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**Crack Shape Evolution Studies with NASGRO 3.0**

Elizabeth Watts and Chris Wilson Mechanical Engineering Tennessee Tech University Cookeville, TN

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**Outline Problem Statement Background Analysis Approach Results**

Conclusions (Newman and Raju, NASA TR-1578)

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**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,

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

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**Newman-Raju/Paris Estimate**

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**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

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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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**(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

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

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**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

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

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**Geometries Flat Plates Cylinder Width = 6 in. Thickness = .5 in.**

Outer Diameter = 4 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 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

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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**

Less width effect for a/t<.4

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Paris vs. NASGRO Example of inconsistency

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

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**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

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**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)

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**PPP Comparison for Different R Values**

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**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

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**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)

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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?

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