Influence of Overload Induced Residual Stress Field on Fatigue Crack Growth

in Aluminum Alloy

Jinhee Park (M.S. Candidate)

Date of joining Masters’ program : Fall 2002

Thesis advisor : Dr. M. A. Wahab

Dr. S. S. Pang

The experimental facility (MTS 810)

Instrumented Specimen in the Corrosion Cell

< Overview >

• Introduction• Theoretical Review• Numerical Modeling (FEM)• Design of Experimental Methodology • Numerical Result• Comparison of Numerical Result with Theory• Conclusion & Comment• Further Work

< Introduction >

• Concept of Fatigue Crack Growth

∆a

∆a

loading

unloading

loading

unloading

smax

smin

s

Time

RSfNa ,

)(maxmin

RatioStressSSR

)(minmax

RangeStressSSS

• 2D - Modeling of Center Crack Specimen

W

a

Crack Tip

ASTM Standard E 1823 M(T)

• Material Behavior Modeling (elastic-perfect plastic) Bilinear Inelastic

Isotropic Hardening

Linear elastic material

Elastic plastic material stress-strain loop

Load

ing

Unl

oadi

ng

Permanent Set

Dis

sipa

ted

Ene

rgy

y

• Plastic Zone Size for Plane Stress

r p2

Crack

y

Distance from crack tip

At cyclic loading (+)

(--)

y

At cyclic unloading

(+)

: Irwin’s plastic zone radius (1960)

σK

π2ry

Ip

1

• Compressive Residual Stresses ahead of Crack Tip after Overload

Distance from crack tip

Com

pre

ssiv

e S

tres

sT

ensi

le

Str

ess

(+)

(--)

Overload Plastic Zone

Cyclic loading plastic zone

Cra

ck L

engt

h(a)

• Fatigue-life Extension due to Periodic Overloads

The slower crack growth continues until the crack grows beyond the overload plastic region(The wheeler model of crack growth inside an overload plastic zone). This beneficial residual stress effect of overload is called crack growth retardation.

Number of cycles(N)

Overload

Periodic overload retardation

Constant amplitude cycles

• The wheeler model of crack growth inside an overload plastic zone

•

a’ '2r p

After second overload

•(-)

(+)

a

Before overload

•

a

After first overload

•

a’

r p2

After some crack growth

< Theoretical Review >

• Consequences of Overload for Crack Tip Plastic Strain Loop

Before overload After overloadF

AE

A E

F

Cyclic elastic strain range

F

EA

E

F

< Numerical Modeling >

Elastic Modulus (E)

Poisson Ratio ()

Yield Stress ( )

RoomTemp.(T)

Tangent Modulus (H)

70 0.33 200 20c 0

• Mechanical Properties of Aluminum Alloy

(2024-T3, 7050-T7451)

y

MPaGPa GPa

Cu Mn Mg Zn Cr

7075-T7451 1.6% 2.5% 5.6% 0.23%

2024-T3 4.4% 0.6% 0.45%

- Chemical Composition of Aluminum Alloy

• Finite Element Model for Center-Crack Plate

Symmetric Boundary Condition

Element Size around crack tip : 0.5mm

Element type :

8 node PLANE 82

10mm

40mm

20

mm

40

mm

Crack Tip

Node just front crack tip

• Cyclic loading condition with two overloads history

Overload ratio = 80 / 3080MPa

30MPa

t

< Design of Experimental Methodology >

• Influence of low cycle fatigue(LCF) damage on high cycle fatigue(HCF) crack growth.

• Modeling of overloading effects on crack growth, and considering various load amplitudes.

• Formulating equations for lifetime prediction.

• Providing recommendations for service life extension and developing improved fatigue life assessment tools.

< Numerical Results >

After one overload, cyclic strain range was considerably reduced and

the crack growth rate will decrease accordingly (Retardation).

Before overload

After overload (80MPa)

• Stress-total strain curve with two overloads (80MPa, 60MPa)

After overload (60MPa)After overload

(80MPa)

Before overload

• Stress-total strain curve with two overloads (80MPa, 100MPa)

After overload (100MPa)

After overload (80MPa)

Before overload

• Stress-strain curve with two overloads (80MPa, 80MPa)

This curve didn’t show any more decreased strain after the second overload.

After overload (80MPa)

Before overload

• Substep time-total strain curve with two overloads

0 5 10 15 20 25-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Substep Time

Tot

al s

trai

n

80MPa - 100MPa

80MPa - 80MPa

80MPa - 60MPa

0 5 10 15 20 25 30 35 4020

40

60

80

100

120

140

160

180

200

Distance from the crack tip (mm)

Von

-mis

es s

tres

s (M

Pa) Before overload

After first overload (80MPa) After second overload (100MPa)

• Von-mises stress distribution along the crack plane

• Two overloads (80MPa - 100MPa)

The plastic zone disappeared after each overload.

< Comparison of Numerical Results with Theory >

After overload

F

After overload (80MPa), strain range moves to the left. It becomes negative. The strain hardening should be considered.

After overload (80MPa)

Before overload

F

< Conclusion and Comments >

• After one overload, strain was decreased.

(Crack growth retardation)

• After the second overload, the second reduced strain was recorded in 80MPa & 100MPa.

• Von-mises stress redistribution along the crack plane after first overload (80MPa) was reduced. After the second overload (100MPa), the stress redistribution was smaller than the first one.

• Two overloads effects on the crack plane and crack growth rate was not well checked in this work.

• This paper was accepted by ICCE 10, July 2003.

< Further Work >

• Cyclic strain hardening and path dependent plasticity should be considered later on.

• Various loading conditions like overload ratio, stress ratio, and stress range should be conducted later on.

• To advance crack, the crack tip advance scheme (involving node release immediately after maximum load on each cycle) needs to be carried out.