Investigation of Change Mechanism of Magnetic Flux Density Distribution around Fatigue Cracks...
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Investigation of Change Mechanism of Magnetic Flux Density Distribution
around Fatigue Cracks
Investigation of Change Mechanism of Magnetic Flux Density Distribution
around Fatigue Cracks
H.TanabeH.Tanabe, Yui Izumi, , Yui Izumi, T.Takamatsu, J.ShimadaT.Takamatsu, J.Shimada
The University of Shiga Prefecture, JAPANThe University of Shiga Prefecture, JAPAN
K.Kida, E.C.SantosK.Kida, E.C.SantosKyushu University, JAPANKyushu University, JAPAN
IntroductionIntroduction
Specimen
Artificial slit
Crack tip
500m
Our previous studyTo evaluate the stress intensity factor of fatigue crack non-destructivelyusing a Magnetic Flux Density (MFD) distribution around fatigue crack,
・ Four-point bending fatigue test・ Observation of the MFD distribution around the fatigue crack
[mT]0.55
0.48
0.41
0.34
0.27
0.20
0.13
0.06
-0.01
-0.08 YcYcYc
Yc
N 0 1.0× 105 2.4× 105 3.4× 105
a (mm) 2.00 2.22 4.35 9.00
Yc (mm) 1.08 1.22 1.84 3.77
: Artificial slit : Fatigue crack
: Centre of gravity of the distribution of Bx
a: Crack length including slit length
Changes in MFD distribution around fatigue crack(Pmax=15.8 kN, R=0.1)
Center of gravity of the MFD distribution (Bx)
Crack propagation
10 20 30 40 50 600
0.5
1.0
1.5
2.0
2.5
3.0
Maximum stress intensity factor Kmax , MPa・m1/2
Yc1/
2 , m
m1/
2
0.1 15.8 kN0.2 15.8 kN0.4 15.8 kN0.1 19.7 kN0.2 19.7 kN0.4 19.7 kN
R Pmax
Relationship between Yc1/2 and Kmax
Non-destructive evaluation of the stress intensity factorof fatigue crack
Changing mechanism of Changing mechanism of magnetic flux density distribution magnetic flux density distribution
remains unclearremains unclear
● To examine the effects of “Annealing after fatigue testing”and “Additional fatigue testing after the annealing” on the MFD distribution
● To discuss the changing mechanisms of MFD distribution based on these results
ObjectiveObjective
To clarify To clarify changing mechanismschanging mechanisms of of MFDMFD distribution distribution around fatigue cracksaround fatigue cracks
““Inverse magnetostrictive effect”Inverse magnetostrictive effect”Mechanical stress(Residual stress)
Change of Spontaneous magnetization
Crack propagation Plastic deformation Residual stress
Flowchart of a series of experimentsFlowchart of a series of experiments
Experimental Experimental methodmethodss
① ① Fatigue testFatigue test
③ ③ AnnealingAnnealing
⑤ ⑤ Additional fatigue testAdditional fatigue test
⑥⑥ Measurement of MFD Measurement of MFD and FWHMand FWHM
④④ Measurement of MFD Measurement of MFD and FWHMand FWHM
② ② Measurement of MFD Measurement of MFD and FWHMand FWHM
Crack length 9mm
Crack length 10mm
873K, 5hoursin N2 atmosphere
SpecimenSpecimen
Material: Chromium molybdenum steelJIS SCM440
Hardness: HV200 Artificial slit: Wire electric discharge machining
Length = 2.0 mm Tip radius = 100 m
Shape and dimensions of specimen
Crack growth testsCrack growth tests
Four-point bending fatigue test Electro-hydraulic servo fatigue testing machine Load span: 50 mm Support span: 100 mm Frequency : 20Hz Stress ratio R : 0.1 Maximum load Pmax: 15.8kN
Specimen
Artificial slit
50mm
100mm
Four-point bending loading jigs
Measurement of MFD (Magnetic Flux Density)Measurement of MFD (Magnetic Flux Density)
MI sensor (Magneto-Impedance sensor)AMI201 (Aichi Micro Intelligent Corporation)
MI sensor
XY stageSpecimen
3mm
Apparatus for measurement of Magnetic flux density distributionSmall, Extremely high sensitivity
Measuring region of MFDMeasuring region of MFD
A
BC
CB
A D
D A
BC
3D Displaying3D Displaying of of BBxx 2D Displaying of 2D Displaying of BBxx
Measurement ofFWHM
Measurement of FWHMMeasurement of FWHM
Characteristic X-ray Cr-Ka
Diffraction plane 2 1 1
Diffraction angle 2q , deg. 156.4
Tube voltage, kV 30
Tube current, mA 30
h/2
h/2
FWHMFWHM
X-raydiffraction profile
FWHM (FWHM (FFull ull WWidth at idth at HHalf alf MMaximum)aximum)
Measurement conditions
Indicator ofDislocation density
or Plastic deformation
Measurement position
2 4 6 8 10 121.5
1.6
1.7
1.8
1.9
y , mm
FW
HM
, deg
ree
Crack tip
FWHMon the specimen’s end
Experimental resultsExperimental results
Effects of Annealing on FWHM distribution
Before Annealing(After Fatigue test)
After Annealing
Plastic deformation Plastic deformation generated in crack propagationgenerated in crack propagation
RelaxationRelaxation ofofplastic deformationplastic deformation
Measurement results of FWHM before and after the annealing
Crack tip
2 4 6 8 10 121.5
1.6
1.7
1.8
1.9
y , mm
FW
HM
, deg
ree
FWHMon the specimen’s end
[T]
400
300
200
100
0
-100
-200
400
300
200
100
0
-100
-200
Mag
netic
flu
x de
nsity
T 400
300
200
100
0
-100
[T]
400
300
200
100
0
-100
After AnnealingAfter AnnealingBefore AnnealingBefore Annealing
Effects of Annealing on MFD distribution
AnnealingAnnealing Decrease of MFDDecrease of MFD
Effects of Additional fatigue test on FWHM
FWHM increased FWHM increased in the range where the fatigue in the range where the fatigue crack propagated in the additional fatigue testcrack propagated in the additional fatigue test
Measurement results of FWHMbefore and after the additional fatigue test
Crack tip
2 4 6 8 10 121.5
1.6
1.7
1.8
1.9
y , mm
FW
HM
, deg
ree
FWHMon the specimen’s end
Crack propagatedin additional fatigue test
FWHMon the specimen’s end
New
cra
ck ti
p
2 4 6 8 10 121.5
1.6
1.7
1.8
1.9
y , mm
FW
HM
, deg
ree
After additional fatigue testBefore additional fatigue test(After Annealing)
400
300
200
100
0
-100
-200
400
300
200
100
0
-100
-200
N =3.4×105
a =9.00 mmN =3.5×105
a =10.1 mm
[T]
400
300
200
100
0
-100
[T]
400
300
200
100
0
-100
After additional After additional fatigue testfatigue test
Before additional Before additional fatigue testfatigue test
Mag
netic
flu
x de
nsity
T
Effects of Additional fatigue test on MFD
Measurement results of MFDMeasurement results of MFDbefore and after the additional fatigue testbefore and after the additional fatigue test
Increase of MFD Increase of MFD in the partin the partwhere the fatigue crack propagated where the fatigue crack propagated
in the additional fatigue testin the additional fatigue test
FWHMFWHM MFDMFD
AnnealingAnnealing DecreaseDecrease DecreaseDecrease
Additional Additional Fatigue TestFatigue Test IncreaseIncrease IncreaseIncrease
Crack propagationCrack propagationPlastic deformation(Change of FWHMFWHM)
Residual stress
Inverse magnetostrictive effectChange of MFDChange of MFD
Changing mechanism of MFD distributionChanging mechanism of MFD distribution
Experimental resultsExperimental results
Consideration of the changing mechanism of MFDConsideration of the changing mechanism of MFD
Good correspondenceGood correspondence
ConclusionsConclusions
1. The magnetic flux density around the fatigue crack decreased through annealing, and a clear correlation between the change of the magnetic flux density and FWHM by the annealing was observed.
2. An obvious increase of the magnetic flux density was observed around the part where the crack propagated during the additional fatigue test after the annealing. In this region, FWHM also increased, and a good correlation was observed between the change of the magnetic flux density and FWHM by the additional fatigue test, as well as by annealing.
3. It was concluded that the change of the magnetic flux density around the fatigue crack in its propagation process was a result of the inverse magnetostrictive effect caused by the plastic deformation generated around the crack tip and accumulated along the crack path.
Plastic zone caused by crack propagation
( a ) Before loading
s s( b ) Loading
( c ) Only elastic deformation
( d ) With plastic deformation
Magnetic domain
Plastic zone caused by crack propagation
Plastic zone
Crack
19
Unloading
Experimental result
0 2 4 6 8 100
1
2
3
4
5
6Pmax
Crack length a, mm
Yc
, m
m
0.1 15.8 kN0.2 15.8 kN0.4 15.8 kN0.1 19.7 kN0.2 19.7 kN0.4 19.7 kN
R
Relationship between Yc and a
aYc aK
cYK
G ood correlation between Yc and a
10 20 30 40 50 600
0.5
1.0
1.5
2.0
2.5
3.0
Maximum stress intensity factor Kmax , MPa・m1/2
Yc1/
2 , m
m1/
2
0.1 15.8 kN0.2 15.8 kN0.4 15.8 kN0.1 19.7 kN0.2 19.7 kN0.4 19.7 kN
R Pmax
Relationship between Yc1/2 and Kmax