Minimum Bondline Length Study

Minimum Bondline Length Study
22-24 August 2017, Hill AFB DoD Advanced Composite Maintainers Technical Interchange Meeting Alexandru Popescu Aerospace Engineer (619) NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

NAVAIR Public Release 17-0008
Summary Motivation Review of “Introduction to Adhesive Bonding,” by Pierre Cyr, L-3 MAS (09 June 2010) 6/β Bondline Length Input Trends A4EI Doubler vs. Lap Method: Doubler Breakdown A4EI Doubler Forcing Zero Shear Stress NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Motivation Speed brake well repair patches required relatively short bondline. A4EI breakdown with short bondline observed. “Preferred minimum patch overlap is 1.50 inches” according to the BJAM manual (pg Revision Date: 25 September 2015) Why 1.5 in.? Can smaller patch overlap be safely utilized? Can A4EI analyze smaller bondlines? Is there an explanation for the shear stress mismatch at joint center? NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Impact on Repairability
Reducing the patch overlap length may be necessary in order to satisfy repair parameters, including geometric restrictions Providing a check for bondline lengths less than 1.25 in. means that parts that previously may have been unrepairable can now be analyzed and possibly repaired, reducing scrap rates NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

“Introduction to Adhesive Bonding” by Pierre Cyr, L-3 MAS
Derivation of β2: Volkersen model shear strain: 𝛾 𝑎 = 𝑢 𝑜 − 𝑢 𝑖 η and 𝜏 𝑎 = 𝐺 𝑎 𝛾 𝑎 = 𝑑𝑁 𝑜 𝑑𝑥 = − 𝑑𝑁 𝑖 𝑑𝑥 so 𝜏 𝑎 = 𝐺 𝑎 η 𝑢 𝑜 − 𝑢 𝑖 Now differentiate with respect to x, knowing 𝑑 𝑢 𝑜 𝑑𝑥 = 𝜀 𝑥𝑜 = 𝜎 𝑜 𝐸 𝑜 = 𝑁 𝑜 𝐸 𝑜 𝑡 𝑜 and likewise for 𝑑 𝑢 𝑖 𝑑𝑥 resulting in 𝑑𝜏 𝑎 𝑑𝑥 = 𝐺 𝑎 η 𝑁 𝑜 𝐸 𝑜 𝑡 𝑜 − 𝑁 𝑖 𝐸 𝑖 𝑡 𝑖 Now use first definition of 𝜏 𝑎 and equilibrium equations to find: 𝑑 2 𝜏 𝑎 𝑑𝑥 2 = 𝛽 2 𝜏 𝑎 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 (Cyr Eq. 8) Cyr Fig. 4 (Hart-Smith) Cyr Fig. 5 NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

“Introduction to Adhesive Bonding”, cont.
Maximum elastic load that can be transferred between adherends was defined in Cyr’s document as: 𝐹 𝑒 = 0 ∞ 𝜏 𝑝 𝑒 −𝛽𝑥 𝑑𝑥 = 𝜏 𝑝 β (Cyr Eq. 17) With the length, L, required for 95% load transfer: 𝐹 95% = 0 𝐿 𝜏 𝑝 𝑒 −𝛽𝑥 𝑑𝑥 = 𝜏 𝑝 1− 𝑒 −𝛽𝐿 β = 0.95 𝜏 𝑝 β (Cyr Eq. 18) 1− 𝑒 −𝛽𝐿 =0.95→ 𝑒 −𝛽𝐿 =0.05 (Cyr Eq. 19) 𝐿= −ln0.05 β ≈ 3 𝛽 (Cyr Eq. 20) for each end of the single lap bond (6/β total) Cyr Fig. 8 Stress profile: 𝜏=𝜏 𝑝 𝑒 −𝛽𝑥 NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Elastic region (slope) moves inward as the applied load increases. Plasticity begins at joint ends. Elastic region has fixed length until the regions begin to overlap as severe plasticity occurs. Central portion of joint can have zero shear stress. Dr. Kim at UCSD discusses in his SE 171 course. Cyr Fig. 9 NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Further information can be found online in several recorded lectures from Dr. Kim’s SE 171 course from UCSD (Winter 2017) 27 Feb 17 01 Mar 17 NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 A4EI.pdf gives a hint at the reason for this overlap length that “Care and Repair of Advanced Composites,” by Armstrong also states on pg. 568: “…provide a bond overlap length that provides both the load requirements…and contains an elastic trough large enough to defend against the negative effects of creep and bond defects…” A4EI.pdf Fig. 3-2 6/β is completely independent of joint loading. It is solely dependent on adhesive and adherend material properties and thicknesses NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Maximum elastic strength (with thermal consideration): 𝑃 𝑒 𝑇 = 𝜏 𝑝 β 1+ 𝐸 1 𝑡 1 𝐸 2 𝑡 2 + 𝐸 1 𝑡 1 𝛼 2 − 𝛼 1 ∆𝑇 (Cyr Eq. 27). Swap subscripts for adherend 2. Lower of the two is the maximum elastic joint strength. Elastic-plastic strength (with thermal consideration): 𝑃 𝑝 𝑇 = 2η 𝐸 1 𝑡 1 1+ 𝐸 1 𝑡 1 𝐸 2 𝑡 2 𝜏 𝑝 𝛾 𝑒 2 + 𝛾 𝑝 1/2 + 𝐸 1 𝑡 1 𝛼 2 − 𝛼 1 ∆𝑇 (Cyr Eq. 53). Swap subscripts for adherend 2. Lower of the two is the maximum elastic-plastic joint strength. Elastic-plastic load transfer length (includes elastic overlap length). Is dependent on the applied load, P: 𝐿 𝑜𝑣𝑒𝑟𝑙𝑎𝑝 = 𝑃 𝜏 𝑝 + 4 𝛽 (Cyr Eq. 64) Plasticity Check: 𝑃> 2 𝜏 𝑝 𝛽 (Cyr Eq. 68). Rough approximation of when plasticity can be expected in the joint. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Conclusions & Recommendations: 6/β bondline length for elastic load transfer is intended to improve fatigue resistance and damage tolerance. Good starting point for determining alternative bondline length. Could be problematic if this bondline check recommends a length shorter than the BJAM manual recommended 1.5 in. Provides some insight as to how A4EI calculates joint strength. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

6/β Bondline Length Input Trends
𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 Goal is to study bondline length trend for different patch-skin combinations and adhesive inputs. Chose skin-patch configuration for four adhesives (EA9394 (5 day, 4 hr, 1 hr), and FM300-2 (2 hr)) then performed the following analyses: Changing Skin Thickness: 12-ply AF/ 9-ply RB 12-ply AF/ 8-ply RB 16-ply AF/ 3-ply RB 14-ply AF/ 3-ply RB 12-ply AF/ 3-ply RB 10-ply AF/ 3-ply RB 8-ply AF/ 3-ply RB 6-ply AF/ 3-ply RB 4-ply AF/ 3-ply RB Changing Patch Thickness: 12-ply AF/ 7-ply RB 12-ply AF/ 6-ply RB 12-ply AF/ 5-ply RB 12-ply AF/ 4-ply RB Variable Studied: Thickness Ratio Stiffness Ratio Parenthesis Value NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

6/β Bondline Length Input Trends, cont.
𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 Varied adherend thickness ratio (by changing skin thickness, patch thickness) Conclusion: No observable trend due to stiffness summation. FM300-2 requires larger bondline length. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 Varied adherend stiffness ratio (by changing skin thickness, patch thickness) Conclusion: No observable trend due to stiffness summation. FM300-2 requires larger bondline length. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 Varied “parenthesis value” (by changing skin thickness, patch thickness) Conclusion: No observable trend due to stiffness summation. FM300-2 requires larger bondline length. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 Conclusions & Recommendations: We cannot predict the bondline length for elastic load transfer from just the skin-patch stiffness ratios or any of the ratios I analyzed. -The individual adherend stiffnesses are required This means that we have to calculate this bondline length for each proposed repair. However, A4EI has been observed to exhibit a breakdown at short bondline lengths. Several examples have been studied to determine if this event happens below certain bondline lengths NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline
A4EI has been observed to exhibit a breakdown at short bondline lengths. Several examples have been studied to determine if this event happens below certain bondline lengths. Performed a study with an example from DED-F with Nxy’ RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond). Studied all 4 adhesives in A4EI: 0.6 in. AFM Cyr 6/β bondline length: in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.6 in. AFM AFM Greater than 1% difference between Doubler and Lap methods Cyr 6/β bondline length: in. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.6 in. CFM CFM Greater than 1% difference between Doubler and Lap methods CFM Cyr 6/β bondline length: in. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.8 in. AFM Cyr 6/β bondline length: 1.05 in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.8 in. CFM Cyr 6/β bondline length: 1.05 in. Greater than 1% difference between Doubler and Lap methods NOTE: Elastic-Plastic is N/A for this CFM case NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 1.2 in. AFM = CFM Cyr 6/β bondline length: in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 1.6 in. AFM Cyr 6/β bondline length: in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Example from A4EI.pdf pg Reduced the bondline and recorded the elastic and potential strengths calculated by A4EI for both the doubler and lap methods: Cyr 6/β bondline length: 1.39 in. 1.5 in. 1.2 in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Example from A4EI.pdf pg. 172 with adherend thicknesses reduced to 0.046”. Reduced the bondline and recorded the elastic and potential strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): Cyr 6/β bondline length: 1.19 in. 1.3 in. 1.0 in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example H-stab patch-skin combination with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): 0.7 in. AFM Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example H-stab patch-skin combination with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): CFM 0.7 in. Greater than 1% difference between Doubler and Lap methods NOTE: Elastic-Plastic is N/A for this CFM case NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example speed brake well repair patch with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): 0.5 in. AFM Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example speed brake well repair patch with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): 0.5 in. CFM Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline: Data Summary
Example L_6/β, in. Bondline Length at 1% deviation, in. % Deviation at 1.25 in. Bondline Length DED-F RTD AFM with EA day cure cycle 0.805 0.6 0.01 DED-F RTD CFM with all EA9394 cure cycle DED-F RTD AFM with EA & 4 cure cycles 0.02 DED-F RTD AFM with FM hr cure cycle 1.054 0.8 0.09 DED-F RTD CFM with FM hr cure cycle DED-F ETW with EA day cure cycle 1.554 1.2 0.85 DED-F ETW AFM with FM hr cure cycle 2.059 1.6 2.91 DED-F CTD AFM with EA day cure cycle 0.701 0.55 0.00 A4EI Stepped-Lap Joint Analysis PDF pg.172 1.388 0.93 A4EI Stepped-Lap Joint Analysis PDF pg.172 Modified 1.186 1.0 0.37 H-stab RTD AFM with FM hr cure cycle 0.896 0.7 0.04 H-stab RTD CFM with FM hr cure cycle Speed Brake Well RTD AFM with EA day cure cycle 0.646 0.5 Speed Brake Well RTD CFM with EA day cure cycle NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline: Discussion and Thoughts The BJAM 1.5 in. preferred minimum patch overlap may be due to this A4EI limitation. For all but one example, the 1 % deviation between the doubler and lap methods happened at less than 1.25 in. Furthermore, even at 1.25 in., only one example had greater than a 1% deviation Because the A4EI Doubler method calculates either EOH or EOP depending on the patch-skin selection, the output may display the non-critical end of the joint. This shortcoming is resolved by switching the patch-skin configurations We have seen evidence that a relatively short bondline yields inaccurate results with AFM (EOH) properties. When Doubler and Lap methods in A4EI diverge, the Doubler results become invalid as evidenced by increasing strength with shorter bond length. We lose our ability to differentiate between CFM and AFM because Doubler method can model both CFM and AFM if patch-skin configuration is swapped, while Lap shows the worst-case NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler Forcing Zero Shear Stress
Cyr pg. 7: “In an ordinary lap joint, the boundary conditions are hard to find. Numerical methods may be used to solve this equation for finite joints or joints that do not have a constant geometry (the A4EI software uses this technique). Fortunately, the following boundary condition exists in the case of an infinite doubler”: 𝜏= 𝐾 1 𝑒 −𝛽𝑥 + 𝐾 2 𝑒 𝛽𝑥 lim 𝑥→∞ 𝜏 =0→ 𝐾 2 =0 𝜏 0 = 𝜏 𝑝 →𝐾 1 = 𝜏 𝑝 𝜏= 𝜏 𝑝 𝑒 −𝛽𝑥 (Cyr Eq ) These two boundary conditions are commonly used NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Discussion & Thoughts 𝐿= 6 𝛽 with 𝛽 2 = 𝐺 𝐴 η 1 𝐸 1 𝑡 𝐸 2 𝑡 2 Will CFM have a different bondline length according to 6/β elastic load transfer length? CFM will have same bondline length because the formula does not consider How do we account for a discontinuity in shear stresses mismatching at the joint center when we have CFM and AFM adhesive properties? True solution would be to model the z-axis stresses and failure mode limited by adherend surface ply failure (due to peel stresses). This was the motivation behind studying Cyr’s paper and 6/β bondline length. Some non-A4EI investigation since CFM properties apply to half of the joint may be useful stop-gap solution until advanced modeling that accounts for peel stresses. Possible future investigation: Can they be equal and not equal to zero? It seems like the A4EI doubler method forces them to be equal by assuming the shear stress goes to zero near the joint center as a boundary condition. 𝜏 𝑚𝑎𝑥 NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Other Strategies Wung, E. C., and O’Callaghan, P. J., “Adhesively Bonded Composite Doubler Loaded by Remote In-Plane Loads,” CAMX, NG , May 2016. Solution presented for in-plane loading is superposition of Volkersen/Hart-Smith for bi-axial, Levy for shear loading Employs trigonometric series from Timoshenko to approximate shear stress Wung, E. C., and O’Callaghan, P. J., “A Greatly Improved A4EI Code for the Analysis of Bonded Composite Joints,” SAMPE, SE , May 2017. Created Excel VBA Macro that matches A4EI results and eliminates A4EI convergence issues by employing closed-form solutions to solve for shear stress NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

Backup Slides NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited. 37

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.6 in. AFM AFM Greater than 1% difference between Doubler and Lap methods Cyr 6/β bondline length: in. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.6 in. CFM CFM Greater than 1% difference between Doubler and Lap methods CFM Cyr 6/β bondline length: in. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 0.8 in. AFM Cyr 6/β bondline length: 1.05 in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : 1.2 in. AFM = CFM Cyr 6/β bondline length: in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. DED-F : Greater than 1% difference between Doubler and Lap methods at all tested lengths AFM Cyr 6/β bondline length: in. NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example H-stab patch-skin combination with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): AFM 0.7 in. Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example speed brake well repair patch with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): 0.5 in. AFM Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Doubler vs. Lap Method: Doubler Breakdown at Short Bondline, cont. Performed a study with an example speed brake well repair patch with RTD material properties then reduced the bondline and recorded the elastic and elastic-plastic strengths calculated by A4EI for both the doubler and lap methods (stepped, single bond): 0.5 in. CFM Greater than 1% difference between Doubler and Lap methods NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited.

A4EI Lap, Doubler Logic BJAM pg. 59, 95: CFM is typically edge of patch and based on double lap shear BJAM pg. 60, 95: AFM is typically edge of hole and based on adhesive capability BJAM pg. 118: Lap joint uses doubler model but uses two material property configurations to capture both EOP/EOH Fig NAVAIR Public Release DISTRIBUTION A. Approved for public release; distribution is unlimited. Fig

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