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

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

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

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)

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

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

Newman-Raju/Paris Estimate

where C, n, p, and q are fitting constants and 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 Using this because it is what was available; Closed form hard to get

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

(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

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

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

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

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

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

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

Typical Crack Shape Evolution

Geometry Comparison in NASGRO

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

Paris vs. NASGRO Example of inconsistency

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

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

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)

PPP Comparison for Different R Values

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

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)

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

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

Questions?

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)

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