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17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China
Study on Magnetic Memory Method (MMM)
for Fatigue Evaluation Bin HU 1, Gang CHEN 1, Gongtian SHEN 1, Luming LI 2 , Xing CHEN 2
1China Special Equipment Inspection & Research Institute, Beijing China
Phone: +86-10-59068300, Fax: +86-10-59068323
e-mail: [email protected], [email protected], [email protected] 2 School of Aerospace, Tsinghua University, Beijing China
e-mail: [email protected], [email protected]
Abstract:
In lab experiments to evaluate the fatigue, the surface magnetic field on specimens would
be changed with different cycle numbers (N). Good correlation between resulting fatigue
level and MMM signals has been demonstrated. In the M (magnetic)N (cycle) curve derived
from the experimental data, three stages corresponding to the fatigue process can be clearly
distinguished. A similar situation was found in the practical inspections of train axles in
service. This technique could be used for fatigue evaluation.
Key Words: MMM; Fatigue; M-N Curve, Nondestructive Evaluation
1 introduction
Stress concentration which is able to lead to failure of a work piece occurs in
dangerous regions due to the accumulation of fatigue damages during operation of
the work piece subjected to periodic loading. Accompanying with the applications of
stress, fatigue develops with the loading of cycle stress, in this process, glide of
crystals generates firstly, and then micro-cracks which eventually grows into
macro-cracks causing failure of the work piece. Fatigue of train axles, which may play
part in train derailment, got more and more attention because of the speed-up railway transport.
Analysis for train axle defects represents that apart from defects due to friction;
approximately 70% of the defects are brought about by fatigue, 90% of which are
due to the present of stress concentration. Traditional nondestructive test (NDT)
methods can hardly carry out effective evaluation of earlier damage caused by the
concentration of mechanical stress. Recent studies are focused on how to detect
concentration of stress and to evaluate fatigue stats and accordingly fatigue life of a
work piece [1~3].
In the past century, various NDT methods, such as X-ray [4], ultrasonic [5], laser[6],
Barkhausen effect and magnetic emission[7] and so on, are proposed for investigation
of earlier fatigue stats. As changes in density and glide of dislocation would affect
magnetic properties of ferromagnetic material, magnetic measurements has nature
advantages in the evaluation of ferromagnetic material.
Metal magnetic memory (MMM) method [8] is a novel magnetic NDT means
which determines stress concentration stats according to a weak change of magnetic
field due to concentration of stress at the region with stress concentration. Prior study [9~15]indicates that MMM signal is sensitive to micro-structure and local stress of
ferromagnetic material, both of which are closely associated with fatigue stats of the
material. Hence, MMM method may be a potential method for NDT of fatigue stats.
In this paper, MMM method is attempted for fatigue evaluation of ferromagnetic
samples and proved to be extraordinary effective on fatigue evaluation and Fatigue
life assessment of ferromagnetic material. The M-N curve derived from the
experiment data can be clearly distinguished to three stages which are corresponding
to three stages of fatigue process respectively. Furthermore, field examination are also
carried out, in which magnetic field distribution of real train axles are measured and
analyzed.
Fig.1 instruments for fatigue experiment and MMM signal measurement
2 Fatigue experiment
2.1 experiment design
Selected samples have a rectangular cross-section and are loaded in three-point
bend manner. As shown in Fig.1,fatigue test was carried out on Instron1603
Electro-Magnetic Resonator which is able to apply a maximum load of 100kN and
loading frequency range from 50 to 250Hz, with average load18averageF KN=
,load
amplitude9amplitudeF KN=
under load frequency of 130Hz. A micro-magnetic
measurement system, as shown in Fig.1,was used to test magnetic field vertical to the
surface of the specimen along the lines indicated in fig2 with a lift-off of 2mm. The
magnetic sensor controlled by a three-dimensional scanning system so as to facilitate
the comparison of the resulting data has a measuring range from 20nT to 6Gs. If there
is no special explanation, the surface magnetic field in this paper means magnetic
field perpendicular to the surface of sample.
The specimen used in the experiment is a medium carbon steel bar with
rectangular cross-section as shown in Fig.2.
Fig. 2 shape and dimensions of the specimen for fatigue test
An arc-shape recess with depth of 1mm and radius of 14mm are formed in the
middle portion of the specimen so as to control the generation of initial crack at a load
cycle number N less than 107.
For the study of the variation of surface magnetic field of ferromagnetic material
under loading with high frequency and high cycle number, surface magnetic field
of the specimen under various loading and various outside magnetic field. In
addition, all parts which is brought into contact with the specimen in the fatigue test
are replace with parts of stainless steel so as to minimum the influence of the
adjacent parts in the experiment. Some of the specimens are demagnetized so as to
analyze effects of initial magnetization of ferromagnetic specimen.
2.2 Result of fatigue experiment
Fig.3 is a typical graph of surface magnetic field under different loading cycles.
Fig.3 surface magnetic field versus loading cycle number N with respect to specimen
without demagnetization
Results of fatigue experiment (as shown in Fig 3) shows that the sample got
demagnetized in the first several cycles, and then the distribution of surface
magnetic field changes slightly along with loading cycles of stress. Although, in
most cycles, variation of surface magnetic field is relative small, in the enlarged
view of the central portion of surface magnetic field which corresponding to the
medium portion of the specimen, i.e. where the arc-shape recess locates, variation
of magnetic field along stress loading cycles are found to be much greater than
other portions. Hence, the magnitude of the central portion are derived and plotted
in Fig 4 and 5 in connection with loading cycles N.
Fig.4 and 5 shows that field magnitude signals change along with stress cycles N
and there is a leap of magnetic signal before fracture. A primary conclusion can be
drawn that the magnetic signals of the concentration location is sensitive to fatigue
evaluation. From these two figures, three stages of M value are clearly
distinguished. During the early stage of fatigue process, the amplitude of magnetic
field increases and then reaches a flat roof. The flat roof continues in the middle
stage of fatigue, the change of magnetic field in this stage is slow and neglectable.
0 1 0 0 2 0 0 3 0 0
-4
-2
0
2
4
磁场
强度
（Ga
uss）
行 程 （ 点 ）
N = 0 N = 1 0 N = 5 0 N = 1 0 0 N = 5 0 8 N = 8 1 1 N = 9 2 0 N = 1 0 1 5 N = 1 2 1 0 × 1 0 0 0 N = 1 4 3 9 N = 1 8 0 5 N = 2 2 0 1 N = 2 4 0 9 N = 2 8 7 6 N = 3 2 0 3 N = 3 3 2 8
12 0 140 1 60
-0.4
-0.2
0.0
0.2
After coming into the last stage, the amplitude of magnetic field raises rapidly. The
flat roof initials at 10% of fatigue life and terminates at 90% of fatigue life, which
is highly consistent with three stages of fatigue development.
Fig.4 magnitude of magnetic field in the central portion M as a function of loading cycles N
of specimens without demagnetization
Fig.5 magnitude of magnetic field in the central portion M as a function of loading cycles N
of specimens with demagnetization
Surface magnetic field of specimen with demagnetization and variation thereof
due to stress cycles are significantly smaller than that of specimen without
demagnetization. However, the M-N curve still indicates three stages mentioned
above with their boundaries mixed up which makes distinction of these stages more
difficult.
2.3 Discussion
According to principal of ferromagnetism [16], magnetic elastic energy (Ems)
associated with magnetostriction in Ferro magnets is obtained by following equation:
Ems = B1 ∑eii (α²i －1/3) + 2B2 ∑eij αi αj
In which, B1 and B2 indicates magnetic elastic couple factors
αi, αj — cosine of the included angle between a direction of magnetization and
crystal axle
eii, eij — components of deformation
As can see from above equation, displacement of magnetic domain walls is
induced by deformation due to action of stress. Thus the direction of spontaneous
magnetization varies and consequently forms fixed nodes of magnetic domains which
lead to the increase of magnetic energy. With the application of loadings, stress
concentration and residual stress with high stress energy are formed in the specimen,
which still exist even after the loading is removed. Hence displacement of magnetic
domain walls is induced in the region of stress concentration, forms magnetic poles
and thus disturbs surface magnetic field of a specimen. The above described
phenomenon is basic principle of MMM method.
Theoretically, it is considered that fatigue initials due to movement of
dislocations, which gather together and form initial cracks. Consequently, stress
concentration generates again by the cracks, this process is repeated and finally lead
to macro cracks [2].
An explanation to the M-N curve derived from fatigue experiment can be drawn
on the basis of fatigue theory in combination with MMM principle：during 0-10% of
fatigue life, density and configuration of dislocations varies significantly as
microstructure of specimen adapted to the present of stress loading, which leads to the
increasing of the degree of stress concentration along with loading cycles N and thus
leads to variation of magnitude of surface magnetic field M at the region of stress
concentration; during 10-90%,substructure of dislocations develops slowly and lead to
the formation of stable slip bands without macroscopic changes of stress, hence, there
is a flat roof in the portion of M-N curve corresponding to this stage of fatigue life; at
last stage, a relative large leakage of magnetic field generates due to the occurrence of
macro cracks.
The consistence between M-N curve and fatigue life with three stages makes it
possible to evaluate fatigue stats of ferromagnetic material by using M-N curves.
3 Field examination
In order to approve above result, a field examination was carried out in Feb. 7th
Rolling Stock Works. In the examination, magnetic field distribution of off –load slot
of total of 140 pairs of axles with different time on active service are tested, wherein
the time on active service of an axle can partly represents fatigue stats of the axle.
2 4 6 8 10 12 14 16 18 20 22
0 . 7
0 . 8
0 . 9
1 . 0
1 . 1
1 . 2
1 . 3
峰 峰 值 十 点 平 均
磁场
强度
（G）
服 役 年 限 （ 年 ）
Fig 6 magnitude of circumference magnetic field at off-load slot as a function of time on
service
Generally, result of field examination are in consistent with the M-N curve
derived in fatigue experiments。The plot of Fig.6 are quite similar to the M-N curve of
Fig.4 and 5,which approves the applicability of M-N curve in the evaluation of fatigue
life of ferromagnetic specimens.
4 conclusion
According to the results of fatigue experiment, the M-N curve derived from
ferromagnetic specimens are found indicating three stages corresponding to the three
stages in the development of fatigue, which is also approved by field examination of
real axles. MMM method shows great advantages in the evaluation of fatigue stats of
ferromagnetic materials.
However, there are still problems, such as how to determine current position of a
specimen in the extent of M-N curve without historic data, need to be solved to
evaluate fatigue stats effectively by using MMM method.
Acknowledgement
This work was supported by National Key Technology R&D Program (2006BAK02B02).
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