1. 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

4. 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)

5. Determining PPP Crack Shape Evolution using Paris equation ratio
Assuming that the PPP is equilibrium,

6. Tension PPP Equations
Newman-Raju coupled with Paris Equation with Crack Closure Factor
ASTM E740
Irwin’s Solution

7. Newman-Raju/Paris Estimate

8. where C, n, p, and q are fitting constants and
NASGRO 3.0 Background
General purpose Fracture Mechanics software from NASA JSC
Version released March 2000
Crack growth rate
where C, n, p, and q are fitting constants and
Using this because it is what was available; Closed form hard to get

9. 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

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

11. da/dN – ΔK Plots for A533B
0.01
1e-9
0.01
1e-9
da/dN
da/dN ΔK ΔK

12. Plate Geometries Surface Crack in Tension or Bending
Surface Crack with Nonlinear Stress
Expect consistency between these when similar loadings, but these loadings are arbitrary t t

13. Cylinder Geometry
Longitudinal Surface Crack in a Hollow Cylinder with Nonlinear Stress

14. Geometries Flat Plates Cylinder Width = 6 in. Thickness = .5 in.
Outer Diameter = 4 in.
ri/t = 3  Implies a thick-walled cylinder

15. 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

16. Outline Results Problem Statement Background Analysis Approach
Conclusions
72 NASGRO runs
Show sample CSE
Compare geometries
Compare width effects
Compare Paris and NASGRO
Show sample PPP
Compare PPP solutions

17. Typical Crack Shape Evolution

18. Geometry Comparison in NASGRO

19. Width Effects Comparison in NASGRO
Less width effect for a/t<.4

20. Paris vs. NASGRO
Example of inconsistency

21. Sample PPP
PPP
Found by ‘eye-balling’ it. Looking for point where slope is zero starting out

22. Comparison of PPP for Tension
Irwin’s Solution (a/c=1)
ASTM E740 Solution
N-R/Paris doesn’t fully capture it either because for the path to match, the value needed for n doesn’t match da/dN- DK
Newman-Raju/Paris with Closure Factor, n=2
NASGRO
Newman-Raju/Paris with Closure Factor, n=3.75

23. PPP Equations for Flat Plate in Tension
ASTM E740
Best Fit Equation from Excel
(2024-T351,Tension, R=.1)
(2024-T351,Tension, R=.4)
E740 independent of n, a mat’l constant which makes a difference
(2024-T351,Tension, R=.7)
(A533B ,Tension, R=.1)

24. PPP Comparison for Different R Values

25. PPP Comparison with Different R Values
for Internal Pressure
PPP for plate in tension,
R=0.1
R=0.1
R=0.4
R=0.7

26. SC04 Results Consistent in SC04 geometry also Best fit lines
(2024-T351, Internal Pressure, R=0.1)
(2024-T351, Internal Pressure, R=0.4)
(2024-T351, Internal Pressure, R=0.7)

27. 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

28. Acknowledgements Kristen Batey, Jeff Foote, and
Sai Kishore Racha for NASGRO analysis

29. Questions?

30. 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)

31. Recommendations
Check consistency with more challenging stress gradients and weight functions
Check the effects of an overloading – still consistent?