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