three-dimensional elastoplastic analysis of rolling...

University of Illinois at Urbana-Champaign

Huseyin Sehitoglu,D. Canadinc, Y.Jiang**,J.Kristan*University of Illinois at Urbana-Champaign,**University of Nevada, Reno, *TransportationTechnology Center Inc.

TRB Meeting, January 13, 2003

THREE-DIMENSIONAL ELASTOPLASTICANALYSIS OF ROLLING CONTACT


TALK OUTLINE

• SHAKEDOWN, RESIDUAL STRESS• DEFORMATION STUDIES RELEVANT TO CONTACT• BAINITIC AND PEARLITIC RAIL MATERIALS• CONCLUSIONS

• SHAKEDOWN, RESIDUAL STRESS• DEFORMATION STUDIES RELEVANT TO CONTACT• BAINITIC AND PEARLITIC RAIL MATERIALS• CONCLUSIONS


H. F. Moore’s Book, p.224


Excessive Wear in Crossings


DEFINITION OF RATCHETTING : INCREMENTOF STRAIN PER CYCLE DUE NONCLOSURE OF

THE HYSTERESIS LOOP

600

400

200

0

0.0350.0340.0330.0320.031Axial Plastic Strain

cycle 256600

400

200

0Axi

al S

tres

s, M

Pa

0.0200.0190.0180.0170.016Axial Plastic Strain

cycle 3

A B

1070 Steel

RATCHETTING STRAIN PER CYCLE


Significant Texture ( Orientation) Develops in the Material Under Contact (Tyfour &Benyon)


MOTIVATION

• To Model the Ratchetting PlasticDeformation Involved in Rolling Contactand Other Complex MultiaxialNonproportional Loading

• Specific Emphasis on Long TermRatchetting and Multiple Step Loading


Contact Stress History in wheel -rail contact(Johnson, 1985)


1.0

0.5

0.0

0.60.50.40.30.20.10.0Normalized Maximum Shear Stress Range, ∆τmax

∆τmax

q/p=0 q/p=0.1 q/p=0.2 q/p=0.3

Variation of Maximum Shear Stress with Increasing Tractions


(a)

Low Adhesion

Self Steering Trucks

High Adhesion

Operation Regimes in Railroad Locomotives


2.5

2.0

1.5

1.0

0.5

0.0

z/a

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15( σx) r

G=79.6GPa µ=0.3H=25.7Gp0/k=4.124 Q/P=f=-0.2

FEM, Kumar et al. Proposed Method Merwin & Johnson's

2.5

2.0

1.5

1.0

0.5

0.0

z/a

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15( σy) r

G=79.6GPa µ=0.3H=25.7Gp0/k=4.124 Q/P=-0.2


2.0

1.5

1.0

0.5

0.0

z/a

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15( σx) r

G=79.6GPa µ=0.3H=25.7Gp0/k=4.5 Q/P=f=-0.2


2.0

1.5

1.0

0.5

0.0

z/a

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15( σy) r

G=79.6GPa µ=0.3H=25.7Gp0/k=4.5 Q/P=f=-0.2


(a) Case I: p0/k=4.124 Q/P=-0.2

(b) Case II: p 0/k=4.5 Q/P=-0.2

Residual Stress Profiles in Rolling Contact

Jiang, Sehitoglu, ASME J.Tribology, 116:3, 1994


-600

-400

-200

0

Axi

al S

tres

s, M

Pa

-400 -200 0 200 400Shear Stress, MPa

Stress-ControlledLoading Path

∆σ/2= 225MPa σm=-225MPa∆τ /2= 215MPa τm=0

-0.04

-0.03

-0.02

-0.01

0.00

Axi

al S

trai

n

0.0200.0150.0100.0050.000-0.005-0.010Shear Strain

cycle1-2832

128256

512

1024

2048

EXPERIMENTAL RATCHETTING FOR A NOPROPORTIONAL AXIAL-TORSIONAL LOADING PATH

Jiang, Y. and H. Sehitoglu, ASME JAM, 63, 726_733, 1996. Jiang, Y. and H. Sehitoglu, ASME JAM, 63, 720_725, 1996.

1070 Steel


EXPERIMENTAL OBSERVATIONS

• The ratchetting direction is coincident with the mean stressdirection under single-step proportional loading.

• For 1070 Steel , the ratchetting rate decreases withincreasing number of loading cycles for both proportionaland nonproportional loadings.

• Under multiple-step loadings, the material exhibits amemory of the previous loading history.


EXPERIMENTAL “ELLIPSE PATH”

600

500

400

300

200

100

0

Axia

l Str

ess,

MPa

-400 -200 0 200 400Shear Stress, MPa

1070 Steel ∆σ/2=222MPa σm=222MPa ∆τ /2=224MPa τm=0

0.010

0.008

0.006

0.004

0.002

0.000

Axi

al S

trai

n

-0.010 -0.005 0.000 0.005 0.010Shear Strain

cycle1-10

16

1070 SteelExperiment


0.05

0.04

0.03

0.02

0.01

0.00

Axi

al R

atch

etti

ng S

trai

n

10080604020Number of Cycles

Chaboche Mroz/Garud

Experiment

Bower

A-F

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

She

ar R

atch

etti

ng S

trai

n

10080604020Number of Cycles

Mroz/GarudChaboche

Armstrong-Frederick

Bower

Experiment

PREDICTION OF THE “ELLIPSE” PATH


10-6

10-5

10-4

10-3

Rat

chet

ting

Rat

e, 1

/cyc

le

1 10 100 1000 10000Number of Cycles

χ(i)

=+∞

Experiment20

1

2

4

8

∆σ/2=205MPaσm=205MPa

1070 Steel

χ0(i)

=0 (i=1,2,...,10)

CAPABILITY OF PROPOSED MODEL IN UNIAXIAL LOADING


CAPABILITY OF PROPOSED MODEL IN NONPROPORTIONAL LOADING

10-6

10-5

10-4

10-3

Axi

al R

atch

etti

ng R

ate,

1/c

ycle


Experiment4

χ(i)

=+ ∞ 8

1

21070 Steel

∆σ/2=0 σm=300MPa∆τ /2=230MPa τm=0 20

χ0(i)

=0 (i=1,2,...,10)

τ

σ


10-6

10-5

10-4

10-3

Axi

al R

atch

etti

ng R

ate,

1/c

ycle


1070 Steel

∆σ/2=225MPa σm=-225MPa∆τ /2=215MPa τm=0

Experiment New Model

-0.010

-0.005

0.000

0.005

0.010

She

ar R

atch

etti

ng S

trai

n


Experiment New Model

CAPABILITY OF PROPOSED MODEL IN NONPROPORTIONAL LOADING

τσ


Deformed Meshes x-z Plane

x

z

x100

xy

z

Figure 14(b) Deformed Mesh: x-z Plane


Shear Strain Accumulation with Cycles

2.0

1.5

1.0

0.5

0.0

z/a

-6 -5 -4 -3 -2 -1 0 1(γ

xz)rG/k

p0/k=6Qx/P=0.4Qy/P=0.25y=0

pass16 3


0.1 0.1

2 2

4 46 6

1 1

2 2

4 46 6

10 10

2 2

4 46 6

100 100

2 2

4 4

6 6

1000 1000

2 2

100

101

102

103

104

105

106

Number of Cycles

Q/P = 0.3

p0/k = 5.0

6.0

7.0

8.0

9.0

Ratchetting as a Function of Cycles (Passes)


1400

1200

1000

800

600

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Q/P , Shear/Normal Traction Ratio

Pearlitic Wheel Steel, Failure Envelope for 10^6 Cycles corresponding to a shear strain at fracture of 1.25

Permissible Contact Pressure Based on a Ratchetting Strain Criteria


Sawley and Kristan (TTCI), 2001


TEM images of Pearlitic steel virgin rail specimens cut from the surface showing different alignments oflamellae in the throughout the microstructure.

RAIL MATERIALS


Figure showing the extraction convention for thevirgin rail tensile specimens.

h

Specimen

Picture showing the orientation of specimens cut from the virgin rails.


Monotonic room temperature tensile test results for the Bainitic and Pearliticsteel virgin rail specimens cut parallel to longitudinal direction.

1600

1400

1200

1000

800

600

400

200

0

0.200.180.160.140.120.100.080.060.040.020.00Engineering Strain

Room Temperature Tensile Stress-Strain Responseof Bainitic and Pearlitic Steel Samples cut from Virgin Railparallel to the longitudinal direction

Strain Rate=10-3

1/sSpecimens loaded until fracture

∆h=0.00 mm ∆h=0.83 mm ∆h=1.66 mm ∆h=2.49 mm ∆h=3.32 mm ∆h=4.15 mm

∆h: Distance between the rail surface and the top surface of the specimen

Bainitic Steel Pearlitic Steel


Bainitic Steel Virgin Rail RollingDirection Texture

Intensity Peaks (110) Pole Figure


Pearlitic Steel Virgin Rail RollingDirection Texture

Intensity Peaks (110) Pole Figure


Bainitic Steel Virgin Rail SurfaceTexture

(110) Pole Figure (211) Pole Figure


Pearlitic Steel Virgin Rail SurfaceTexture



Change of Texture with PlasticDeformation


After 50% Compressive StrainAfter Superimposed Shear

and Compression

dx

dy

σ

σ

τ

τdx

dy

σ

σ


Conclusions

(1)As the shear tractions (adhesion levels above 35%) increase, for the same wheel loads, the plastic strains increase.

(2) The severity of rail surface displacements becomespronounced as both the longitudinal and lateral shear tractions are increased.

(3) Factors other than yield strength could play a significant role in rolling contact behavior and wear.

three-dimensional elastoplastic analysis of rolling...

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