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

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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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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)

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

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

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7 Newman-Raju/Paris Estimate n=3.75

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8 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

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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

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

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

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

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

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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

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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

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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

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17 Typical Crack Shape Evolution

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18 Geometry Comparison in NASGRO

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19 Width Effects Comparison in NASGRO

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20 Paris vs. NASGRO Example of inconsistency

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21 Sample PPP PPP

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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

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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)

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24 PPP Comparison for Different R Values

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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

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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)

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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

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

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29 Questions?

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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)

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

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