuities and
subsurface discontinuities. The leakage
Larger particles are difficult to hold in fields at such discontinuities are weaker
suspension. Even 20 µm (0.0008 in.) and more diffuse. The formation of
particles tend to settle out of suspension particle strings based on internal poles
rapidly and are stranded as the suspension makes more intense indications.
drains off the test object. Stranded
Fundamentals of Magnetic Testing 61
Dry Powder Shapes applications, black, red or blue is used.
The choice of color depends on the
The superiority of elongated particles in surface colors of the test objects and on
diffuse magnetic fields holds true for dry the prevailing test site lighting.
powder testing. However, there is another
effect that must be considered. Dry The ability to bond fluorescent dyes to
powders are often applied to object magnetic powders has produced a particle
surfaces by releasing them out of material that provides the best possible
mechanical or manual blowers. It is visibility and contrast under proper
essential that the particles be dispersed as lighting conditions. When test objects are
a uniform cloud that settles evenly over examined in ultraviolet light, it is difficult
the object surface. Magnetic powder not to see the light emitted by a few
containing only elongated particles tends particles collected at a discontinuity.
to become mechanically linked in its
container and is then expelled in uneven Fluorescent particles are magnetically
clumps. less sensitive than visible particles but the
reduction in magnetic sensitivity is more
Wet Method Particle Shapes than offset by the increase in visibility
and contrast.
The performance of particles suspended in
a liquid vehicle is not as shape dependent Visibility and contrast of fluorescent
as that of dry particles. The suspending particles are directly related to the
liquid is much denser and more viscous darkness of the testing site. In a totally
than air; the movement of particles darkened area, even a small amount of
through the liquid is slowed so that they ultraviolet energy activates fluorescent
accumulate more reliably at dye to emit a noticeable amount of visible
discontinuities. light. When the test site is partially
darkened, the amount of required
Because of this slower movement, wet ultraviolet energy increases dramatically
method particles form minute elongated yet the emitted visible light is only barely
aggregates. Even unfavorable shapes align noticeable, especially in the conventional
magnetically into elongated aggregates yellow-to-green range.
under the influence of local, low level
leakage fields. In suspension, the particles Most military and commercial
are kept dispersed by mechanical agitation specifications require the test site to be
until they flow over the surface of the darkened to 20 lx (2 ftc) or less, with a
magnetized object. There is no need to minimum ultraviolet intensity of
add certain shapes to improve the 1000 µW·cm–2 at the test object surface.
dispersion of the particles.
Particle Mobility
Visibility and Contrast
When magnetic particles are applied to
Visibility and contrast are properties that the surface of a magnetized object, the
must be considered when selecting a particles must move and collect at the
magnetic particle material for a specific leakage field of a discontinuity in order to
testing application. Magnetic properties, form a visible indication. Any interference
size and shape may all be favorable for with this movement has an effect on the
producing the best indication, but if an sensitivity of the test. Conditions
indication is formed and the inspector promoting or interfering with particle
cannot see it, then the test procedure has mobility are different for dry and wet
failed. method particles.
Visibility and contrast are enhanced by Dry Powder Mobility
choosing a particle color that is easy to
see against the test object surface. The Dry particles should be applied in a way
natural color of metallic powders is silver that permits them to reach the
gray. The colors of iron oxides commonly magnetized object surface in a uniform
used in wet method powders are black or cloud with minimum motion. When this
red. Manufacturers bond pigments to the is properly done, the particles come under
particles to produce a wide selection of the influence of leakage fields while
other colors: white, black, red, blue and suspended in air and are then said to
yellow, all with comparable magnetic possess three-dimensional mobility. This
properties. condition can be approximated on
surfaces that are vertical or overhead.
The white or yellow colors provide
good contrast against mill surface objects. When particles are applied to
They are not effective against the silver horizontal surfaces, they settle directly
gray of grit blasted or chemically etched onto the surface and do not have mobility
surfaces or against bright, polished in three dimensions. Some extension of
machine ground surfaces. For those mobility can be achieved by tapping or
vibrating the test object, agitating the
particles and allowing them to move
62 Magnetic Testing
toward leakage fields. Alternating current of subsurface discontinuities. The wet
and half-wave rectified alternating current method also offers the advantage of
(pulsed direct current) can give particles complete coverage of the object surface
excellent mobility when compared to and good coverage of test objects with
direct current magnetization. irregular shapes.
Wet Method Particle Mobility Visible or Fluorescent Particles
The suspension of particles in a liquid The decision between visible particles and
vehicle allows mobility for the particles in fluorescent particles depends on
two dimensions when the suspension convenience and equipment. Testing with
flows over the test object surface and in visible particles can be accomplished
three dimensions when the test object is under common shop lighting while
immersed in a magnetic particle bath. fluorescent particles require a darkened
area and an ultraviolet light source.
Wet method particles have a tendency
to settle out of the suspension either in Both wet method visible and wet
the tank of the test system or on the test method fluorescent tests have about the
object surface short of the discontinuity. same sensitivity, but under proper lighting
To be effective, wet method particles must conditions fluorescent indications are
move with the vehicle and must reach much easier to see.
every surface that the vehicle contacts.
The settling rate of particles is directly Magnetic Particle Testing
proportional: (1) to their dimensions and Processes
(2) to the difference between their density
and the lower density of the liquid A test object may be magnetized first and
vehicle. Their settling rate is inversely particles applied after the magnetizing
proportional to the liquid’s viscosity. As a current has been stopped (called the
result, the mobility of wet method residual method) or the object may be
particles is never ideal and must be covered with particles while the
balanced against the other factors magnetizing current is present (known as
important to wet method test results. the continuous method). With test objects
that have high magnetic retentivity, a
Media Selection combination of the residual and
continuous methods is sometimes used.
The choice between dry method and wet
method techniques is influenced Residual Test Method
principally by the following
considerations: In the residual method, the test object is
magnetized, the magnetizing current is
1. Type of discontinuity (surface or stopped and then the magnetic particles
subsurface): for subsurface are applied. This method can only be used
discontinuities, dry powder is usually on materials having sufficient magnetic
more sensitive. remanence. The residual magnetic field
must be intense enough to produce
2. Size of surface discontinuity: wet discontinuity leakage fields sufficient for
method particles are usually best for producing visible test indications. As a
fine or broad, shallow discontinuities. rule, the residual method is most reliable
for detection of surface discontinuities.
3. Convenience: dry powder with portable
half-wave equipment is easy to use for Hard materials with high remanence
tests on site or in the field. Wet are usually low in permeability, so higher
method particles packaged in aerosol than usual magnetizing currents may be
spray cans are also effective for field necessary to obtain an adequate level of
spot tests. residual magnetism. This difference
The dry powder technique is superior between hard steels and soft steels is
usually not critical if only surface
for locating subsurface discontinuities, discontinuities are to be detected.
mainly because of the high permeability
and favorable elongated shape of the Either dry or wet method particle
particles. Alternating current with dry application can be used in the residual
powder is excellent for surface cracks that method. With the wet method, the
are not too fine but this combination is of magnetized test object may be immersed
little value for cracks lying wholly in an agitated bath of suspended magnetic
beneath the surface. particles or may be flooded with particle
suspension in a curtain spray.
When the requirement is to find
extremely fine surface cracks, the wet In the immersion technique, the
method is superior, regardless of the intensity of discontinuity indications is
magnetizing current in use. In some cases, directly affected by the object’s dwell time
direct current is considered advantageous in the bath. By leaving the object in the
because it also provides some indications
Fundamentals of Magnetic Testing 63
bath for extended periods, leakage fields The wet continuous method requires
have time enough to attract and hold the more operator attention than the residual
maximum number of particles, even at method. If bath application continues,
fine discontinuities. If the test object has even momentarily, after the current is
high retentivity, longer dwell time stopped, particles held by a discontinuity
increases the sensitivity over that of the leakage field can be washed away. If there
wet continuous method. Note that the is a pause between stopping the bath
location of the discontinuity on the application and applying the magnetizing
object during immersion affects the current, the suspension can drain off the
accumulation of particles. Indications are test object, leaving insufficient particles
more intense on upper horizontal surfaces for producing discontinuity indications.
and weaker on vertical or lower horizontal Careless handling of the bath and current
surfaces. sequence can seriously hinder the
production of reliable test results.
Care must be exercised when removing
the test object from the bath or particle The highest possible sensitivity for very
spray. Rapid movement can literally wash fine discontinuities is typically achieved
off indications held by weak discontinuity by the following sequence: (1) immerse
leakage fields. the test object in the bath, (2) pass
magnetizing current through the object
Continuous Test Method for a short time during immersion,
(3) maintain the current during removal
When a magnetizing current is applied to from the bath, (4) maintain the current
a ferromagnetic test object, the magnetic during drainage of the suspension from
field rises to a maximum. Its value is the test object and (5) stop the
derived from the magnetic field intensity magnetizing current.
and the magnetic permeability of the test
object. When the magnetizing current is Conclusion
removed, the residual magnetic field in
the object is always less than the field Magnetic particle tests are effective
produced while the magnetizing current nondestructive procedures for locating
was applied. The amount of difference material discontinuities in ferromagnetic
depends on the BH curve of the material. objects of all sizes and configurations. It is
For these reasons, the continuous a flexible technique that can be
method, for any specific value of performed under a variety of conditions,
magnetizing current, is always more using a broad range of supplementary
sensitive than the residual method. components.
Continuous magnetization is the only Application of the magnetic particle
method possible for use on low carbon method is deceptively simple — good test
steels or iron having little retentivity. It is results can sometimes be produced with
frequently used with alternating current little more than practical experience. In
on these materials because of the fact, the development of the technique
excellent mobility produced by has been almost entirely empirical rather
alternating current. than theoretical.
With the wet method, the surface of However, the method is founded on
the test object is flooded with particle the complex principles of
suspension. The bath application and the electromagnetics and the magnetic
magnetizing current are simultaneously interactions of at least three materials
stopped. The magnetic field intensity simultaneously. In addition, there is the
continues to affect particles in the bath as critical consideration of the operator’s
it drains. In some continuous method ability to qualitatively and quantitatively
procedures, the magnetizing current evaluate the results of the inspection.
remains on during interpretations.
64 Magnetic Testing
PART 9. Magnetic Test Techniques
Successful testing requires the test object perpendicular to each other. A grid is
to be magnetized properly. The usually drawn on the test object to
magnetization can be accomplished using facilitate the tests.
one of several approaches: (1) permanent
magnets, (2) electromagnets and Magnetizing Coil
(3) electric currents used to induce the
required magnetic field. A commonly used encircling coil is shown
in Fig. 30. The field direction follows the
Excitation systems that use permanent right hand rule. (The right hand rule
magnets offer the least flexibility. The states that, if someone grips a rod, holds it
major disadvantage with such systems lies out and imagines an electric current
in the fact that the excitation cannot be flowing down the thumb, the induced
switched off. Because the magnetization is circular field in the rod would flow in the
always turned on, it is difficult to insert direction that the fingers point.) With no
and remove the test object from the test test object present, the field lines form
rig. closed loops that encircle the current
carrying conductors. The value of the field
Electromagnets, as well as electric at any point has been established for a
currents, are used extensively to great many coil configurations. The value
magnetize the test object. Figure 29 shows depends on the current in the coils, the
an excitation system where the test object number of turns and a geometrical factor.
is part of a magnetic circuit energized by Calculation of the field from first
current passing through an excitation principles is generally unnecessary for
coil. The physics of magnetization are nondestructive testing; a hall element
described elsewhere in this volume. tesla meter will measure this field.
To obtain maximum sensitivity, it is Two totally different situations,
necessary to ensure that the magnetic flux common in magnetic flux leakage testing,
is perpendicular to the discontinuity. This are described below.
direction is in contrast to the orientation
in techniques that use an electric current FIGURE 30. Encircling coil using direct
for inspection of a test object, where it current to produce magnetizing force.
may be more advantageous to orient the
direction of current so that a
discontinuity would impede the current
as much as possible. Because the
orientation of the discontinuity is
unknown, it is necessary to test twice
with a yoke, in two directions
FIGURE 29. Electromagnetic yoke for PI R
magnetizing of test object. QS
Coil
Air gap where test Legend
object is inserted I = electric current
P, Q = points of discontinuities in example
R = point at which magnetic field intensity H is
measured
S = point at which magnetic flux density B is
measured
Fundamentals of Magnetic Testing 65
Testing in Active Field tubular test object to magnetize the test
object circularly. Figure 33 shows a central
In this technique, the test object is conductor energized by a current source
scanned by probes near position R in to establish a circular magnetic field
Fig. 30. Application of small fields is intensity in a tubular test object.
sufficient to cause magnetic flux leakage
from transversely oriented surface Capacitor Discharge Devices
breaking discontinuities. For subsurface
discontinuities or those on the inside For the circular magnetization of tubes or
surface of tubes, larger fields are required. the longitudinal magnetization of the
The inspector must experiment to ends of elongated test objects, a capacitor
optimize the applied field for the discharge device is sometimes used.4,5 The
particular discontinuity. capacitor discharge unit represents a
practical advance over battery packs and
Testing in Residual Field consists of a capacitor bank charged to a
voltage V and then discharged through a
Test objects are passed through the coil rod, a cable and a silicon controlled
field and tested in the resulting residual rectifier of total resistance R. Typical
field. Elongating the coil and placing the configurations are shown in Fig. 34.
test object next to the inside surface of
the coil will expose the test object to the Larger capacitances at lower voltages
largest field that the coil can produce. provide better magnetization than smaller
capacitances at higher voltages because
This technique is often used in larger capacitances at lower voltages lead
magnetic particle testing. The main to longer duration pulses and therefore to
problem to avoid is the induction of so lower eddy currents. The lower voltage is
much magnetic flux in the test object that an essential safety feature for outdoor use.
the magnetic particles stand out like fur A maximum of 50 V is recommended.6
along the field lines that enter and leave
the test object, especially close to its ends. FIGURE 32. Current carrying clamp electrodes used for
Optimum conditions require that the test testing ferromagnetic tubular objects with small diameters.
object be somewhat less than saturated.
The inspector should experiment to Magnetic flux lines
optimize the coil field requirements for
the test object because this field depends
on test object geometry.
Applied Direct Current Clamp
Current I out
If an electric current is used to magnetize
the test object, it may be more Current I in
advantageous to orient the direction of
current in a manner where the presence
of a discontinuity impedes the current
flow as much as possible. Bars, billets and
tubes are often magnetized by application
of a direct current I to their ends (Fig. 31).
Figure 32 shows a system where the
current I is passed directly through a
FIGURE 31. Circumferential magnetization by application of FIGURE 33. Simple technique for circumferential
direct current: (a) rectilinear bar; (b) round bar; (c) tube. magnetization of ferromagnetic tube.
(a) I r
H
H
(b) I
H
(c) I I
Current source
H
Legend
Legend H = magnetic field intensity
H = magnetic field intensity I = electric current
I = electric current r = tube radius
66 Magnetic Testing
Magnitudes of Magnetic Optimal Operating Point
Flux Leakage Fields
Consider raising the magnetization level
The magnitude of the magnetic flux in a block of steel containing a
leakage field under active direct current discontinuity (Fig. 35). At low flux
excitation naturally depends on the density, the field lines tend to crowd
applied field. An applied field of 3.2 to together in the steel around the
4.0 kA·m–1 (40 to 50 Oe) inside the discontinuity rather than go through the
material can cause leakage fields with nonmagnetic region of the discontinuity.
peak values of tens of millitesla (hundreds The field lines are therefore more crowded
of gauss). However, in the case of residual above and below the discontinuity than
induction, the magnetic flux leakage they are on the left or right. The material
fields may be only a few hundred can hold more flux as the permeability
microtesla (a few gauss). Furthermore, rises, so there is no significant leakage
with residual field excitation, an flux at the surfaces (Fig. 35a).
interesting field reversal may occur,
depending on the value of the initial However, an increase in the number of
active field excitation and the dimensions lines causes permeability to fall. At about
of the discontinuity. this point, magnetic flux leakage is first
noticed at the surfaces. Although the lines
FIGURE 34. Capacitor discharge are now closer together, representing a
configurations causing magnetization higher magnetic flux density, they do not
perpendicular to current direction: have the ability to crowd closer together
(a) conductor internal to test object creates around the discontinuity where the
circular field; (b) flexible cable around test permeability is low.
object creates longitudinal field.
(a) Capacitor discharge unit At higher values of applied field, the
permeability continues to fall. It is,
C SCR l c however, still large compared to the
permeability of air, so the reluctance of
the path through the discontinuity is still
larger than through the metal. As a result,
magnetic flux leakage at the outside
surface helps provide a sufficiently high
flux density in the material for the
leakage of magnetic flux from
discontinuities (Fig. 35b) while partially
suppressing long range surface noise.
le
le FIGURE 35. Effects of induction on magnetic
flux lines at discontinuity: (a) no surface flux
Circular field
(b) SCR l c leakage occurs where magnetic flux lines are
compressed at low levels of induction
around discontinuity; (b) lack of
C compression at high magnetization results in
surface magnetic flux leakage.
(a)
(b) Flux leakage
Longitudinal field
Legend
C = capacitor
Ic = capacitor discharge current
Ie = eddy current
SCR = silicon controlled rectifier
Fundamentals of Magnetic Testing 67
For residual field testing, it is best to The output of the pickup coil is
ensure that the material is saturated. The proportional to the spatial gradient of the
magnetic field starts to decay as soon as flux along the direction of the coil
the energizing current is removed. movement as well as the velocity of the
coil. Two issues arise as a result.
Magnetic Test Probes
1. It is essential that the probe scan
The purpose of probes for magnetic velocity (relative to the test object)
testing is to detect and possibly quantify should be constant to avoid
the magnetic flux leakage field generated introducing artifacts into the signal
by heterogeneities in the test object. The through probe velocity variations.
leakage fields tend to be local and
concentrated near the discontinuities. The 2. The output is proportional to the
leakage field can be divided into three spatial gradient of the flux in the
orthogonal components: normal direction of the coil.
(vertical), tangential (horizontal) and axial The output of the pickup coil can be
directions. Probes are usually either
designed or oriented to measure one of integrated for measurement of the leakage
these components. Typical plots of these flux density rather than of its gradient.
components near discontinuities are Figure 37 shows the output of a pickup
shown in this volume’s chapter on probes. coil and the signal obtained after
integrating the output.8 The coil is used to
A variety of probes (or transducers) are measure, in units of tesla (or gauss), the
used in industry for detecting and magnetic flux density B leaking from a
measuring leakage fields. rectangular slot.
Pickup Coils The sensitivity of the pickup coil can
be improved by using a ferrite core. Tools
One of the simplest and most popular for designing pickup coils, as well as
means for detecting leakage fields is to use predicting their performance, are
a pickup coil.7 Pickup coils consist of very described elsewhere in this volume.
small coils that are either air cored or use
a small ferrite core. The voltage induced Magnetodiodes
in the coil is given by the rate of change
of flux linkages associated with the pickup The magnetodiode is suitable for sensing
coil. Only the component of the flux leakage fields from discontinuities because
parallel to the axis of the coil (or of its small size and its high sensitivity.
alternately perpendicular to the plane of
the coil) is instrumental in inducing the FIGURE 37. Pickup coil and signal integrator (magnetic flux
voltage. This induction direction makes it leakage) output for rectangular discontinuity.7
possible to orient the pickup coil so as to
measure any of the three leakage field 0.3 (3) 30
components selectively (Fig. 36).
Magnetic flux density B, T (kG)0.2 (2)Magnetic flux20
FIGURE 36. Effect of pickup coil orientation Output from search coil (mV)leakage
on sensitivity to components of magnetic
flux density: (a) coil sensitive to normal 0.1 (1) 10
component; (b) coil sensitive to tangential
component. 00
(a) Pickup coil
Test object Discontinuity –10
width –20
(b) Pickup coil
Search coil output
Test object –30
0 2 4 6 8 10
(8) (16) (24) (32) (40)
Coil position, mm (10–2 in.)
68 Magnetic Testing
Because the coil probe is usually larger the effect of the bias. The resistance of the
than the magnetodiode, it is less sensitive device, therefore, decreases with
to longitudinally angled discontinuities increasing field intensity values. Figure 38
than the magnetodiode is. However, the shows a typical response of a giant
coil probe is better than the magnetoresistive probe.
magnetodiode for large discontinuities,
such as cavities. Magnetic Tape
Hall Effect Detectors For the testing of flat surfaces, magnetic
tape can be used. The tape is pressed to
Hall effect detector probes are used the surface of the magnetized billet and
extensively in industry for measuring then scanned by small probes before
magnetic flux leakage fields in units of being erased. This technique is sometimes
tesla. Hall effect detector probes are called magnetography.
described in this volume’s chapter on
probes for electromagnetic testing. In automated systems, magnetic tape
can be fed from a spool. The signals can
Giant Magnetoresistive Probes be read and the tape can be erased and
reused.
Magnetic field sensitive devices called
giant magnetoresistive probes,9,10 at the Unfortunately, the tangential leakage
most basic level, consist of a nonmagnetic field intensity at the surface of the
layer sandwiched between two magnetic material is not constant. To optimize the
layers. The apparent resistivity of the response, the amplification of the signals
structure varies depending on whether the can be varied.
direction of the electron spin is parallel or
antiparallel to the moments of the Scabs or slivers projecting from the test
magnetic layers. When the moments surface can easily tear the tape
associated with the magnetic layers are
aligned antiparallel, the electrons with Magnetic Particles
spin in one direction (up) that are not
scattered in one layer will be scattered in Magnetic particles are the most popular
the other layer. This increases the means used in industry for making
resistance of the device. This is in contrast magnetic indications. The descriptions
to the situation when the magnetic below are cursory.
moments associated with the layers are
parallel and the electrons that are not Magnetic particle testing involves the
scattered in one layer are not scattered in application of magnetic particles to the
the other layer, either. test object before or after it is magnetized.
The ferromagnetic particles preferentially
Giant magnetoresistive probes use a adhere to the surface of the test object in
biasing current to push the magnetic areas where the flux is diverted, or leaks
layers into an antiparallel moment state out. The magnetic flux leakage near
and the external field is used to overcome discontinuities causes the magnetic
particles to accumulate in the region and
FIGURE 38. Resistance versus applied field for in some cases form an outline of the
2 µm (8 × 10–5 in.) wide strip of discontinuity. Heterogeneities can
antiferromagnetically coupled, multilayer therefore be detected by looking for
test object composed of 14 percent giant indications of magnetic particle
magnetoresistive material.9 accumulations on the surface of the test
object either with the naked eye or
4.2 through a camera. The indications are
easier to see if the particles are bright and
4.1 reflective. Alternately, particles that
fluoresce under ultraviolet or visible
Resistance (kΩ) 4.0 radiation may be used. The test object has
to be viewed under appropriate levels of
3.9 illumination with radiation of appropriate
wavelength (visible, ultraviolet or other).
3.8
Application Techniques
3.7
Magnetic particles are applied to the
3.6 surface by two different techniques in
industry.
–32 –16 0 16 32 Dry Testing. Dry techniques use particles
(–0.4) (–0.2) (0.2) (0.4) applied in the form of a fine stream or a
cloud. They consist of high permeability
Applied magnetic field, kA·m–1 (kOe) ferromagnetic particles coated with either
reflective or fluorescent pigments. The
particle size is chosen according to the
Fundamentals of Magnetic Testing 69
dimensions of the discontinuity sought. can be used to image the surface very
Particle diameters range from Յ50 to rapidly.
180 µm (Յ0.002 to 0.007 in.). Finer
particles are used for detecting smaller In very simple terms, charge coupled
discontinuities where the leakage devices each consist of a two-dimensional
intensity is low. Dry techniques are used array of tiny pixels that each accumulates
extensively for testing welds and castings a charge corresponding to the number of
where discontinuities of interest are photons incident on it. When a readout
relatively large. pulse is applied to the device, the
Wet Testing. Wet techniques are used for accumulated charge is transferred from
detecting relatively fine cracks. The the pixel to a holding or charge transfer
magnetic particles are suspended in a cell. The charge transfer cells are
liquid (usually oil or water) that can be connected in a manner that allows them
sprayed on the test object. Particle sizes to function as a bucket brigade or shift
are significantly smaller than those used register. The charges can, therefore, be
with dry techniques and vary in size serially clocked out through a
within a normal distribution, with most charge-to-voltage amplifier that produces
particles measuring from 5 to 20 µm a video signal.
(2 × 10–4 to 8 × 10–4 in.). As in the case of
dry powders, the ferromagnetic particles In practice, charge coupled device
are coated with either reflective or cameras can be interfaced to a personal
fluorescent pigments. computer through frame grabbers, which
are commercially available. Vendors of
Imaging of Magnetic Particle frame grabbers usually provide software
Indications that can be executed on the personal
computer to process the image. Image
The magnetic particle distribution can be processing software can be used to
examined visually after illuminating the improve contrast, highlight the edges of a
surface or the surface can be scanned with discontinuity or to minimize noise in the
a flying spot system11,12 or imaged with a image.
charge coupled device camera.
Flying Spot Scanners. To illuminate the Test Calculations
test object, flying spot scanners use a
narrow beam of radiation — visible light In determining the magnetic flux leakage
for nonfluorescent particles and from a discontinuity, certain conditions
ultraviolet radiation for fluorescent ones. must be known: (1) the discontinuity’s
The source of the beam is usually a laser. location with respect to the surfaces from
The wavelength of the beam is chosen which measurements are made, (2) the
carefully to excite the pigment of the relative permeability of the material
magnetic particles. The incidence of the containing the discontinuity and (3) the
radiation beam on the test object can be levels of magnetic field intensity H and
varied by moving the scanning mirror. magnetic flux density B in the vicinity of
the discontinuity. Even with this
The photocell does not sense any light knowledge, the solution of the applicable
when the test object is scanned by the field equations (derived from Maxwell’s
narrow radiation beam until the beam is equations of electromagnetism) is difficult
directly incident on the magnetic particles and is generally impossible in closed
adhering to the test object near a algebraic form. Under certain
discontinuity. When this occurs, a large circumstances, such as those of
amount of light is emitted, called discontinuity shapes that are easy to
fluorescence if excited by ultraviolet handle mathematically, relatively simple
radiation. The fluorescence is detected by equations can be derived for the magnetic
a single phototube equipped with a filter flux leakage if simplifying assumptions are
that renders the system blind to the made. This simplification does not apply
radiation from the irradiating source. The to subsurface inclusions.
output of the photocell is suitably
amplified, digitized and processed by a Finite Element Techniques
computer.
Charge Coupled Devices. An alternative An advance in magnetic theory since
approach is to flood the test object with 1980 has been the introduction of finite
radiation whose wavelength is carefully element computer codes to the solution
chosen to excite the pigment of the of magnetostatic problems. Such codes
magnetic particles. Charge coupled device came originally from a desire to minimize
cameras,13,14 equipped with optical filters electrical losses from electromagnetic
that render the camera blind to radiation machinery but soon found application in
from the source but are transparent to magnetic flux leakage theory. The
light emitted by the magnetic particles, advantage of such codes is that, once set
up, discontinuity leakage fields can be
calculated by computer for any size and
70 Magnetic Testing
shape of discontinuity, under any discontinuity is constant or when
magnetization condition, so long as the nonlinear permeability effects can be
BH curve for the material is known. ignored. The major problem that remains
is how to deal with real discontinuity
In the models of magnetic flux leakage shapes often impossible to handle by
discussed so far, the implicit assumptions classical techniques.
are (1) that the field within a
discontinuity is uniform and (2) that the Such deficiencies are overcome by the
nonlinear magnetization characteristic use of computer programs written to
(BH curve) of the tested material can be allow for nonlinear permeability effects
ignored. Much of the early pioneering around oddly shaped discontinuities.
work in magnetic flux leakage modeling Specifically, computerized finite element
used these assumptions to obtain closed techniques, originally developed for
form solutions for leakage fields. studying magnetic flux distributions in
electromagnetic machinery, have also
The solutions of classical problems in been developed for nondestructive
electrostatics have been well known to testing. Both active and residual
physicists for almost a century and their excitation are discussed above. The
magnetostatic analogs were used to extension of the technique to include
approximate discontinuity leakage fields. eddy currents is detailed elsewhere.
Such techniques work reasonably well
when the permeability around a
Fundamentals of Magnetic Testing 71
PART 10. Techniques of Magnetic Testing15
Magnetic flux leakage testing is a suited for pumping well sucker rods and
commonly used technique. Signals from other elongated oil field test objects.
probes are processed electronically and
presented to indicate discontinuities. After a well is drilled, the sides of the
Although some techniques of magnetic well are lined with a relatively thin steel
flux leakage testing may not be as casing material, which is then cemented
sophisticated as others, it is probable that in. This casing can be tested only from
more ferromagnetic material is tested with the inside surface. The cylindrical
magnetic flux leakage than with any other geometry of the casing permits the flux
technique. loop to be easily calculated so that
magnetic saturation of the well casing is
Magnetizing techniques have evolved achieved.
to suit the geometry of the test objects.
The techniques include yokes, coils, the As with inservice well casing, buried
application of current to the test object pipelines are accessible only from the
and conductors that carry current through inside surface. The magnetic flux loop is
hollow test objects. Many situations exist the same as for the well casing test
in which current cannot be applied system. In this case, a drive mechanism
directly to the test object because of the must be provided to propel the test
possibility of arc burns. Design system through the pipeline.
considerations for magnetization of test
objects often require minimizing the Threaded Regions of Pipe
reluctance of the magnetic circuit,
consisting of (1) the test object, (2) the An area that requires special attention
magnetizing system and (3) any air gaps during the inservice testing of drill pipe is
that might be present. the threaded region of the pin and box
connections. Common problems that
Test Object Configurations occur in these regions include fatigue
cracking at the roots of the threads and
Short Asymmetrical Objects stretching of the thread metal. Automated
systems that use both active and residual
A short test object with little or no magnetic flux techniques can be used for
symmetry may be magnetized to detecting such discontinuities.
saturation by passing current through it
or by placing it in an encircling coil. If Ball Bearings and Races
hollow, a conductor can be passed
through the test object and magnetization Systems have been built for the
achieved by any of the standard magnetization of both steel ball bearings
techniques (these include half-wave and and their races. One such system uses
full-wave rectified alternating current, specially fabricated hall elements as
pure direct current from battery packs or detectors.
pulses from capacitor discharge systems).
For irregularly shaped test objects, testing Relatively Flat Surfaces
by wet or dry magnetic particles is often
performed, especially if specifications The testing of welded regions between flat
require that only surface breaking or curved plates is often performed using
discontinuities be found. a magnetizing yoke. Probe systems
include coils, hall effect detectors,
Elongated Objects magnetic particles and magnetic tape.
The cylindrical symmetry of elongated Discontinuity Mechanisms
test objects such as wire rope permits a
relatively simple flux loop to magnetize a In the metal forming industry,
relatively short section of the rope. discontinuities commonly found by
Encircling probes are placed at some magnetic flux leakage include overlaps,
distance from the rope to permit the seams, quench cracks, gouges, rolled-in
passage of splices. Such systems are also slugs and subsurface inclusions. In the
case of tubular goods, internal mandrel
marks (plug scores) can also be identified
when they result in remaining wall
72 Magnetic Testing
thicknesses below some specified Typical Magnetic
minimum. Small marks of the same type Techniques
can also act as stress raisers: cracking can
originate from them during quench and Short Parts
temper procedures. Depending on the use
to which the material is put, subsurface For many short test objects, the most
discontinuities such as porosity and convenient probe is magnetic particles.
laminations may also be detrimental. The test object can be inspected for
Such discontinuities may be acceptable in surface breaking discontinuities during or
welds where there are no cyclic stresses after it has been magnetized to saturation.
but may cause injurious cracking when For active field testing, the test object can
such stresses are present. be placed in a coil carrying alternating
current and sprayed with magnetic
In the metal processing industries, particles. Or it can be magnetized to
grinding especially can lead to surface saturation by a direct current coil and the
cracking and to some changes in surface resulting residual induction can be shown
metallurgy. Such discontinuities as with magnetic particles. In the latter case,
cracking have traditionally been found by the induction in the test object can be
magnetic flux leakage techniques, measured with a flux meter. Wet particles
especially wet magnetic particle testing. perform better than dry ones because
there is less tendency for the wet particles
Service induced discontinuities include to fur (that is, to stand up like short hairs)
cracks, corrosion pitting, stress induced along the field lines that leave the test
metallurgy changes and erosion from object. These techniques will detect
turbulent fluid flow or metal-to-metal transversely oriented, tight
contact. In those materials placed in discontinuities.
tension and under torque, fatigue
cracking is likely to occur. A discontinuity The magnetic flux leakage field
that arises from metal-to-metal wear is intensity from a tight crack is roughly
sucker rod wear in tubing from producing proportional to the magnetic field
oil wells. Here, the pumping rod can rub intensity Hg across the crack, multiplied
against the inner surface of the tube and by crack width Lg. If the test is performed
both the rod and tube wear thin. In wire in residual induction, the value of Hg
rope, the outer strands will break after (which depends on the local value of the
wearing thin and inner strands sometimes demagnetization field in the test object)
break at discontinuities present when the will vary along the test object. Thus, the
rope was made. Railroad rails are subject sensitivity of the technique to
to cyclic stresses that can cause cracking discontinuities of the same geometry
to originate from otherwise benign varies along the length of the test object.
internal discontinuities.
For longitudinally oriented
Loss of metal caused by a conducting discontinuities, the test object must be
fluid near two slightly dissimilar metals is magnetized circumferentially. If the test
a very common form of corrosion. The object is solid, then current can be passed
dissimilarity can be quite small, as for through the test object, the surface field
example, at the heat treated end of a rod intensity being given by Ampere’s law:
or tube. The result is preferential
corrosion by electrolytic processes, ∫(1) H dℓ = I
compounded by erosion from a contained
flowing fluid. Such loss mechanisms are where dℓ is an element of length (meter),
common in subterranean pipelines, H is the magnetic field intensity (ampere
installed petroleum well casing and in per meter) and I is the current (ampere) in
refinery and chemical plant tubing. the test object.
The stretching and cracking of threads If the test object is a cylindrical bar, the
is a common problem. For example, when symmetry of the situation allows H to be
tubing, casing and drill pipe are constant around the circumference, so the
overtorqued at the coupling, the threads closed integral reduces:
exist in their plastic region. This causes
metallurgical changes in the metal and (2) 2π RH = I
can create regions where stress corrosion
cracking takes place in highly stressed or:
areas at a faster rate than in areas of less
stress. Couplings between tubes are a (3) H I
good example of places where material 2πR
may be highly stressed. Drill pipe threads
are a good example of places where such
stress causes plastic deformation and
thread root cracking.
=
Fundamentals of Magnetic Testing 73
where R is the radius (meter) of the transverse discontinuities, such as
cylindrical test object. A surface field ultrasonic or eddy current techniques.
intensity that creates an acceptable
magnetic flux leakage field from the Alternating Current versus Direct
minimum sized discontinuity must be Current Magnetization
used. Such fields are often created by
specifying the amperage per meter of the Alternating current magnetization is more
test object’s outside diameter. suitable for detection of outer surface
discontinuities because it concentrates the
Transverse Discontinuities magnetic flux at the surface. For equal
magnetizing forces, an alternating current
Because of the demagnetizing effect at the field is better for detecting outside surface
end of a tube, automated magnetic flux imperfections but a direct current field is
leakage test systems do not generally better for detecting imperfections below
perform well when scanning for the surface.
transverse discontinuities at the ends of
tubes. The normal component Hy of the In practice, the ends of tubes are tested
field outside the tube is large and can for transverse discontinuities by the
obscure discontinuity signals. Test following magnetic flux leakage
specifications for such regions often techniques.
include the requirement of additional
longitudinal magnetization at the tube 1. Where there is a direct current active
ends and subsequent magnetic particle field from an encircling coil, magnetic
tests during residual induction. This particles are applied to the tested
situation is equivalent to the material while it is maintained at a
magnetization and testing of short test high level of magnetic induction by a
objects as outlined above. direct current field in the coil. This
technique is particularly effective for
The flux lines must be continuous and internal cracks. Fatigue cracks in drill
must therefore have a relatively short pipe are often found by this
path in the metal. Large values of the technique.
magnetizing force at the center of the coil
are usually specified. Such values depend 2. Where there is an alternating current
on the weight per unit length of the test active field from an encircling coil,
object because this quantity affects the magnetic particles are applied to the
ratio of length L to diameter D. Where the tested material while it lies inside a
test object is a tube, the L·D–1 ratio is coil carrying alternating current. Using
given by the length between the poles 50 or 60 Hz alternating current, the
divided by twice the wall thickness of the penetration of the magnetic field into
tube. (The distance L from pole to pole the material is small and the
can be longer or shorter than the actual technique is good only for the
length of the test object and must be detection of outside surface
estimated by the operator.) As a rough discontinuities.
example, with L = 460 mm (18 in.) and When tests for both outer surface and
D = 19 mm (0.75 in.), the L·D–1 ratio is
24. inner surface discontinuities are necessary,
it may be best to test first for outer surface
The effective permeability of the metal discontinuities with an alternating current
under test is small because of the large field, then for inner surface
demagnetization field created in the test discontinuities with a direct current field.
object by the physical end of the test
object. An empirical formula is often used Liftoff Control of Scanning Head
to calculate approximately the effective
permeability µ: To obtain a stable detection of
discontinuities, liftoff between the probe
(4) µ = 6 L −5 and the surface of the material must be
D kept constant. Usually liftoff is kept
constant by contact of the probe with the
so effective permeability µ = 139 in the surface but the probe tends to wear with
above example. this technique. A magnetic floating
technique has been used for noncontact
For wet magnetic particle testing, the scanning. In this technique, liftoff is
surface tension of the fluids that carry the measured by a gap probe and the probe
particles is large enough to confine the holder is moved by a coil motor,
particles to the surface of the test object. controlled by the gap signal.16 This system
This is not the case with dry particles, and related technology are described in
which have the tendency to stand up like this volume’s chapter on primary metals
fur along lines of magnetizing force. applications.
In many instances, it may be better to
use some other test technique for
74 Magnetic Testing
PART 11. Magnetic Testing Applications
Discontinuities2 5. Forging laps occur when gouges or fins
created in one metal working process
For magnetic testing, discontinuities may are rolled over at an angle to the
be broadly categorized according to their surface in subsequent processes.
origin in the stages of fabrication and
service. 6. Inclusions are pieces of nonmagnetic
or nonmetallic materials embedded
1. Primary production and processing tests inside the metal during cooling.
are used to inspect the stages of Inclusions are not necessarily
processing from pouring and detrimental to the use of the material.
solidification of the ingot to
production of basic shapes, including 7. The pouring and cooling processes can
sheet, bar, pipe, tubing, forgings and also result in lack of fusion within the
castings. These tests are typically used steel. Such regions may be worked
to locate two discontinuity subgroups: into internal laminations.
(a) those formed during solidification Discontinuities in used materials
are called inherent discontinuities;
(b) those formed during mill reduction include fatigue cracks, pitting, corrosion,
are called primary processing erosion and abrasive wear.
discontinuities.
Much steel is acceptable to the
2. Secondary processing, or manufacturing producer’s quality assurance department if
and fabrication tests, are used to inspect no discontinuities are found or if
the results of processes that convert discontinuities are considered to be of a
raw stock into finished components. depth or size less than some prescribed
Forming, machining, welding and maximum. Specifications exist for the
heat treating discontinuities are acceptance or rejection of such materials
detected. and such specifications sometimes lead to
debate between the producer and the end
3. Service tests are widely used for user. Discontinuities can either remain
detecting overstress and fatigue benign or can grow and cause premature
cracking. Magnetic particle tests are failure of the part. Abrasive wear can turn
not used to detect corrosion, benign subsurface discontinuities into
deformation or wear, three of the most detrimental surface breaking
common service induced problems. discontinuities.
Flux leakage testing, however, can be
used to detect material loss resulting For used materials, fatigue cracking
from corrosion or abrasion — in wire commonly occurs as the material is
rope, for example. cyclically stressed. Fatigue cracks grow
Discontinuities caused during rapidly under stress or in the presence of
corrosive materials such as hydrogen
manufacture include cracks, seams, sulfide, chlorides, carbon dioxide and
forging laps, laminations and inclusions. water. For example, drill pipe failure from
fatigue often initiates at the bases of pits,
1. Cracking occurs when quenched steel at tong marks or in regions where the
cools too rapidly. tube has been worn by abrasion. Pitting is
caused by corrosion and erosion between
2. Seams occur in several ways, the steel and a surrounding or containing
depending on when they originate fluid. Abrasive wear occurs in many steel
during fabrication. structures. Good examples are (1) the
wear on drill pipe caused by hard
3. Discontinuities such as piping or formations when drilling crooked holes or
inclusions within a bloom or billet can (2) the wear on both the sucker rod and
be elongated until they emerge as long the producing tubing in rod pumping oil
tight seams or gouges during initial wells. Specifications exist for the
forming processes. They may later be maximum permitted wear under these
closed with additional forming. and other circumstances. In many
instances, such induced damage is first
4. Their metallurgical structures are often found by automated magnetic techniques.
different but the origin of
manufactured discontinuities is not
usually taken into account when
rejecting a part.
Fundamentals of Magnetic Testing 75
Basic Ferromagnetic Materials Nonmetallic Inclusions
Production
All steel contains nonmetallic matter that
In the production of ferrous alloys, iron mainly originates in deoxidizing materials
ore is converted to steel in one or more added to the molten metal during the
furnaces where it is melted and refined refining operation. These additives are
and where alloying elements are added. easily oxidized metals such as aluminum,
While in the liquid state, the metal is silicon, manganese and others. The oxides
poured into a mold and allowed to and sulfides of the metals make up the
solidify into a shape typically called an majority of nonmetallic inclusions. When
ingot or is continuously cast. finely divided and well distributed, these
discontinuities are often not
Ingots are quite large and must be objectionable.
formed into more manageable shapes by
hot working through a series of rolls or However, sometimes the additives
mills. These semifinished shapes are called collect during solidification and form
blooms, billets or slabs, depending on size large clumps in an ingot. During primary
and shape. A bloom is an intermediate processing these large clumps are rolled
product, rectangular in shape with a cross out into long discontinuities called
sectional area typically larger than stringers. In highly stressed components,
0.02 m2 (36 in.2). A billet can be round or stringers can act as nucleation points for
square with a cross sectional area from fatigue cracking. In certain test objects,
1600 mm2 to 0.02 m2 (2.5 to 36 in.2). A stringers are acceptable in a limited
slab is an intermediate shape between an amount. Government and industry
ingot and a plate with a width at least specifications on steel cleanliness define
twice its thickness. the amount of inclusions or stringers that
may be accepted.
Inherent Discontinuities
The addition of lead or sulfur to
This group of discontinuities occurs molten steel is a common practice for the
during the initial melting and refining alloys known as free machining steels.
processes and during solidification from These alloys contain a large number of
the molten state. Such discontinuities are nonmetallic inclusions that break or chip
present before rolling or forging is during machining operations. Magnetic
performed to produce intermediate particle tests of free machining alloys
shapes. often indicate an alarming number of
discontinuities that are not considered
Pipe detrimental in service.
When molten metal is continuously cast Blowholes
or poured into a mold, solidification
progresses gradually, starting at the sides As molten steel is poured into an ingot
and progressing upward and inward. and solidification commences, there is an
There is progressive shrinkage during evolution of gases. These gases rise
solidification. For ingots, the last metal to through the liquid in the form of bubbles
solidify is at the top and center of the and many escape or migrate to the
mold. Because of the shrinkage, there is cropped portion of the ingot.
typically insufficient liquid metal
remaining to fill the mold and a However, some gases can be trapped in
depression or cavity is formed. the ingot, forming the discontinuities
known as blowholes. Most blowholes are
In addition, impurities such as oxides clean and will weld or fuse shut during
and entrapped gases tend to migrate to primary and secondary rolling. Those near
the center and top of a mold and may the surface may have an oxidized skin
become embedded in the last portions to and will not fuse, appearing as seams in
solidify. After solidification, the upper the rolled, forged or extruded product.
portion is cut off or cropped and Oxidized blowholes in the interior of slabs
discarded, removing most of the appear as laminations in plate products.
shrinkage cavity and impurities. However,
if the cavity is deeper than normal or if Ingot Cracks
the cropping is short, some of the
unsound metal will show up in the Contraction of the metal during
intermediate shape as a void called pipe. solidification and cooling of the ingot
Pipe is almost always centered in the generates significant surface stresses and
semifinished shape and is undesirable for internal stresses that can result in
most purposes. cracking. If the cracks are internal and no
air reaches them, they are usually welded
shut during rolling and do not result in
discontinuities. If they are open to the air
or otherwise become oxidized, they will
not seal but remain in the finished
product.
76 Magnetic Testing
During the rolling of an ingot into a service. These seams can initiate fatigue
billet, oxidized cracks form long seams. It cracks.
is common practice to use magnetic
particle tests of billets before additional Laminations
processing. Such preprocessing tests
permit the removal of seams by grinding, Laminations in plate, sheet and strip are
chipping or flame scarfing. If not removed formed when blowholes or internal cracks
before rolling or working, seams are are not fused shut during rolling but are
further elongated in finished shapes and flattened and enlarged. Laminations are
this may make the final product large and potentially troublesome areas of
unsuitable for many applications. horizontal discontinuity.
Primary Processing Magnetic particle testing detects
Discontinuities lamination only when it reaches and
breaks the edges of a plate. Laminations
When steel ingots are worked down to that are completely internal to the test
shapes such as billets, slabs and forging object typically lie parallel to its surface
blanks, some inherent discontinuities may and cannot be detected by magnetic
remain in the finished product. In particle procedures.
addition, rolling or forming operations
may themselves introduce other Cupping
discontinuities. The primary processes
considered here include the hot working Cupping occurs during drawing or
and cold working methods of producing extruding operations when the interior of
shapes such as plate, bar, rod, wire, tubing the shape does not flow as rapidly as the
and pipe. surface. The result is a series of internal
ruptures that are serious whenever they
Forging and casting are also included occur. Cupping can be detected by the
in this category because they typically magnetic particle method only when it is
require additional machining or other severe and approaches the surface.
subsequent processing. All the primary
processes have the potential for Cooling Cracks
introducing discontinuities into clean
metal. Bar stock is hot rolled and then placed on
a bed or cooling table and allowed to
Seams reach room temperature. During cooling,
thermal stresses may be set up by uneven
Seams in bar, rod, pipe, wire and tubing rates of temperature change within the
are usually objectionable. They originate material. These stresses can be sufficient
from ingot cracks and despite for generating cracks.
preprocessing tests, some cracks can be
overlooked or incompletely removed. Cooling cracks are generally
longitudinal but because they tend to
Rolling and drawing operations can curve around the object shape, they are
also produce seams in the finished not necessarily straight. Such cracks may
product. If the reduction on any of the be long and often vary in depth along
rolling passes is too great, an overfill may their length. Magnetic particle indications
then produce a projection from the billet. of cooling cracks therefore can vary in
This projection can be folded or lapped intensity (heavier where the crack is
on subsequent passes, producing a long deepest).
deep seam.
Forging Discontinuities
The reverse also occurs if the shape
does not fill the rolls, resulting in a Forgings are produced from an ingot, a
depression or surface groove. On billet or forging blank that is heated to
subsequent rolling passes, this underfill the plastic flow temperature and then
produces a seam running the full length pressed or hammered between dies into
of the shape. Seams originating from the desired shape. This hot working
overfilled rolls usually emerge at an acute process can produce a number of
angle to the surface. Seams caused by discontinuities, some of which are
underfilled rolls are likely to be normal to described below.
or perpendicular to the surface.
Flakes
Seams or die marks can be introduced
by defective or dirty dies during drawing Flakes are internal ruptures that some
operations. Such seams are often fairly believe are caused by cooling too rapidly.
shallow and may not be objectionable, Another theory is that flakes are caused by
especially when subsequent machining the release of hydrogen gas during
removes the seam. Seams are always cooling.
objectionable in components that
experience repeated or cyclic stresses in
Fundamentals of Magnetic Testing 77
Flakes usually occur in fairly heavy liquid solidifies before joining with the
sections and some alloys are more remaining liquid. The presence of an
susceptible than others. These ruptures are oxidized surface, even though it is liquid
usually well below the surface, typically or near liquid, prevents fusion when two
more than halfway between the surface surfaces meet. This condition can result
and the center. Because of their from splashing, interrupted pouring or
positioning, flakes are not detectable by the meeting of two streams of metal
magnetic particle techniques unless coming from different directions.
machining brings the discontinuity close
to the surface. Cold shuts can be shallow skin effects
or can extend quite deeply into the
Forging Bursts casting. Shallow cold shuts called scabs
can be removed by grinding. Deep cold
When steel is worked at improper shuts cannot be repaired.
temperatures, it can crack or rupture.
Reducing a cross section too rapidly can Hot Tears and Shrinkage Cracks
also cause forging bursts or severe
cracking. Hot tears are surface cracks that occur
during cooling after the metal has
Forging bursts may be internal or solidified. They are caused by thermal
surface anomalies. When at or near the stresses generated during uneven cooling.
surface, they can be detected by the Hot tears usually originate at abrupt
magnetic particle method. Internal bursts changes in cross section where thin
are not generally detected with magnetic sections cool more rapidly than adjacent
particles unless machining brings them heavier masses.
near the surface.
Shrinkage cracks are also surface cracks
Forging Laps that occur after the metal cools. They are
caused by the contraction or reduction in
During the forging operation, there are volume that the casting experiences
several factors that can cause the surface during solidification.
of the object to fold or lap. Because this is
a surface phenomenon, exposed to air, Weldment Discontinuities
laps are oxidized and do not fuse when
squeezed into the object (Fig. 1). Welding can be considered a localized
casting process that involves the melting
Forging laps are difficult to detect by of both base and filler metal. Welds are
any nondestructive testing method. They subject to the same type of discontinuities
lie at only slight angles to the surface and as castings but on a slightly different
may be fairly shallow. Forging laps are scale. In addition, other discontinuities
almost always objectionable because they may be formed as a result of improper
serve as fatigue crack initiation points. welding practices. Some of the
discontinuities peculiar to weldments are
Flash Line Tears described below.
As the dies close in the final stage of the Lack of Fusion and Lack of
forging process, a small amount of metal Penetration
is extruded between the dies. This
extruded metal is called flash and must be Failure to melt the base metal results in a
removed by trimming. void between the base and filler materials.
This lack of fusion can be detected by
If the trimming is not done or not magnetic particle methods if it is close
done properly, cracks or tears can occur enough to the weld surface.
along the flash line. Flash line tears are
reliably detected by magnetic particle With lack of penetration, the root area
testing. of the weld is inadequately filled.
Magnetic particle testing does not
Casting Discontinuities generally detect lack of penetration.
Castings are produced by pouring molten Heat Affected Zone Cracks and
metal into molds. The combination of Crater Cracks
high temperatures, complex shapes, liquid
metal flow and problematic mold Cracks in the base metal adjacent to the
materials can cause a number of weld bead can be caused by the thermal
discontinuities peculiar to castings. Some stresses of both melting and cooling. Such
of these are described below. cracks are usually parallel to the weld
bead. Heat affected zone cracking is easily
Cold Shuts detected by magnetic particle testing.
Cold shuts originate during pouring of Cracks in the weld bead caused by
the metal when a portion of the molten stresses from solidification or uneven
78 Magnetic Testing
cooling are called crater cracks. Cracks the distortion is too great or the objects
caused by solidification usually occur in are very hard, cracking can occur during
the final weld puddle. Cracks caused by the straightening operation.
uneven cooling occur in the thin portion
at the junction of two beads. Magnetic Surface cracks can also occur in
particle testing is widely used to detect hardened objects during improper
crater cracks. grinding operations. Such thermal cracks
are created by stresses from localized
Manufacturing and overheating of the surface under the
Fabrication Discontinuities grinding wheel. Overheating can be
caused by using the wrong grinding
Discontinuities associated with various wheel, a dull or glazed wheel, insufficient
finishing operations, e.g., machining, heat or poor coolant, feeding too rapidly or
treating or grinding are described below. cutting too heavily. Grinding cracks are
especially detrimental because they are
Machining Tears perpendicular to the object surface and
have sharp crack tips that propagate
Machining tears occur if a tool bit drags under repeated or cyclic loading.
metal from the surface rather than cutting
it. The primary cause of this is improperly Another type of discontinuity that may
shaped or dull cutting edges on the bit. occur during grinding is cracking caused
by residual stresses. Hardened objects may
Soft or ductile metals such as low retain stresses that are not high enough to
carbon steel are more susceptible to cause cracking. During grinding, localized
machining tears than harder medium heating added to entrapped stresses can
carbon and high carbon steels. Machining cause surface ruptures. The resulting
tears are surface discontinuities and are cracks are usually more severe and
reliably detected by magnetic particle extensive than typical grinding cracks.
testing.
Plating, Pickling and Etching
Heat Treating Cracks Cracks
When steels are heated and quenched (or Hardened surfaces are susceptible to
otherwise heat treated) to produce cracking from electroplating, acid pickling
properties for strength or wear, cracking or etching processes.
may occur if the operation is not suited to
the material or the shape of the object. Acid pickling can weaken surface fibers
The most common sort of such cracking is of the metal, allowing internal stresses
quench cracking, which occurs when the from the quenching operation to be
metal is heated above the critical relieved by crack formation. Another
transition point and is then rapidly cracking mechanism is the interstitial
cooled by immersing it in a cold medium absorption of hydrogen released by the
such as water, oil or air. acid etching or electrodeposition process.
Absorption of nascent hydrogen adds to
Cracks are likely to occur at locations the internal stresses of the object and
where the object changes shape from a subsequently may cause cracking. This
thin to a thick cross section, at fillets or mechanism, called hydrogen embrittlement,
notches. The edges of keyways and roots can result in cracking during the etching
of splines or threads are also susceptible to or plating operation or at some later time
quench cracking. when additional service stresses are
applied.
Cracks can also originate if the metal is
heated too rapidly, causing uneven Service Discontinuities
expansion at changes of cross section. In
addition, rapidly increasing heat can Discontinuities also occur from service
cause cracking at corners, where heat is conditions. Some discontinuities such as
absorbed from three surfaces and is deformation and wear are not detected by
therefore absorbed much more rapidly the magnetic particle test, but the
than by the body of the object. Corner technique is useful for indicating the
cracking can also occur during quenching discontinuities listed below.
because of thermal stresses from uneven
cooling. Overstress Cracking
Straightening and Grinding All materials have load limits (called
Cracks ultimate strength). When service stressing
exceeds this limit, cracking occurs.
The uneven stresses caused by heat Usually the failure is completed by surface
treating frequently result in distortion or fracture of the object. In this case, the
warping and the metal forms must be crack is easy to detect and magnetic
straightened into their intended shape. If particle testing is not required. However,
Fundamentals of Magnetic Testing 79
there are instances where surfaces do not applications and elevators for personnel
visibly separate and magnetic particle and raw material transportation. Testing is
testing is needed to detect and locate the performed to determine cross sectional
cracking. loss caused by corrosion and wear and to
detect internal and external broken wires.
Fatigue Cracking The type of flux loop used (electromagnet
or permanent magnet) can depend on the
Objects subjected to repeated alternating accessibility of the rope. Permanent
or fluctuating stresses above a specific magnets might be used where taking
level eventually develop a crack. The crack power to an electromagnet might cause
continues to grow until the object logistic or safety problems.
fractures. The stress level at which fatigue
cracks develop is called the fatigue strength By making suitable estimates of the
of the material and is well below the parameters involved, a reasonably good
ultimate strength of the material. There is estimate of the flux in the rope can be
an inverse relationship between the made. Because discontinuities can occur
number of stress applications (cycles) and deep inside the rope material, it is
the stress level necessary to initiate essential to maintain the rope at a high
cracking: low cycles and high stress value of magnetic flux density, 1.6 to
produce the same results as high cycles 1.8 T (16 to 18 kG). Under these
and low stress. conditions, breaks in the inner regions of
the rope will produce magnetic flux
Another factor contributing to fatigue leakage at the surface of the rope.
cracking is the presence of surface
anomalies such as copper penetration The problem of detecting magnetic
sharp radii, nicks and tool marks. These flux leakage from inner discontinuities is
act as stress raisers and lower both the compounded by the need to maintain the
number of cycles and the stress level magnetic probes far enough from the rope
needed to initiate cracking. Fatigue for splices in the rope to pass through the
cracking typically occurs at the surface test head. Common probes include hall
and is reliably detected by magnetic effect detectors and encircling coils.
particle testing.
The cross sectional area of the rope can
Corrosion be measured by sensing changes in the
magnetic flux loop that occur when the
Magnetic particle procedures are not used rope gets thinner. The air gap becomes
to detect surface corrosion or pitting. larger and so the value of the field
However, there are secondary intensity falls. This change can easily be
discontinuities that can be revealed by the sensed by placing hall effect probes
magnetic particle method. When objects anywhere within the magnetic circuit.
are under sustained stress, either internal
or external, and are at the same time Internal Casing or Pipelines
exposed to a corrosive atmosphere, a
particular kind of cracking results. Known The testing of inservice well casing or
as stress corrosion cracking, this buried pipelines is often performed by
discontinuity is easily detected by magnetic flux leakage techniques. Various
magnetic particle testing. types of wall loss mechanisms occur,
including internal and external pitting,
Another occurrence related to erosion and corrosion caused by the
corrosion is pitting. Pitting itself does not proximity of dissimilar metals.
usually produce magnetic particle
indications (in some applications, sharp From the point of view of magnetizing
edged pits can hold particles). Pitting can the pipe metal in the longitudinal
serve as a stress raiser and often initiates direction, the two methods are identical.
fatigue cracks. Fatigue cracks originating The internal diameters and metal masses
at corrosion pits are reliably detected by involved in the magnetic flux loop
the magnetic particle method. indicate that some form of active field
excitation must be used. Internal
Applications of Magnetic diameters of typical production or
Flux Leakage Testing transportation tubes range from about
100 mm (4 in.) to about 1.2 m (4 ft).
Wire Ropes
If the material is generally horizontal,
An interesting example of an elongated some form of drive mechanism is
steel product inspected by magnetic flux required. Because the test device (a robotic
leakage testing is wire rope. Such ropes are crawler) may move at differing speeds, the
used in the construction, marine and oil magnetic flux leakage probe should have
production industries, in mining a signal response independent of velocity.
For devices that operate vertically, such as
petroleum well casing test systems, coil
probes can be used if the tool is pulled
from the bottom of the well at a constant
speed. In both types of instrument, the
80 Magnetic Testing
probes are mounted in pads pressed shallower, the signal will eventually be
against the inner wall of the pipe. indistinguishable from the rifle bore
noise. In magnetic flux leakage testing,
Because both line pipe and casing are cannon tubes can be magnetized to
manufactured to outside diameter size, saturation and scanned with hall elements
there is a range of inside diameters for to measure residual induction.
each pipe size. Such ranges may be found
in specifications. To make the air gap as Round Bars and Tubes
small as possible, soft iron attachments
can be screwed to the pole pieces. In some test systems, round bars and
tubes have been magnetized by an
For the pipeline crawler, a recorder alternating current magnet and rotated
package is added and the signals from under the magnet poles. Because the
discontinuities are tape recorded. When leakage flux from surface discontinuities is
the tapes are retrieved and played back, very weak and confined to a small area,
the areas of damage are located. Pipe the probes must be very sensitive and
welds provide convenient magnetic extremely small. The system uses a
markers. With the downhole tool, the differential pair of magnetodiodes to
magnetic flux leakage signals are sent up sense leakage flux from the discontinuity.
the wire line and processed in the logging The differential output of these twin
truck at the wellhead. probes is amplified to separate the leakage
flux from the background flux. In this
A common problem with this and system, pipes are fed spirally under the
other magnetic flux leakage equipment is scanning station, which has an
the need to determine whether the signals alternating current magnet and an array
originate from discontinuities on the of probe pairs. The system usually has
inside or the outside surface of the pipe. three scanning stations to increase the
Production and transmission companies test rate.
require this information because it lets
them determine which form of corrosion In one similar system, round billets are
control to use. The test shoes sometimes rotated by a set of rollers while the billet
contain a high frequency eddy current surface is scanned by a transducer array
probe system that responds only to inside moving straight along the billet axis.
surface discontinuities. Thus, the Seamless pipes and tubes are made from
occurrence of both magnetic flux leakage the round billets.
and eddy current signals indicates an
inside surface discontinuity whereas the In another tube test system, the
occurrence of a magnetic flux leakage transducers rotate around the pipe as the
signal indicates only an outside surface pipe is conveyed longitudinally.
discontinuity. Overlapping elliptical printed circuit coils
are used instead of magnetodiodes and are
Problems with this form of testing coupled to electronic circuits by slip rings.
include the following. The system can separate seams into
categories according to crack depth.
1. The magnetic flux leakage system
cannot measure elongated changes in Billets
wall thickness, such as might occur
with general erosion. A relatively common problem with square
billets is elongated surface breaking
2. If there is a second string around the cracks. By magnetizing the billet
tested string, the additional metal circumferentially, magnetic flux leakage
contributes to the flux loop, especially can be induced in the resulting residual
in areas where the two strings touch. magnetic field.
3. A relatively large current must be sent Magnetic flux leakage systems for
down the wire line to raise the pipe testing tubes exhibit the same general
wall to saturation. Temperatures in ability to classify seam depth. It is
deep wells can exceed 200 °C (325 °F). generally accepted that even with the lack
of correlation between some of the
4. The tool may stick downhole or instrument readings and the actual
underground if external pressures discontinuity depths, the automatic
cause the pipe to buckle. readout of these two systems still
represents an improvement over visual or
Cannon Tubes magnetic particle testing.
In elongated tubing, the presence of One technique, often called
rifling affects the ability to perform a magnetography, for the detection of
good test, especially for discontinuities discontinuities uses a belt of flux sensitive
that occur in the roots of the rifling. material, magnetic tape, to record
Despite the presence of extraneous signals indications. Discontinuity fields
from internal rifling, however, rifling magnetize the tape, which is then
causes a regular magnetic flux leakage scanned with an array of microprobes or
signal that can be distinguished from
discontinuity signals. As a simulated
discontinuity is made narrower and
Fundamentals of Magnetic Testing 81
hall effect detectors. Finally, the tape surface), it may be possible to correlate
passes through an erase head before magnetic flux leakage signals and
contacting the billet again. Because the discontinuity depths. This correlation is
field intensity at the corners is less than at normally impossible.
the center of the flat billet face, a
compensation circuit is required for equal Commercially available equipment
sensitivity across the entire surface. does not reconstruct all the desired
discontinuity parameters from magnetic
Damage Assessment flux leakage signals. For example, the
signal shape caused by a surface breaking
In most forms of magnetic flux leakage forging lap is different from that caused
testing, discontinuity dimensions cannot by a perpendicular crack but no
be accurately measured by using the automated equipment uses this difference
signals they produce. The final signal to distinguish between these
results from more than one dimension discontinuities.
and perhaps from changes in the
magnetic properties of the metal As with many forms of nondestructive
surrounding the discontinuity. testing, the detection of a discontinuity
and subsequent followup by either
Signal shapes differ widely, depending nondestructive or destructive methods
on location, dimensions and pose no serious problems for the
magnetization level. It is therefore inspector. Ultrasonic techniques,
impossible to accurately assess the damage especially a combination of shear wave
in the test object with existing and compression wave techniques, work
equipment. Under special circumstances well for discontinuity assessment after
(for example, when surface breaking magnetic flux leakage has detected them.
cracks can be assumed to share the same In some cases, however, the discontinuity
width and run normal to the material is forever hidden. Such is very often the
case for corrosion in downhole and
subterranean pipes.
82 Magnetic Testing
References
1. Nondestructive Testing Handbook, 11. Flaherty, J. and E.J. Strauts. United
second edition: Vol. 6, Magnetic Particle States Patent 3774162, Laser Scan
Testing. Columbus, OH: American Testing System Having Pattern
Society for Nondestructive Testing Recognition Means (1973).
(1989).
12. Flaherty, J. and E.J. Strauts. “Automatic
2. Stanley, R.K. Section 21, “Diverted Scanning of Fluorescent Indications.”
Flux Theory.” Nondestructive Testing Proceedings of the ASM Metals Show.
Handbook, second edition: Vol. 4, Materials Park, OH: ASM International
Electromagnetic Testing. Columbus, OH: (October 1971).
American Society for Nondestructive
Testing (1986): p 607-630. 13. Bloke, M.M., N. Sampat and J. Canosa.
Sensors and Camera Systems for Systems
3. Hausman, E. and E. Slack. Physics, for Scientific Industrial and Digital
second edition. Princeton, NJ: Van Photography Applications. Bellingham,
Nostrand Publishing Company (1939). WA: SPIE Press (2001).
4. Stanley, R.K. and G.L. Moake. 14. Donati, S. Photodetectors: Devices,
“Inspecting Oil Country Tubular Circuits and Applications. Upper Saddle
Goods Using Capacitor Discharge River, NJ: Prentice Hall (2000).
Systems.” Materials Evaluation. Vol. 41,
No. 7. Columbus, OH: American 15. Stanley, R.K., T. Hiroshima and
Society for Nondestructive Testing M.L. Mester. Section 22, “Diverted
(1983): p 779-782. Flux Applications.” Nondestructive
Testing Handbook, second edition:
5. Moake, G.L. and R.K. Stanley. Vol. 4, Electromagnetic Testing.
“Capacitor Discharge Magnetization of Columbus, OH: American Society for
Oil Country Tubular Goods.” Nondestructive Testing (1986):
Electromagnetic Methods of p 631-651.
Nondestructive Testing. New York, NY:
Gordon and Breach (1985): p 151-160. 16. Sakamoto, T. and T. Hiroshima.
“Rotating Eddy Current Machine for
6. NFPA 70, National Electric Code, 2002 Hot Steel Rods and Wires.” Paper 5.
edition. Quincy, MA: National Fire QualTest-2 Conference Proceedings
Prevention Association (2001). [Dallas, TX, October 1983]. Columbus,
OH: American Society for
7. Beissner, R.E., G.A. Matzkanin and Nondestructive Testing (1983): p 1-11.
C.M. Teller. NDE Applications of
Magnetic Leakage Field Methods: A State Bibliography
of the Art Survey. San Antonio, TX:
Southwest Research Institute (1980). Blitz, J. “Magnetic Methods.” Electrical and
Magnetic Methods of Nondestructive
8. Owston, C.N. “The Magnetic Leakage Testing. New York, NY: Adam Hilger
Field Technique of NDT.” British (1991): p 44–88.
Journal of Non-Destructive Testing.
Vol. 16, No. 6. Northampton, United Hopwood, T., V.G. Oka, R.C. Deen.
Kingdom: British Institute of Reliability Assessment of High-Risk Steel
Non-Destructive Testing (November Bridges by Nondestructive Test Methods.
1974): p 162-168. PB 89-117717/GAR. Lexington, KY:
Kentucky Transportation Research
9. Daughton, J., J. Brown, R. Beech, A. Program (October 1987).
Pohm and W. Kude. “Magnetic Field
Sensors Using GMR Multilayer.” IEEE Jiles, D. Introduction to Magnetism and
Transactions on Magnetics. Vol. 30, Magnetic Materials. London, United
No. 6. New York, NY: Institute of Kingdom: Chapman & Hall (1991).
Electrical and Electronics Engineers
(1994): p 4608-4610. Mackintosh, D.D., D.L. Atherton,
P.C. Porter and A. Teitsma. “Test Rigs
10. Smith, C. and J. Daughton. “Low-Field for Magnetic Flux Leakage Inspection
Magnetic Sensing with GMR Sensors.” Tools for Pipelines.” Materials
Proceedings of the Sensors Expo Evaluation. Vol. 50, No. 1. Columbus,
[Baltimore, MD, May 1999]. OH: American Society for
Cleveland, OH: Advanstar Nondestructive Testing (January 1992):
Communications (1999). p 13-17.
Fundamentals of Magnetic Testing 83
Shannon, R.W.E. and L. Jackson. “Flux CESLIC Report OR6. London, United
Leakage Testing Applied to Kingdom: Engineering Structures
Operational Pipelines.” Materials Laboratories, Department of Civil
Evaluation. Vol. 46, No. 12. Columbus, Engineering, Imperial College
OH: American Society for (February 1988).
Nondestructive Testing (November Lord, W., J.M. Bridges, W. Yen and
1988): p 1516-1518, 1520-1522, 1524. R. Palanisamy [P. Samy]. “Residual and
Active Leakage Fields around Defects
Stanley, R.K. “Simple Explanation of the in Ferromagnetic Materials.” Materials
Theory of the Total Magnetic Flux Evaluation. Vol. 36, No. 7. Columbus,
Method for the Measurement of OH: American Society for
Ferromagnetic Cross Sections.” Nondestructive Testing (July 1978):
Materials Evaluation. Vol. 53, No. 1. p 47-54.
Columbus, OH: American Society for Lovejoy, D.J. Magnetic Particle Inspection:
Nondestructive Testing (January 1995): A Practical Guide. London, United
p 72-75. Kingdom: Chapman and Hall (1993).
Lovejoy, D.J. ”Standardisation of Light
Magnetic Particle Testing Levels for Magnetic and Penetrant
Inspection.” British Journal of
Astroem, T. “Use and Misuse of Settling Nondestructive Testing. Vol. 36, No. 1.
Measurements of Magnetic Particle Northampton, United Kingdom:
Suspensions.” Non-Destructive Testing: British Institute of Nondestructive
Proceedings of the 4th European Testing (January 1994): p 8-9.
Conference [London, United Kingdom, Magnetic Particle Inspection Symposium
September 1987]. Vol. 4. J.M. Farley Reference Book. Columbus, OH:
and R.W. Nichols, eds. London, United American Society for Nondestructive
Kingdom: Pergamon Press (1988): Testing (1993).
p 2748-2753. Stanley, R.K. “Magnetic Particle
Inspection: Some Unsolved Problems.”
Bayliss, M., D. Short and M. Bax, eds. Materials Evaluation. Vol. 52, No. 8.
Underwater Inspection. London, United Columbus, OH: American Society for
Kingdom: Plymouth Ocean Projects Nondestructive Testing (August 1994):
Limited (1988). p 917-920.
Stanley, R.K. “Circumferential
Betz, C.E. Principles of Magnetic Particle Magnetization of Tubes and the
Inspection, first edition. Chicago, IL: Measurement of Flux Density in Such
Magnaflux Corporation (1967). Materials.” Materials Evaluation.
Vol. 44, No. 8. Columbus, OH:
Bray, D.E. and R.K. Stanley. Nondestructive American Society for Nondestructive
Evaluation — A Tool for Design, Testing (July 1986): p 966-970.
Manufacturing and Service. New York, Stanley, R.K. “Circumferential
NY: McGraw-Hill Publishing Company Magnetization of Tubes and the
(1989). Measurement of Flux Density in Such
Materials.” Materials Evaluation.
Chedister, W.C. and J. Long. “Issues of Vol. 44, No. 8. Columbus, OH:
Magnetic Particle Weld Inspection.” American Society for Nondestructive
Materials Evaluation. Vol. 51, No. 9. Testing (July 1986): p 966-970.
Columbus, OH: American Society for Stanley, R.K. “Magnetic Field
Nondestructive Testing (September Measurement: The Gauss Meter in
1993): p 976-977. Magnetic Particle Testing.” Materials
Evaluation. Vol. 46, No. 12. Columbus,
Forshaw, M.E. and P.J. Mudge. OH: American Society for
“Optimisation of Magnetic Particle Nondestructive Testing (November
Inspection.” Non-Destructive Testing: 1988): p 1509-1512.
Proceedings of the 4th European Swartzendruber, L.J. “Quantitative
Conference [London, United Kingdom, Problems in Magnetic Particle
September 1987]. Vol. 4. J.M. Farley Inspection.” Proceedings of the 15th
and R.W. Nichols, eds. London, United Annual Review of Progress in
Kingdom: Pergamon Press (1988): Quantitative Nondestructive Evaluation
p 2729-2740. [La Jolla, CA, 1988]. Vol. 8B. New
York, NY: Plenum (1989): p 2133-2140.
Goldberg, L. Inspection of Fixed Offshore Wong, L.C. “Test Parameters of Wet
Structures: Inspector/Diver Training. Magnetic Particle Inspection of Steel
Columbus, OH: American Society for Billets.” Materials Evaluation. Vol. 46,
Nondestructive Testing (1994). No. 12. Columbus, OH: American
Society for Nondestructive Testing
Hagemaier, D.J. “Quality Indicators for (November 1988): p 1548-1557.
Magnetic Particle Inspection.”
Materials Evaluation. Vol. 49, No. 3.
Columbus, OH: American Society for
Nondestructive Testing (March 1991):
p 346-350.
Kountouris, I.S. and M.J. Baker. Defect
Assessment: Analysis of the Dimensions
of Defects Detected by Magnetic Particle
Inspection in an Offshore Structure.
84 Magnetic Testing
3
CHAPTER
Magnetism1
Nathan Ida, University of Akron, Akron, Ohio
PART 1. Fundamentals of Electromagnetism
Coulomb’s Law The approach in this chapter is to start
with Maxwell’s equations and derive from
The nature of electromagnetism can be them all the necessary relations. In doing
summarized by four vector quantities, so, the equations are accepted as the basic
their interaction, their relations with each postulates. In particular, at low
other and with matter. These four time frequencies, Maxwell’s equations are
dependent vector quantities are referred to identical to those of Coulomb, Faraday,
as electromagnetic fields and include: Gauss and Ampere. The results derived
electric field intensity E, electric flux here are general and, within the
density D, magnetic field intensity H and assumptions made in their derivation,
magnetic flux density B. apply to a wider range of applications.
Only those electric and magnetic
The study of electromagnetic fields phenomena most directly related to
begins with the study of basic laws of nondestructive testing and, in particular,
electricity and magnetism and with the to magnetic particle testing are considered
use of some basic postulates. In particular, in detail here. Other electromagnetic
it is customary to start with Coulomb’s phenomena are mentioned briefly for
law. This law states that the force between completeness of treatment.
two stationary charges is directly proportional
to the size of the charges and is inversely Maxwell’s equations are a set of
proportional to the square of the distance nonlinear, coupled, first order, time
between them. dependent partial differential equations
whose general solution is difficult to
Adding Gauss’ and Ampere’s laws obtain. Some methods for the solution of
provides a complete set of relations the electromagnetic field equations are
describing all electrostatic, magnetostatic discussed below.
and induction phenomena, but not wave
propagation. To include wave propagation Measurement Units
in electromagnetic field equations, the
displacement current (continuity One major source of confusion when
equation) is added to Ampere’s law. Doing applying electromagnetic field theory has
so obtains Maxwell’s equations. been the units for measurement.
Centimeter gram second (CGS) units, the
Alternatively, Maxwell’s equations may electromagnetic system of units (EMU)
serve as the basic postulates and, because and meter kilogram second ampere units
they form a complete set describing all (MKSA) are the most familiar, but other
electromagnetic phenomena, the required systems such as the absolute magnetic, the
relations may be deduced. By choosing absolute electric and the so-called
Maxwell’s equations as the starting point, normalized system have also been used.
an assumption of the equations’ accuracy
is implicitly made. This is not more More disturbing is the fact that mixed
troublesome than assuming that units have also been used. For example,
Coulomb’s law applies or that practitioners used to use MKSA units such
displacement currents exist. In either case, as the ampere for electrical quantities and
the proof of correctness is experimental. EMU units such as the gauss for magnetic
This is an important consideration: it quantities.
specifically states that Maxwell’s equations
and therefore the electromagnetic field Only the International System (SI) of
relations cannot be proven Units is used in this section. The benefit
mathematically. gained in consistency far outweighs any
inconvenience.
Use of Maxwell’s Equations
Another problem encountered in
Maxwell’s equations do not take motion practice is the confusion between magnetic
into account and therefore do not include field intensity H, sometimes called field
the induction of currents due to motion. strength, and magnetic flux density B. The
To do so, it is necessary to add the lorenz term magnetic field is often used for H or B
force equation and the so-called or both, depending on the situation. To
constitutive relations. It may also be useful avoid such confusion, the quantity B is
to note that, by proper interpretation, used consistently for the magnetic flux
relativistic effects can also be handled (this density while H is the magnetic field
application is found in the literature).2-6 intensity. Similarly, E is the electric field
intensity and D is the electric flux density.
86 Magnetic Testing
PART 2. Field Relations and Maxwell’s Equations
Maxwell’s equations are summarized in contribution to the original laws of
Eq. 1 through Eq. 4 in differential form electricity. The displacement current,
and in Eq. 5 through Eq. 8 in integral although often taken as an assumption, is
form. Equation 9 is the lorenz force nothing more than an expression that can
equation which describes the interaction be derived from the continuity equation.
of electric and magnetic fields with Equations 4 and 8 are Gauss’ law for
electric charge: magnetic sources and they state the
nonexistence of isolated magnetic charges
(1) ∇×E = − ∂B or poles. Equations 3 and 7 are Gauss’ law
∂t for electric charges.
(2) ∇×H = J + ∂D At this point, the equations are neither
∂t linear nor nonlinear. This important
behavior is determined through material
(3) ∇ ⋅ D = ρ properties and is not inherent in the
equations. The material properties follow
the constitutive relations:
(10) B = µH
(4) ∇ ⋅ B = 0 (11) D = ⑀ E
∫(5) E ⋅ dℓ = − dΦ (12) J = σE
dt
c If any of these relations is nonlinear,
the field relations are nonlinear. In
∫ ∫(6) ∂D ds particular, the permeability is known to
H ⋅ dℓ = I + ∂t ⋅ be highly nonlinear for ferromagnetic
materials. In some cases, the conductivity
c S and permittivity ⑀ may also be nonlinear.
∫(7) D ⋅ ds = Q The electric conductivity σ, magnetic
s permeability µ and the electric
permittivity ⑀ are generally tensor
∫(8) B ⋅ ds = 0 quantities. Although for many practical
s purposes it can be assumed that they are
scalar quantities, materials are
(9) F = q(E + v × B) encountered in practice that behave
differently. These exceptions are defined
where dℓ is differential length (meters), ds through linearity, homogeneity and
is differential area (square meters), E is isotropy of the materials. Only for linear,
electric field intensity (V·m–1), F is force isotropic, homogeneous materials are the
(N), I is current (A), J is current density material properties single-valued scalar
(A·m–2), q is electric charge (coulomb) v is quantities.
charge velocity (meter per second) and ٌ
is the del operator. Linearity, Homogeneity and
Isotropy
Equations 1 and 5 are a statement of
Faraday’s law of induction. Equations 2 A medium is said to be homogeneous if its
and 6 are a modified form of Ampere’s properties do not vary from point to point
law. The addition of the displacement within the material. A medium is linear in
current term ∂D·(∂t)–1 was Maxwell’s a property when that property remains
constant as the field changes. The
permeability of most nonmagnetic
materials is considered to be independent
of the field. These materials are usually
considered to be linear in permeability. A
material is isotropic if its properties are
Magnetism 87
independent of direction. This means that As with the general system of
the permeability of an isotropic material equations, the lorenz equation has to
must be the same in all three spatial supplement these equations. Because of
directions. the decoupling of the two sets, the force
equation (Eq. 9) should be used in its
A good example of an anisotropic electrostatic form for electrostatic fields:
material is a permanent magnet. Most
materials, including iron, are anisotropic (21) F = qE
on the crystal level. Because these crystals For magnetostatic fields, only the
are randomly oriented, it may often be
assumed that a macroscopic material is magnetic force exists:
isotropic. This is not necessarily the case (22) F = qv × B
for hard steels or for steels with large,
preferred orientations. The electric current or, more
conveniently, the electric current density J
Static Fields is the source of the magnetic field
intensity (Eq. 14).
By setting to zero all time derivatives in
Maxwell’s equations, the equations for the Equation 18 is particularly useful
static electric and magnetic fields are because it allows the calculation of the
obtained. The four equations become: magnetic field intensity and the
(13) ∇ × E = 0 determination of its direction. If the
(14) ∇ × H = J integration is taken such that the normal
(15) ∇ ⋅ D = ρ to the surface enclosed by the contour C
is in the direction of the current, then the
(16) ∇ ⋅ B = 0 field is described by the right hand rule: if
the current is in the direction of the
thumb, the field is in the direction of the
fingers (Fig. 1). The total current I in
Eq. 18 is the current enclosed within the
contour.
∫(17) E ⋅ dℓ = 0 Magnetic Vector Potential
c
Equation 14 is a cross product and results
∫(18) H ⋅ dℓ = I in a vector quantity J. Because the cross
c product of a vector is also a vector, the
magnetic flux density B may be written as
the curl (cross product) of another
vector A:
∫(19) D ⋅ d s = Q (23) B = ∇ × A
s Thus, Ampere’s law (Eq. 14) can be
∫(20) B ⋅ ds = 0 written as:
s
Equations 13 and 15 are the governing FIGURE 1. Right hand rule: if the thumb of
the right hand is in the direction of the
equations for electrostatic fields (Faraday’s current, the fingers show the direction of
and Gauss’ laws). Equations 14 and 16 are the magnetic field.
Ampere’s and Gauss’ (magnetic) laws for
magnetostatic applications. Note that Magnetic flux lines
Eqs. 13 and 15 do not contain the R
magnetic field whereas Eqs. 14 and 16 do
not depend on the electric field. Thus, the I
equations for electrostatics and
magnetostatics are completely decoupled
and electrical quantities can be calculated
without resorting to the magnetic field
and vice versa.
88 Magnetic Testing
(24) ∇ × 1 (∇ × A) = J In Eq. 27, the definition of the magnetic
µ vector potential in Eq. 23 has been used.
In order to find the total magnetic vector
The vector A is called a magnetic vector potential, this differential is integrated
potential. For an isotropic linear medium, over the closed contour formed by the
the following vector identity can be used current to obtain:
to simplify this expression:
µI dℓ
A∫(28)=4π R
(25) ∇ × ∇ × A = ∇(∇⋅ A) − ∇2 A c
A vector is only defined when both its In order to find the field intensity or
divergence and curl are specified. The the flux density, it is necessary to find the
divergence may be specified in different curl of this expression by performing the
ways. The simplest is to set it equal to operations in Eq. 23.
zero in Eq. 25. Ampere’s law then
becomes: If the magnetic vector potential in
Eq. 28 is substituted back into its
(26) ∇2 A = −µJ definition, the following expression is
which is the vector poisson equation. obtained for the flux density:
Equation 23 defines the magnetic µI dℓ × R
vector potential. This definition of the ∫(29)B=
magnetic vector potential A allows the 4π R2
use of a simpler poisson equation instead
of the original field equations. c
Biot-Savart Law where R^ denotes a unit vector in the
direction of R in Fig. 2.
The purpose of field relations is to solve
field problems. Any of the relations This expression, known as the
obtained previously may be used for this Biot-Savart law, allows the calculation of
purpose. In particular, Eq. 14 can be used the flux density directly. It is particularly
for general field problems while Eq. 18 is useful for situations where the current
useful for solution of highly symmetric paths are clear and the required contour
problems. In problems where no such integration is in the direction of the
symmetry can be found but which are currents.
simple enough not to require the solution
of the general Eq. 26, another method can FIGURE 2. Straight current carrying wire and
be used. For these types of problems, the relation of current and field at point P.
magnetic vector potential is used in still
another form. Considering the current in IP
a straight wire in Fig. 2, the following can
be written at point P: R
dℓ
(27) dA = µI dℓ
4π R
Magnetism 89
PART 3. Electromagnetic Fields and Boundaries
Steady State Alternating This version of Maxwell’s equations is
Current Fields often called the quasistatic form and is
very convenient for many alternating
Low frequency alternating current fields current calculations at low frequencies,
are unique in that a simpler form of including alternating current leakage
Maxwell’s equations can be used. The fields. The following equation is obtained
displacement current term (∂D·∂t –1) in by a method similar to that used to obtain
Eq. 2 or Eq. 6 depends on frequency and is Eq. 26:
very small for low frequencies. In fact,
this term may be neglected within ( )(36) ∇ × 1 ∇× A = J + jσω A
conducting materials and for all µ
frequencies below about 10E + 13 Hz. If This equation, often called the curl-curl
this assumption is introduced and the equation is a diffusion equation and is the
term neglected, the pre-Maxwell set of basis of many analytical and numerical
equations is obtained. methods. By using the vector relation in
Eq. 25, Eq. 36 can be written as:
By introducing a phasor notation for
all vectors, the time dependency is not ( )(37) ∇2A − ∇ ∇⋅ A = −µJ + jωµσ A
explicitly used and the transformed
system is both simpler in presentation Here, the divergence of the magnetic
and in solution. A general vector can be vector potential may be chosen in any
expressed as a phasor by the following convenient, physically sound method. By
definition: cthheoolaspinlagcaiaznerٌo2A~diivnerigtsendcifefearnedntrieawl froitrimng, a
partial differential equation can be written
(30) A(x,y,z,t ) = real ⎡ A ( x, y, z) e jωt ⎤ for two-dimensional (Eq. 38),
⎣ ⎦ axisymmetric (Eq. 39) and
three-dimensional geometries (Eq. 40).
where j is current density (A·m –2), t is time Equations 37 through 40 assume linear
(seconds) and ω is angular frequency permeability:
(radians per second).
Maxwell’s equations (in differential
form) can now be written as:
(31) ∇ × E = − jωB (38) 1 ⎛ ∂2 Az + ∂2 Az ⎞ = − Js
µ ⎜ ∂ x2 ∂y2 ⎟ + jωσ Az
⎝ ⎠
(32) ∇ × H = J + jωD
(33) ∇ ⋅ D = ρ (39) 1 ⎛ ∂2 Aφ + 1 ∂Aφ +
µ ⎜ ∂r 2 r ∂r
⎜⎝
(34) ∇ × B = 0 ∂2 Aφ − Aφ ⎞ = − Js + j ω σAφ
In this form, all time derivatives were ∂z2 r2 ⎟
⎠⎟
written as:
1 ⎛ ∂2 A ∂2 A ∂2 A ⎞
(40) µ ⎜⎜⎝ ∂x2 + ∂y 2 + ∂z2 ⎠⎟⎟ = − Js + jωσA
(35) ∂A = jωA
∂t
90 Magnetic Testing