nondestructive characterization of fatigue processes in cyclically ...

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 1
NONDESTRUCTIVE CHARACTERIZATION
OF FATIGUE PROCESSES IN CYCLICALLY
LOADED WELDED JOINTS BY THE
BARKHAUSEN NOISE METHOD
C. Lachmann, Th. Nitschke-Pagel, H. Wohlfahrt
Institute of Welding Technology,
Technical University of Braunschweig
ABSTRACT
The fatigue behaviour of welded joints is dependent on the weld geometry, its microstructure,
the cyclic material properties of the different weld zones and residual
stresses in the weldment. In this investigation, a new nondestructive testing method
is presented for a in-situ characterisation of fatigue damage in cyclically loaded
welded joints. This micromagnetic method is based on the Barkhausen-Noise effect
and with a new multi-parameter testing system, microstructure- and stress-sensitive
parameters can be measured. The system is mobile, computer-controlled, has a high
spatial resolution and needs no shielding, what makes it especially suited for diagnostics
at existing steel constructions, e.g. buildings, steel bridges, cranes, steel parts
of airplanes, etc.. Fatigue tests were performed on GTA-welds as single-step tests
for a evaluation of the feasibility of the new method for characterising fatigue processes.
Local plastic deformations in softened zones of the weld causing material
damage were identified by a significant change of the micromagnetic parameters.
Additionally, the static and cyclic mechanical deformation behaviour for the welded
joints was studied by local strain measurements and FEM-calculations. The results
of the present investigations indicate that material damage caused by microstructural
changes and microcrack growth is strongly connected with the micromagnetic parameters
and can be correlated to the mechanical behaviour and the fatigue life of
welded joints. Furthermore, the micromagnetic testing method can be used for the
identification of the different stages of the fatigue process in the material before
failure of the weldment.
1 INTRODUCTION
Nondestructive techniques for the assessment of fatigue-related damage become
increasingly important since many structural components, e.g. bridges, aircraft
structures or offshore platforms, need to be inspected periodically to prevent major
damage or even failure. For inspection in the field or on large constructions, small,
mobile and easy to handle devices are essential. Additionally, cost minimizing requires
short measuring times without time-consuming preparation of the part prior to
the test. The Barkhausen noise method is well-suited for this task and is already established
in controlling wear of bearing parts, the indentification of grinding burn,
the measurement of hardness, case hardening depth and residual stresses, and the

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 2
control of machining, heat treatment processes and material characteristics within
the production line [1, 2].
An especially complex task is the identification of fatigue damage in welded joints
with the aim of a fatigue life estimation for that part. The reason for this is that
welded joints consist of different zones with different material properties, e. g. yield
strength, ductility, hardness, grain structure, chemical composition etc., and residual
stresses [3]. In general, these zones of a weld can be divided into the formerly molten
weld bead, the heat affected zone (HAZ) which was not molten and the unaffected
base material. Besides the material properties, the fatigue life of a weld is
influenced by the size and sharpness of notches especially at the weld toe where
certain welding processes can produce undercutting or high reinforcement angles
reducing the fatigue strength. Additionally, so-called metallurgical notches at the
intersections of two microstructures with significantly different material properties,
can lead to local stress concentrations reducing the fatigue life, too.
To assess the fatigue behaviour of the entire welded joint it is essential to characterize
the microstructural processes and their influence on the residual stresses in each
zone of the weld during cyclic loading. Changes in microstructure and residual
stresses can be observed both in the period before crack initiation and during the
micro- and macrocrack growth period [4]. Additionally, it is well known that residual
stresses can influence the fatigue life of welded joints significantly [5]. Therefore,
an observed change in microstructural parameters and residual stresses could
be used to characterize the actual stage of fatigue of a loaded weldment. A major
drawback of nearly all nondestructive techniques for characterising microstructural
changes and residual stresses is the limitation to near-surface regions. The analysing
depths vary from a few microns using common X-ray diffraction to approximately 1
mm with micromagnetic or eddy current devices. Only neutron diffraction enables a
nondestructive investigation of residual stresses up to a few centimeters below the
surface. But since a nuclear reactor and extensive shielding is necessary for this
method, it is limited to small parts on a laboratory scale. For a further interpretation
of microstructural changes in near-surface regions, a study of the deformation behaviour
and the relaxation or build-up of residual stresses in the entire weld volume
by a FEM-simulation is essential. The present paper presents investigations on the
fatigue of cyclically loaded welds by the nondestructive testing methods using micromagnetic
Barkhausen noise analysis and X-ray diffraction with the further aim of
a fatigue life prediction.
2 EXPERIMENTAL SETUP AND EVALUATION PROCEDURE
The investigations were carried out using flat specimens of the structural steel
S355J2G3 with transverse butt welds according to Fig. 1. The pulsed gas-tungsten-
F m + F a·sin(t)
Strain Gauges
BNA and X-Ray
Measurements
thickness 10 mm
Fig. 1
Specimen geometry and location of strain gauges

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 3
arc (GTA-) welding process was applied to generate test welds with a high reproducibility
and bead quality.
Fig. 2 shows a micrograph of a transverse section of the weld bead and the adjacent
zones HAZ and base material. Additionally, a hardness distribution of the transverse
section was measured by an automated hardness testing system [6] and is displayed
in Fig. 2. The cyclic tests (pure pulsating tension and tension-compression) were
carried out using a 400 kNservohydraulic
material testing
system. For an evaluation of
the static deformation behaviour,
a 2D-FEM-simulation
was conducted. Fig. 3 shows
the different zones of the FEmesh
of the investigated GTAweld,
developed on the basis of
the micrograph and hardness
distribution depicted in Fig. 2.
Each zone of the welded joint
(weld meaterial of cap and
final pass, 2 HAZ’s and base
material) were assigned mechanical
characteristics deriving
from tensile tests and
welding-TTT-diagrams [7]. In
these TTT-diagrams, mechanical
properties and hardness
values are correlated with the
cooling rate and chemical
composition of a weld zone.
The results were compared to
local strain measurements in
the weld, the weld toe and the
Depth [mm]
6
4
2
0
-2
-4
-6
Final Pass
Cap Pass
Hardness Distibution, GTA-DV-Weld
-10 -8 -6 -4 -2 0 2 4 6 8 10
Distance from weld centerline[mm]
Vickers
Hardness HV1
330.0 -- 350.0
310.0 -- 330.0
290.0 -- 310.0
270.0 -- 290.0
250.0 -- 270.0
230.0 -- 250.0
210.0 -- 230.0
190.0 -- 210.0
170.0 -- 190.0
150.0 -- 170.0
Fig. 2 Transverse section of the weld bead of a 6-layer GTA-
DV-weld in the steel S355 and corresponding Vickers hardness
distribution
1
1000
1 - Weld material final pass
2 - HAZ 1 of final pass and weld material of cap pass
3 - HAZ 2
4 - Base material
2
4 3
4
True stress [MPa]
800
600
2
400
0 0.02 0.04 0.06 0.08 0.1
Logarithmic plastic strain [-]
Fig. 3 FE-Mesh and material data of the investigated GTA-weld-zones; 1. weld material of final pass; 2.
weld material of cap pass; HAZ of final pass; 3. HAZ of cap pass; 4. base material

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 4
base material determined by strain gauges. After each decade of loading, the nondestructive
parameters from X-ray residual stress determination [8] and micromagnetics
were measured on a line transverse to the weld (see Fig. 1). In the present work,
variations of the internal stresses along the loading axis of cyclically loaded welded
joints were studied by the use of the micromagnetic Barkhausen noise method [9].
Fig. 4 schematically shows the design of a micromagnetic sensor. A U-shaped yoke
is excited by a coil connected to a bipolar power-supply unit. By the orientation of
the poles, the direction of the resulting alternating magnetic field is defined and thus
the corresponding stress component can be measured. The Barkhausen noise is detected
by a small air coil whereas the tangential field strength is measured by a Hall
probe. Both signals are amplified, filtered and evaluated in the micromagnetic testing
system.
A basic requirement for performing the micromagnetic analysis is a ferromagnetic
material that also has to be magnetostrictive. In general, the ferromagnetic properties
of the investigated material are dependent on the microstrucure, the hardness and
residual stresses since theses these material characteristics interact with the magnetic
domain structure in the material. The magnetic domains are seperated by so-called
Bloch walls which can be trapped by Lattice faults like foreign atoms, vacancies or
dislocations. With a further increase of the magnetic field strength they can overcome
these faults which induces small electrical pulses in the micromagnetic sensor
(air coil) and can be recorded as the
so-called Barkhausen noise. In
many technical steels investigated
so far with coercivities greater than
5 A/cm, the Barkhausen noise corresponds
to the coercive field
strength H c (see Fig. 5). The microstructural
parameter H cm is derived
from the coercive field strength at
the maximum Barkhausen noise
level M max [11]. Since stacking
faults hinder the magnetization of a
ferromagnetic material, they lead to
a broadening of the magnetic hysteresis
and hence to an increase of
the coercivity H cm . Analogous to this
effect, these faults within the lattice
lead also to a higher hardness due to
their interaction with dislocation
movement. Therefore, a close relationship
between the coercivity H cm
and the hardness of the material can
be expected. Additionally, the magnetic
properties of a ferromagnetic
material are influenced by internal or
residual stresses. The Barkhausen
noise intensity increases with tensile
stresses due to a higher density of
Air coil and Hall probe
Bipolar power
supply and with
control device
Amplifier
and filter
Signal
processing
Fig. 4 Schematic diagram of the Barkhausen noise
sensor [9]
Fig. 5 Magnetic hysteresis loop with Barkhausen
noise and derived parameters

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 5
1 - Coercivity HC
2 - Max. magnetic Barkhausen noise
3 - Max. acoustic Barkhausen noise
4 - Max. incremental permeability, µ
∆
5 - Ht-field value at 50% of µ
∆max
6 - Ht-field value at 75% of µ
∆max
7 - Max. of λL in between |H
max| and HC
8 - Max. of λL in between H
Cand |H
max|
9 - H-field at λL
= 0
10 - H-field at maximum dynamic λL
11 - Maximum dynamic λL
12 - H-field at minimum dynamic λL
13 - Minimum dynamic λL
14 - Dynamic λ at 200 A/cm
180°-Bloch wall movements. On the contrary, compressive stresses lead to a decrease
of the noise intensity because of a higher density of 90°-Bloch walls in the
magnetizing direction. Hence, M max correlates with the magnitude of the residual
stresses in the investigated material volume. However, due to the high gradients in
the microstructure and the distribution of residual stresses in a weld, a clear separation
of microstructural and stress-related magnetic phenomena followed by quantitative
approach has not been successful in the past [9].
Newer approaches using neural networks and multiparameter least squares analysis
can be applied to find the best correlation between micromagnetic paramters and
material properties if multi-parameter testing systems are used. As an example, Fig.
6 shows that different micromagnetic parameters derived from Barkhausen noise
and incremental permeability measurements have different capabilities to measure
hardness [1].
3MA Ferrotest Dur III
L
Fig. 6 Significance of micromagnetic parameters for
hardness evaluation [1]
max
1
2 3 4 5 6
Raw Data
Control
36
PC with evaluating
Software
30
Evaluating
Micromagnetic
Parameters
Fig. 7 3MA-testing system and Sensor

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 6
The analysing frequency of the evaluating unit in the 3MA-system directly influences
the depth to where the micromagnetic signals can be detected, the so-called
interaction depth. The excitation frequency of the power supply could be varied
between 1 and 160 Hz and also has to be adapted to the maximum field strength and
the material properties. From former parameter studies, an excitation frequency of
100 Hz and an analysing frequency of 0.4 MHz was found to be at an optimum
leading to a interaction depth of ≈10 µm, which is similar to the penetration depth of
the X-rays used in the residual stress measurements.
The commercial 3MA-testing system used here is shown in Fig. 7 The raw data
from the 3MA device could be transferred into a computer for further data evaluation.
Using a specially designed software, the shape of the Barkhausen noise curve
and the time signal of the tangential field strength could be analysed to derive further
parameters [1, 10, 11].
3 SIMULATION OF THE DEFORMATION BEHAVIOUR OF
THE WELDED JOINT
Depending on the load stress, often the greatest magnitude of local plastic derformations
and corresponding residual stress relaxation in a welded joint can be detected
after the first load cycle and thus determines the further fatigue process to a
great extent. For this reason, it is essential to investigate this static load step for an
assessment of the fatigue behaviour. Fig. 8 shows the calculated distribution of the
total residual strains after loading including the elastic strains resulting from residual
stresses at the surface of the weld for different maximum nominal loading stresses.
According to the material properties (see Fig. 2 and 3), the hard weld bead of the
final pass exhibits very small plastic deformations in comparison to the soft base
material. At the weld toe, the geometrical notch at the transition from weld material
to HAZ leads to a local stress concentration and thus high local (plastic) strains. A
similar effect can be observed at the transition zone from HAZ to base material. The
400 MPa
500 MPa
550 MPa
400 MPa
500 MPa
550 MPa
Base Mat. HAZ Weld
Base Mat. HAZ Weld
Fig. 8 Calculated strains (elastic and plastic) after different loading stresses across the surface of the
weld FEM-model (left: final pass, right: cap pass)

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 7
strain gradient from hard weld bead to soft base material is much less severe in the
softer cap pass where no geometrical notch is present, the weld bead of the cap pass
plastically deforms proportional with growing nominal stress with a magnitude approximately
half of that of the base material.
4 BEHAVIOUR OF NONDESTRUCTIVE PARAMETERS IN
CYCLICALLY LOADED WELDED JOINTS
Fig. 9 shows the distributions of
the tranverse residual stresses and
the micromagnetic parameters
coercivity H cm and the Barkhausen
noise amplitude M max across
the weld determined after different
decades of pure pulsating tension
loading with an upper stress
of 400 MPa. The investigated 6-
layer GTA double vee weldment
was welded with a filler metal of
a higher strength than the base
material (see hardness distribution
in Fig. 2). Despite the fact that
compressive residual stresses are
found in the weld seam and the
load stress is of a pure tension
type, a relaxation of these compressive
residual stresses can be
observed. This relaxation indicates
local plastic deformation in
the weld seam, which is in
agreement with the result of the
FEM-simulation in Fig. 8. Until
10 5 load cycles, the compressive
residual stresses further relax but
begin to increase again after
σ RS t [MPa]
Mmax [V]
Hcm [A/cm]
300
200
100
0
-100
-200
-300
-400
S 355,
GTA-DV-Weld,
Cap Pass,
σ o = 400 MPa,
N = 10 5 until fracture. On the
Distance from weld centerline [mm]
other side, in the base material,
tensile residual stresses up to
200 MPa continously arise during
fatigue loading. Analogous to the
behaviour of the residual stresses,
both micromagnetic parameters
change significantly after the first
load cycle. Additionally, a continous change of H cm and M max throughout the fatigue
process can be observed. The Barkhausen noise amplitude M max continuously increases
across the whole weld area until 10 5 load cycles and decreases to an intermediate
level at fracture of the specimen. In opposite to the behaviour of M max , the
coercivity decreases in the weld seam and the HAZ until shortly before fracture.
7.5
7
6.5
6
5.5
5
4.5
4
9.5
9
8.5
8
7.5
7
Weld toe
Weld HAZ Base Mat.
Weld HAZ Base Mat.
0 5 10 15 20
N = 0
N = 1
N = 1000
N = 100000
N = 102234
(cracked)
Fig. 9 Distribution of the transverse residual stresses and
the micromagnetic parameters H cm and M max at different
load cycles until fracture (steel S355, pure tension loading
with maximum stress of 400 MPa)

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 8
Between N = 10 5 and failure of the specimen, however, the coercivity in the weld
seam remains relatively constant, whereas a remarkable increase of H cm in the HAZ
can be found.
To assess the cycle-dependent behaviour, the nondestructive measuring quantities
are plotted versus the number of load cycles in Fig. 10. The transverse residual
stresses and the micromagnetic parameters Barkhausen noise amplitude M max and
coercivity H cm were determined in the weld center after each decade during cyclic
loading with four different maximum load stresses. After the first load cycle, the
residual stresses in the weld seam relax significantly dependent on the load stress.
The magnitude of this stress relaxation increases with a higher load stress, accompanied
by stronger plastic deformations (see also Fig. 8). The results of the micromagnetic
measurements also indicate microstructural changes caused by the fatigue process.
Depending on the load stress, after a certain number of load cycles, in Fig. 10
the Barkhausen noise amplitude and the coercivity begin to change significantly,
M max begins to increase whereas H cm drops constantly until shortly before fracture.
The magnitude of this drop in H cm is dependent on the load stress and the corresponding
degree of plastic deformation in the specimen. The lowest cyclic load
stress of 350 MPa, leading to an increase of the fatigue life of 50 % with respect to
the 400 MPa load, causes no relevant changes in both micromagnetic parameters;
just before fracture, H cm shows a moderate decrease which can be interpreted by the
beginning formation of microcracks.
Parallel to the investigation of the fatigue behaviour of welds under pulsating tension
loading (R = 0), experiments with alternating load (tension-compression,
R = -1) were conducted. Fig. 11
shows the result for a load amplitude
of 300 MPa. The
changes in the micromagnetic
parameters maximum Barkhausen
noise amplitude and coercivity
at distinctive locations of
the fatigued weld are compared
to the local cyclic strain behaviour
measured by strain gauges.
Firstly, the initial values of H cm
correspond to the hardness in
the inspected zones (see Fig.
2). Until a number of 100 load
cycles, Barkhausen noise amplitude
and coercivity change
only gradually – for all locations,
M max decreases slightly,
whereas H cm increases slightly
in the weld seam and at the
weld toe and decreases in the
base material. Between 100 and
1000 load cycles, however, the
plastic strain amplitude increases
significantly in all
σ RS t [MPa]
Mmax [V]
Hcm [A/cm]
100
0
-100
-200
-300
-400
7.5
6.5
5.5
4.5
3.5
9.0
8.0
7.0
6.0
5.0
1E-1 1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6
Load Cycles
S355,
Cap Pass,
Weld Center
350 MPa
400 MPa
500 MPa
550 MPa
Fracture
Fig. 10 Distribution of the parameters determined by X-ray
diffraction and micromagnetic testing in the cap pass (5 th pass)
of the weld versus the number of load cycles

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999 9
zones, indicating a beginning softening. These microstructural processes also affect
the magnitude of Barkhausen noise amplitude and coercivity. M max increases slightly
in all observed zones, whereas H cm
exhibits a significant drop in the weld
seam and the weld toe and an increase
of this parameter in the base material.
During further loading until fracture,
another characteristic behaviour of
both parameters can be observed. Especially
in the weld center but also in
the weld toe and in the base material,
a significant increase followed by a
remarkable drop of M max shortly before
fracture of the specimen can be
observed. Analogous, in the weld
center and at the weld toe, the coercivity
firstly increases and then, after
a slight decrease, H cm grows rapidly
with a magnitude of ≈30 %. This behaviour
of M max and H cm after a former
cyclic softening process can be
explained by the formation of microcracks
shortly before failure of the
specimen. Obviously, the small gaps
in the material introduced by the
cracks lead to a relaxation of residual
stresses, indicated by the drop of
M max , but also influence the coercivity
due to a grow of microstructural defects
and an increase of the dislocation
density.
Mmax [V]
Hcm [A/cm]
2ε p l [10 -3 ]
3.5
3.0
2.5
2.0
1.5
1.0
0.5
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1 10 100 1000 10000
Load Cycles
S 355,
GTA-DV-Weld,
Pure Tension-
Compression
Loading
σ a = 300 MPa
Weld Seam
Weld Toe
Base Material
Fig. 11 Comparison between Barkhausen noise amplitude,
coercitivity and plastic strain amplitude of a
GTA-weld under pure tension-compression loading
5 SUMMARY AND CONCLUSIONS
The present investigations show that the characteristic changes of macro-residual
stresses, micromagnetic parameters and plastic strains under cyclic loading are
strongly connected to each other. In certain cases, however, a definite relationship
between the micromagnetic parameters Barkhausen noise amplitude M max and coercivity
H cm and those resulting from X-ray diffraction cannot be derived. The basic
problem is that the investigated micromagnetic parameters react on both residual
stresses and microstructural changes.
Under cyclic loading, the residual stresses within a weld can relax due to local plastic
deformation. In the weld seam of the investigated structural steel S355, such a
relaxation took place in corresponence with the magnitude of the calculated strains
in the FEM-simulation. This change of the residual stress level leads to a significant
increase of the Barkhausen noise amplitude that is especially sensible to residual
stresses. In the base material where the lower yield strength leads to a higher degree

2 nd International Workshop on Structural Health Monitoring, Stanford University, 1999
10
of plastic deformation and thus to an increase of the dislocation desity, a build-up of
tensile residual stresses in connection with an increasing Barkhausen noise amplitude
can be detected. The initial values of the coercivity H cm on the other side correlate
very clearly with the hardness in the weld seam, the HAZ and the base material.
After a significant change after the first load cycle, the residual stresses remain relatively
constant in the course of further loading until fracture. In contrast to this, the
micromagnetic parameters exhibit a greater sensivity to microstructural changes,
even at early stages of the fatigue process. A relatively continous drop of H cm until
fracture was observed under pure pulsating tension loading. Additionally, the Barkhausen
noise amplitude M max shows a characteristic behaviour before the formation
of cracks in the material. Under pure alternating load, a change in the magnitude of
the coercivity is strongly connected with the increase of the plastic strain amplitude.
In nearly all investigated examples, the visible appearance of cracks leads to a relatively
strong alteration of both micromagnetic parameters.
The presented results in this first overview illustrate the potential use of the micromagnetic
testing system for the assessment on fatigue processes in cyclically loaded
weldments. Both micromagnetic parameters show a good sensivity with respect to
microstructural changes during fatigue and thus this nondestructive method can be
used to characterize the stages of fatigue in a fast and easy way. Further investigations
will be carried out within an ongoing project with the aim of a fatigue life prediction
for welded steel constructions.
The authors would like to thank the Deutsche Forschungsgemeinschaft (DFG) for
the support of the investigations.
REFERENCES
1. Theiner, W. A.: Physical Basis of Micromagnetic Methods and Sensor Systems and their Application
Areas, Proceedings of the 1 st International Conference on Barkhausen noise and Micromagnetic
Testing, Hannover, 1998, 197-218
1. Karpuschewski, B.: Introduction to Micromagnetic Techniques, Proceedings of the 1 st International
Conference on Barkhausen noise and Micromagnetic Testing, Hannover, 1998, 85-100
3. Nitschke, T., Wohlfahrt, H.: The Generation of Residual Stresses due to Joining Processes, in:
Residual Stresses - Measurement, Calculation, Evaluation, DGM Informationsgesellschaft,
1991, 121-134
4. Christ, H.-J.: Wechselverformung von Metallen, Werkstofforschung und -technik, Springer,
1991
5. Nitschke-Pagel, T.: Eigenspannungen und Schwingfestigkeitsverhalten geschweißter Feinkornstähle,
Diss. TU Braunschweig, 1994
6. König., J., Weiler, W., Winckler, I.: Das UCI-Verfahren – ein automatisiertes Härteprüfverfahen
nach Vickers unter Prüfkraft, Materialprüfung, Heft 10 (1972), 265-276
7. Seyffarth, P.: Großer Atlas Schweiß-ZTU-Schaubilder, DVS-Verlag, 1992
8. Hauk, V., Macherauch, E.: Die Zweckmäßige Durchführung röntgenographischer Spannungsermittlungen
(RSE), in: HTM-Beiheft: Eigenspannungen und Lastspannungen, hrsg. v. V.
Hauk und E. Macherauch, Hanser, 1982, 1-19
9. Theiner, W., Höller, P.: Magnetische Verfahren zu Spannungsermittlung, in: HTM-Beiheft:
Eigenspannungen und Lastspannungen, hrsg. v. V. Hauk und E. Macherauch, Hanser, 1982,
156-163
10. Tönshoff, H. K., Karpuschewski, B.: Magnetisches Verfahren zur Prozeßnahen Überwachung
des Eigenspannungszustandes nach dem Schleifen, HTM 50 (1995) 3, 145-150
11. Altpeter, I., Theiner, W. A.: Micromagnetic Measurement of Residual Stresses in Components,
in: Residual Stresses: Measurement, Calculation, Evaluation, DGM Informatiosgesellschaft,
1991, 33-36