Stress Intensity Factors for Finite Width Plates

Transcription

1 Stress Intensity Factors for Finite Width Plates 10 September 2013 AFGROW Workshop 2013 US Air Force Academy CAStLE Matthew Hammond * Scott Fawaz * James Greer, Technical Director, CAStLE ** *SAFE Inc. **Presenter The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official polices and endorsements, either expressed or implied of the US Air Force Academy or the US Government. Approved for public release, distribution is unlimited. USAFA-DF-PA

2 Acknowledgements Mr. Dan Dunmire, Director, OSD-CPO Mr. Rich Hays, Deputy Director, OSD-CPO Dr. Greg Shoales, Director, CAStLE, USAFA This material is based on research sponsored by the US Air Force Academy under agreement number FA The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon 2

3 Background Current stress intensity factor solutions (K) for corner cracks in narrow finite width plates are inaccurate Can improve correlation of predicted vs. measured Crack shapes Crack growth lives Extrapolating to small plate width / hole diameter (W/D) ratios is inaccurate Newly calculated finite width Ks for corner cracks at holes in narrow plates will reduce the uncertainty in inspection intervals and life limits 3

4 Original Motivation K final = 10~15 MPa m K initial = ~3 MPa m 4

5 Experimental Results Final Crack Predictions not perfect Improve K solution Improve da/dn input data Using R = 0.65 data Tests are constant amplitude + marker banding Periphery Crack Under-predicting crack size Under-predicting K AFGROW predicited crack evolution vs observed aspect ratios Error 10% Advanced 2point model Hypothesis - If crack shape predictions are good, crack length predictions are too aspect ratio, a/c measured pit 6* 10* 6# Predicted a/c is too large Predicted c-tip K is too small a (mm) 5

6 Does 10% Error in K Matter? % 47% Crack Length (in.) ksi 11 ksi 15 ksi 16.5 ksi Material 2024 T3 Bare Sheet Loading Tension, Constant Amplitude Geometry W = 1.0" W / D 5 T= 0.125" D = , , , , , , ,000 Cycles 6

7 K Calculation Error Sources Interpolation within the K solution space Mitigation dense solution space Extrapolation outside the K solution space Mitigation plate and crack geometry ranges cover expected aircraft structural cracking scenarios FEM Discretization Mitigation Convergence study numerically converged solutions Mesh density study adequate representation of vertex Degrees of freedom 150K 2.4M 7

8 Analysis Process Geometry & Crack Definition MATLAB TrueGrid Input File TrueGrid Mesh Generation NASTRAN Neutral File Translator NASTRAN Neutral File to ZIP3D ZIP3D 3D FEA Post Processor Calculate K using VCCT PC HPC PC or HPC Implement in AFGROW 8

9 Solution Space Single corner crack at a centrally located hole in a plate of varying width new finite width correction factor Three load types are considered Remote Tension Remote Bending Pin Loading P*cos 2 (θ) 9

10 Solution Space - Crack Geometry a/t ϵ [0.01, 0.99] a/t = [0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99] a/c ϵ [0.1, 10] a c = [0.1, 0.111, 0.125, , , 0.2, 0.25, 0.333, 0.5, 0.667, 0.75, 0.8, 1, 1.25, 1.333, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10] 10

11 Solution Space - Plate Geometry L/W = 2 (fixed) Eliminate finite height effect W/D ϵ [1.1, 20] W/D = [1.1, 1.25, 1.5, 1.667, 2, 3, 4, 10, 20*] * Large W/D ratio used for comparison to existing AFGROW solutions 11

12 Solution Space - Plate Geometry r/t ϵ [0.1, 10] r/t = [0.1, 0.111, 0.125, , , 0.2, 0.25, 0.333, 0.5, 0.667, 0.75, 0.8, , 1, 1.25, 1.333, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10] 12

13 FE Automatic Mesh Generation Crack Plane w/ Auto-Mesh Crack Front w/ Auto-Mesh L t r W/2 Crack Front 13

14 Stress Intensity Factor at Vertex 14

15 FEA Convergence C-tip A-tip 15

16 Verification / Correlation 16

17 Finite Width Effect: a/c = 2 Compare well with wide plates, differences with narrow plates 17

18 Finite Width Effect: a/c = 1 Compare well with wide plates, differences with narrow plates 18

19 Interpolated Solution Space 19

20 Beta-A Table for AFGROW 20

21 Gulfstream G4 So What? - Real World Significant Corrosion Lower Wing Panel & Stringers (Both Wings) 21

22 Repair Scheme Stringer Splices Lower Panel Doublers 22

23 Stringer Splice Example Parameters Cross-Sectional Geometry T = 0.125in W = 0.750in D in (#6 Hi-Lok) R/T = 0.75 W/D = 4 e/d =

24 SIF Solutions 24

25 Stringer Splice DTA No significant changes at: a/c = 1 and W/D 4 25

26 Stringer Splice Example - O/S Parameters Cross-Sectional Geometry T = 0.125in W = 0.750in D 0.250in (#8 Hi-Lok) R/T = 1.0 W/D = 3 e/d =

27 SIF Solutions O/S 27

28 Stringer Splice DTA - O/S 12% Life Reduction Finite Width effect appears at: a/c = 1 and W/D = 3 28

29 Parameters T = 3.2mm W = 10mm D = 6mm Lab Corrosion Specimen R/T 0.94 W/D 1.66 e/d

30 Corrosion Specimen - DTA 60% Life Reduction 51% Life Reduction Naturally evolving aspect ratio a/c constant 30

31 Conclusions Automated mesh generation Reduces FE discretization error Aids in K error control Simplifies additional geometry cases if increased fidelity is needed to reduce K interpolation error Automated run-stream Reduced user input Robust data management 31

32 Conclusions Initial results indicate that part-through crack finite width corrections can be improved Improvement relevant to any life prediction code using the Newman/Raju corner crack K solutions Finite width correction factor is embedded in these solutions Significant differences in Ks for (>> 12%, Life hit): Smaller r/t (thick plates & small holes) Naturally evolving a/c ratios (a/c constant) Naturally evolving crack aspect ratios capture the physics of the problem more accurately 32

33 Questions? 33