1 Crack Shape Evolution Studies with NASGRO 3.0 Elizabeth Watts and Chris Wilson Mechanical...

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Crack Shape Evolution Studies with NASGRO 3.0

Elizabeth Watts and Chris Wilson

Mechanical Engineering

Tennessee Tech University Cookeville, TN

2

Outline• Problem Statement

• Background

• Analysis Approach

• Results

• Conclusions

(Newman and Raju, NASA TR-1578)

3

Problem Statement• Purpose and Goals of Analysis

– To predict crack shape evolution (CSE) and preferred path propagation (PPP) using NASGRO 3.0

– To check for self-consistency within NASGRO 3.0

– To compare NASGRO 3.0 with closed-form estimates of CSE and PPP

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Background• Equations

– Newman-Raju K-solution– Paris vs. NASGRO, da/dN-ΔK– dc/dN – has correction for width based on closure

(McClung and Russell, NASA CR-4318)

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Determining PPP• Crack Shape Evolution using Paris equation ratio

• Assuming that the PPP is equilibrium,

c

a

c

a

c

a

cc

aa

KC

KC

c

an

c

na

6

Tension PPP Equations• Newman-Raju coupled with Paris Equation with Crack

Closure Factor

• ASTM E740

• Irwin’s Solution

2

2.01

t

a

c

a

09.0

01.02.09.0

35.01.135.01.1

42

2122

R

RRR

t

a

c

a

t

a

c

a

c

a

R

nn

R

n

R

1c

a

7

Newman-Raju/Paris Estimate

n=3.75

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NASGRO 3.0 Background• General purpose Fracture Mechanics software

from NASA JSC

• Version 3.0.4 released March 2000

• Crack growth rate

where C, n, p, and q are fitting constants and

q

c

p

thn

KK

KK

KR

fC

dN

da

max1

1

1

1

)(max

RgK

Kf open

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Analysis Approach• Two Materials

– 2024-T351– A533B, C11 & C12

• Three Geometries– Surface Cracks – SC01, SC02, and SC04 (with both

internal and external cracks)• Constant Amplitude Loading• Three Load Ratios

– R = -1, 0.1, 0.7• Varying Loads

– Tension, Bending, Combined Tension and Bending– Internal Pressure, Calculated Internal Pressure, and a

Nonlinear Pressure Gradient

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Material Properties• 2024-T351

• A533B, C11 & C12

(kpsi, in./cycles, and kpsi(in)1/2)

UTS YS KIc C n p q

68.0 54.0 34.0 .922e-08 3.353 .50 1.0

UTS YS KIc C n p q

100.0 70.0 150.0 .1e-08 2.7 .50 .50

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da/dN – ΔK Plots for A533B0.01

1e-9

0.01

1e-9ΔK ΔK

da/d

N

da/d

N

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Plate Geometries

tWM

M

S 0

S 0

a2c

S = 6 M

W t21

<<0.05 1.2ac

<2c

W0 < 1

S C 0 1 S C 0 2

a

Y

2c

x

tW

S (X) i

= 0, 1, 2, 3i

X = x/t

S (X) i

0.05 1.2c

< < a

2cW

0 < 1<

Surface Crack in Tension or Bending

Surface Crack with Nonlinear Stress

t t

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Cylinder Geometry

S C 0 3

S0

S0

R(sphere)

S = p4 (internal pressure)

2c

a

M

M

t

W t2

6 MS =

1

<<0.05 1.2ac

internal or external crack

S C 0 4

pD

2c

a

internal or external crack

S (X) = Stresses due to internal pressure, pS (X) = Other stresses

0

i

S (X)i

i = 1, 2 ,3

X = x/t(from inner wall)

x

a<<0.05 1.2c

>D 4 t

t

Longitudinal Surface Crack in a Hollow Cylinder with Nonlinear Stress

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Geometries• Flat Plates

– Width = 6 in.– Thickness = .5 in.

• Cylinder– Outer Diameter = 4 in.– Thickness = .5 in.

– ri/t = 3 Implies a thick-walled cylinder

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Load Ratios• Expected similar results for R = -1.0 and

R = 0.1 because of closure

• Expected results for R = 0.7 to be different because of little closure

• An intermediate value of R = 0.4 used for 2024-T351 plate in tension

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Outline• Problem Statement

• Background

• Analysis Approach

• Results• Conclusions

-72 NASGRO runs

-Show sample CSE

-Compare geometries

-Compare width effects

-Compare Paris and NASGRO

-Show sample PPP

-Compare PPP solutions

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Typical Crack Shape Evolution

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Geometry Comparison in NASGRO

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Width Effects Comparison in NASGRO

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Paris vs. NASGRO

Example of inconsistency

tWM

M

S 0

S 0

a2c

S = 6 M

W t21

<<0.05 1.2ac

<2c

W0 < 1

S C 0 1 S C 0 2

a

Y

2c

x

tW

S (X) i

= 0, 1, 2, 3i

X = x/t

S (X) i

0.05 1.2c

< < a

2cW

0 < 1<

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Sample PPP

PPP

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Comparison of PPP for Tension

ASTM E740 Solution

Newman-Raju/Paris with Closure Factor, n=2

Irwin’s Solution (a/c=1)

Newman-Raju/Paris with Closure Factor, n=3.75

NASGRO

tWM

M

S 0

S 0

a2c

S = 6 M

W t21

<<0.05 1.2ac

<2c

W0 < 1

S C 0 1 S C 0 2

a

Y

2c

x

tW

S (X) i

= 0, 1, 2, 3i

X = x/t

S (X) i

0.05 1.2c

< < a

2cW

0 < 1<

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PPP Equations for Flat Plate in Tension

• ASTM E740

• Best Fit Equation from Excel

12.02

t

a

c

a

1.0047 0.0124 - 0.1544- =

0.9324 0.0797 - 0.1568- =

0.976 0.043 - 0.2001- =

0037.10124.02153.0

2

2

2

2

t

a

t

a

c

a

t

a

t

a

c

a

t

a

t

a

c

a

t

a

t

a

c

a(2024-T351,Tension, R=.1)

(2024-T351,Tension, R=.4)

(2024-T351,Tension, R=.7)

(A533B ,Tension, R=.1)

tWM

M

S 0

S 0

a2c

S = 6 M

W t21

<<0.05 1.2ac

<2c

W0 < 1

S C 0 1 S C 0 2

a

Y

2c

x

tW

S (X) i

= 0, 1, 2, 3i

X = x/t

S (X) i

0.05 1.2c

< < a

2cW

0 < 1<

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PPP Comparison for Different R Values

tWM

M

S 0

S 0

a2c

S = 6 M

W t21

<<0.05 1.2ac

<2c

W0 < 1

S C 0 1 S C 0 2

a

Y

2c

x

tW

S (X) i

= 0, 1, 2, 3i

X = x/t

S (X) i

0.05 1.2c

< < a

2cW

0 < 1<

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PPP Comparison with Different R Values

R=0.7

R=0.1

R=0.4

PPP for plate in tension, R=0.1

for Internal Pressure

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SC04 Results• Consistent in SC04 geometry also• Best fit lines

0.9077 t

a0.1315 -

t

a0.143- =

c

a2

(2024-T351, Internal

Pressure, R=0.7)

0.9898 + t

a0.1471 -

t

a0.0933- =

c

a2

0.9615 t

a0.1741 -

t

a0.0726- =

c

a2

(2024-T351, Internal

Pressure, R=0.4)

(2024-T351, Internal Pressure, R=0.1)

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Conclusions• K-solution between SC01 and SC02 self-

consistent

• Each of the NASGRO runs converged towards a PPP

• NASGRO PPPs are a function of R, unlike PPP equation in E740

• Width effects are small if a/t < 0.4

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Acknowledgements• Kristen Batey, Jeff Foote, and

Sai Kishore Racha for NASGRO analysis

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Questions?

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End Conditions Encountered

• Net section stress > yield

• Unstable crack growth

• Crack depth + yield zone > thickness

• Broke through (transition to through crack)

• Crack outside geometric bounds (2c > W)

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Recommendations• Check consistency with more challenging

stress gradients and weight functions

• Check the effects of an overloading – still consistent?