ASNT NDT Handbook Volume 8 Magnetic Testing

These equations were obtained by (43) ∇⋅A + µ⑀ ∂V = 0
substituting the magnetic vector potential ∂t
in Maxwell’s equations. Because other
potentials (vectors or scalars) can be Equation 42 then becomes:
defined, the field equations may be
Hot~eb.rtmAaispnooeifdstsihonnetioearrnmig(isonroafllatfphielealdsceiqafnuu)annfcottiritominessaBs~oiraninnEdq. (44) ∇2 A − µ⑀ ∂2 A = −µJ
40 is particularly useful because of the ∂t 2
standard methods available for their
solution. This is a heterogeneous wave equation
for the magnetic vector potential. It is
Time Dependent Fields considered a wave equation because its
solution represents waves traveling at a
Instead of neglecting terms in Maxwell’s velocity 1·(µ⑀)–0.5.
equations, if the complete sets in Eqs. 1
through 4 or Eqs. 5 through 8 are used, This particular form was found by
then the general time dependent form of choosing to use the magnetic vector
Maxwell’s equations is obtained. As was potential. Similar wave equations may be
mentioned above, this form is completely found in terms of the electric scalar
general and, when combined with the potential (Eq. 45), the magnetic field
appropriate boundary conditions, can be intensity (Eq. 46) or the electric field
solved to obtain all electromagnetic intensity (Eq. 47):
phenomena, including those related to
static fields. In practice, exact solutions are (45) ∇2V − µ⑀ ∂ 2V = −ρ
rarely obtained because of the complexity ∂t 2 ⑀
involved. Approximations or numerical
methods are often required for the solutions (46) ∇2H − µ⑀ ∂2 H =0
of this type of problem. ∂t 2

Wave Propagation (47) ∇2E − µ⑀ ∂2 E = 0
∂t
When describing wave propagation, the 2
time dependent form must be used. A wave
equation may be obtained by using the The last two equations were obtained
definition of the magnetic vector potential under source-free conditions and are
in Eq. 23. By substituting this into Eqs. 1 therefore homogeneous wave equations for
and 2 and using the constitutive relations the magnetic field intensity and electric
in Eqs. 10 and 11, the following equation is field intensity respectively.
obtained for linear, isotropic material
(where permeability µ is constant): If phasors are used in Eqs. 46 and 47,
instead of time dependent vectors, similar
(41) ∇×∇× A = µJ + µ⑀ ∂ ⎛ −∇V − ∂A ⎞ forms are obtained for wave equations
∂t ⎝⎜ ∂t ⎟⎠ where the time derivative is replaced by jω.
Thus, the wave equations in Eq. 46 and 47
where V is magnetic scalar potential (volt). can be written as:
Using the vector identity in Eq. 25,

Eq. 41 can be written as:

(42) ∇2 A − µ⑀ ∂2 A = − µJ (48) ∇2 H − k2 H = 0
∂t and:
2
(49) ∇2 E − k2 E = 0
+∇ ⎛ ∇ ⋅ A + µ⑀ ∂V ⎞ where the constant k is defined as:
⎝⎜ ∂t ⎟⎠

Because the magnetic vector potential (50) k = ω µ⑀
requires the definition of the curl and the These equations are known as the
divergence, it is possible to define its
divergence in whatever way the situation homogeneous helmholz equations and describe
requires, if consistent with the field the harmonic form of the electromagnetic
equation. The following form may be waves.
chosen:

Magnetism 91

Skin Depth Electromagnetic Boundary
Conditions
In a linear isotropic material, after
substitution of the constitutive relations Electromagnetic fields behave differently
in Eqs. 10 through 12 and using the in different materials. The constitutive
vector identity in Eq. 25, Eqs. 1 and 2 relations in Eqs. 10 through 12 are a
become: statement of this behavior. When
different materials are present, the fields
(51) ∇2E − σµ ∂E − ⑀µ ∂2 E = 0 across the boundaries between these
∂t ∂t materials must undergo some changes to
2 conform to both materials. In such cases,
the field may experience a discontinuity
(52) ∇2H − σµ ∂H − ⑀µ ∂2 H = 0 at the boundary. In order to find the
∂t ∂t 2 necessary conditions that apply at
material boundaries, assume two different
Thus, E and B satisfy identical wave materials as in Fig. 3 and apply Maxwell’s
equations with a damping (dissipative) equations at the boundary. For
term proportional to the conductivity and convenience, the integral form is used. By
magnetic permeability of the material. In doing so, the following four conditions
a good conductor such as most metals, are obtained:
the second order derivative may be
neglected for low frequencies since it is (55) E1τ = E2τ
due to the displacement current in
Maxwell’s second equation. For example, (56) nˆ × (H1τ − H2τ ) = Js
Eq. 52 becomes:
(57) nˆ ⋅ (D1n − D2n ) = ρs
(53) ∇2 H − σµ ∂H = 0
∂t (58) B1n = B2n
The boundary conditions are the same
This is a simple diffusion equation. If an
alternating magnetic field intensity for the magnetostatic and time varying
H0exp (jωt) or E0(jωt) is applied parallel to fields. These conditions are summarized as
the surface of the conductor, the electric follows:
field intensity E or the magnetic field
intensity H is attenuated exponentially 1 The tangential component of the
with distance below the surface. The electric field intensity E and the
attenuation is exp (–x·δ–1) where x is the normal component of the magnetic
distance below the surface and δ is the flux density B are continuous across
skin depth given by: the boundary.

(54) δ = 2 2. The normal component of the electric
flux density D and the tangential
σµω component of the magnetic field
intensity H are discontinuous across
This is an important factor to consider the boundary. The discontinuity
for alternating current magnetic particle depends on the existence of surface
testing because, even at 60 Hz, the skin charges and currents. For situations
depth can be quite small. For example, for where no such charges or currents
a typical ferromagnetic material with a exist, either component may be
conductivity σ = 5 × 106, a relative continuous, depending on the
permeability µr = 100 and a frequency materials and the fields involved.
f = 60 Hz, the skin depth δ = 3 mm. This is The four conditions presented in
probably an overestimate because a linear
material was assumed in the derivation. Eqs. 55 through 58 can be used in order
to describe the fields in different materials
For this reason, alternating current and across their boundaries.
magnetic particle methods, such as the
so-called swinging field methods, generally The four conditions are not entirely
detect only discontinuities which are independent and should be specified with
open to the surface. These methods are care. For example, in time varying fields,
more sensitive to surface breaking specification of the tangential component
discontinuities because the applied field is of E (Eq. 55) is equivalent to the
relatively more intense at the surface. specification of the normal component of
B (Eq. 58). Similarly, specification of the

92 Magnetic Testing

tangential component of H is equivalent (64) nˆ × (H1τ − H2τ ) = Js
to that of the normal component of D.
Only two of the four may be specified (65) nˆ ⋅ D1n = ρs
independently (the tangential component
of E and the tangential component of H (66) B1n = B2n
or any other acceptable combination). Note that while Eqs. 63 through 66 are
Overspecification of boundary conditions
may result in contradiction of conditions correct for the static field, for the time
and may therefore be in error. varying field, both B and H must also be
zero inside a perfect conductor. Thus,
The boundary conditions in Eqs. 55 Eqs. 63 through 66 must be modified for
through 58 were obtained by using the time varying case to:
Maxwell’s equations directly. In order to
render these relations more useful, it is (67) E1τ = E2τ = 0
convenient to introduce the constitutive When H2τ = 0, then:
relations in these conditions and find the
interface conditions for some special (68) nˆ × H1τ = Js
classes of common materials. Two such When D2n = 0, then:
groups of materials often found in
practice are: (69) nˆ ⋅ D1n = ρs
(70) B1n = B2n = 0
1. boundary conditions between two
lossless media (a lossless medium is Note that the boundary conditions in
one that has zero conductivity with Eqs. 67 through 70 only apply for perfect
arbitrary permittivity and conductors. This rarely arises except for
permeability; two perfectly insulating simplified problems and for
materials are considered here); and superconductors. In the case of a
superconductor, these boundary
2. boundary conditions between a conditions are also correct for the static
lossless material and a good field.
conductor.
At the boundary between two good Proper application of the field
equations and imposition of the correct
insulators, no current densities and free
charges are normally present. Thus, all
four components in Eqs. 55 through 58
are continuous. These then can be
rewritten using the constitutive relations
in Eqs. 10 and 12 as:

(59) D1τ = ⑀1
D2 τ ⑀2

(60) B1τ = µ1
B2 τ µ2

(61) ⑀1 E1n = ⑀2 E2n Figure 3. Boundary conditions between
(62) µ1H1n = µ2H2n two materials.

At the interface between a good ⑀2 A2n
conductor and an insulator, both surface µ2 A2
current densities and free charges may σ2 n1
exist. The electric field is zero inside a
perfect conductor and both the tangential A1τ A2τ
component of the electric field intensity A1n A1
and the normal component of the electric ⑀1
flux density must be zero inside the n2 µ1
conductor. The boundary conditions
(Eqs. 55 to 58) then become: Legend σ1
A = magnetic vector potential
(63) E1τ = 0 n = normal component of vector
⑀ = permittivity
µ = permeability
σ = conductivity

Magnetism 93

boundary conditions result in a correct Thus, this equation can be written as:
solution to the field equations.
(74) ∇ ⋅(∇ × H) = ∇⋅J + ∂ρ = 0
The Continuity Equation ∂t

Since charge cannot be destroyed or From Gauss’ law (Maxwell’s third
created, the only possible way to charge a equation), this can be written as:
body is through flow of charge from one
point to another. This is stated
mathematically by the continuity
equation:

∂ρ (75) ∇ ⋅ (∇ × H) = ∇ ⋅ ⎛ J + ∂D ⎞
∂t ⎜⎝ ∂t ⎠⎟
(71) ∇⋅J = −

This often neglected relation is And the following is the correct form
fundamental to understanding field of Ampere’s law:
behavior and is responsible for two
important aspects of electromagnetic (76) ∇×H = J + ∂D
fields: Kirchoff’s current law and the ∂t
linking of electric and magnetic
quantities. Observing that the continuity Note that this form is only necessary
equation is in fact a statement of the when both electric and magnetic
divergence of the current density, the quantities are present. The continuity
displacement current term in Maxwell’s equation need not be taken into account
equations is shown to be a statement of explicitly for purely electrostatic solutions
the continuity equation or preservation of because this implies static charges and
charge. Ampere’s law, before Maxwell’s therefore Eq. 71 is always satisfied
modification is: implicitly. For direct current magnetic
applications, Eq. 71 is again satisfied
(72) ∇ × H = J because any flow of charges is constant.
The divergence of the curl of a vector is The only time the equation needs to be
introduced directly is when the
zero (identically): displacement currents are large compared
to conduction currents (at very high
frequencies).

(73) ∇ ⋅ (∇ × H ) = 0

94 Magnetic Testing

PART 4. Effect of Materials on Electromagnetic
Fields

Material Properties and TABLE 1. Relative permeabilities of magnetic materials.
Constitutive Relations Values given for ferromagnetic materials represent
approximate maximum relative permeabilities.
Magnetic properties are important because
of their effect on the behavior of materials Magnetic Material Relative
under an external field (under active Permeability
excitation) or when the external field is
removed (residual magnetism). The Diamagnetic materials 0.999964
magnetic properties are often discussed Gold 0.99998
using the magnetic permeability of Silver 0.999991
materials. This important quantity is Copper 0.999983
defined through the constitutive relation Lead 0.999991
in Eq. 10. Water 0.999968
Mercury 0.99983
Permeability governs two important Bismuth
features of the magnetic field and 1.0
therefore affects any application that uses Paramagnetic materials 1.00000036
the magnetic field. For ferromagnetic Vacuum (nonmagnetic) 1.000021
materials below saturation, flux density B Air
is generally the quantity of interest and Aluminum 250
has higher values for high values of the 600
permeability for a given source field Ferromagnetic materials 6000
intensity H. Secondly, the permeability Cobalt (99 percent annealed)
also defines whether the field equation is Nickel (99 percent annealed) 2.0 × 105
linear or nonlinear. Iron (99.8 percent annealed)
Iron (99.95 percent annealed in hydrogen) 1.0 × 106
The permeability of free space is Nickel alloy 100
µ0 = 4π × 10 –7 H·m–1. Other materials may Annealed nickel alloy (controlled cooling)a 2000
have larger or smaller permeabilities. Steel (0.9 percent carbon)
Table 1 lists the relative permeabilities of Iron (98.5 percent, cold rolled)
some important materials.
a. By weight 79 percent nickel; 5 percent molybdenum; iron.
The magnetic properties of materials
are defined through the interaction of (78) Hin = M = N m
external magnetic fields and moving The magnetic flux density of the material
charges in the atoms of the material is then given by:
(static charges are not influenced by the
magnetic field since no magnetic forces (79) Bin = µ M
are produced in Lorenz’ law). Atomic scale The terms Hin, m and M are vectors.
magnetic fields are produced inside the
material through orbiting electrons. These This implies that a net magnetic field or
orbiting electrons produce an equivalent flux density can only exist if these vectors
current loop that has a magnetic moment: are aligned in such a way that a total net
vector M exists. If the independent
(77) m = zˆ Iπa2 vectors m are randomly oriented, as is
where πa2 is the area of the loop, I is the often the case, the net magnetization is
equivalent current (Fig. 4a) and z^ is a unit zero.
vector normal to the plane of current
flow. Materials

Many such atomic scale loops or For the purposes of this chapter, three
magnetic moments exist and the material types of magnetic materials are important:
volume contains a certain magnetic diamagnetic, paramagnetic and
moment density. If N magnetic moments ferromagnetic.
per unit volume are present, and if these
moments are aligned in the same
direction, a total magnetization is
generated. The magnetization M is then
given by:

Magnetism 95

Diamagnetic Materials susceptibility of –1 and a permeability of
0. A superconductor expels magnetic flux
In these materials, the internal magnetic (the meissner effect) from its interior.
field due to electrons is zero under normal
conditions. In an external magnetic field, Paramagnetic Materials
an imbalance occurs and a net internal
field opposing the external field is This group of materials exhibits properties
produced. Thus, M in Eq. 78 is negative similar to diamagnetics except that the
with respect to the applied field. The magnetic susceptibility is positive. In the
magnetization is proportional to the presence of an applied magnetic field
external field through a quantity called intensity, the atomic magnetic dipole
the magnetic susceptibility of the moments can align to form a net
material xm: magnetic dipole density. The effect is still
(80) M = xm Hex relatively small, producing observed
In terms of the applied flux density, this relative permeabilities slightly larger than
becomes: 1.0.

(81) B = µ0 (1 + xm ) Hex The permeability of paramagnetic
materials remains constant over a large
The magnetic permeability of any range of applied magnetic field intensities.
material can be written as: Examples of materials in this group are
air, aluminum and some stainless steels.
(82) µ = µ0 (1 + xm )
Ferromagnetic Materials
In diamagnetic materials, the magnetic
susceptibility is very small and negative. Ferromagnetic materials vary from
Its magnitude is usually on the order of diamagnetic and paramagnetic materials
10–5. The net effect is that the relative in two critical ways: (1) their susceptibility
permeabilities exhibited by diamagnetic is very large and (2) there is a pronounced
materials are slightly smaller than 1.0. variation in the internal structure of their
This group of materials includes many magnetic moments. In these materials,
familiar metals including pure copper and many atomic moments are aligned in a
lead. certain direction within a very small
region called a magnetic domain.
Under special conditions such as Neighboring domains have a similar
temperatures less than –150 °C, some structure, with the net magnetic domain
materials may become superconducting. in one direction. In the demagnetized
An ideal superconductor has a magnetic state, the magnetic domains tend to be
aligned randomly, exhibiting a net
Figure 4. Representation of material internal field that is either very small or
properties: (a) field due to current loop; zero.
(b) current loops created by spinning
electrons. This domain model is depicted in
(a) Fig. 5. When an external magnetic field is
applied, those domains that have a net
I field aligned in the direction of the
applied field grow in size while the other
(b) B domains shrink. The internal field and the
external field H are aligned in the same
I direction producing a larger total flux

Legend Figure 5. Magnetic domains in
B = magnetic flux density ferromagnetic material: domain 8 is aligned
I = current with field and will grow as magnetic field
intensity H is increased; domain 3 is aligned
against field and will shrink as H is
increased.

I 2 4
7 5
8
3 6
H

96 Magnetic Testing

density B. The above argument is related As is evident from any hysteresis curve,
to the hysteresis curve of a ferromagnetic the permeability of ferromagnetic
material and explains why any such curve materials is not constant but varies with
has a saturation region: beyond a certain the field. This is exhibited through the
field, all the magnetic domains are slope of the initial magnetization curve to
aligned with the field and an increase in which the permeability is tangent. Thus,
the magnetic field intensity cannot most ferromagnetic materials are highly
increase the net magnetization. Materials nonlinear materials.
typical of this group are iron, steels, nickel
and some stainless steels. Table 1 TABLE 3. Dielectric constants (relative
summarizes some of the more important permittivities) for some materials.
ferromagnetic materials and their
permeabilities. Table 2 lists conductivities Material Relative
of various materials and Table 3 is a listing Permittivity
of dielectric constants.

TABLE 2. Electrical conductivities of some Vacuum 1
materials. Air 1.0006
Rubber 3
Material Conductivity Paper 3
(S·m–1) Phenolic resin, cured 5
Quartz 5
Silver 6.1 × 107 Glass 6
Copper (pure) 5.8 × 107 Mica 6
Gold 4.1 × 107 Water 81
Aluminum 3.5 × 107 Barium titanate 1200
Tungsten 1.8 × 107 Barium strontium titanate 10 000
Brass 1.1 × 107
Iron (pure) 1.0 × 107
Soft steel 0.8 × 107
Carbon steel (1 percent carbon) 0.5 × 107
Nickel chromium stainless steela 1.4 × 106
Nickel chromium alloyb 0.9 × 106
Mercury 1.0 × 106
Graphite 1.0 × 105
Carbon 3.0 × 104
Sea water 4.0
Germanium
Silicon 2.3
Phenolic resin, cured
Glass 3.9 × 10–4
Rubber 1.0 × 10–9
Mica 1.0 × 10–12
Quartz 1.0 × 10–13
1.0 × 10–15
1.0 × 10–17

a. 18 percent nickel, 8 percent chromium.
b. 80 percent nickel, 20 percent chromium.

Magnetism 97

PART 5. Magnetic Circuits and Hysteresis

Magnetic Circuits assumed to be the same. This assumption
in effect neglects any fringing effects in
The two equations that define the static the gap. If the field intensity is denoted in
magnetic field are Eq. 14 and Eq. 16. the gap as Hg abnedcainlcuthlaetetodrionidtearsmHsℓ,otfhtehne
These are written below in differential and the fields can
integral forms in terms of B: pfleurxmdeeanbsiiltityieBsℓ in the toroid and the
(83) ∇ × B = µ J (µ0 and µ) as: of the gap and of the toroid

(84) ∇ ⋅ B = 0 (88) Hℓ = Bℓ
µ
∫(85) B ⋅ dℓ = µ I
c and:

∫(86) B ⋅ ds = 0 (89) Hg = Bℓ
s µ0
These are Ampere’s and Gauss’ laws for
By substituting these in Eq. 87, the
the static field. They can also be viewed as magnetic flux density is found to be
defining a vector quantity B through its related to gap lengths ℓg and the length
curl and divergence. (2πr – ℓg) of toroid material, where r is the
mean radius of the toroid:
The line integral of the magnetic field
intensity around a closed path is defined µ0 µ NI
as a magnetomotive force. µ0 2πr − ℓg + µℓg
( )(90)Bℓ =

∫(87) Vm = H ⋅ dℓ = NI Figure 6. Toroid with air gap used to define
c magnetic circuit concept.

The units of the magnetomotive force A
are customarily expressed as ampere turns A
although the correct unit is the ampere.
The modification from I to NI simply Φ A s
states that, if the total current inside the Ig µo A
closed contour is divided into N wires, I
then the number of turns may be used for
convenience. r
µ
Circuit Theory
Legend
A magnetomotive force Vm = NI causes a A = reference point
magnetic flux Φ to exist within the closed Ig = gap distance
contour mentioned in Eq. 87. If for any r = radius of toroid
reason this flux is contained within a s = cross sectional area of toroid
material, it may be assumed that a flux µ = permeability
flows within the material. This concept Φ = flux
allows flux to be treated much the same
way as current and therefore circuit
theory concepts may be used for the
solution of some specific field problems.

To develop this concept, it is
convenient to use a toroid (Fig. 6). The
gap is assumed to be small and the flux
densities inside the toroid and the gap are

98 Magnetic Testing

If it is assumed that the magnetic flux ∑ ∑(96)
density is uniform within a material (it is NiIi = RjΦ j
often uniform inside a toroid but rarely in
other shapes), the flux can be calculated: ij

(91) Φ = Bs Similarly, by using the divergence of
The total flux through the toroid or the the magnetic flux density ∇·B = 0, the law
gap is therefore: for a junction is:

∑(97) Φi = 0

NI i

(92) Φ = 2πr − ℓg ℓg For simplicity, an analogous magnetic
µs µ0s circuit can be defined as in Fig. 7. Because
+ of its simplicity, this approach has found
considerable use in many areas, especially
Written in terms of the magnetomotive in devices with closed paths (transformers
force Vm, the equation for the flux can be and machines). The approach is quite
written as: limited in scope because of the
approximations used to derive the
(93) Φ = Vm concept. First, the fringing effects cannot
Rℓ + Rg be neglected for large air gaps. Second,
there are always some leakage fields that
where: cannot be taken into account. Finally, the
permeability has been assumed to be
(94) Rℓ = ℓℓ constant. In most cases of practical
µs importance, the permeability of a material
is field dependent (Eq. 98).

and:

(95) Rg = ℓg Hysteresis
µ0s
The constitutive relation between the
The forms of Eqs. 94 and 95 are magnetic field intensity and the magnetic
analogous to that of the direct current flux density is shown in Eq. 10. The
resistance (R = ρℓ·a–1) and are therefore behavior of the field within different
called magnetic resistances or reluctances. materials has been described above.
The reluctance of the mgaapteirsiaRlginantdheRℓ is However, these do not describe all
the reluctance of the phenomena that exist within materials.
toroid. The units for reluctance are 1 per
henry (1·H–1). Similarly, if magnetomotive Inspecting Eq. 10 shows that by
force is considered analogous to voltage increasing the magnetic field intensity H,
and flux analogous to current, Eq. 93 is the flux density B increases by a factor of
analogous to Ohm’s law. µ. However, for ferromagnetic materials,
For any closed magnetic path, the Eq. 10 must be written as a nonlinear
equation can be written as: equation:

Figure 7. Equivalent magnetic circuit (98) B = µ (H ) H
representation.
An alternative way to look at this
+Φ Rt phenomenon is to inspect the domain
Vm Rg behavior of a ferromagnetic material.
Initially, the domains are randomly
– oriented. As the applied field increases,
domains begin to grow by displacing
Legend other domains and eventually occupying
Rg = gap resistance most of the material volume. Any further
Rt = toroid resistance increase of the field has little effect on the
Vm = magnetomotive force domains and therefore has little effect on
Φ = flux the flux density in the material; thus the
permeability depends strongly on the
applied field.

Magnetization Curves

A plot of the relation in Eq. 98 describing
the flux density as a function of the field
intensity is a useful way to look at

Magnetism 99

magnetic materials. For linear materials Hysteresis Curves
(materials for which the permeability is
constant at any field value), this curve is a Reducing the applied field moves the
straight line whose slope is equal to the curve to the left, rather than retracing the
permeability. Ferromagnetic materials initial magnetization curve (Fig. 8b). The
behave differently. The curves in Fig. 8 flux density is reduced up to the point Br,
describe the behavior of iron. Initially, the where the applied field is zero. This
applied field intensity is zero and so is the residual flux is called remanence or
flux density. retentivity and is typical of all
ferromagnetic materials. Applying a
As the field is increased, the flux reverse magnetic field further reduces the
density also increases but, unlike linear flux density to the point Hc, where an
materials, the curve is not linear. At some applied field intensity exists without an
field value H1, the curve starts bending associated flux density. The field intensity
and the slope of the curve is reduced at this point is called the coercivity or the
significantly. Any increase beyond the coercive force of the material. Further
field H3 increases the flux density but not increase in the negative field intensity
at the same rate as at lower points on the traces the magnetization curve through
curve. In fact, the slope in this section of point P2 where a saturation point has
the curve approaches unity, meaning that again been reached, except that in this
the relative permeability approaches 1. case the field intensity and the flux
This region is called saturation and is density are negative.
dependent on the material tested. The
whole curve described in Fig. 8a is called a If the applied field is decreased to zero,
magnetization curve. Since it starts with a point symmetric to Br is reached.
zero applied field it may also be called an Similarly, by increasing the applied field
initial magnetization curve. intensity to a value equal (but positive) to
Hc, the flux density is again zero. Further
Figure 8. Hysteresis curve: (a) initial increase in the field intensity brings it
magnetization curve; (b) hysteresis curve. back to the point P1. Repeating the
(a) B process described above results in a
retracing of the outer curve but not that
H1 H3 H of the initial magnetization curve. This
unique magnetization curve is called the
(b) B P1 hysteresis curve and is typical of all
H1 H ferromagnetic materials (hysteresis curves
Br of different materials, including their
coercive forces and remanence, are
–Hc markedly different).
Hc
The slope of this curve at any point is
–Br the magnetic permeability. The slope is
relatively high in the lower portions of
P2 the initial magnetization curve and is
Legend gradually reduced to unity. At this point,
the material has reached magnetic
B = magnetic flux density saturation. A curve describing the slope of
H = magnetic field intensity the initial magnetization curve of Fig. 8a
P = saturation point is shown in Fig. 9. Figure 9 shows that for
this material (iron), the initial relative
permeability is low, increases gradually
and then, as the field approaches
saturation, decreases and approaches 1.

The hysteresis curve in Fig. 8b has four
distinct sections described by the four
quadrants of the coordinate system.
Particularly important are the first and
second. The curve in the first quadrant is
created by an applied field or source and
is therefore called a magnetization curve. In
particular, the initial magnetization curve
can only be described by starting with an
unmagnetized sample of the material and
then increasing the field within the
material. This section of the curve is
referred to as the active part of the curve.
All direct current applications of magnetic
particle testing that depend on active
magnetization are governed by this
section of the curve.

100 Magnetic Testing

The second quadrant (with the limits dissipated, primarily in the magnetic core
at Br and Hc) is called the demagnetization of the device. In other cases, including
curve. It is important for two reasons. permanent magnets or switching
First, any magnetic material, after being magnetic devices, this property is useful.
magnetized, relaxes to the point Br or
more commonly to a point in the second Magnetization
quadrant. Secondly, this is the quadrant
in which permanent magnets operate. The In order to magnetize a sample, it is
coercivity and remanence of necessary to apply a magnetic field to the
ferromagnetic materials are very different sample. The form in which this field is
from each other and define to a large applied may vary depending on practical
extent the classification of magnetic considerations but the same basic effect
materials. The coercivity and remanence must be obtained: the field in the sample
of some important materials are shown in must be increased to a required value.
Table 4.
In general, if a sample is initially
The area under the hysteresis curve demagnetized, the field is gradually
represents energy. This is understood by increased through the initial
referring to the poynting theorem. In magnetization curve to a required point.
devices such as transformers, this is a If a residual method is being used, the
detrimental property because the energy is field is reduced to zero and the material
relaxes to a point in the second quadrant
Figure 9. Initial permeability curve for iron. of the hysteresis loop. For previously
magnetized samples, it is usually better to
µ demagnetize the sample first and then to
magnetize it to the required point.
Permeability (relative scale)
Demagnetization
H1 H3 H
The hysteresis curve indicates that when
Magnetic field intensity (relative scale) the source of a field is reduced to zero,
there is a remanent flux density in the
material. This remanent or residual field is
sometimes used for testing purposes but
in many cases it is desirable to
demagnetize a test object before a
controlled field is applied or to
demagnetize it after a test.

Demagnetization cannot be achieved
simply by creating a field opposing the
original source field. The demagnetization
process is complicated by shape effects
that usually cause different operating

TABLE 4. Coercivity and remanence of some important materials. Values for Hc and Br are
approximate and strongly depend on thermoelectrical history.

Coercive Remanent Saturation
Force Flux Density Flux Density
Hc
(A·m–1) Br Bs
(Wb·m–2) (Wb·m–2)

Soft magnetic materials 0.2 10–4 0.8
Annealed nickel alloy (controlled cooling)a 16 0 0.34
Nickel zinc ferrite 20 0.5 1.95
Silicon iron (4 percent silicon) 100 1.2 2.16
Iron (pure annealed) 4000 1.0 2.0
Steel (0.9 percent carbon, hot rolled)
4000 1 —
Hard magnetic materials 44 000 1.2 —
Carbon steel (0.9 percent carbon) 126 000 1.04 —
Aluminum nickel alloy, type 5 560 000 0.84 —
Aluminum nickel alloy, type 8
Samarium cobalt

a. 79 percent nickel; 5 percent molybdenum; iron.

Magnetism 101

points to exist in different sections of the loops to distinguish them from the normal
material (see the curve in Fig. 8). (or major) hysteresis loop. Because
permeability is defined as the ratio of |B|
Effective demagnetization of materials and |H|, the permeability of a minor loop
can be achieved by heating the material may be defined as ∆B·∆H–1:
beyond the curie temperature and then
cooling it in a zero field environment. (99) µinc = ∆B
Under most circumstances, this method is ∆H
impractical because of the metallurgical
effects associated with it. Also called an incremental permeability,
this quantity depends on the location of
A practical demagnetization approach the minor curve on the hysteresis loop
is to cycle the material through the and decreases as the normal
hysteresis curve while gradually reducing magnetization increases. The slope of
the magnetic field intensity to zero. The minor loops is always smaller than that of
effect is shown in Fig. 10. If started with a the major loop at a given point. Thus, the
high enough field intensity and reduced incremental permeability is lower than
slowly, this procedure results in a properly the normal permeability at any point on
demagnetized sample. In practice, the hysteresis curve. As the material
demagnetization is performed by applying approaches saturation, the relative
an alternating current field and gradually incremental permeability approaches
reducing its amplitude to zero. Complete unity.
demagnetization is usually a very time
consuming process. In practical situations, Hysteresis Curve As Classifier
it is usually limited to reducing the flux
density to some acceptable level. When applying electromagnetic fields, it
is necessary to distinguish between
Minor Hysteresis Loops applications, specialties and frequency
ranges. For example, electromagnetic
It often happens while a sample is at nondestructive testing is classified as a
some operating point on the hysteresis discipline separate from paleomagnetism
curve (either on the initial magnetization (terrestrial magnetism), even though
curve or on the outer loop) that a exactly the same principles are involved
relatively small change in magnetization and, often, the same methods are used.
occurs. An example of this is a large direct Moreover, within each discipline different
current corresponding to a point on the applications are distinguished.
hysteresis curve and a small alternating
current superimposed on it. In nondestructive testing, active leakage
field, residual leakage field, eddy current and
Alternatively, if the magnetizing other electromagnetic phenomena are
current is suddenly decreased and then used. This distinction helps focus the
increased again, the same effect is created. treatment of different problems. Often,
This situation results in a change in the the distinction parallels that of the
hysteresis curve as shown in Fig. 11. Thus, various areas of electromagnetic fields:
a small oval curve similar to the hysteresis active leakage fields are associated with
curve is described at the initial point. magnetostatics; residual leakage fields
These loops are called minor hysteresis

Figure 10. Demagnetization of Figure 11. Major and minor hysteresis
ferromagnetic materials. loops.

B B ∆H

∆B
HH

Legend Legend
B = magnetic flux density B = magnetic flux density
H = magnetic field intensity H = magnetic field intensity

102 Magnetic Testing

with source-free magnetostatics; and eddy apply a field to an initially magnetized
currents with steady state alternating sample but this is usually not done
current fields. because of the difficulty in determining
the exact operating point.
It is far more practical to distinguish
between the various applications based on Residual leakage fields are obtained
the point of operation on the hysteresis when an active excitation is removed and
curve. This offers a visual description as the operating points of the material are
well as some physical insight into the allowed to relax into the second quadrant
application. (Fig. 12b). Similarly, alternating current
leakage methods may be defined as those
Active leakage field methods are those that employ a normal hysteresis curve.
that employ the initial magnetization The operating point is on the major loop
curve (Fig. 12a). The point on the initial (Fig. 12c).
magnetization curve is obtained by
increasing the current that increases Eddy current methods require
intensity H from zero to some alternating current excitation but this is
predetermined value. It is possible to usually very low. In terms of the hysteresis
curve, it may be said that the operating
Figure 12. Classification of testing point is at the origin although small
methods: (a) active leakage fields (direct hysteresis loops are described around the
current); (b) residual leakage fields; origin as in Fig. 12c.
(c) alternating current operation.
(a) B Energy Lost in Hysteresis Cycle

The energy stored in the magnetic field is
given as a volume integral of an energy
density w:

∫(100) W = wdv
v

H After integrating over the hysteresis
curve or over any part of it, the area
under the curve may be written as:

(b) B B

(c) B ∫(101) w = HdB
0
Legend
B = magnetic flux density The units of this integral are those of a
H = magnetic field intensity volume energy density and, under
linearity assumptions (dB = µdH), the
energy density becomes w = 0.5 µH2.
If this is then integrated over the
H volume of material in which the magnetic

field exists, the total work done by
external sources can be written as:

⎛B ⎞

∫ ∫(102) W = ⎜ HdB⎟ dv
v ⎝⎜ 0 ⎠⎟

The fact that energy is transformed in
the process becomes apparent by
considering that work needs to be
performed in order to change the
H magnetic field in the volume of a
material. The expression in Eq. 102 is the
work done for a complete cycle over the
hysteresis loop. If the field changes at a
certain frequency, the energy per cycle in
Eq. 102 must be multiplied by the
frequency to obtain:

Magnetism 103

(103) Pd = Wf The dissipated energy due to heating
This equation is exact but of limited losses (I2R) is related to the square of the
electric field. In terms of Eq. 105 and the
use because it requires integration over magnetic field, this becomes:
the hysteresis loop. Being a complex
function and in many cases only known (106) σE2 ∝ σf 2B2
experimentally, the hysteresis loop is This relation clearly indicates that the
difficult to integrate. For practical
purposes, an approximate expression in losses due to eddy currents can be very
terms of the maximum induced flux large, especially for large flux densities
density Bmax is often used. The dissipated and higher frequencies. Eddy current
power is: losses may be reduced: (1) by reducing the
conductivity of the materials involved
(104) Pd = ηf Bm1.6ax (ferrites); (2) by special alloying to
This expression is credited to Charles produce very narrow hysteresis curves
(silicon steels); and (3) by breaking the
Steinmetz and assumes that the constant eddy current paths (laminated cores).
η is known. It ranges from 0.001 for
silicon steels to about 0.03 for hard steels. The total losses in magnetic materials
It is an experimental value and the due to hysteresis and eddy current losses
equation is only correct for relatively large can be summarized in terms of the actual
saturation fields (above 0.1 T, or 1 kG). field as:
For low saturation flux densities, the
equation cannot be used. (107) Pd = Nf + k B2f 2
ρ

Eddy Current Losses where N is the number of turns.
In terms of the saturation flux density
In addition to hysteresis losses, the
change in flux density inside conducting Bmax, total losses may be written as:
materials generates induced
electromagnetic forces in those materials. (108) Pd = k1f Bm1.6ax + k2f 2 Bm2 ax
The existence of this electromagnetic ρ
force, and the relatively large conductivity
of most metals, results in a relatively large The constants k, k1 and k2 depend on
current flowing inside the material in a geometry as well as on material
path that is a mirror image of the source properties.
generating the field. It is difficult to
calculate the eddy current generated for
any particular situation but the relative
quantity involved is easy to obtain.

For any conductor, the electric field
due to the induced electromagnetic force
is directly proportional to the magnetic
field as:

(105) E ∝ dB ∝ fB
dt

104 Magnetic Testing

PART 6. Characteristics of Electromagnetic Fields

Energy in Electromagnetic stored magnetic energy and the stored
Field electric energy. These energy densities
reduce to simpler expressions for the
In order to examine the energy in a static electric and magnetic fields:
magnetic field it is convenient to look
first at the general time dependent (113) we = ⑀ E2
expression for energy. This expression 2
includes stored magnetic energy, stored
electric energy and dissipated energy. The µH2
following vector identity is used: 2

(114) wm =

(109) ∇ ⋅(E × H ) = H ⋅∇ × E − E ⋅∇ × H The second term on the right side of
Eq. 111 is the power dissipated and the
Into this expression, a substitution is power due to sources that may exist in the
made: the expression for the curl of E and volume v. If no such sources exist, this
H from Maxwell’s first and second term represents ohmic losses.
equations:
The poynting theorem describes all of a
(110) ∇ ⋅(E × H ) = − H ∂B − E ⋅ ∂D − E ⋅ J system’s energy relations: electrostatic,
∂t ∂t magnetostatic or time dependent. Because
the cross product between the electric
Assuming the energy flows in a volume field and the magnetic field is taken, these
v bounded by an area s, it is then possible two quantities must be related, otherwise
to integrate this expression over the the results have no meaning.
volume v. Before this, transform the left
side from a volume integral to an area The expression in Eq. 111 is an
integral using a divergence theorem. instantaneous quantity. For practical
purposes, a time averaged quantity is
more useful. This can be done by
averaging over a time T (usually a cycle of
the alternating current field):

(E × H )⋅∂s ∂ ⎛ H⋅B E⋅D⎞
∫ ∫(111) = − ∂t ⎝⎜ 2 + 2 ⎠⎟ 1 T
T
sv ∫(115) Pav= P(t )dt

∫× dv − E⋅ Jdv 0
v
Force in Magnetic Field
The left side of the expression
represents the total flow of energy The force in the magnetic field is
through the area bounding the volume. governed by the lorenz force equation
The expression E × H is a power density given in Eq. 9. For the purposes here, the
with units of W·m–2. The power density is electric force (Coulomb’s law) Fe = qE is
called a poynting vector: not important and was removed from the
equation. This in effect assumes that the
(112) P = E × H charge q only experiences a magnetic
The advantage of such an expression is force:

that it also indicates the direction of the (116) F = q(v × B)
energy flow, information that is
important for wave propagation Here, v is the velocity of the charge.
calculations. While forces on charges are important in
themselves, the force on current carrying
The first term on the right side of
Eq. 111 represents the time rate of
increase in the potential or stored energy
in the system. It has two components: the

Magnetism 105

conductors is more important in where ω is angular frequency (radians per
conjunction with magnetic fields. If it is second).
assumed that an element of conductor dℓ,
with a cross sectional area s carries N The force due to this reduction in the
charge particles per unit volume moving stored energy is therefore:
with an average velocity v, then the
magnetic force that this conductor (123) F = − ∇ω
experiences is: This expression for the force is

(117) d F = Nqs v dℓ × B particularly convenient when the actual
Since Nqsv is the total current in the current distributions are not known or are
conductor, the magnetic force becomes: too complicated to permit calculation of
(118) dF = Idℓ × B the flux densities of each current
separately.
To obtain the force due the complete
conductor, integration is taken over the Because the magnetic field energy may
length of the conductor: be expressed in terms of inductances
(Eq. 131), the force in the magnetic field
may also be expressed in terms of
inductances. Thus, for example, the force
between two conductors carrying currents
I1 and I2, having inductances L1, L2 and
mutual inductance L12 can be written as:

∫(119) F = I dℓ × B (124) F = I1 I2 (∇L12)
C
Another important consideration is The stored energy is calculated as:

that of the force exerted on a current (125) W = 1 L1I12 + L12I1I2 + 1 L2 I22
carrying conductor due to the field of a 2 2
second conductor. This is treated by
assuming that the field B is due to one Torque in Magnetic Field
conductor. If there are two conductors,
the force on conductor 1 due to the field The torque on a current carrying system
of conductor 2 is: may be calculated by using the definition
of torque: the product of force and the
∫ ∫ ( )(120) F21 moment arm length. For simplicity,
= µ I1I2 dℓ1 × dℓ2 × Rˆ21 consider the square loop in Fig. 13. If this
4π R221 definition is used, the torque is equal to:
C1 C2
(126) T = sˆIs B sin θ
Similarly, the force on conductor 2 due where s is the area of the loop and s is a
to conductor 1 is: unit vector normal to the plane of the
current loop. The product of current and
∫ ∫ ( )(121) F12 area is defined as a magnetic moment m.
= µ I2 I1 dℓ2 × dℓ1 × Rˆ12
4π R122 (127) m = Is
C2 C1 The magnetic moment has a direction

In these equations, the integration is normal to the area s and in the direction
assumed to be over the entire (closed) described by the right hand rule. Thus,
path of the currents. This is not merely a torque is a vector quantity and can be
convenience but is required to ensure that written as:
the forces F12 and F21 are equal and
opposite in direction. In other words, (128) T = m × B
integration over part of the contours
violates Newton’s third law (action and
reaction forces).

Forces in the magnetic field may also
be expressed in terms of the energy stored
in the magnetic field. A system’s
mechanical work is done at the expense
of its potential energy, so that:

(122) F ⋅ dℓ = − (∇ω) ⋅ dℓ

106 Magnetic Testing

Inductance The inductance in Eq. 130 can be
calculated, provided that the flux linkages
Inductance is a property of the can be obtained. In many practical
arrangement of conductors in a system. It situations, it is more convenient to use an
is a measure of the flux linked within the energy relation.
circuit when excited and a measure of the
magnetic energy stored in the system of (131) W = L I2
conductors. Flux linkage is defined as the 2
flux that links the whole system of
conductors, multiplied by the number of Figure 13. (a) Rectangular loop;
conductors or turns in the system. For a (b) direction of forces and torque on
simple solenoid, this is defined as: rotating loop.
(a) (b)
∫(129) Λ = NΦ = N B ⋅ d s
s F

In effect, this includes only the flux that mB
passes through the center of the solenoid. s
The integration is over the cross sectional
area of the solenoid. A more complicated F
definition can be used, one that includes
flux linkages that do not link all the I
conductors, but this has little practical use
because of the difficulties in calculation.If Legend
the system under consideration is linear, B = magnetic flux density
the field is directly proportional to the F = mechanical force
current and the inductance in henries (H) m = magnetic movement (Eq. 127)
of a system (a coil) may be defined as the I = current
ratio of the flux linkage and the current: s = area within loop

∫N B⋅ds
(130) L = s

I

Magnetism 107

References

1. Ida, N. Ch. 5, “Basic Bastos, J.P.A. and N. Sadowski.
Electromagnetism.” Nondestructive Electromagnetic Modeling by Finite
Testing Handbook, second edition. Element Methods. New York, NY: Marcel
Columbus, OH: American Society for Dekker (2003).
Nondestructive Testing (1989):
p 101-145. Davidson, D.B. Computational
Electromagnetics for RF and Microwave
2. Morse, P.M. and H. Feshbach. Methods Engineering. Cambridge, United
of Theoretical Physics. New York, NY: Kingdom: Cambridge University Press
McGraw-Hill (1953). (2007).

3. Jackson, J.D. Classical Electrodynamics, Gross, P.W. and P.R. Kotigua.
third edition. New York, NY: Wiley Electromagnetic Theory and
(1998). Computation: A Topological Approach.
Cambridge, United Kingdom:
4. Abraham, M. and R. Becker. Classical Cambridge University Press (2004).
Theory of Electricity and Magnetism,
second edition. Glasgow, United Hayt, W.H., Jr. and J.A. Buck. Engineering
Kingdom: Blackie and Son (1961). Electromagnetics, seventh edition.
Boston, MA: McGraw Hill (2006).
5. Clemnow, P.C. An Introduction to
Electromagnetic Theory. New York, NY: Ida, N. Numerical Modeling for
Cambridge University Press (1973). Electromagnetic Nondestructive
Evaluation. London, United Kingdom:
6. Elliott, R.S. Electromagnetics: History, Chapman and Hall (1995).
Theory, and Applications. New York, NY:
Wiley, for IEEE Press (1999). Ida, N. and J.P.A. Bastos. Electromagnetics
and Calculation of Fields. New York, NY:
Bibliography Springer (1997).

Binns, K.J., P.J. Lawrenson and Jin, J. The Finite Element Method in
C.W. Trowbridge. The Analytical and Electromagnetics, second edition. New
Numerical Solution of Electric and York, NY: Wiley (2002).
Magnetic Fields. Chichester, United
Kingdom: Wiley (1992). Sadiku, M.N.O. Numerical Techniques in
Electromagnetics, second edition. Boca
Raton, FL: CRC Press (2000).

Westgard, J.B. Electrodynamics: A Concise
Introduction. New York, NY: Springer
(1997).

108 Magnetic Testing

4

CHAPTER

Magnetization1

Volker Deutsch, Karl Deutsch and Company,
Wuppertal-Elberfeld, Germany
Roderic K. Stanley, NDEIC, Houston, Texas

PART 1. Description of Magnetic Fields

The magnetic particle testing method material is placed across the poles of a
uses magnetic fields to reveal material horseshoe magnet, the lines of flux flow
discontinuities in ferromagnetic materials. from the north pole of the magnet
The common horseshoe magnet attracts through the material to the south pole.
most ferritic materials to its ends or poles. Magnetic lines of flux flow preferentially
Magnetic lines of flux flow from the south through magnetic material rather than
pole through the magnet to the north nonmagnetic material or air.
pole as illustrated in Fig. 1a.
Magnetized Ring
Magnets attract certain materials at the
poles, where the lines of flux leave or If a horseshoe magnet is bent so that its
enter the magnet. When magnetic poles are close together (Fig. 1b), the poles
FIGURE 1. Magnetism in various shapes: still attract magnetic materials. Iron filings
(a) horseshoe magnet; (b) ring magnet with or other magnetic materials cling to the
air gap; (c) closed magnetized ring; poles and bridge the gap between them.
(d) magnetic particles attracted to radial In the absence of a slot, the magnetic flux
crack in circularly magnetized object. lines are enclosed within the ring (Fig. 1c).
(a) No external poles exist, and magnetic
particles dusted over the ring are not
NS attracted to the ring even though there
are magnetic flux lines through it.
(b) Magnetized materials attract externally
only when poles exist. A ring magnetized
NS in this manner is said to contain a circular
magnetic field which is wholly within the
(c) Magnetic particles object.

(d) Magnetic particles Small changes in the cross section of
the ring or in the permeability of its
SN material may cause external flux and the
attraction of magnetic particles.
Legend
N = north pole Effect of Cracks
S = south pole
A radial crack in a circularly
magnetized object creates north and
south magnetic poles at the edges of the
crack. This forces some of the magnetic
lines of force out of the metal path. These
disrupted lines of force are called magnetic
flux leakage. Magnetic particles are
attracted to the poles created by such a
crack, forming an indication of the
discontinuity in the metal test object
(Fig. 1d).

Bar Magnet

When a horseshoe magnet is straightened,
it becomes a bar magnet with poles at
each end. Magnetic flux lines exist
through the bar from the south pole to
the north pole but the flux density is not
uniform along the bar. Magnetic particles
are attracted to any location where flux
emerges and particularly to the ends of
the magnet where the concentration of

110 Magnetic Testing

external flux lines is greatest. Since the FIGURE 2. Straightening horseshoe magnet
magnetic flux within a bar magnet may results in bar magnet: crack in bar magnet
run the length of the bar, it is said to be creates magnetic poles that attract magnetic
longitudinally magnetized or to contain a particles outside the bar.
longitudinal field.
Magnetic
Effect of Cracks in Magnetized Bar particles
SN
A crack in a bar magnet (Fig. 2) distorts
the magnetic flux lines of force and Crack
creates poles on either side of the crack.
These poles attract magnetic particles to
form an indication of the crack. The
intensity of poles formed at a crack
depends on the number of magnetic flux
lines interrupted. A crack at right angles
to the magnetic lines of force interrupts
more flux lines and creates stronger poles
than a crack more nearly parallel to the
flux lines. Test indications of maximum
size are formed when discontinuities are
at right angles to the magnetic lines of
flux and the discontinuity is at the
surface.

Magnetization 111

PART 2. Magnetization with Electric Current

Electric currents are used to create or prods and into the area of the object in
induce magnetic fields in electrically contact with the prods. This establishes a
conducting materials. Since it is possible circular magnetic field in the test object
to alter the directions of magnetic fields around and between each prod electrode.
by controlling the direction of the
electrical magnetizing current, the The use of alternating current limits
arrangement of current paths is used to the prod technique to the detection of
induce magnetic flux lines at right angles
to expected discontinuities in the test FIGURE 3. Circumferential magnetic field
object. surrounding straight conductor carrying
electric current.
Circular Magnetization
Magnetic field
Electric current passing through a straight
conductor (a wire or bar, for example) + –
creates a circumferential magnetic field Magnetizing
around that conductor (Fig. 3). The current Test object
magnetic lines of force are always at right
angles to the direction of the current that FIGURE 4. Circular magnetization of typical
induces the magnetic field. test objects: (a) circular magnetization
caused by passing electric current from
To determine the direction taken by contact plates through test object;
magnetic lines of force around a (b) production of localized circular field by
conductor, imagine that the conductor is passing electric current between contact
grasped with the right hand so that the prods.
thumb points in the direction of the
electric current. The fingers then point in (a) Contact plate Magnetic field Contact
the direction taken by the magnetic field plate
lines, surrounding the conductor. This is
known as Fleming’s right hand rule.

The passage of current induces a
magnetic field intensity in the conductor
as well as in surrounding space. An object
magnetized in this manner is said to have
a circular field or to be circularly magnetized
(Fig. 3).

Circular Magnetization of Magnetic Crack
Solid Test Objects particles

To induce a circular magnetic field in a Magnetizing
solid test object, current may be passed current
through the object. This creates poles on
both sides of discontinuities that are (b) Magnetizing
parallel to the length of the test object. current
These poles attract fine magnetic particles Switch
and form an indication of the
discontinuity (Fig. 4a). It is also possible Weld Magnetic lines of force
to generate a circular field in localized
areas of the object using prods to pass
current through the area being tested
(Fig. 4b).

The prod electrodes (generally solid
copper or braided copper tips) are first
pressed firmly against the test object. The
magnetizing current is passed through the

112 Magnetic Testing

surface discontinuities. Half-wave rectified Circular Magnetization with
direct current is more desirable here Induced Current
because its greater depth of penetration
helps indicate near surface discontinuities. A current flowing circumferentially
around the ring can be induced by
The prod technique generally is used making the ring a single-turn, short
with dry magnetic particle materials circuited secondary transformer (Fig. 6
because of increased particle mobility on illustrates this effect). To accomplish this
rough surfaces and better penetration. In effect, a standard magnetizing coil can be
the United States, wet magnetic particles used.
are not normally used with the prod
technique because of electrical and fire The ring is placed inside the coil with
hazards. In Europe, wet particles are its axis parallel to that of the coil. When
regularly used with prods to achieve the coil is energized with alternating
higher sensitivity. Care should be taken current, the arrangement constitutes an
to maintain clean prod tips, to minimize air core transformer. The magnetizing
heating at the point of contact and to coil is the primary circuit and the ring is
prevent arc strikes and local heating of the single-turn secondary circuit. The
the test surface. Aluminum or copper total current induced in the ring is greatly
braided tip prods or pads (rather than increased by inserting a laminated core of
solid copper tips) are recommended ferromagnetic material through the ring.
because of the possibility of copper
penetration if arcing occurs. For materials with high magnetic
retentivity, direct current can be applied
A remote control switch should be in the technique known as quick break and
built into the prod handles to permit the objects may then be tested by the
control of the current after positioning residual technique. Quick break is when a
and before removing, to minimize arcing. direct current field is caused to collapse
Additional magnets, called leeches, can be suddenly due to an abruptly interrupted
attached to prod electrodes for the same magnetizing current. The circular field
purpose. generated by the induced current leaves
the test object with a strong residual
Circular Magnetization with Prods induction. A bearing race is a good
example of the type of object that can be
In circular magnetization with prods, the tested advantageously by this technique.
field intensity is proportional to the
current used but varies with prod spacing For test objects made of soft material,
and the thickness of the section being with little retentivity, the continuous
tested. A magnetizing current of 90 to technique must be used and the
110 A for each 25 mm (1 in.) of prod collapsing direct current field technique is
spacing is recommended for material not applicable. By using alternating
under 20 mm (0.75 in.) thick. A current (or half-wave direct current) in the
magnetizing current of 100 to 125 A for magnetizing coil, the current may be
each 25 mm (1 in.) of prod spacing is left on and an alternating current (or
recommended for material over 20 mm half-wave direct current) of the same
(0.75 in.) in thickness. Prolonged frequency as the magnetizing current is
energizing cycles may cause localized induced in the ring. This current should
overheating. Prod spacing should not be allowed to flow long enough to
exceed 200 mm (8 in.). produce indications by the continuous
technique.
Prod spacing less than 75 mm (3 in.) is FIGURE 5. Direct contact method of
usually not practical because the particles magnetizing ring shaped test objects to
tend to band around the prods, making locate circumferential discontinuities.
interpretation difficult.
Circular magnetic field
Circular Magnetization with Direct
Contact Discontinuities
Magnetizing current
Figure 5 shows the direct contact
technique for producing circular fields in
a ring to indicate circumferential cracks.
To achieve a reliable examination of the
entire cylindrical surface, two
magnetizations are required.

This is done because the points of
contact (where the current enters and
leaves the ring) are not adequately
magnetized for discontinuity indication.
The ring must therefore be turned
90 degrees and then retested.

Magnetization 113

Circular Magnetization of passed through the test object and
Hollow Test Objects connected to receptacles in the magnetic
particle unit (Fig. 7b). For large diameter
With hollow objects or tubes, the inside cylinders, the cable can be brought back
surfaces may be as important for testing as on the outside of the test object, then
the outside surfaces. When such an object threaded through again — the second
is circularly magnetized (by passing the pass through increases the effective field
magnetizing current through it), no by a factor of two. For long finished tubes,
magnetic flux is produced on the inside uninsulated conductors are not permitted
surface. because of arc burns.

Since a magnetic field surrounds a Longitudinal
current carrying conductor, it is possible Magnetization
to induce a satisfactory magnetic field by
sliding the test object onto an internal Electrical current can be used to create a
conducting bar (Fig. 7a). Passing current longitudinal magnetic field in magnetic
through the bar induces a circular materials. When electric current is passed
magnetic field throughout the volume through a coil, a magnetic field is
of the test object. established lengthwise or longitudinally
within the coil (Fig. 8).
When a conducting bar is not
available, an electrical cable may be The nature and direction of this field
are the result of the field around the
FIGURE 6. Magnetizing with induced current conductor which forms the turns of the
method to locate circular discontinuities in coil. Application of the right hand rule to
ring shaped objects: (a) magnetizing core; the conductor at any point in the coil
(b) magnetizing coil. (Fig. 8a) shows that the field within the
coil is longitudinal.
(a) Test object

Line of flux FIGURE 7. Circular magnetization of
cylindrical objects by using an internal
Discontinuity current carrying conductor: (a) internal bar
conductor; (b) internal cable conductor.

(a)

Head

Bar conductor (copper bar)
Magnetic field

Alternating Laminated Magnetizing current
current iron core Outside or inside diameter cracks
Alternating
current (b)

(b) Discontinuity Cable

Magnetic Magnetizing coil
field
Ring shaped object
Induced current path Current

Flux lines

Circumferential Current
discontinuity

Laminated
core

114 Magnetic Testing

Coil Magnetization Test objects too large to fit in a fixed
coil can be magnetized longitudinally by
When ferromagnetic material is placed making a coil from several turns of
within a coil, most of the magnetic lines flexible cable (Fig. 8b). The use of portable
of force created by the electric current magnetizing equipment with cables and
concentrate themselves in the test object prods or clamps has broadened the use of
and induce longitudinal magnetization magnetic particle testing — there is no
(Fig. 8b). theoretical limit to the size of the object
that can be tested in this manner.
Testing of a long cylindrical object with
longitudinal magnetization is shown in Field Flow Magnetization
Fig. 8c. With a transverse discontinuity in
the test object, magnetic poles are formed Another means of producing a
on both sides of the crack. These poles longitudinal field in a test object is the
attract magnetic particles to form an field flow technique. Here, the field is
indication of the discontinuity. Figure 8c produced by electromagnets and passed
shows that a magnetic field has been through objects as if they were the
induced at right angles to the keepers in a yoke. (A keeper is magnetic
discontinuity. filler put next to a pole to reduce the air
gap.) The field is almost wholly contained
FIGURE 8. Longitudinal or coil within the test object.2
magnetization: (a) longitudinal magnetic
flux within current carrying magnetizing While there is theoretically no limit to
coil; (b) longitudinal magnetization with the length of a test object that can be
coil; (c) typical arrangement of coil and test magnetized this way, as a practical matter
object for longitudinal magnetization. with an alternating current source, power
requirements limit the effective length to
(a) Wire coil about 1.3 m (4 ft). However, special
techniques using direct current have
Magnetic field accomplished longitudinal magnetization
in one step for lengths over 3 m (10 ft).
Magnetizing current
The field flow (or yoke) technique may
(b) Wire coil have some advantages over the current
flow (coil) technique in some production
Test object applications because: (1) moving a
magnetizing coil several times may be
Magnetizing current impractical and time consuming, (2) test
objects with length-to-diameter ratios less
than 3:1 require no special handling and
(3) a consistent field wholly contained
within a test object may be required.
Frequently the field flow technique is
indicated in multidirectional
magnetization.

A reference standard called a quantitive
quality indicator containing known
artificial discontinuities should be located
in the center of the test object during
setup to ensure adequate field intensity
along its entire length.

(c) Coil

Magnetizing
current

Crack
N

SN
S

Legend
N = north pole
S = south pole

Magnetization 115

PART 3. Factors Controlling Magnetization

Factors that should be considered when Half-wave rectified alternating current
selecting a technique of magnetization with a single-phase circuit is shown in
include: (1) alloy, shape and condition of Fig. 9b. The direct current proportion
the test object, (2) type of magnetizing amounts to about 30 percent of the peak
current, (3) direction of the magnetic value.
field, (4) sequence of operations,
(5) value of the flux density, (6) desired Figure 9c shows full-wave rectified
throughput and (7) type of discontinuities alternating current with a single-phase
anticipated. Material properties, current bridge circuit. The direct current
type and direction of the magnetic field proportion amounts to about 64 percent
are covered below. of peak value.

Material Properties Alternating current with a frequency of
50 to 60 Hz (Fig. 9d) shows excellent
The alloy, its heat treatment, cold working uniform magnetization of the surface
and other conditioning treatments even with large changes of cross section.
determine the magnetic permeability of Penetration depth is frequency dependent
a test object. It is necessary to consider and equals about 2 mm at 50 Hz (skin
these when selecting the sequence of effect). There is rapid reduction in
operations, the value of flux density or indication sensitivity with increasing
the magnetic field intensity. They, in turn, depth when using alternating current
affect selection of the magnetization magnetization.
means.
Pulsed current is illustrated in Fig. 9e.
The size and shape of the test object Because of the pulse train at
determine the most practical technique predetermined intervals, the danger of
of magnetization with the available heating from current flow at the contact
equipment. The surface condition of the points is minimized. Thin walled test
test object influences the selection of objects can therefore be tested using
particles as well as the magnetization higher currents.
means. Surface coatings such as paint,
chemical conversion or lacquer coatings Impulse current is normally used
are poor electrical conductors and affect with the residual technique (Fig. 9f). The
testing because it is difficult or impossible magnetization effect results from a high
to pass magnetizing current through such intensity single-current pulse of short
coatings. Whenever a test object can be duration (millisecond range).
properly magnetized with an induced
technique, coating thickness is a concern Direct Current Magnetization
for the inspector.
Direct current obtained from storage
Types of Magnetizing batteries was first believed to be the most
Current desirable current to use for magnetic
particle testing because direct current
Many types of magnetizing current can be penetrates more deeply into test
used for each type of testing (Fig. 9).1 specimens than alternating current. The
Most magnetizing equipment since 1990 big disadvantage of storage batteries as a
is solid state, controlled by thermistors.2,3 source of current is that there is a definite
Full-wave rectified alternating current limit to the magnitude and duration of
with three-phase bridge circuitry is shown current that can be drawn from a battery
in Fig. 9a. With a ripple of 5 percent, before recharging. Battery maintenance is
nearly the entire cross section can be costly and can be a source of trouble.
magnetically saturated. This means that
the probability of detecting subsurface Today, direct current is generally
discontinuities may be improved over produced with silicon diode rectification.
other forms of current. Because only Current obtained by passing three-phase
ohmic resistance is involved, large lengths alternating current through special
can be tested at high current values. rectifiers is called simply rectified current.

A three-phase circuit demands lower
power consumption to achieve an
equivalent current density.

116 Magnetic Testing

Half-Wave Rectified Magnetizing section is much greater in the case of
Current direct current magnetization.

Half-wave rectified current is the most For the same value of direct current,
effective current to use for the detection the field intensity is inversely
of subsurface and surface discontinuities proportional to the square of the
when dry magnetic particles are used. diameter: an alternating current field is
This type of current is produced by FIGURE 9. Theoretical types of current used
putting single-phase alternating current for magnetic particle testing: (a) full-wave
through a rectifier. The rectifier is a rectified alternating current with three-phase
nonlinear electronic component that bridge circuit; (b) half-wave rectified
permits unimpeded current flow in one alternating current with single-phase circuit;
direction and thus simulates direct (c) full-wave rectified alternating current and
current characteristics for purposes of single-phase bridge circuit; (d) alternating
testing. Half-wave rectified current current at frequency of 50 to 60 Hz;
imparts a very noticeable pulse to the (e) pulsed current; (f) impulse current.
particles. This gives them mobility, aids in (a) Waveforms
the formation of indications and helps
prevent the formation of nonrelevant t
indications. Five percent ripple

Alternating Current (b)
Magnetization
t
Alternating current at line frequency is
the most effective current to use for the (c)
detection of surface discontinuities,
particularly fatigue cracks. t

An advantage of alternating current (d)
testing is the ease with which test objects
can be demagnetized. t

It is important that alternating current (e) I
testing equipment be built to include
proper current controls. ττ t

Choosing Alternating or Direct (f)
Current2,3
I
A direct current is distributed uniformly
across the entire cross section of the test t
object. The field and flux density it τ
creates are maximum at the outer surface
and zero along the object’s central axis, as
required by Ampere’s law. An alternating
current field is forced to the surface
because of the skin effect. This fact has
technical consequences for the current
flow in a billet of square cross section, for
example. Figure 10 shows the difference
in field intensity distribution along the
test object surface in cases of alternating
and direct current.

For direct current flow, the magnetic
field near the billet corners is considerably
lower than in the middle of each side;
it is nearly constant in the case of an
alternating current field. For corner
cracks to be accurately indicated by direct
current fields, an overmagnetization in
the center area of each side may be
unavoidable. With the alternating current
technique, the same field intensity is
obtained across the surface of the billet
at half the current density.

Figure 11 shows the distribution of
field intensity on the surface of a stepped
sample. The difference in magnetic field
intensity for the largest and smallest cross

Magnetization 117

inversely proportional only to the also on the crack’s shape, size and its
diameter. When maximum and minimum relations to the test object dimensions.
field intensities for a specimen are given The indications from subsurface cracks are
in test specifications, a complicated test relatively blurred and indefinite and can
object can often be inspected only in be recognized reliably only on a
sections, if the test is carried out with a sufficiently smooth surface.
direct current magnetic field.
Direct current field magnetization
More obviously, this effect can be seen cannot guarantee the ability to indicate
on objects with sudden enlargements in all subsurface discontinuities, particularly
cross section. In camshafts, for example, as depth increases. Magnetic particle
the alternating current field (in testing should be for detecting surface or
accordance with the skin effect) follows near surface discontinuities. Wet
the contour; the direct current field technique indications of discontinuities
follows a more direct path. As a deeper than 0.2 mm (0.01 in.) should be
consequence, alternating current systems relied on only when other nondestructive
are often found at airline and automotive testing techniques cannot be used.
overhaul stations, where surface fatigue
cracks can occur at various locations on Depth of Penetration5
complex shapes such as landing gear and
actuating mechanism components. Figure 12 is a plot of threshold values for
the magnetizing currents necessary to
Furthermore, the magnetic pole areas produce a readable indication of holes in
at the ends of a test object are much a tool steel ring standard. Holes parallel to
smaller with an alternating current field. the cylindrical surface are drilled 1.8 mm
The indications of cracks near the (0.07 in.) in diameter at increasing depths
contacting area are much better with an below the surface. The depths vary from
alternating current field. 1.8 to 21 mm (0.07 to 0.84 in.), in
1.8 mm (0.07 in.) increments, from hole 1
An advantage of the direct current field to hole 12.
is its increased depth of penetration. This
provides the ability to test for subsurface The results plotted in Fig. 12 were
cracks with magnetic particle techniques. obtained using the dry continuous testing
Such tests are generally used to find cracks technique with an internal conductor
under chromium plating, subsurface using 60 Hz alternating current, and three
cracks in flash welds and lack of root forms of direct current: (1) direct current
penetration or lack of fusion in
weldments. FIGURE 11. Distribution of field intensity on surface of
stepped sample: (a) alternating current field; (b) direct
Extensive research has shown that the current field.
depth effect not only depends on the (a)
distance of the crack from the surface but
Magnetic field H ≅ 3.7 3.9
FIGURE 10. Tangential magnetic field intensity (kA·m–1)
intensity (kA·m–1) on surface of current flow 4.3
in square billets (f = 50 Hz). Current flow is 4.8
through length of billet. 5.3

HDC (HAC) I
7.4 (5.2)
5.2 (5.2) Current (relative scale)
2.7 (5.2) (b)

Billeta Magnetic field H ≅ 1.1 1.4
I = 2040 A intensity (kA·m–1)
Htheo = 0.25 a 1.8 5.5
2.8
= 6.4 kA·m–1

Legend I Current (relative scale)
a = distance = 80 mm (3 in.)
Legend
HAC = alternating current magnetic field intensity (A·m–1) H = magnetic field intensity (A·m–1)
HDC = direct current magnetic field intensity (A·m–1) I = electric current (A)
Htheo = theoretical magnetic field intensity (A·m–1)

I = electric current (A)

118 Magnetic Testing

from batteries, (2) three-phase rectified FIGURE 12. Comparison of sensitivity of alternating current,
alternating current with surge and direct current, direct current with surge and half-wave
(3) half-wave rectified single-phase rectified current for locating discontinuities wholly below
alternating current. surface of test object. Threshold indications produced using
dry particles and continuous magnetization on unhardened
The alternating current test required tool steel ring with artificial discontinuity diameter of
about 475 A to indicate hole 1 and over 1.8 mm (0.07 in.).5
1000 A to indicate hole 2. Hole 3 could
not be shown at any available alternating Depth to center of artificial 2 (0.08) DirHeDcairtlefc-cwut rcaruverenretdnsiturercgtecurrentAlternating current
current value. Hole 2 was indicated with discontinuity, mm (in.) 4 (0.16)
475 A straight direct current, with 275 A 6 (0.24) 250 500 750 1000
full-wave rectified alternating current 8 (0.32) Magnetizing current (A)
preceded by a surge of double this 10 (0.40)
amount, and by 175 A using half-wave 12 (0.48)
rectified alternating current. Half-wave 14 (0.56)
rectified alternating current of 750 A 16 (0.64)
indicated hole 12, while 975 A of direct 18 (0.72)
current from batteries was needed to 20 (0.80)
indicate hole 10. 22 (0.88)

These comparisons verify the 0
importance of choosing the right current
for producing the best indications. The
comparisons also show how current
should vary, depending on the nature
and location of the discontinuities.

Magnetization 119

PART 4. Direction of Magnetic Field

The proper orientation of the magnetic Prod Magnetization of Large Test
flux in relation to the direction of a Objects
discontinuity is the most important factor
affecting discontinuity detection, even When an object is too big to fit into
more than the magnitude of the available test equipment, the test object
magnetizing current. (or areas of it) can be circularly
magnetized by either of two means.
For reliable testing, the magnetic flux
should be at right angles to the One means is to use prod contacts with
discontinuity. If the magnetic flux is cables to transmit the magnetizing current
parallel to the discontinuity, there is little from the source to the test object
magnetic leakage: if an indication is (Fig. 4b). Prods are attached to the ends of
formed at all, it is likely to be extremely the cables so that magnetizing current can
small or indefinite. To ensure that proper be passed through the test object or
field direction exists at the desired through an area of it. Portable equipment
magnitude, reference standards should have a remote control switch on
containing artificial discontinuities are the prods, enabling the operator to
needed. control the current while moving the
prods or viewing the test indications.
Circular Magnetization
Another means of local magnetization
Fundamentals of Circular is to use contact clamps with cables,
Magnetization particularly when the test objects are
relatively small in diameter. Tubular
The magnetizing technique that is easiest structures can be tested this way by
to control is circular magnetization. This positioning the clamps so that the current
is the technique in which the passes through the area of interest and
magnetizing current is passed directly along the line of suspected discontinuities
through the test object, setting up circular (Fig. 13).
magnetic field lines at right angles to the
direction of current flow (Fig. 4a). Internal Conductor Magnetization

A good way to circularly magnetize the In a tubular test object, a circular
outer regions of a test object is to place magnetic field may be set up by passing
the object between the contact plates of a current through the tube itself; no field is
stationary magnetic particle testing induced on the inside surface of the tube.
system. Care should be taken to clamp the If the test object is hollow or has holes
test object firmly between contact plates through which an internal conductor can
made of lead or copper. Copper pads are be passed, it is best to induce a circular
coated with thermal rubber to reduce magnetic field in the object by passing
arcing. Enough of the object’s surface area the magnetizing current through the
must contact the plates to permit passage conductor. Circular magnetization with a
of the magnetizing current without
burning. As the area of the surface FIGURE 13. Current carrying clamp electrodes used for
decreases, the probability of burning testing tubular objects with small diameters.
increases.
Flux lines
On irregular test objects, it may be
helpful to use copper braid contact pads Clamp
between the objects and plates to prevent
overheating. When testing objects with Current
irregular cross section, it may be necessary
to circularly magnetize with a low current
to inspect the thin areas. A technique
specific to the application must be devised
to pass a higher current through the
heavier sections for testing of those areas.

Current

120 Magnetic Testing

central conductor has the following Longitudinal
advantages over passing current through Magnetization
the test object itself.
A longitudinal field can be induced in a
1. It induces flux at the inside diameter test object by placing the object in a fixed
of the test object, permitting testing of current carrying coil. The coil may be
inner as well as outer surfaces. mounted on the rails of a stationary unit
or attached by cables to a portable unit
2. Direct electrical contact is not made (Fig. 8). The effective magnetic field
with the test object, thereby induced by a coil extends from 150 to
eliminating the likelihood of burning. 220 mm (6 to 9 in.) beyond either end of
the coil. Depending on fill-factor, if the
3. Several small ring shaped test objects test object is long, it is necessary to
(washers or nuts, for example) can be magnetize and test it in sections along its
suspended on the same conductor and length.
tested for transverse discontinuities in
groups (Fig. 14). Longitudinal magnetization with
portable equipment is accomplished by
Capacitor Discharge Circular wrapping current carrying cable in a coil
Magnetization around the test object. Portable,
alternating current coils are commercially
Capacitor discharge techniques are used available.
for the circumferential magnetization of
oil field pipes. The technique is discussed Important Considerations in Coil
in detail elsewhere is this volume. Magnetization

Limitations of Parallel To induce an adequate longitudinal
Magnetization magnetic field with a coil, the long
dimension of the test object should be at
A circular magnetic field surrounds any least twice as great as its short dimension
electrical conductor and this is the or end pieces should be added and the
magnetic principle underlying circular long axis of the test object should be
magnetization with an internal conductor. parallel to the coil axis. This is especially
Knowing this, some operators have true in the case of irregularly shaped test
assumed that they can induce a circular objects, because the shape of the object
field in a test object by placing it next to affects the direction of the induced flux.
instead of around a conductor. This is not
true. When a wheel, smaller in diameter
than a coil, is placed in the coil (as shown
Some field is induced in the test object in Fig. 15), a field is induced in the white
by such a procedure, but because a areas of the test object in such a direction
portion of the magnetic flux path is in air, that radial discontinuities create
the field in the object is greatly reduced,
distorted and unevenly distributed. This FIGURE 15. Coil magnetization of circular
procedure is sometimes called parallel shape. Radial discontinuities will be
magnetization. It is not dependable and indicated only in white areas; to reveal radial
should not be used. discontinuities in dark areas, test object
must be rotated 90 degrees and
FIGURE 14. Internal conductor method used remagnetized. Circular discontinuities will be
to produce circular magnetization: indicated in shaded areas; to reveal circular
(a) several ring shaped test objects discontinuities in white areas, part must be
magnetized simultaneously; (b) closeup of rotated 90 deg and remagnetized.
ring with cracks in several locations and
orientations. Coil
(a)
Current
(b)
Magnetic field Circular
discontinuities

Radial
discontinuities

Magnetization 121

indications. However, radial cracks in the Combined Circular and
shaded areas of the test object are parallel Longitudinal
(or nearly so) to the induced magnetic Magnetization
field, so that few or no indications are
formed. Furthermore, magnetic poles and Complete testing for discontinuities in
attractive forces occur in these areas. To different directions requires that two or
indicate radial discontinuities in the more magnetizations and tests be
shaded areas, it is necessary to rotate the performed. The test object should first be
test object through 90 degrees and circularly magnetized and examined for
remagnetize it, although this technique is indications, then longitudinally
not recommended. magnetized and inspected.
Demagnetization is the final step.
The detection of radial cracks in a test
object of this shape is more accurately It is critical to remember that
and rapidly done using an internal discontinuities are best detected when
conductor (Fig. 14). Better techniques for they are at right angles to the magnetic
finding circumferential discontinuities in lines of force.
ring shaped test objects are shown in
Figs. 5 and 6. Ring shaped objects, disks, FIGURE 16. Longitudinal lines of force
wheels or races are best checked for induced by yoke magnet: (a) electrically
circumferential cracks using the induced energized yoke magnet; (b) permanent
technique of Fig. 6. An iron core, for magnet yoke.
example, is used with a coil surrounding
it to produce a toroidal field. This Nonmagnetic
technique has an advantage over the
direct contact technique (Fig. 5) in that (a) handle
no danger of arcing or burning exists, and
the field is constant throughout the test Coil
object.
Flux field Magnetic
Yoke Magnetization particles collect
(b) at crack
A longitudinal magnetic field can be
induced in a test object or in a limited Test object
area of an object by using a handheld
yoke. A yoke is a U shaped piece of soft
magnetic material, either solid or
laminated, around which is wound a coil
carrying the magnetizing current (Fig. 16).

When a test object is placed across the
opening of the U shape and the coil is
energized, the object completes the path
of the magnetic lines of force. This sets up
a longitudinal field in the test object
between the ends of the yoke. Permanent
magnetic yokes can also be used to create
a longitudinal magnetic field (Fig. 16b).
Such yokes are often specified by their
lifting power or by the tangential field
intensity midway between the legs.

Magnetic lines
of force

122 Magnetic Testing

PART 5. Multidirectional Magnetization6,7

With all magnetizing techniques, especially when induced in complex
discontinuities perpendicular to the shapes.
magnetic flux are optimally indicated.
However, discontinuity detection depends Two or three field directions may be
on flux density and the properties of the superimposed by sequencing. If the fields
testing medium (Table 1).8,9 vary in intensity with time, a swinging
vector field is created. It is essential that
It is true that magnetic excitation also multiple imposed fields be balanced in
permits the detection of discontinuities intensity, duration or both.
that are not exactly perpendicular to the
flux direction. In this case, the lines of FIGURE 17. Superimposition of direct current
flux can be decomposed into two magnetic fields: (a) addition of field vectors;
components, one of them parallel and the (b) relationship of field directions.
other perpendicular to the direction of (a)
the crack. The perpendicular component
contributes to the indication of the Vector of circular field Strength and
discontinuity. In some cases, even cracks direction of
appearing to be parallel to the flux resulting field
direction may be weakly indicated. The
reason is that most cracks are ragged in Vector of longitudinal field
outline (intercrystalline cracks) so that
some sections may be properly oriented (b) Resulting Test object
for detection. However, at best cracks can Force lines field
only be detected when the angle between of circular
them and the direction of magnetization
is more than 30 degrees. Experiments magnetization
suggest the optimum angle is over
50 degrees.10 Force lines of
longitudinal
Combined Direct Current
Fields magnetization

When a direct current magnetic field
of a certain direction and intensity is
superimposed on one of a different
direction and intensity, both fields can be
combined to form another field as shown
in Fig. 17. Physically, the resulting field
is formed by the addition of the two
magnetic field vectors. The resulting field
has a direction and intensity different
from either of the primary fields, and is
therefore very difficult to predict,

TABLE 1. Techniques for multidirectional magnetization. Means
Technique

Circular magnetization technique current flow technique (for solid and tubular test objects)
internal conductor technique (recommended for tubular test objects)
Longitudinal magnetization technique yoke or coil magnetization
Current induction technique circulating current induced in ring using laminated core and influence of

Combination for single, overall test fluctuating longitudinal alternating current yoke field (Fig. 6)
yoke or coil magnetization with current flow or internal conductor technique
internal conductor with current induction technique

Magnetization 123

Combined Direct Current Combined Alternating
and Alternating Current Current Fields
Fields
It can be advantageous to magnetize in
For combined direct and alternating two directions with alternating current
current magnetic particle testing, two fields. An effective combination for
perpendicular magnetic fields are periodic alternation of the resulting field
superimposed in such a way that the vector cannot be realized if the two fields
resulting field changes its direction with are in phase or in counter phase.
time (generally in rhythm with the
alternating frequency). The direction At a phase shift between 50 and
change again occurs in such a way that, 130 degrees, a rotating magnetizing vector
for at least a short time, some field of sufficient uniformity can be obtained.
component is perpendicular to any At a phase shift of 90 degrees and for
existing crack direction. This in turn equal field intensities, a circularly rotating
causes a magnetic particle accumulation vector is generated, as illustrated in
and subsequent detection. Fig. 20. When three-phase current from
the mains of a phase shift of 120 degrees
In the case of a combination of direct is used, the behavior is similar (elliptical
current yoke (or coil) with an alternating rotation).
current flow (Fig. 18), the resulting field
swings around the axis of the test object Yoke for Combined Alternating
(Fig. 19). This combination of static and Current Fields1,6
dynamic fields results in a vector swinging
over an angle. The magnetic vector swings For structural reasons, a direct current
around the position of the direct current yoke of solid steel has been used for many
field and, in any given position, a years to indicate transverse cracks.
sufficient component of it is at right Alternating current yokes have recently
angles to a possible discontinuity. If both been used but they must be assembled
fields have the same intensity, a total from laminated transformer sheet to
angle range of ±45 degrees (totally prevent eddy current losses. These
90 degrees) is covered. constructions are more expensive than
direct current yokes.
The disadvantages of direct current
yokes are that (1) stray fields may form at Alternating current yokes are usually
the rounded ends of the test objects or at built to operate over limited clamping
cross-sectional differences between the lengths, because a longitudinally oriented
yoke and the object and (2) considerable alternating current field is reduced with
field reduction occurs with large increasing clamping lengths.
cross-sectional changes of the test object.
Similar situations can also occur with coil FIGURE 19. Combined crack detection by circular alternating
magnetization. current and longitudinal direct current field.

FIGURE 18. Complete discontinuity detection Amplitude (relative scale) R CD
by traditional swinging field technique A
(combination of direct current yoke and
alternating current head current flow).

Crack Test object L
indications Clamping device with
current contacts

AB CD

Time (relative scale)
A

Insulating layer GA B C D
RA RB GB L L
Direct current for yoke GD
= L L RC GC
~
RD
Alternating current for current flow
Legend
G = vector of resultant field (at times ABCD)
L = vector of longitudinal magnetization
R = vector of circular magnetization

124 Magnetic Testing

An alternating current yoke has several does possess a certain inertia: the
advantages. magnetic vector has already left the
parallel direction when the particles begin
1. Field distribution is uniform, even to move away.
over test objects with geometrically
complicated shapes and over changes Experience in Germany and more
of cross section. recently in the United States indicates
two advantages for the multidirectional
2. Induced field flow is possible. magnetization technique. The technique
3. Demagnetization of the test object is can detect very small discontinuities
because at some period in the
simple and rapid. magnetization cycle the field vector is
4. Testing times are short. normal to the discontinuity direction.
Also, in comparison with the single
With clamping lengths from 900 mm magnetization procedures (head and coil
to 1200 mm (36 to 48 in.), longitudinal magnetizations), the combined current
magnetization may better be achieved technique presents considerable economic
using a movable alternating current coil. advantages since it requires only one
processing step instead of two or
Testing Procedures with more.11,12
Multidirectional Magnetization6
Combined Auxiliary
With multidirectional magnetization Magnetization
techniques, the resulting magnetic field
changes its direction in the rhythm of An exceptional variation of the
the frequency of the current application, multidirectional magnetization technique
becoming alternately perpendicular to is called combined auxiliary magnetization,
certain cracks. However, the direction of used for cylindrical test objects. Here, the
such a vector is also parallel to a particular auxiliary alternating current flow
crack for a very short time. For this technique is combined with the
reason, when using the multidirectional alternating current induction technique
technique, the application of the testing (Fig. 21). A magnetizing bar is put
medium must always take place during through the test object. This laminated
magnetization. An indication previously steel, copper coated bar serves as both a
established cannot be held by magnetic current conductor and a phase shifted
force and could theoretically be flushed magnetic field conductor.
away by the testing fluid. The procedure
This reliable technique is
FIGURE 20. Alteration of the magnetic field by combination noncontacting, pole free and can indicate
of two phase shifted alternating current fields (rotating cracks of any direction on inside surfaces,
vector). outside surfaces and face areas of
cylindrical test objects. Combined
HR auxiliary magnetization can be carried
Circular out only by systems equipped with an
magnetic alternating current yoke — contributing
field still further to the trend toward
alternating current yoke techniques
(Table 1).

HL FIGURE 21. Combined auxiliary

Longitudinal magnetization by combination of alternating
magnetic current flow and current induction
field techniques.

G G=L L
R R
G=R
L G

Legend Alternating current
G = vector of resultant field Alternating current
H = magnetic field intensity (A·m–1)
L = vector of longitudinal field Magnetization 125
R = vector of circular field

PART 6. Circumferential Magnetization of Pipe

The drilling and production of natural (1) H = I
hydrocarbons generally require that the 2πR0
tubular product (casing, tubing and drill
pipe) be tested for discontinuities. where I is the current (amperes) and Ro is
Magnetic flux leakage techniques are the the outer radius of the tube (meters).
most commonly used tests for detection
of outer and inner surface discontinuities. Figure 23 illustrates some of the values
Ultrasonic testing is used for regions used in this discussion. In Eq. 1, the field
difficult to inspect with magnetic flux intensity is given in amperes per meter
leakage. because Ro is expressed in meters.
However, this field intensity is sometimes
A common form of testing for measured with a hall element tesla meter,
longitudinally oriented, surface breaking, and because one gauss is numerically
tight discontinuities (seams, laps and equal to one oersted in air, conversion to
cracks) involves magnetization of the tube gaussian units yields:
circumferentially by the internal
conductor technique, followed by testing (2) H = 2I
with some form of magnetic flux leakage 10 R0
sensor. The use of ferroprobes, coils and
solid state sensors for this application is FIGURE 22. Two techniques for establishing
summarized elsewhere in the circumferential magnetization in elongated
Nondestructive Testing Handbook.13 The text tubes: (a) central conductor with battery
below deals with the magnetization of oil pack to provide high current; (b) internal
field tubes and treats magnetic particles as conductor with capacitor discharge system.
the sensor. Peak and duration meter may be used to
measure pulse amplitude and duration.
Specifications for Testing (a)
Oil Field Tubulars
Ro H = I · (2πRo)–1
Specifications and recommended practices
for the testing of oil field materials are
written by oil companies and the
American Petroleum Institute (API).14–17

Magnetization Techniques I Battery pack
for Oil Field Applications Ie
(b) I
Two distinct techniques18 are used for the
circumferential magnetization of tubes up I Capacitor t
to 14 m (45 ft) long (Fig. 22). Both discharge
techniques use an insulated rod (generally
made from aluminum although this is not Meter
required) which passes through the bore
of the tube. In Fig. 22a, the rod is Legend
reasonably well centered in the bore and H = magnetic field intensity (A·m–1)
fed with some form of direct current. In I = electric current (A)
mill installations, this might be full-wave Ie = electric current (A) induced in cylinder
or half-wave rectified alternating current Ro = outer radius (m)
with the subsequent test being done using t = time (s)
wet fluorescent magnetic particles.

In field operations, banks of batteries
have been used for current. When the
magnetizing current is pure direct current,
the magnetic field intensity H at the outer
surface of the tube, when the conductor is
centered within the bore, is given in
amperes per meter by:

126 Magnetic Testing

where I is in amperes and R0 is in ground through the rack and there is a
centimeters. real possibility of arc burn at the point of
contact.
The second magnetization technique is
shown in Fig. 22b. The motive force is BH Curve in Setting
provided by a capacitor discharge unit.19 Specifications
The effect of rod centralization is minimal
and has been shown to affect field There is an important fact about the
intensity by 4.2 percent for pipe larger magnetization of test objects by the
than 340 mm (13.37 in.).20 Magnetization capacitor discharge, internal conductor
by this technique obeys no scientifically technique: the ring sample BH curve
simple rules because the rapid rise of rod governs the flux density value in the
current during magnetization causes the material. In effect, knowing the BH
induction of an eddy current in the tube properties of the material from a ring
and this detrimentally affects penetration sample investigation allows field intensity
of the magnetizing field intensity into the levels to be set. Figure 24 shows the BH
material. properties of two typical oil field tubular
materials: a 620 MPa (90 000 lbf·in.–2)
The direction of the induced eddy proprietary material and a 390 MPa
current Ie with respect to the rod current (55 000 lbf·in.–2) casing material.
I is shown in Fig. 23 for a centered rod. By
Lenz’s law, the eddy current induced on The important point that can be made
the inner surface of the tube must create a from these curves is that after application
field within the material which opposes of about 3200 A·m–1 (40 Oe), the materials
the field caused by the rod current I. The are effectively saturated.21 It is generally
field intensity H at some radius r at some true of oil field tubular materials that
instant, whereas the rod and eddy current 3200 to 4000 A·m–1 (40 to 50 Oe) are
fields are finite, is given in amperes per required within the material to magnetize
meter by: to a level sufficient for subsequent
residual induction testing. It is required
(3) H = I + He that this field intensity level be reached at
2πr
FIGURE 23. Eddy current Ie created in steel
The He term is the field intensity created tube at beginning of pulse I in rod centered
by the eddy current itself. within bore of tube. Direction of Ie on inner
surface opposes that of I; outer surface
Eddy Current Effect forms return path.

In considering Fig. 23, Ampere’s law Return current
indicates that the field at the radius r is together with Ie forms
caused by the currents inside that radius
(rod current and inner wall eddy current). eddy currents in
The outer wall eddy current is the return tube wall
loop for the inner wall eddy current, and
plays no role in the theory so far outlined. T
However, since it does represent an Ro
unwanted current flowing in the tube, its
presence does lead to two very practical Ie r
considerations.
Ri
First, pipes being magnetized before
testing should be insulated from each Rod
other by an air gap. If this does not occur, current I
then the outer surface eddy current can
jump from protrusions in the pipe being Legend
magnetized to the next pipe in the string. I = electric current (A) in rod
The resulting arc can cause burns on both Ie = eddy current (A) induced on inner surface
tubes. This in turn can cause hard spots r = radius (m) from axis to point inside tube wall
on the materials at which corrosion might Ri = radius (m) from axis to tube inner surface
preferentially occur. This is particularly to
be avoided with corrosion resistant Ro = radius (m) from axis to outer surface
materials, some of which require a T = wall thickness
hardness less than 22 on the rockwell
C scale for longevity in corrosive
environments.

Secondly, the material should be
insulated from the metal racks that carry
it. If pipe racks are not insulated with a
layer of nonconductive material (rubber
or wood, for example), then the outside
diameter surface eddy current can flow to

Magnetization 127

each point in the tube wall, despite the FIGURE 24. Curves of magnetizing force H versus flux
demagnetizing effect of the eddy current. density B: (a) high strength tube steel material is a sour gas
grade of special chemistry and heat treatment; (b) lower
This requirement does not lead to a strength oil field casing. Dashed lines indicate that the
simple current equation that can be used materials are magnetized almost to saturation by application
by a typical operator in the field of 3.2 to 4.0 kA·m–1.
(experimental specifications found
effective in saturating tubes are presented (a) Br
below).
1.4 (14)Flux density B, T (kG)
Typical Requirements for
Direct Current 1.0 (10)
Magnetization 0.6 (6)

If the central conductor technique is used 0.2 (2)
for the magnetization of tubes, then the
values given in Table 2 reflect the 0 3.2 6.4 9.6
magnetizing field at the outside diameter Magnetizing field intensity H (kA·m–1)
of either 3200 A·m–1 (40 Oe) for I1 or
4800 A·m–1 (60 Oe) for I2 for typical pipe (b)
sizes. Because the magnetization uses
direct current, the wall thickness, mass Flux density B, T (kG) 1.4 (14)
per meter (weight per foot) and tube
grade — which affect the magnetic and 1.0 (10)
electrical properties of the material — do
not affect the field intensity. The actual 0.6 (6) 3.2 to 4.0 kA·m–1
value used is often determined by 0.2 (2)
specifications, as agreed between the
manufacturer of the material and the user. 0 3.2 6.4 9.6
A typical specification is given by:
(4) I = 7500 D [mm] Magnetizing field intensity H (kA·m–1)

= 300 D [in.] TABLE 2. Current requirements for direct
where D is tube diameter. This amperes per current magnetization of oil field tubes.
diameter unit specification is equivalent to Direct current or long pulse (> 0.5 s) only.
3760 A·m–1 (47 Oe) at the tube surface. It Not valid for capacitor discharge
can be seen from Fig. 24 that such a field magnetization.
intensity raises the value of the flux
density in the tube to a high level, so that __T_u_b_e__D_i_a_m__e_t_e_r_ I1a I2b
after the field has fallen to zero, the flux mm (in.) (A) (A)
density in the material is at a value close
to remanence (Br). 60 (2.4) 600 910
73 (2.9) 730 1100
Full-Wave and Half-Wave Rectified 89 (3.5) 890 1340
Alternating Current 102 (4.0) 1020 1530
114 (4.5) 1150 1720
For the central conductor technique 127 (5.0) 1280 1910
outlined above, some form of rectified 140 (5.5) 1400 2100
alternating current is often used. It should 168 (6.6) 1690 2530
be noted that such current waveforms 178 (7.0) 1790 2680
induce eddy currents in the test object. 194 (7.6) 1940 2920
The field intensity waveform at the outer 219 (8.6) 2200 3300
surface can be seen by positioning a hall 244 (9.6) 2450 3680
element to detect the field and feeding 273 (10.8) 2740 4110
the output of the tesla meter to an 298 (11.8) 3000 4500
oscilloscope. 340 (13.4) 3410 5120

Pulsed Current a. 3.2 kA·m–1 (40 Oe) at outside diameter.
Magnetization b. 4.8 kA·m–1 (60 Oe) at outside diameter.

Internal conductor magnetization (using
single pulses of current) differs from direct
current or continuous magnetization by
the central conductor technique because

128 Magnetic Testing

account must be made for the fact thatCurrent I (A) The fall in induction from F to Br is
the induced eddy current may not have that which is normally expected when the
time to die away before the field intensity magnetizing field intensity falls to zero, as
from the conductor current dies away. it does after the passage of a pulse. This is
Figure 25 shows two time variations that determined by the BH curve for the
are measurable for single pulses, such as material undergoing magnetization.
are provided by capacitor discharge units. Should the point F not represent
The first variation is that of the saturation (Bs), then the material reaches
magnetizing current (I versus t). In this some average bulk flux density lower than
variation, a relatively rapid rise of current Br. This is often not a problem: while the
to its maximum value Imax is followed by surfaces are magnetized sufficiently for
a much slower fall toward zero, the entire longitudinally oriented discontinuities to
pulse length being on the order of hold magnetic particles, no information
200 ms. This time variation is the of the interior condition is required.
response to the discharge of a capacitor C, However, when relatively thin elongated
initially charged to V0 volts through a tubulars can be tested from the outside
resistor R in a circuit containing surface only, saturation of the material is
inductance L. A simple mathematical necessary for inside diameter
analysis is provided later. discontinuities to produce magnetic flux
leakage at the outside diameter.
The second variation is that of the
average bulk flux density within the Practical Testing Situations
material (B versus t). This quantity rises at
a much slower rate than I(t) due to the Commonly encountered testing situations
shielding effect of Ie. A high level of for the magnetization or remagnetization
magnetization is reached when the flux of tubes are discussed below, including
density at the point F is close to the (1) material at unknown induction,
material’s saturation value Bs. The (2) material at zero induction and
consequences of conditions shown in (3) material not saturated by pulse.
Fig. 25 are that deep magnetization of the
tube only occurs when the detrimental The magnetic condition in which a
effect of the eddy current is overcome by sample arrives is often not known to the
elongating the electrical pulse in time so inspector, who must assume the worst
that the magnetizing current is still possible case: the material is at saturation
effective as the eddy current is dying in a direction directly opposed to that
away. caused by the magnetic particle test
equipment. This is resolved by taking the
FIGURE 25. Plots of capacitor discharge material from an unknown value of
internal conductor current (I versus t) and remanence in one direction to remanence
average flux density induced (B versus t) in in the other direction as is shown in the
tube. Imax and t are measured with peak and schematic BH curve for the material
duration meter. Flux density peaks well after (Fig. 26).
current.
A material might also arrive with an
Imax I versus t induction between zero and –Br and it is
F desired to perform testing at +Br. During
Bs magnetization, the material should take
the path –BrHcPBsBr. That is, through
τ Br saturation Bs to remanence Br.

B versus t In the case of material initially at zero
0 induction, the tube is at 0 on Fig. 26 and
during magnetization takes the path
Time t (µs) OPBsBr.
Legend
In cases where the pulse is
B = magnetizing flux density insufficiently strong, the material may
Br = point of flux density lower than saturation follow a magnetization path such as
Bs = point of magnetic saturation –BrHcPQ or OPQ. It is then essential to
F = high magnetization point pulse more than once. A possible
I = current (A) magnetization path during a second pulse
Imax = maximum current (A) is QBsBr. The net final induction is raised
t = time (s) as shown.
τ = mean lifetime (s)
Analysis of Pulse Current
Magnetization

In the text below, an analysis of the pulse
current internal conductor technique for

Magnetization 129

magnetizing elongated tubes is presented. inductance between cables and ground
Simplified equations are given for the can be minimized. Because inductance is
types of current pulses available for time dependent, it is included in the
magnetization. From the theoretical derivative term. The resistance is the
viewpoint, the current pulse time combined resistance of the rod, cables and
dependence (I versus t of Fig. 25) is their connection, and any internal
discussed and then formulas are presented resistance in the capacitor discharge box.
for the inductance experienced by the Resistance in the discharge box may be
magnetizing circuit. due to the forward resistance of a silicon
controlled rectifier included to eliminate
These formulas illustrate the the possibility of current oscillation. The
dependence of such inductances (1) on capacitance of the system is generally in
the average value of the differential the region of 2 to 8 F.
permeability dB·(dH)–1 of the object under
magnetization and (2) between the field Equation 5 has three solutions if the
intensity and flux density limits imposed time dependence of L is ignored. These
by the exciting current and BH properties solutions depend on the relative values of
of the material. L, C and R.

Current Pulse Time Dependence (6) I= 2Vo exp (−βt )

For inductance capacitance resistance 4L − R2
circuits, the time variation of the current C
pulse obeys the equation:
sin 4L − R2t
C
d(LI ) dt
dt C
∫(5) + IR + I =0

The three terms on the left of Eq. 5 (7) I = VoC(β2t ) exp (−βt )
represent the instantaneous voltages
across the inductance, the resistance and (8) I= 2Vo exp (−βt )
the capacitance in the circuit (Fig. 22b).
The inductance in the circuit is mainly R2 − 4L
that of the rod tube system, because by C
careful design the presence of additional
sin h R2 − 4L t
C

FIGURE 26. Possible paths taken by where Vo is the voltage to which
circumferentially magnetized material from the capacitor bank is charged and
various initial magnetization conditions to ␤ = R·(2L)–1.
saturation Bs and then remanence Br in
known direction. Point P indicates weak The solution to Eq. 6 is oscillatory, but
pulse followed by second pulse. the presence of the SCR limits the pulse to
only the first positive-going peak. This is
B Bs shown in Fig. 27. In this example, the
Br P pulse has a length of 17 ms and reaches
Q 10 500 A. Such pulses are ideal for
magnetizing objects of low electrical
conductivity, such as ferrite magnets.
However, with highly conducting
materials such as steel tubes, the initial

O H FIGURE 27. Typical pulses from capacitor
Hc discharge systems: long pulse is more
effective in magnetizing of line pipe.

10 Short pulse
66 percent duration

–Br Current (kA) 5
Long pulse
Legend 97 percent duration
B = magnetic flux density
H = magnetic field intensity 50 100 150
Time (µs)
Hc,O,P,Q = reference points
= material at remanence in opposite direction
= material at zero induction

130 Magnetic Testing

rapid current rise (up to millions of National Electric Code should be consulted
amperes per second) induces a shield of for details. However, it appears essential
eddy currents that does not permit field for field use to limit the charging voltage
penetration into the bulk of the material. of the capacitor bank to 50 V. The
The net effect of this is a magnetized tendency of this restriction is to add
outer layer only. capacitance to the system.

The exponential solution (Eq. 7) is The resistance of the magnetization
known in its mechanical analog as critical system is a factor in permitting high
damping. It is difficult to achieve in this currents to flow. It is minimized for field
situation because it depends on the value use by using parallel strands of 11.7 mm
of L which in turn is dependent on the (0.46 in.) diameter (AWG [American wire
physical and magnetic parameters of the gage] 0000) copper welding cable for the
test object. The formula for the connections between the rod and the
inductance of a tube is given below. capacitance discharge box. The rod is
made of aluminum (mainly because of the
The sin h solution (Eq. 8) leads to continued need to make and break the
the longest pulses because there is no rod) but any highly conductive material
oscillation. Pulses of full length up to would work equally well. The requirement
160 ms are commonly used in the oil of elongating the pulse length to ensure
tube testing industry. the presence of its field after eddy
currents have died away far outweighs the
Definition of Pulse Length requirement of minimizing the overall
resistance of the magnetizing circuit.
It has become commonplace to define the Typical values, which might include that
length of such pulses as the time taken for of 5 m (16 ft) of cable and 15 m (49 ft) of
the pulse to reach 0.5 Imax during decay ␶ rod, are 1 to 5 m⍀.
(Fig. 25). Both Imax and ␶ are measurable
with an inductive ammeter or peak and The capacitance within the capacitance
duration meter (Fig. 22b). Such pulses discharge supply is generally within the
are effective in magnetizing tubular test range of 2 to 8 F, which is comparatively
objects because the field intensity from large. This occurs because of the need to
the rod current is still high as the eddy maintain relatively low voltages around
current in the test object dies away, so the circuit and to elongate the pulse.
that penetration of the field into the bulk
of the material occurs. While the values R and C can be
controlled by the manufacturer, the value
Since the inductance is a function of of L cannot, mainly because it depends on
time, a full solution for the variation of the test object undergoing magnetization.
the pulse current I(t) can only be obtained In the case of tubulars, the inductance is
by modeling the effect that the induced given by:
eddy current has on the instantaneous
value of L. Experimental evidence (9) L = ℓ ⎛ dB ⎞ ln Ro
indicates that, at least for elongated tubes, 2π ⎝⎜ dH ⎠⎟ Ri
the physics of the magnetization process
can be illustrated by a discussion of the where dB·(dH)–1 is the differential
constant L case. permeability, ᐉ is the length of the tube,
Ro is the outer radius and Ri is the inner
Typical Values for L, C radius (Fig. 23).
and R
It often occurs that the wall thickness
In the design of a capacitor discharge T is much smaller than the average radius
pulsing system, it is essential to aim at a of the tube. Under these circumstances,
pulse that has sufficient length to deeply Eq. 9 may be converted to:
magnetize the material. There are two
reasons for this. First, the material to be (10) L = ℓ ⎛ dB ⎞ ln r + T
tested may arrive at the test site in a 2π ⎜⎝ dH ⎟⎠ r − 2
longitudinally magnetized condition and T
it may be necessary to remagnetize it 2
circumferentially prior to testing. Second,
some specifications call for relatively low which reduces to:
emergent longitudinal field intensities at
the ends of such elongated test objects. (11) L ≅ ℓT ⎛ dB ⎞
Rotation of the bulk flux density into the 2πr ⎝⎜ dH ⎟⎠
circumferential direction may be simplest
way to achieve this. Using the International System of Units
(SI), Eq. 11 becomes:
An additional consideration unrelated
to the physics of the magnetization of the
test object is the safety of the system in
both installed and field situations. The

Magnetization 131

(12) L ≅ 0.16 ⎛ ℓT ⎞ ⎛ dB ⎞ Design Considerations
⎜⎝ r ⎟⎠ ⎜⎝ dH ⎠⎟
Good equipment design must include
where r is 0.5(Ro ϩ Ri). All lengths are in user input about the material being
meters and dB·(dH)–1 is dimensionless. magnetized. The worst case for the
internal and external resistances of the
The inductance of thin walled tubes is magnetizing system should be known to
seen from Eq. 11 to be proportional to the the manufacturer and worst values of
length ᐉ and wall thickness T of the tube, inductance should be investigated. Under
and inversely proportional to its radius or no circumstances should peak currents be
diameter. Neither of these physical stated for the purpose of magnetization
parameters nor the value of dB·(dH)–1 can without an electrical and magnetic load
be controlled by the designer of the being used for the system evaluation.
magnetizing equipment.
Depending on the use of the
For much of the tubular product used equipment, the relevant regulations
in oil fields, the value of T·(R)–1 does not should be consulted about insulation,
vary a great deal, perhaps only by a factor isolation, explosion proofing, intrinsic
of two. The average value of dB·(dH)–1 safety and purging. Such regulations are
encountered during magnetization can found in a variety of places, depending on
be seen from Fig. 26 to vary widely, the use of the product. Notable among
depending on (1) the point P reached these are the Occupational Safety and
on the BH curve by the material during Health Administration (OSHA), the
magnetization and (2) the starting point National Institute of Occupational Safety
for magnetization (anywhere from –Br to and Health (NIOSH), the Code of Federal
Q on the B axis). Examples of typical Regulations (CFR) and a variety of
inductances follow. international specifications, many of
Example 1. Pipe magnetized to saturation which are much more stringent than
following the path –BrHcPQ. Flux density those in the United States.
Br at point Br = 1.2 T (12 kG); dH =
2400 A·m–1 (30 Oe); ᐉ = 10 m (33 ft); Equipment designers should
P = 1.2 T (12 kG); r = 136.5 mm (5.4 in.); particularly note the requirements of the
T = 12.6 mm (0.5 in.). Canadian standards when designing for
Canada. The requirements of the United
Here, dB is 24 000 G, so dB·(dH)–1 = Kingdom, Norway and Germany are
800, and L = (2 ϫ 10–7)(10 m)(12.6 mm) applicable when designing for the North
(800)·(136.5)–1 mm = 148 ␮H. Sea.
Example 2. Same tube as example 1 is
taken from Q through P and Bs to Br by a Magnetization
second pulse. Bs = 1.5 T (15 kG); Recommendations
dH = 4000 A·m–1 (50 Oe); Q = 1.0 T
(10 kG). Tubular product has such wide limits of
diameter and wall thickness that it is
The average value of dB·(dH)–1 is now difficult to provide a universal
only 100. Dividing the value obtained in specification for the measurable
example 1 by 8, the ratio of the two parameters of current pulses for a high
values of dB·(dH)–1 exhibited by the steel level of residual induction. However,
yields: L = 18.5 ␮H. broad guidelines based on research with a
Example 3. Pipe is initially unmagnetized variety of tubes indicate that the values
follows path OPBsBr with: Bs = 1.5 T given in Table 2 provide adequate
(15 kG) = 9.09 m (30 ft); dH = 3200 A·m–1 magnetization.
(40 Oe); R = 27.7 mm (1.1 in.);
T = 4.83 mm (0.2 in.). Pulse Duration

Consequently, L = (2 ϫ 10–7)(9.09 m) In Table 3, pulses are classified by
(4.83 mm) (15 000·(40)–1)·(27.7)–1 mm = duration. Long duration pulses are those
119 ␮H. in excess of 100 ms. For such pulses, the
induced eddy current can be assumed to
The relatively large change in have died away while the magnetizing
inductance exhibited by the tube in field intensity is still high enough to
examples 1 and 3 affects the shape of cause saturation. Moderate duration
the pulse waveform, notably the easily pulses are those between 40 and 100 ms.
measurable parameters of peak current For magnetization, the longevity of the
Imax and pulse duration ␶. These induced eddy current is acknowledged by
parameters are shown in Fig. 25. its effect on the tube (shown through the
use of the lineal mass of the tube rather
than the outer diameter). Short pulses are
those below 40 ms. The maximum current

132 Magnetic Testing

requirement for the single short pulse hollow product by the internal conductor
compared to that for the single moderate technique, the search coil can be a
pulse is higher for the same lineal mass of single-turn coil through the test object.
tube. In effect, the higher current causes a Flux changes are given by:
larger magnetizing field intensity in an (13) ∆Φ = A∆B
attempt to overcome the eddy current. where ⌬␾ is changes in flux, A is the area
of the test object perpendicular to the
Should it be necessary to use two such search coil (A = Tᐉ), where ᐉ is tube
pulses, the peak current requirement falls length, and ⌬B is the change in flux
because the material is partially density of the test object induced during
magnetized. If the peak current can only magnetization.
reach Imax = 180 (W), then two such
pulses are required. Should the pulse be of Commercially available flux meters can
insufficient magnitude to magnetize the generally be compensated for the test
tube with two pulses, then a third pulse is object area so that the device can be made
necessary so that the three pulses meet to read the average flux density directly. A
the requirement of Imax = 145 (W). problem with this approach to the
measurement of the final flux density is
These requirements are designed to that the initial flux density in the test
ensure that the bulk induction following object, with respect to the vector direction
the pulses is at least 90 percent of the of the search coil, must be zero. This
remanence value. In most cases it is problem occurs because, when flux
higher. changes are to be measured, the initial
value must be known. However, if the
Current Pulse Effectiveness tube shown in Fig. 28 is initially
unmagnetized or the prior magnetization
There are two techniques used to evaluate is longitudinal, then the flux meter reads
the effectiveness of a current pulse. A the average density of induced
third technique, which detects surface circumferential magnetization.
fields only, is also outlined here. The first
technique is a variation on the rowland Should the output of the flux meter be
ring technique for the evaluation of the presented on an oscilloscope, it should
magnetic parameters of magnetizable be noted that flux values (caused by the
materials and involves the measurement passage of a pulse) between the beginning
of magnetic flux. The second technique is and the end of the magnetization process
an indirect technique using an inductive represent the flux linked by the
ammeter (peak and duration meter). The single-turn coil and contain the effect of
third technique uses simulated contact the flux in the air between the terminals
discontinuities. of the flux meter.

Flux Meter During the pulse, the air field caused
by the current I in the rod and eddy
Magnetic flux meters measure the total currents Ie in the test object affects the
magnetic flux threading an area defined instantaneous flux meter reading. When
by a search coil. In the case of these currents have died away, only flux
circumferential magnetization of a perpendicular to the single-turn coil
affects the final result. If the operator has
TABLE 3. Pulse classification by duration time to wind more than one turn around
with current requirement. the test object, the resulting error in final

Magnetization Duration Current FIGURE 28. Measuring of flux density
(ms) Requirement induced in circumferential direction by
techniques shown in Fig. 22.
Long pulse > 100 I = 11.8 D1
I = 300 D2 Flux meter
Moderate pulse 40 to 100 I = 74 W1
I = 110 W2
Single short pulse 0 to 40 I = 161 W1
I = 240 W2
Double short pulse 0 to 40 I = 121 W1 T
I = 180 W2 I
Triple short pulse 0 to 40 I = 97 W1 B
D1 = outer diameter (mm) I = 145 W2 Legend
D2 = outer diameter (in.) B = magnetic flux
I = current (A) I = electric current
W1 = tube weight (kg·m–1) T = wall thickness
W2 = tube weight (lb·ft–1)

Magnetization 133

bulk flux can be reduced. However, for diameter surface to the outside diameter
the purpose of establishing the presence surface. The vertical axes show either the
of a residual induction in the test object fraction of H required to saturate the
to excite magnetic flux leakage from material or the flux density B. The lowest
discontinuities, this procedure is not lines indicate time from the very start of
necessary. the pulse. The uppermost lines indicate
the field intensity and flux density levels
Inductive Ammeter at later time increments.

In an inductive ammeter or peak and It can be seen from Fig. 29 that
duration meter, as shown in Fig. 22b, the three phenomena occur during pulse
pickup coil is threaded onto any magnetization: (1) both inner and outer
convenient part of the magnetizing circuit surfaces are rapidly magnetized, (2) the
and when the pulse is fired the meter midwall region is the last part of the
reads the peak current (Imax of Fig. 25) and material to be magnetized and (3) the
the duration of the pulse (␶ of Fig. 25).21 midwall region can be left with a low

Saturation of the material occurs when FIGURE 29. Plots of tube wall thickness: (a) versus
successive readings on the ammeter are magnetizing force; (b) versus resultant flux density. Lower
identical. This can be explained as lines represent field and induction at beginning of pulse
follows. When the first pulse is fired, the (time proceeds up to the figures); central (midwall) regions
material exhibits its highest value of are the last to be magnetized.
dB·(dH)–1 because of the inclusion of the
steep part of the BH curve into the value (a) Inside Outside
of L (Fig. 27). The average value of diameter
dB·(dH)–1 is effective in determining the diameter
value of the inductance in Eqs. 6 to 8.
This value is relatively large compared to 8
what the material might exhibit during a
second pulse. In effect, the second pulse 7
experiences a lower inductance than the
first pulse. Magnetizing force H, kA·m–1 6

The effect of the lowered inductance 5
experienced by a second pulse is to permit
the peak current Imax to reach a higher 4
value than it reached on the first pulse — 3 Time
in effect, the material is different — but
the system response is also to lower the 2
duration ␶. By monitoring Imax and ␶, it is
possible for inspectors to determine the 1
relative degree of magnetization of the
test object. 0
20 40 60 80 100
Simulated Test Discontinuity Thickness (percent)

Flexible laminated strips of high (b) Inside Outside
permeability material are commercially diameter
available and these may be placed in diameter
intimate contact with the test object after 1.6 (16)
magnetization. Such strips contain three
test discontinuities encapsulated in brass 1.4 (14)
so that the liftoff between the test object
and the strip is minimized to that of the Magnetizing flux B, T (kG) 1.2 (12)
brass encapsulation.
1.0 (10)
Under such circumstances, the
magnetized material shares flux with the 0.8 (8) Time
strip and, if the test discontinuities give 0.6 (6)
an indication with magnetic particles,
then so will a similarly sized discontinuity 0.4 (4)
in the test object.
0.2 (2)
Use of Inductive Ammeters
0 (0)
When magnetizing with pulse techniques,
the value of the material’s field intensity 20 40 60 80 100
H and flux density B both change with Thickness (percent)
time. In Fig. 29, the horizontal axes show
the percent distance from the inside

134 Magnetic Testing

state of magnetization if the pulse field Fig. 22, the material must be exhibiting its
intensity is insufficient to saturate the lowest inductance to the magnetizing
material. circuit and must therefore be at
remanence Br.
This last phenomenon contributes to
magnetic fields from discontinuities at Operation of Inductive Ammeters
one surface, producing no leakage field at
the other surface, when the material is The inductive ammeter is a
not saturated. The leakage field into the microprocessor based instrument that
midwall section of the material merely employs an inductive pickup coil. This
raises the local magnetization level to a coil contains a large number of turns
higher degree. wound onto a nonconducting
nonmagnetic ring shaped core. It is
During magnetization, if parts of the threaded onto the cables from the
material do not reach a field intensity capacitor discharge system or onto the
level that ensures saturation (at the point rod itself. When a pulse is fired, the flux
P in Fig. 26), then the ensuing bulk caused by the current surge links with the
residual flux density is low and the ring and the voltage induced in the coil
material requires additional pulses to (Fig. 30) is given by:
saturate it. The magnetization process
calls for the highest values of the ( )(17) E = dI b
inductance L in Eqs. 5 through 12 during 2 × 10−7 Nd dt ln a
the first pulse and lower values during
subsequent pulses. The general effect of a where a is the inner radius of the ring;
high value of inductance is to lower the and b is the outer radius of the ring; d is
value of Imax and elongate the value of ␶. the axial length of the ring; dI·(dt)–1 is the
rate of change of the current; N is the
In order to show that this is the case, number of turns in the ring.
and to limit the necessary mathematical
computation, Eq. 7 is selected and from it This equation is derived from Faraday’s
the closed form results for Imax and ␶ are law of induction. To provide a signal
found. First, the time t (in seconds) at related to the current itself, Eq. 17 must
which Imax occurs is found by be integrated:
differentiation of Eq. 7 to be:

(14) t = 2L ∫(18) e = E · dt
R

where L is self inductance (henry) and R is ( )=⎡ b ⎤
resistance (ohm). ⎣⎢ 2 × 10−7 Nd ln a ⎥⎦ I

When this value is used in Eq. 7, the Here, e is the output voltage of the
result for Imax is: integration circuit. Because all the terms
in the brackets are known, the output of
(15) Imax = V0C R the integration of the induced voltage is
2 Le proportional to the instantaneous current,
and the instrument can be calibrated to
where C is capacitance (farad) and V0 is read current. Electronic circuits are used
voltage. to measure the peak current Imax and the
pulse duration ␶.
This result indicates that the value of
Imax is inversely proportional to that of L FIGURE 30. Diagram of inductive pickup coil
(the greater is L, the lower is Imax). To find (dimensions used in Eq. 17).
␶, I(t) must be set at 0.5 Imax. The result in
seconds is: I Readout
calibrated
(16) τ = 5.36 L in amperes
R

In this case, the pulse duration as b
defined by ␶ is proportional to the value a
of L. Larger values of L, such as are found
for the initial pulse, lead to the longest d
pulse durations.

The B-H curve indicates that the lowest
value of inductance that can occur under
these magnetization conditions is that
exhibited by saturated material, when the
value of dB·(dH)–1 is at its lowest (Eq. 11).
If two identical readings are obtained
from an inductive ammeter as shown in

Magnetization 135

PART 7. Magnetic Flux in Test Objects with
Complex Shapes

When a discontinuity lies perpendicular the external flux fields are measured using
to the magnetic field and is at or near the circular and longitudinal magnetization
surface of an adequately magnetized test by means of a transverse hall probe tesla
object, the leakage field attracts and holds meter. The magnitude of the current pulse
magnetic particles applied to the test is determined from empirical rules in
object surface. The capturing and holding order to ascertain the validity of the rule
power of the leakage field is determined in each case. The determination of the
by both the magnitude of the magnetic field direction and magnitude does not
flux in the test object and the relative reveal the magnetic field level required for
orientation of the discontinuity and flux. crack detection but does uncover problem
The gradient and magnitude of the areas caused by part geometry. Locations
leakage field are important for indication having cross-sectional areas significantly
formation. There is, however, larger than those where the current enters
disagreement on whether the axial or the test object exhibit fields whose
tangential component is the one of magnitudes are extremely low compared
interest. to those at the entry area (points 5, 6 and
7 in Fig. 31).
There are rules used to define the
current needed and how it is applied to Magnetization was performed using
produce the desired direction and flux full-wave direct current techniques. Low
density in the test object. Those rules, fields were also observed in deep cutouts
along with recommended particle (between points 6 and 7 of Fig. 31) and at
concentrations, are specified in military the extremity areas not directly in the
and commercial specifications. path of the current flow (points 4, 6 and 7
Unfortunately, many complex of Fig. 31). Any area producing a field of
ferromagnetic aircraft components have less than 10–3 T (10 G) was deemed
varying cross sections, large cutouts and inadequately magnetized. It was also
protruding extremities. With these, it is determined that when the current
difficult to apply empirical rules that branched into different directions at an
guarantee effective testing of the object in intersection, the field at this intersection
its entirety. was zero (Fig. 32 and points 1, 2, 3 and 5
of Fig. 31). These particular areas required
The testing of the object shown in additional tests using portable
Fig. 31 has been detailed in the electromagnetic yokes.
literature.13 The direction and intensity of
FIGURE 31. Complex shape of steel forging When dealing with complex test
for aircraft. Numbers are cited in text. objects, initial investigations concerning
the direction of the flux field and
adequacy of field intensity should be
determined using artificial discontinuity

8 FIGURE 32. Typical geometry problem in
6 magnetic particle testing.

7

5 Magnetic flux lines
1

4 Area of
2 zero field

Current

3

136 Magnetic Testing

shims placed at a sufficient number of rates, special magnetizing tools may need
locations on the test object. Special to be fabricated to achieve reliable testing
techniques are required to establish of the entire test object. This is important
adequate field intensity and direction in because areas containing changes in shape
some areas of the test object. The or thickness are likely locations for
techniques should be documented for development of cracks during fabrication
future reference when identical objects are or service.
to be tested. In cases of high production

Magnetization 137

References

1. Hagemaier, D.[J.], V. Deutsch and 9. Stanley, R.[K.] “Circumferential
R.[K.] Stanley. Chapter 6, Magnetization of Tubes and the
“Magnetization Methods.” Measurement of Flux Density in Such
Nondestructive Testing Handbook, Materials.” Materials Evaluation.
second edition: Vol. 6, Magnetic Particle Vol. 44, No. 8. Columbus, OH:
Testing. Columbus, OH: American American Society for Nondestructive
Society for Nondestructive Testing Testing (July 1986): p 966-970.
(1989).
10. Moake, G. and R.[K.] Stanley.
2. Deutsch, V., A. Becker and M. Vogt. “Inspecting OCTG Using Capacitive
Crack Detection by Magnetic Particle Discharge Systems.” Materials
Examination. Wuppertal-Elberfeld, Evaluation. Vol. 41, No. 7. Columbus,
Germany: Karl Deutsch GmbH (1979). OH: American Society for
Nondestructive Testing (June 1983):
3. Deutsch, V. and M. Vogt. “A p 779-782.
Comparison of AC and DC Fields for
Magnetic Particle Methods.” British 11. Stanley, R.K. “Basic Principles on
Journal of Non-Destructive Testing. Magnetic Flux Leakage Inspection
No. 4. Northampton, United Systems” and “Capacitor Discharge
Kingdom: British Institute of Magnetization of Oil Country Tubular
Non-Destructive Testing (July 1982). Goods.” Electromagnetic Methods of
Nondestructive Testing. Vol. 3.
4. Nondestructive Testing Handbook, third Langhorne, PA: Gordon and Breach
edition: Vol. 5, Electromagnetic Testing. (1985): p 97-160.
Columbus, OH: American Society for
Nondestructive Testing (2004). 12. Schindler, J. United States Patent
4 502 004, Current Pulse Monitor
5. API SPEC 5CT, Specification for Casing (June 1980).
and Tubing. Dallas, TX: American
Petroleum Institute (2006). 13. Gregory, C.A., V.L. Holmes and R.J.
Roehrs. “Approaches to Verification
6. API SPEC 5D, Specification for Drill Pipe. and Solution of Magnetic Particle
Dallas, TX: American Petroleum Inspection Problems.” Materials
Institute (2001). Evaluation. Vol. 30, No. 10. Columbus,
OH: American Society for
7. API SPEC 5L, Specification for Line Pipe. Nondestructive Testing
Dallas, TX: American Petroleum (October 1972): p 219.
Institute (2004).

8. API RP 5A5, Field Inspection of New
Casing, Tubing and Plain-End Drill Pipe.
Dallas, TX: American Petroleum
Institute (2005). From ISO 15463
(2003).

138 Magnetic Testing

5

CHAPTER

Magnetic Leakage
Field Measurements1

Roderic K. Stanley, NDE Inspection Consultants,
Houston, Texas

PART 1. Fundamentals of Magnetic Flux
Leakage Fields

Magnetic particle testing is not an isolated density B(t) around a discontinuity. The
technical discipline. It is a combination of flux density may or may not be time
two distinct nondestructive testing dependent but should be at such a level
techniques: magnetic flux leakage testing that some of the flux is displaced by the
and visual testing. The basic principle of discontinuity’s higher magnetic
the magnetic particle technique is to reluctance. The displaced flux is forced
magnetize an object to a flux density that out of the object’s surface into the
causes magnetic flux leakage from a surrounding environment (air or water),
discontinuity. Powdered ferromagnetic where it can be detected (Fig. 1).4
material is then passed through the
leakage field and those particles held over Magnetizing Current
the discontinuity are visually interpreted
by the operator. To induce flux leakage, magnetizing
current can be passed through the test
From a theoretical point of view, the object by direct contact. This is
only difference between magnetic flux commonly done but because of the
leakage testing and magnetic particle danger of arc burns, it is not always
testing is the use of iron or iron oxides as recommended (Fig. 2). Insulated current
a sensor. In effect, magnetic particles may carrying rods or cables may be used, by
be considered a commonly used form of passing them through holes in the test
sensor for the detection of magnetic flux object. Other alternatives are the use of
leakage (sometimes called stray fields). coils to carry the current around the test
object and the use of electromagnets or
The key to ideal magnetic particle permanent magnets applied to the test
testing is to provide the highest sensitivity object.5
to the smallest discontinuities by a careful
combination of: (1) applied magnetic field When current is present, there is an
intensity H(t), (2) flux density B(t) in associated field intensity H(t) that raises
the test object, (3) particle size and localized areas to various flux density B(t)
application method and (4) optimal values, based on the BH properties of the
viewing conditions. In order to do this, test material. Figure 1 shows a computer
experiments are necessary with all of the simulation of field lines in and above a
parameters. The best combination is then material at some value below magnetic
chosen for a particular application. saturation, as can be seen from the
bending of the field lines under the
Writers of specifications have often discontinuity.4
over-generalized this empirical process in
order to provide the magnetic particle test FIGURE 1. Field lines around, through and
operator with a set of rules that govern all above discontinuity (an oblique slot), as
situations. This generalization can lead to computed by finite element computer
inappropriate specifications for certain model. The magnetic flux leakage field is
magnetic particle tests. asymmetric.4

There are many forms of magnetic field
sensors, including the hall element, the
magnetodiode, the ferroprobe and the
sensor coil.2,3 Tape recorder heads are
magnetic sensors, as are the triaxial flux
gate magnetometers that are orbited
above the Earth to detect very small
changes in magnetic fields. The purpose
of this chapter is to provide details about
the use of sensors in measuring and
detecting fields for magnetic
nondestructive tests.

Induction of Magnetic Flux
Leakage

The essence of all magnetic flux leakage
testing is to induce a magnetic flux

140 Magnetic Testing