Durability of adhesive bonded joints in aerospace structures

Washington State University Date: 11/08/2017 AMTAS Fall meeting Seattle, WA Durability of Bonded Aircraft Structure

• Principal Investigators & Researchers • Lloyd Smith • Preetam Mohapatra, Yi Chen, Trevor Charest • FAA Technical Monitor • Ahmet Oztekin • Other FAA Personnel Involved • Larry Ilcewicz • Industry Participation • Boeing: Will Grace, Peter VanVoast, Kay Blohowiak

2 Durability of adhesive bonded joints in aerospace structures

1. Influence of yield criteria Yield criterion 2. Biaxial tests (Arcan) Plasticity 3. Cyclic tests Hardening rule 4. FEA model

Nonlinearity in Bonded Joints

1. Creep, non-linear response Tension (closed form) 2. Ratcheting, experiment Time Dependence 3. Creep, model development Shear (FEA) 4. Ratcheting, model application Approach: Plasticity vPrimary Research Aim: Modeling of adhesive plasticity to describe nonlinear stress-strain response.

ØSub Task:

1. Identify the influence of yield criterion and hardening rule on bonded joints (complete)

2. Characterizing hardening rule (complete Dec 2017)

3. Characterizing yield criterion (complete Dec 2017)

4. Numerically combining hardening rule and yield criterion (complete Feb 2017) Approach: Plasticity 1. Identify yield criterion and hardening rule of bonded joints

• Input properties: Bulk and Thin film adhesive properties in Tension.

60 Characterization of Tensile properties 55 50 45 40 35 30

25 Bulk Tension: Tough Adheisve 20 Tensile Stress [MPa] Bulk Tension: Standard Adhesive 15 10 Thin film Tension: Tough Adhesive 5 Thin film Tension: Standard Adhesive 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Axial Strain Approach: Plasticity 1. Identify the influence of yield criterion and hardening rule on bonded joints • Background: Investigate yield criterion and hardening rule of bonded joints.

• Outcome type: Comparison of Test results vs different FEA models Scarf

Experiment: bonded joints in shear 45 40 35 30 25 20 Tough: scarf WALS

Shear Stress [MPa] 15 Tough: lap shear 10 Standard: scarf 5 Standard: lap shear 0 0 0.005 0.01 0.015 0.02 Axial Strain Approach: Plasticity • Validation of Material model: Isotropic vs Kinematic hardening

• Choice of Input property: Bulk vs. Thin film

45 Exp vs. FEA: Tough Scarf 45 Exp vs. FEA: Tough WALS 40 40 35 35 30 30 25 25 Experiment 20 Experiment 20 FEA: Kinematic hardening with thin film 15 FEA: Kinematic hardening with thin film 15 Shear Stress [MPa] FEA: Isotropic hardening with thin film 10 FEA: Isotropic hardening with thin film Shear Stress [MPa] 10 FEA: Kinematic hardening with bulk adhesive FEA: Kinematic hardening with bulk adhesive 5 5 FEA: Isotropic hardening with bulk adhesive FEA: Isotropic hardening with bulk adhesive 0 0 0 0.005 0.01 0.015 0.02 0.025 0 0.003 0.006 0.009 0.012 0.015 Axial Strain Axial Strain • Status: Completed, Journal paper submitted

• Task outcome: Adhesive follows a von Mises yield criterion and kinematic hardening Approach: Plasticity

• Validation of Material model: Isotropic vs Kinematic hardening

• Choice of input property: Bulk = thin film (for Standard adhesive)

45 45 Exp vs. FEA: Standard Scarf Exp vs. FEA: Standard WALS 40 40 35 35 30 30 25 25 20 20 15 Experiment 15 Shear Stress [MPa] Experiment 10 Shear Stress [MPa] FEA: Kinematic hardening 10 5 FEA: Kinematic hardening FEA: Isotropic hardening 5 0 FEA: Isotropic hardening 0 0.001 0.002 0.003 0.004 0.005 0 Axial Strain 0 0.003 0.006 0.009 0.012 0.015 Axial Strain • Status: Completed, Journal paper submitted

• Task outcome: Adhesive follows a von Mises yield criterion and kinematic hardening Approach: Plasticity

2. Characterize hardening rule

• Background: Similar to metals, adhesives could follow isotropic, kinematic or combined hardening rule.

• Lot of research done with metals, but none with bonded joints.

• This has to be verified by studying the movement of the yield surface under cyclic tension compression loading in a biaxial stress space.

Ref: Muransky O. et al [Metal Plasticity] Approach: Plasticity • Outcome type: Cyclic ten-comp tests for scarf joint. Plot of yield surface translation/expansion/both, Journal paper

σ_�

τ

Scarf Joint in cyclic test fixture

〖−σ〗_� σ_�

Black = Original Red = Isotropic • Scarf joint being tested in ten-comp. -τ Blue = Kinematic 〖−σ〗_� • DIC is used for calculating shear Orange = Combined strain Approach: Plasticity • Outcome type: Cyclic ten-comp tests for scarf joint. Plot of yield surface translation/expansion/both, Journal paper

5000 Blue = Red (all cycles) 4500 Stress controlled Exp: Tension: Max 4000 Peaks [+4800 to -4800 psi] 3500 Increasing Strain 3000 2500 2000 1500 Cycle # Yield surface size [psi] 1000 Tension : Yield 1 (Blue: ten peak) 6250 +4800 to -1450 500 0 2 (Red: comp peak) 6250 -4800 to +1450 -500

Shear Stress [psi] Compression : Yield 3 (Blue: ten peak) 6250 +4800 to -1450 -1000 -1500 4 (Red: comp peak) 6250 -4800 to +1450 -2000 Blue 1 5 (Blue: ten peak) 6250 +4800 to -1450 -2500 Red 1 -3000 Blue 2 -3500 Red 2 -4000 Blue 3 Compression : Min -4500 -5000 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Shear Strain

• Status: Documentation in progress

• Task outcome: Yield surface showed translation (kinematic hardening). Approach: Plasticity • Outcome type: Cyclic ten-comp tests for scarf joint. Plot of yield surface translation/expansion/both, Journal paper

st nd 5000 Blue ~ Red (1 and 2 cycle) Test 1 4500 Purple = Orange (3rd and 4th cycle) 4000 Blue 3500 Virtual Strain Red Test 1 Cycles# 3000 Controlled: Yield surface size [psi] (presented here) 2500 Purple Stress peaks [psi] 2000 Orange 4800 1 (Blue: ten peak) 6300 +4800 to -1500 1500 Black 1000 -4500 2 (Red: comp peak) 6250 -4500 to +1750 500 0 4000 3 (Purple: ten peak) 5750 +4000 to -1700

Shear Stress -500 -4000 4 (Orange: comp peak) 5750 -4000 to +1700 -1000 -1500 -2000 -2500 Decreasing -3000 Stress: Test 2 Cycles# Yield surface size [psi] -3500 Stress peaks [psi] -4000 4800 1 (Blue: ten peak) 6200 +4800 to -1400 -4500 -4500 2 (Red: comp peak) 6160 -4500 to +1660 -5000 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 Shear Strain 3425 3 (Purple: ten peak) 4756 +3425 to -1330 -3500 4 (Orange: comp peak) 4800 -3500 to +1300 • Status: Documentation in progress

• Task outcome: Yield surface showed translation after stabilizing cycles in a strain controlled/decreasing stress experiment (Kinematic hardening). Approach: Plasticity 3. Characterizing yield criterion

• Background: Assumption of yield criteria to avoid complex characterization with thin bonded joints

• Test bonded joints with mixed mode Arcan fixture to plot yield surface in biaxial stress space to identify shape of yield surface.

• Outcome type: Test results, Journal paper

Normal component: σ =

Shear Component: σ =

Prospected Test set up Approach: Plasticity

Schematic Yield Surface in Biaxial Stress Space 8000 Solid Black line: Initial Yield Dotted black line: Failure surface 6000

4000 τ 90 67.5 45 2000 22.5

σ 0 Assembly: fixture and coupon [psi] -σ 0 0 τ -22.5 -2000 -45 -67.5 -90 -4000 -τ Tensile stress Compressive Stress -6000 +ve Shear stress -ve Shear stress -8000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 σ [psi] Approach: Plasticity

8000 Tough Adhesive 8000 Tough Adhesive Exp: yield surface 7000 7000 Exp: failure surface Drucker Prager criterion 6000 Exp: yield surface 6000 von Mises criterion

5000 5000

4000 4000

3000 3000 Shear Stress Shear Stress

2000 2000 1000 1000 0 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 Normal Stress Normal Stress

• Status: Documentation in progress

• Task outcome: yield surface shape and size to be plotted from experimental data. Approach: Plasticity Standard Adhesive Standard Adhesive 8000 7000 Exp: failure surface Exp: yield surface

7000 Exp: yield surface 6000 von Mises criterion

Drucker Prager criterion 6000 5000

5000 4000 4000 3000 Shear Stress

Shear Stress 3000 2000 2000 1000 1000 0 0 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 6000 7000 8000 Normal Stress Normal Stress • Status: Documentation in progress

• Task outcome: yield surface shape and size to be plotted from experimental data. Approach: Plasticity

4. Numerically modeling nonlinear hardening rule.

• Background: Modeling of nonlinear hardening is common in metals.

• Nonlinear hardening has not been characterized for bonded joints due to experimental complexities, assumed to be linear.

• To model nonlinear hardening by including possible effects form both Isotropic and or kinematic hardening.

• Outcome type: Numerical modeling, comparison of experiment and simulation, Journal paper

• Status: Identified the modeling technique to use cyclic scarf test data to extract nonlinear hardening parameters by separating isotropic and kinematic hardening components (estimated Feb 2018)

• Task outcome: Numerical modeling-FEA simulation of nonlinear hardening Approach: Time dependence (viscoelasticity/viscoplasticity)

Background

• The time-dependent behavior of adhesives is important for the durability

• Seldom accurate models for adhesives to predict the ratcheting

• The response of shear coupons is more complicated to test

Objectives

The final objective is to build a shear viscoelastic modeling on bonded joints for ratcheting.:

• Viscoelastic response of bulk resin, closed form model (complete)

• FEA Viscoelasticity model of bulk Resin (12/31/2017)

• FEA viscoelastic model of bonded joints in creep (05/31/2018)

• FEA viscoelastic model of bonded joints in ratcheting (12/31/2018) Approach: Time dependence (viscoelasticity/viscoplasticity)

•FM300-2

Strain for 20 % Scarf

820

800 780 Strain for 50 % Scarf strain - 760 Racheting Strain 2200

Micro 740 Creep Strain 2150 2100 720 Ratcheting Strain 2050 700 strain

- Creep strain 0 200 400 600 800 1000 1200 2000 Strain for 80 % Scarf 1950

Cycles Micro 1900 3600 1850 3550 1800 3500 0 200 400 600 800 1000 1200 3450 strain Cycles - 3400 3350 Ratcheting Strain Micro 3300 Creep Strain 3250 3200 0 200 400 600 800 1000 1200 Cycles Ratcheting Efforts (Extensometer)

• Extensometer can slip during ratcheting • Used Digital Image Correlation to try to capture peak strains • DIC does not sample fast enough • Shear strain gauge measurement will begin next week

Good ratcheting result from extensometer Ratcheting result with suspected extensometer slippage Approach: Time dependence (viscoelasticity/viscoplasticity) ØTensile Viscoelasticity Modeling on Bulk Resin

Material Type Material Model Components of Model Nonlinear Time- Tried Results Dependent

Elasticity 22.2 Linear Elasticity Elastic 22.3 Porous Elasticity Porous Elastic ● 22.4 Hypoelasticity Hypoelastic ● 22.5 Hyperelasticity Hyperelastic ● Plasticity 23.2.1 Classical Metal Plasticity Plastic ● 23.2.4 Rate-Dependent Plasticity Creep: time hardening ● ● ● No viscoelastic strain in recovery stage. 23.2.6 Anisotropic Yield/Creep Plastic or Creep ● ● 23.2.11 Two-Layer Viscoplasticity Elastic Difference in creep stage of Plastic ● ● ● 80% loading. Viscous: time hardening Viscoelasticity 22.7 Linear Viscoelasticity Viscoelastic ● ● No permanent strains in recovery. 22.8.1 Hysteresis in Elastomers Hysteresis ● ● ● Can not fit for three kinds Hyperelastic loading simultaneously. 22.8.2 Parallel Rheological Framework Hyperelastic ● ● ● Difference in creep and Viscous: recovery stages of 80% strain hardening loading.

Simulate the tensile creep-recovery behaviors of EA9696 bulk coupons under loading of 20% UTS, 50%UTS and 80% UTS. Approach: Time dependence (viscoelasticity/viscoplasticity) • 23.2.4 Rate Dependent Plasticity

32000 30000 28000 26000 20%-test • Time hardening: 24000 %-RD 20 �̇ = �� � 22000 50%-test 20000 Parameter 20% 50% 80% ) 50%-RD

ue 18000 E0(MSI) 283842.8 269043.2 234234.2 80%-test 16000 A 3.8e-8 3.8e-8 2.8e-8 14000 80%-RD n 1 1 1.17 STRAIN ( m -0.92 -0.92 -0.92 12000 10000 8000 6000 4000 2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 TIME (s) Fig.1 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 23.2.11 Two-Layer Viscoplasticity

32000 30000 28000 26000 20%-test 24000 22000 20%-VP 20000 50%-test

ue) 18000 50%-VP 16000 Fig.3 Model Sketch 80%-test 14000 STRAIN ( 80%-VP 12000 • Viscous part: �̇ = � � � 10000 8000 Parameter Value 6000 A 2.496e-7 4000 n 1.1809 2000 0 m -0.12968 0 200 400 600 800 1000 1200 1400 1600 1800 2000 TIME (s) Fig.2 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 22.7 Linear Viscoelasticity

32000 30000 28000 • 2-branch Prony series 26000 %-test 24000 20 Parameter 20% 50% 80% 22000 20%-VE E0(MSI) 283842.8 269043.2 234234.2 20000 50%-test G1 0.0398 0.0511 0.0487 ) τ1(S) 13.228 20.654 16.6

ue 18000 50%-VE G2 0.057 0.0733 0.0758 16000 80%-test τ2(S) 306.47 318.44 308 14000

STRAIN ( 80%-VE 12000 10000 8000 6000 4000 2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 TIME (s) Fig.4 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 22.8.1 Hysteresis in Elastomers

32000 30000 28000 %-test 26000 20 24000 20%-H 22000 50%-test 20000 50%-H Fig.8 Model Sketch

ue) 18000 16000 80%-test 14000 80%-H STRAIN ( • Network B: �̇ = � (�) � 12000 10000 Parameter Value 8000 A 3.8969e-3 6000 m 3 4000 2000 c -0.082312 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 TIME (s) Fig.7 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 22.8.1 Hysteresis in Elastomers

32000 30000 28000 20%-test 26000 20%-HE 24000 50%-test 22000 50%-HE 20000 Fig.10 Model Sketch 80%-test

ue) 18000 %-HE 16000 80 14000 STRAIN ( • Network B: �̇ = � (� ) � 12000 10000 Parameter Value 8000 A 3.8696e-3 6000 m 8.4 4000 c -0.02312 2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 TIME (s) Fig.9 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 22.8.2 Parallel Rheological Framework

30000 28000 26000 20%-test 24000 20%-PRF 22000 50%-test 20000 50%-PRF 18000

ue) %-test-e4 16000 80 Fig.6 Model Sketch 14000 80%-PRF

STRAIN ( 12000 • Viscous part: 10000 �̇ = �� � + 1 � 8000 6000 Parameter Branch-1 Branch-2 Branch-3 4000 A 2.01e-12 9.7e-14 2.94e-11 2000 n 3.1284 1.4683 1.6875 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 m -0.04 -0.09 -0.007 TIME (s)

Fig.5 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 22.8.2 Parallel Rheological Framework-Ratcheting

1000 cycle ratcheting 28000 26000 24000 22000 20000 20%-test 20%-PRF 18000 50%-test 50%-PRF 16000 Fig.6 Model Sketch 80%-test 80%-PRF 14000 12000 • Viscous part: 10000 8000 �̇ = �� � + 1 � Max Strain Per Cycle [ue] 6000 4000 Parameter Branch-1 Branch-2 Branch-3 2000 A 2.01e-12 9.7e-14 2.94E-11 0 n 3.1284 1.4683 1.6875 0 100 200 300 400 500 600 700 800 900 1000 Cycle m -0.04 -0.09 -0.007

Fig.5 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • 22.8.2 Parallel Rheological Framework-Ratcheting

1000 cycle ratcheting-recovery 20000

18000

16000 20%-test 14000 20%-PRF 12000 50%-test Fig.6 Model Sketch 10000 50%-PRF 8000 80%-test • Viscous part: 6000

Recovery Strain [ue] %-PRF 80 �̇ = �� � + 1 � 4000

2000 Parameter Branch-1 Branch-2 Branch-3

0 A 2.01e-12 9.7e-14 2.94E-11 n 3.1284 1.4683 1.6875 -2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 m -0.04 -0.09 -0.007 Recovery Time [s]

Fig.5 comparison between simulation and test Approach: Time dependence (viscoelasticity/viscoplasticity) • Further Work

Ø Tensile Viscoelasticity Modeling on Bulk Resin (12/31/2017) • Optimize parameters in mentioned Parallel Rheological Framework Model and Two-Layer Viscoplasticity Model • Modify the viscous equations(exponents expression) in PRF and Two-Layer Viscoplasticity Models which have effect on the slope of creep curve and permanent strain • A model with higher strain rate for 80% loading • UMAT

Ø Shear Viscoelastic Modeling on Bonded Joints for Creep (05/31/2018) • Simulate the creep/recovery behavior of WALS coupons, scarf joints. • Verify the linear/ nonlinear model by comparison with the test data.

Ø Shear Viscoelastic Modeling on Bonded Joints for Ratcheting (12/31/2018) • Simulate the ratcheting/recovery behavior of WALS coupons, scarf joints. • Verify this model by comparison with the test data. Summary

• Plasticity • Adhesives we’ve tested follow a von Mises yield criterion • Adhesives we’ve tested follow a kinematic hardening rule

• Viscoelasticity • Adhesives become non-linear about 50% UTS • Ratcheting response is greater in shear than in normal stress Future work

• Plasticity • Complete yield and hardening tests • Incorporate yield and hardening results in a predictive FEA model

• Viscoelasticity • Complete ratcheting experimental tests • Include strength and fracture toughness changes with ratcheting • Develop FEA model of non-linear viscoelastic response under creep • Apply model to shear and ratcheting loading environments