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1 Crack Shape Evolution Studies with NASGRO 3.0 Elizabeth Watts and Chris Wilson Mechanical Engineering Tennessee Tech University Cookeville, TN.

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Presentation on theme: "1 Crack Shape Evolution Studies with NASGRO 3.0 Elizabeth Watts and Chris Wilson Mechanical Engineering Tennessee Tech University Cookeville, TN."— Presentation transcript:

1 1 Crack Shape Evolution Studies with NASGRO 3.0 Elizabeth Watts and Chris Wilson Mechanical Engineering Tennessee Tech University Cookeville, TN

2 2 Outline Problem Statement Background Analysis Approach Results Conclusions (Newman and Raju, NASA TR-1578)

3 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 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 5 Determining PPP Crack Shape Evolution using Paris equation ratio Assuming that the PPP is equilibrium,

6 6 Tension PPP Equations Newman-Raju coupled with Paris Equation with Crack Closure Factor ASTM E740 Irwins Solution

7 7 Newman-Raju/Paris Estimate n=3.75

8 8 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

9 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 10 Material Properties 2024-T351 A533B, C11 & C12 (kpsi, in./cycles, and kpsi(in) 1/2 ) UTSYSK Ic Cnpq 68.054.034.0.922e-083.353.501.0 UTSYSK Ic Cnpq 100.070.0150.0.1e-082.7.50

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

12 12 Plate Geometries Surface Crack in Tension or Bending Surface Crack with Nonlinear Stress t t

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

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

15 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 16 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

17 17 Typical Crack Shape Evolution

18 18 Geometry Comparison in NASGRO

19 19 Width Effects Comparison in NASGRO

20 20 Paris vs. NASGRO Example of inconsistency

21 21 Sample PPP PPP

22 22 Comparison of PPP for Tension ASTM E740 Solution Newman-Raju/Paris with Closure Factor, n=2 Irwins Solution (a/c=1) Newman-Raju/Paris with Closure Factor, n=3.75 NASGRO

23 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) (2024-T351,Tension, R=.7) (A533B,Tension, R=.1)

24 24 PPP Comparison for Different R Values

25 25 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

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

27 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 28 Acknowledgements Kristen Batey, Jeff Foote, and Sai Kishore Racha for NASGRO analysis

29 29 Questions?

30 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 31 Recommendations Check consistency with more challenging stress gradients and weight functions Check the effects of an overloading – still consistent?


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