Newman-Raju Limits Study Exceeding Thickness to Diameter Upper Bound Chad King Robert Pilarczyk James Gyllenskog Joshua Hodges
Issue Approach Overview Finite Element Analysis Solution AFGROW Solution (Implementation) Centered Hole (Newman-Raju) Comparison Offset Hole Comparison Conclusions 2
Issue AFGROW Classic Model, Single Corner Crack at Hole, uses the Newman-Raju Solutions Thru Crack at Hole Solution is not Newman-Raju Newman-Raju Solutions FEA solutions for a wide range of several parameters Fit equations to FEA solutions; e.g. Reference: Newman, J.C., and Raju, I.S., "Stress Intensity Factor Equations for Cracks in Three- Dimensional Bodies Subjected to Tension and Bending Loads," Chapter 9, Computational Methods in the Mechanics of Fracture, Elsvier Science Publishers B.V., 1986 3
Issue (con t) Newman-Raju (N-R) FEA Limits Parameter Lower Bound Upper Bound ϕ 0.0 π/2 a/t 1.0 a/c 0.2 2.0 r/t 0.5 2.0 (r+c)/b 0.5 r/t > 0.5 t/d < 1 Bounds can be exceeded in AFGROW What is the impact on the solution when t/d > 1? 4
Hole Bore Assumptions Approach Corner Crack Solutions Only Crack Aspect Ratio a/c = 1 Tensile Loading Only Angles Surface ϕ K c at 5 K a at 80 Compare FEA Solution and Classic Solution Beta Factors and Crack Growth Life 5
Approach (con t) Matrix of Parameters Analyzed Selection Made Based on Actual FCLs Case Thickness (t, [in]) Diameter (D, [in]) t/d Crack Length (a, c [in]) 1 0.580 0.190 3.05 0.05 to 0.550 2 0.600 0.250 2.40 0.005 to 0.570 3 0.520 0.250 2.08 0.005 to 0.500 4 0.498 0.276 1.80 0.005 to 0.473 5 0.596 0.375 1.59 0.005 to 0.575 6 0.428 0.276 1.55 0.005 to 0.405 7 0.345 0.276 1.25 0.005 to 0.328 8 0.200 0.197 1.02 0.005 to 0.190 9 0.248 0.276 0.90 0.005 to 0.235 6
Finite Element Analysis Corner Crack at Hole in Plate, Tension Load Symmetric Model W=10 Idealized t a L=10 c D Plane of Symmetry 7
FEA (con t) StressCheck Software Used Mesh ~5000 Tetrahedral Elements per FEM 3 Layer Refinement at Crack Front 8
K1 [psi root (in)] FEA (con t) Boundary Conditions P-Level = 4, Convergence of <1% Result = Stress Intensity Factor 6000 ϕ Unconstrained Surface (Crack Face) 5500 A-direction 5000 C-direction 4500 4000 Symmetry Constraint 3500 3000 0 10 20 30 40 50 60 70 80 90 ϕ (degrees) 9
AFGROW Solution AFGROW Implementation Includes Many Factors AFGROW N R F w F offset β N R = Beta Factor, Newman-Raju Solution F w = Width Correction Factor F offset = Hole Offset Correction Factor 10
Beta Factor Centered Hole Typical Beta Factor Comparison 2.5 2.0 1.5 (t/d = 2.40, t = 0.600", D = 0.250") SC Results, c SC Results, a N-R Results, c N-R Results, a -direction -direction -direction -direction 1.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Crack Length / Thickness 11
C-Direction Crack Length Centered Hole Typical Crack Growth Life Comparison (t/d = 2.40, t = 0.600", D = 0.250") SC Results N-R Solution 17% Crack Growth Life 12
Relative Error (+) Error = N-R is conservative ( ) Error = N-R is unconservative Error N R SC SC 100 Error Life Life SC Life Life SC N R 100 13
% Relative Error in Beta Factor Centered Hole Beta Factor 14% 12% 10% 8% 6% 4% 2% % Relative Error in Beta Factor C-Direction t/d = 3.05 t/d = 2.40 t/d = 2.08 t/d = 1.80 t/d = 1.59 t/d = 1.55 t/d = 1.25 t/d = 1.02 t/d = 0.90 0% -2% -4% 0.0 0.2 0.4 0.6 0.8 1.0 Crack Length / Thickness 14
% Relative Error in Beta Factor Centered Hole Beta Factor 14% 12% 10% 8% 6% % Relative Error in Beta Factor C-Direction t/d = 3.05 t/d = 2.40 t/d = 2.08 t/d = 1.25 t/d = 1.02 4% 2% 0% -2% -4% 0.0 0.2 0.4 0.6 0.8 1.0 Crack Length / Thickness 15
% Relative Error in Crack Growth Life Centered Hole Life 20% % Relative Error in Crack Growth Life 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% t/d Upper Bound Exceeded 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 t/d 16
% Relative Error in Crack Growth Life Centered Hole Life 20% % Relative Error in Crack Growth Life 18% 16% 14% 12% 10% 8% 6% 4% 2% IFS = 0.005" IFS = 0.05" t/d Upper Bound Exceeded 0% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 t/d 17
Centered Hole Exceeding Newman-Raju t/d Upper Limit? < 20% Error in Life Conservative for Cases Investigated Conclusion Not Critical Issue 18
Offset Hole More Direct Comparison to Actual Application Involves all beta factor components AFGROW N R F w F offset Used Model Width 19
Offset Hole Matrix of Parameters Analyzed Added Case Thickness (t, [in]) Diameter (D, [in]) t/d Offset (B, [in]) Crack Length (a, c [in]) 1 0.580 0.190 3.05 N/A 0.050 to 0.550 2 0.600 0.250 2.40 0.60 0.005 to 0.570 3 0.520 0.250 2.08 1.70 0.005 to 0.500 4 0.498 0.276 1.80 0.92 0.005 to 0.473 5 0.596 0.375 1.59 1.58 0.005 to 0.575 6 0.428 0.276 1.55 1.15 0.005 to 0.405 7 0.345 0.276 1.25 1.15 0.005 to 0.328 8 0.200 0.197 1.02 0.50 0.005 to 0.190 9 0.248 0.276 0.90 1.58 0.005 to 0.235 10 0.143 0.276 0.52 0.97 0.005 to 0.135 20
% Relative Error in Beta Factor Offset Hole Beta Factor 15% % Relative Error in Beta Factor C-Direction 10% 5% 0% -5% -10% -15% -20% -25% t/d = 3.05 t/d = 2.40 t/d = 2.08 t/d = 1.80 t/d = 1.59 t/d = 1.25 t/d = 1.02 t/d = 0.90 t/d = 0.51-30% 0.0 0.2 0.4 0.6 0.8 1.0 Crack Length / Thickness 21
% Relative Error in Beta Factor Offset Hole Beta Factor 15% 10% 5% 0% % Relative Error in Beta Factor C-Direction t/d = 0.52 is unconservative -5% -10% -15% -20% -25% t/d = 2.40, t = 0.60, B = 0.60 t/d = 1.02, t = 0.20, B = 0.50 t/d = 0.52, t = 0.143, B = 0.97 Short Edge Distance Offset Correction Comes into Play -30% 0.0 0.2 0.4 0.6 0.8 1.0 Crack Length / Thickness 22
% Relative Error in Crack Growth Life Offset Hole Life 20% % Relative Error in Crack Growth Life (Corner Crack Growth Only) 15% 10% 5% 0% -5% -10% t/d Upper Bound Exceeded 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 t/d 23
Conclusions Exceeding Newman-Raju t/d Upper Limit? Conclusion Not Critical Issue for A-10, T-38 Further Work AFGROW Advanced Solutions a/t lower bound was exceeded for most cases selected Angles will be slightly different Thru-Crack Solution Exceeding any bounds for this solution? 24