Analysis of a Lap Joint Including Fastener Hole Residual Stress Effects

Analysis of a Lap Joint Including Fastener Hole Residual Stress Effects Guillaume Renaud, Gang Li, Guoqin Shi, Yan Bombardier, Min Liao Aerospace Portfolio AFGROW User Workshop 214, Layton, UT, September 9-1 214

Outline Introduction Fastener Hole Residual Stress Analysis Hole Cold Expansion Simulation Interference Fit Fastener Installation Simulation Riveting Simulation Example: Crack Growth in Riveted Lap Joint Finite Element Analysis (MSC Marc) Crack Growth Analysis (AFGROW) Probabilistic Analysis (CanGROW) Conclusion and Future Work 2

Hole Cold Expansion (Cx) Simulation 3D Simulations Using MSC Marc PCL: Parameterization, Automation Contact assumed between nosecap and sleeve, and between sleeve and hole bore Boundary conditions representative of FTI process Mandrel entrance side (FTI process) Multiple Cx hole interaction Mandrel Sleeve 3

Model Parameters 1. Plate geometry: Length: L Width: W Plate thickness, Tp Starting hole diameter: D Edge margins: e/d 2. Applied expansion: Cx range from 3 to 6% for aluminum and mild steels (8 ksi Fty max) Cx range from 4.5 to 6.7 % for titanium and high strength steels (24 ksi Fty max) 3. Mandrel shape: Length Slope Cross section shape 4. Sleeve configuration: Split orientation: 36 Gap size Sleeve thickness 5. Lubrication conditions (Friction) Friction model type Friction coefficient 6. Mesh density : Mesh density on plate Mesh density on sleeve 7. Process control Cold expansion process Mandrel contact release Sleeve contact release Sleeve removal Tension load 8. Result data implementation : Residual tangential stress curve on Entrance surface Residual tangential stress curve on middle line Residual tangential stress curve on Exit surface Residual tangential stress curve along plate thickness 4

Baseline Configuration Tool selected: 8--N from Table 4.1-1 in FTI process specification 811D, 22 Original hole dia.:.235 (5.969 mm) min,.238 (6.45 mm) max Mandrel diameter: Major: nom..23 (5.842 mm) Sleeve thickness:.8 (.232 mm) Plate geometry: Dimensions: Thickness:.25 (6.35 mm); Length: 5.51 (14 mm); Width: 2.56 (65 mm) Plate material: 224-T3 extrusion (MIL-HDBK-5H) E = 1.8x1 3 ksi (74.4 GPa); =.33 Fty = 4 ksi (275 MPa) Futs = 68 ksi (47MPa) Sleeve material: elastic steel E = 3.5x1 3 ksi (21 GPa); =.3 stress (Mpa) 5 4 3 2 1 AL 224-T3 extrusion Mandrel: rigid body..5.1.15 strain 5

Parametric Study Matrix 3D FE Models Sleeve split orientation, 45, 9, 135, 18 Sleeve thickness.6,.8,.12,.18 Plate thickness.63,.125,.25 Friction coefficient.1,.3,.5,.8 Baseline: Cx = 4.%, e/d = 2. Cx % = 1% x (Dm+ 2ts D hole) D hole e/d 3. 3.5 4. 4.68 5. x x x x 3. x 2. x x x x 1.75 x 1.5 x 1.2 x x x x.8 x x x x 6

Example of Hole Cx Residual Stress Results Entrance Middle Exit Wide edge Narrow edge 7 DIC FE Comparison

Edge Margin Study: Deformations bulging Cx =4.68%, e/d=.8 Cx =4.68%, e/d=1.2 Cx =4.68%, e/d=2. Cx =4.68%, e/d=5. 8

Edge Margin 3 Cx=4., Narrow edge Effects on hoop (tangential) stress after cold expansion (narrow edge) Compression at hole edge e/d compression at Entrance e/d tensile Tangential stress (MPa) 4 3 2 1-1 -2-3 -4-5 yield Cx=4., Narrow edge Cx=4.%, e/d=5., Middle Cx=4.%, e/d=2., Middle Cx=4.%, e/d=1.2, Middle Cx=4.%, e/d=.8, Middle -6 3 6 9 12 15 Distance from hole edge (mm) Tangential stress (MPa) Tangential stress (MPa) 2 1-1 -2-3 Cx=4.%, e/d=5., Entrance Cx=4.%, e/d=2., Entrance Cx=4.%, e/d=1.2, Entrance Cx=4.%, e/d=.8, Entrance -4 3 6 9 12 15 3 2 1-1 -2-3 -4 yield Distance from hole edge (mm) Cx=4., Narrow edge Cx=4.%, e/d=5., Exit Cx=4.%, e/d=2., Exit Cx=4.%, e/d=1.2, Exit Cx=4.%, e/d=.8, Exit -5 3 6 9 12 15 Distance from hole edge (mm) 9

Tangential stress (MPa) Tangential stress (MPa) Edge Margin Effects on hoop (tangential) stress under 1 MPa tension (narrow edge) Low stress at hole edge e/d tensile e/d compression at Entrance Without Cx Tangential stress (MPa) 4 3 2 1-1 -2-3 With & without Cx, tension, narrow edge yield Cx=4.%, e/d=5., tension, Middle Cx=4.%, e/d=2., tension, Middle Cx=4.%, e/d=1.2, tension, Middle Cx=4.%, e/d=.8, tension, Middle e/d=5., tension, Middle e/d=2., tension, Middle e/d=1.2, tension, Middle e/d=.8, tension, Middle 1 2 3 4 5 6 7 8 9 1 11 12 Distance from hole edge (mm) 4 3 With & without Cx, tension, narrow edge yield 4 3 With & without Cx, tension, narrow edge 2 2 1-1 -2-3 Cx=4.%, e/d=5., tension, Entrance Cx=4.%, e/d=2., tension, Entrance Cx=4.%, e/d=1.2, tension, Entrance Cx=4.%, e/d=.8, tension, Entrance e/d=5., tension, Entrance e/d=2., tension, Entrance e/d=1.2, tension, Entrance 1 2 3 4 5 6 7 8 9 1 11 12 Distance from hole edge (mm) 1-1 -2-3 Cx=4.%, e/d=5., tension, Exit Cx=4.%, e/d=2., tension, Exit Cx=4.%, e/d=1.2, tension, Exit Cx=4.%, e/d=.8, tension, Exit e/d=5., tension, Exit e/d=2., tension, Exit e/d=1.2, tension, Exit e/d=.8, tension, Exit 1 2 3 4 5 6 7 8 9 1 11 12 Distance from hole edge (mm) 1

Cx Level Effects on hoop (tangential) stress after cold expansion (narrow edge) Tangential stress (MPa) Compression at hole edge Cx tension Cx compression 3 2 1-1 -2-3 -4-5 -6 e/d=2., narrow edge Cx=4.68%, e/d=2., Middle Cx=4.%, e/d=2. Middle Cx=3.5%, e/d=2. Middle Cx=3.%, e/d=2. Middle 2 4 6 8 Distance from hole edge (mm) Tangential stress (MPa) Tangential stress (MPa) 2 15 1 5-5 -1-15 3 2 1-1 -2-3 -4 e/d=2., narrowedge Cx=4.68%, e/d=2., Entrance Cx=4.%, e/d=2., Entrance Cx=3.5%, e/d=2., Entrance Cx=3.%, e/d=2., Entrance 2 4 6 8 Distance from hole edge (mm) e/d=2., narrow edge Cx=4.68%, e/d=2., Exit Cx=4.%, e/d=2. Exit Cx=3.5%, e/d=2. Exit Cx=3.%, e/d=2. Exit -5 2 4 6 8 Distance from hole edge (mm) 11

Sleeve Split Orientation Effects on hoop (tangential) stress after cold expansion (narrow edge) Effect on Entrance side Tangential stress (MPa) 2 15 1 5-5 -1-15 -2-25 Cx=4., e/d=2., edge Cx=4.%, e/d=2., gap=, Entrance Cx=4.%, e/d=2., gap=45, Entrance Cx=4.%, e/d=2., gap=9, Entrance Cx=4.%, e/d=2., gap=135, Entrance Cx=4.%, e/d=2., gap=18, Entrance -3 2 4 6 8 1 Distance from hole edge (mm) Tangential stress (MPa) Cx=4., e/d=2., edge 2 1-1 Cx=4.%, e/d=2., gap=, Middle -2 Cx=4.%, e/d=2., gap=45, Middle -3 Cx=4.%, e/d=2., gap=9, Middle -4 Cx=4.%, e/d=2., gap=135, Middle -5 Cx=4.%, e/d=2., gap=18, Middle -6 2 4 6 8 1 Distance from hole edge (mm) Tangential stress (MPa) 2 1-1 -2-3 -4 Cx=4., e/d=2., edge Cx=4.%, e/d=2., gap=, Exit Cx=4.%, e/d=2., gap=45, Exit Cx=4.%, e/d=2., gap=9, Exit Cx=4.%, e/d=2., gap=135, Exit Cx=4.%, e/d=2., gap=18, Exit -5 2 4 6 8 1 Distance from hole edge (mm) 12

Sleeve Split Orientation Effects on hoop (tangential) stress after cold expansion (narrow edge) Effect on Entrance side Tangential stress (MPa) 2 15 1 5-5 -1-15 -2-25 Cx=4., e/d=2., edge Cx=4.%, e/d=2., gap=, Entrance Cx=4.%, e/d=2., gap=45, Entrance Cx=4.%, e/d=2., gap=9, Entrance Cx=4.%, e/d=2., gap=135, Entrance Cx=4.%, e/d=2., gap=18, Entrance -3 2 4 6 8 1 Distance from hole edge (mm) o 45 o 9 o 135 o 18 o 13

Friction (Lubrication) 2 Cx=4., e/d=2., edge Effects on hoop (tangential) stress after cold expansion (between sleeve and mandrel / sleeve and hole bore) (narrow edge) No significant effect Tangential stress (MPa) 15 1 5-5 -1-15 Cx=4.%, e/d=2., frc=.1, Entrance Cx=4.%, e/d=2., frc=.3, Entrance Cx=4.%, e/d=2., frc=.5, Entrance Cx=4.%, e/d=2., frc=.8, Entrance 2 4 6 8 1 Distance from hole edge (mm) Tangential stress (MPa) Cx=4., e/d=2.,, edge 2 1-1 -2-3 Cx=4.%, e/d=2., frc=.1, Middle Cx=4.%, e/d=2., frc=.3, Middle -4 Cx=4.%, e/d=2., frc=.5, Middle -5 Cx=4.%, e/d=2., frc=.8, Middle -6 2 4 6 8 1 Distance from hole edge (mm) Tangential stress (MPa) 2 1-1 -2-3 Cx=4., e/d=2., edge Cx=4.%, e/d=2., frc=.1, Exit Cx=4.%, e/d=2., frc=.3, Exit Cx=4.%, e/d=2., frc=.5, Exit -4 Cx=4.%, e/d=2., frc=.8,, Exit -5 2 4 6 8 1 Distance from hole edge (mm) 14

Sleeve Thickness Effects on hoop (tangential) stress after cold expansion (narrow edge) t compression at Entrance Tangential stress (MPa) 2 15 1 5 Cx=4., e/d=2., edge -5 Cx=4.%, e/d=2., ts=.6, Entrance -1 Cx=4.%, e/d=2., ts=.8, Entrance Cx=4.%, e/d=2., ts=.12, Entrance -15 Cx=4.%, e/d=2., ts=.18, Entrance -2 2 4 6 8 Distance from hole edge (mm) Cx=4., e/d=2.,, edge Cx=4., e/d=2., edge Tangential stress (MPa) 2 1-1 -2 Cx=4.%, e/d=2., ts=.6, Middle -3 Cx=4.%, e/d=2., ts=.8, Middle -4 Cx=4.%, e/d=2., ts=.12, Middle -5 Cx=4.%, e/d=2., ts=.18, Middle -6 2 4 6 8 Distance from hole edge (mm) Tangential stress (MPa) 3 2 1-1 -2 Cx=4.%, e/d=2., ts=.6, Exit Cx=4.%, e/d=2., ts=.8, Exit -3 Cx=4.%, e/d=2., ts=.12, Exit -4 Cx=4.%, e/d=2., ts=.18, Exit -5 2 4 6 8 Distance from hole edge (mm) 15

Strain (mm/mm) Comparison with Analytical Solutions and Digital Image Correlation (DIC) Test Strain Measurements.6 4--N, No ream.6 4-4-N, No ream.4.4.2.2 Strain (mm/mm) 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. -.2 -.4 -.6 ε_r_ana ε_θ_ana -.8 ε_r_exp ε_θ_exp ε_r_entry_fea ε_θ_entry_fea -.1 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. -.2 -.4 -.6 ε_r_ana ε_θ_ana -.8 ε_r_(exp) ε_θ_(exp) -.1 ε_r_entry_fea ε_θ_entry_fea -.12 r/a (mm/mm) -.12 r/a (mm/mm) 16

Strain (mm/mm) Comparison with Analytical Solutions and Digital Image Correlation (DIC) Test Strain Measurements.4 8-1-N, No ream.4 1--N, No ream.2.2 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. -.2 -.4 -.6 ε_r_ana ε_θ_ana ε_r_(exp) ε_θ_(exp) -.8 ε_r_entry_fea ε_θ_entry_fea Strain (mm/mm) 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. -.2 -.4 -.6 ε_r_ana ε_θ_ana ε_r_(exp) ε_θ_(exp) -.8 ε_r_entry_fea ε_θ_entry_fea -.1 r/a (mm/mm) -.1 r/a (mm/mm) 17

Brief Summary from parametric Study Low edge margins can lead to high deformation and high edge tension Entrance side displayed the most variability and least amount of Cx benefit Middle displayed most consistency and greatest amount of Cx benefit Cx technology shows clear benefits; however, there are obvious limitations for low edge margins 18

Residual Stresses Induced by Hole Cx Process Observations from FE Simulations: Uniform radial expansion resulted in higher compressive radial and hoop stresses A considerable through-the-thickness radial and hoop stress variation was observed Compressive hoop residual stresses are larger at the exit face than at the entrance face, which contains the smallest compressive (or even tensile ) hoop residual stresses Fatigue tests show that early crack nucleation and growth tend to occur primarily and more extensively at the mendrel entrance face 19

Interference Fit Fastener Modeling Hi-Lok fastener HL5-8-6 with HL9-8A collar 1- Insert fastener / hold disk 2- Release pusher 2- Apply pre-tension (torque) to fastener / collar Parametric study: Hole diameters (interference fits) 775-T651 plate No load transfer Edge margins Fastener Disk Collar 2

Interference Fit Fastener Modeling e/d = 2. e/d = 1.5 e/d = 1.2 e/d = 1. e/d =.8 21

Summary of Interference Fit Fastener Modeling Properly installed Hi-Lok fasteners will reduce the stress concentration effect at the hole edge by their clamping force and move the largest stressed areas from the surfaces to the mid-plane. A.35 induced interference fit was the best of the four values investigated (,.1,.35,.5 ) Effect of the low edge margin e/d was significant. At a e/d value less than 1.2, a highly localized tensile stress occurred in the remaining ligament, independent of the degree of interference fit 22

Riveting Simulation Countersunk fastener 1- Squeeze fastener 2- Release pusher Parametric study: Hole diameters (clearance) Squeeze displacement (head deformation) Def 1 Def 2 Size 1 Size 2 Size 3 (largest clearance) 23

Hoop stress (MPa) Riveting Simulation General Observations on Residual Stress Smaller diameters / Larger deformation resulted in compression at hole edge Larger compression is balanced by larger tension, at a larger distance from the hole Results agreed well with Neutron Diffraction measurements 15 1 5-5 -1 2 25 3 35 4 Transverse path position (mm) h Size1 Def1 Size 2 Def 1 Size 3 Def 1 Size1 Def2 Size 2 Def 2 Size 3 Def 2 Post-Riveting Residual Stress 24

Example: Crack Growth in Riveted Lap Joint Typical Lap Joint Geometry representative of a fuselage panel Three rows of countersunk rivets Analysis Objective Calculate life to first link-up distribution 25

Analysis Strategy Stress and Residual Stress Profiles Riveting simulation (MSC Marc) Crack Growth Analysis Countersunk geometry correction factor Riveting residual stress correction factor Spectrum modification based on tip position Residual stress correction factor AFGROW AFGROW AFGROW Monte Carlo Simulations (CanGROW) EIFS distribution calculation Life distribution calculation (to first link-up) 26

Riveting Simulation Global Model Shell model Displacements from applied loads Local Model Central region / Nine rivets 3D model / Multi-Step Analysis Riveting simulation Squeeze, release Cyclic loading 1 or 3 rivets 27

Finite Element Analysis Input Parameters Several hole diameters from specifications Squeeze displacement derived from test measurements Material properties from published data Model validated with strain survey 28

Hoop stress (MPa) Finite Element Analysis Local Model Analysis Results Post-riveting stress No load Stress under applied loads Max, min Open hole stress Max, min Include nonlinear effects: Material Geometry Contact 25 2 15 1 5 2 25 3 35 4-5 Hole Transverse path position (mm) Residual Max Min Open hole Max Size 3 Def 2 (low compression at hole edge) Open hole Min 29

Beta Solution Riveting Residual Stress CanGROW: Does not have CSK model or residual stress capabilities yet Approach: Convert AFGROW s results to a Beta correction for constant amplitude loading (compounded with MSD factors) AFGROW: Approach 1: AFGROW CSK model Residual Stress option not available for CSK model Modify spectrum based on tip position (FE min and max stress) Approach 2: AFGROW Straight Hole Model Convert CSK Model to a Beta table Add post-riveting residual stress from FE 3

c (m) Beta Correction for CSK Geometry Countersunk Hole Solution Uses AFGROW s solution in CanGROW (through crack) Correction Factor (CF) = c_afgrow / c_cangrow 2.5 1.E-2 2 Correction Factor CSK 8.E-3 CSK AFGROW CanGROW Through 1.5 6.E-3 Mod CanGROW c 1 4.E-3.5 Thickness Initiation 1% Thickness.E+.2.4.6.8.1 c (m) Correction Factor 2.E-3 1 2 3 4 Cycles Crack Growth 31

SMF (MPa) Stress Ratio Approach 1: AFGROW CSK Model Calculate SMF and R based on tip position Use FE min and max stress in AFGROW Calculated using FE open CSK hole model Incremental growth (VBA Program / COM interface) 16.4 14 12 1 Original SMF Modified SMF.3.2 Original R Modified R 8.1 6 4 2 -.1.2.4.6.8.1.2.4.6.8.1 c (m) -.2 Size 3 Def 2 (low compression at hole edge) c (m) 32

Approach 2: AFGROW Straight Hole Model Manual CSK Beta correction Residual stresses curve from FE Constant D is assumed 2.5 2.5 2 AFGROW Straight Hole - Through Crack AFGROW CSK Extracted points AFGROW output (verification) 2 c direction a direction 1.5 1.5 1 1.5.5.2.4.6.8.1 c (m) Size 3 Def 2 (low compression at hole edge).2.4.6.8.1 a, c (m) 33

Beta Solutions 2.5 2 CSK Hole - AFGROW Auto CSK Hole - AFGROW Step-By-Step + Through CSK Hole + Res Stress - Approach 1 CSK Hole + Res Stress - Approach 2 2.5 2 Correction Factor CSK CSK + Res. Stress - Approach 1 1.5 1.5 CSK + Res. Stress - Approach 2 c c 1 1.5 Thickness "Initiation" (.5 mm) 1% Thickness.2.4.6.8.1 c (m).5 Thickness "Initiation" (.5 mm) 1% Thickness.2.4.6.8.1 c (m) Beta curve (AFGROW) CanGROW Correction Factor Size 3 Def 2 (low compression at hole edge) 34

Crack Growth Approach 2 more severe than Approach 1 D assumed constant in Approach 2 Nonlinearities in FE results 35 Size 3 Def 2 (low compression at hole edge)

Probabilistic Analysis Life to first link-up Option 1: Probabilistic initiation life (strain life using FE results) + Crack Growth Option 2: EIFS distribution based on in-service findings (including censored data) Crack Growth only CanGROW MSD analysis (crack interaction) Monte Carlo simulation life distribution (POF) CanGROW 36

Conclusion An overview of NRC s work on the calculation of residual stresses using 3D finite element modeling was presented These simulations replicate as closely as possible the actual processes by using 3D multi-step nonlinear analysis Hole cold expansion; Interference fit fastener installation; Riveting 3D and through-the-thickness effects were shown to be significant An example was presented, where life to first-linkup is to be calculated for a lap joint, using a series of three software tools: MSC Marc to calculate post-riveting residual stresses AFGROW to build a Beta factor for CSK geometry and FE stresses CanGROW to perform MSD Monte Carlo simulations 37

Possible Future Work Possible verification and improvement steps: Use StressCheck to develop Beta factors that includes the hole geometry and service and/or residual stresses determined by Cx or riveting simulation Additional test validation using digital image correlation, X-ray diffraction, contour method, etc. 38

Thank you Guillaume Renaud Research Officer Tel: 613-99-476 Guillaume.Renaud@nrc-cnrc.gc.ca www.nrc-cnrc.gc.ca 39