Damage Tolerance and Durability of Adhesively Bonded ... · Durability of Adhesively Bonded Composite Structures Thomas Siegmund CT Sun. ... (ABAQUS CAE, ABAQUS Standard) for all

The Joint Advanced Materials and Structures Center of Excellence

Damage Tolerance and Damage Tolerance and Durability of Adhesively Durability of Adhesively

Bonded Composite StructuresBonded Composite StructuresThomas SiegmundThomas Siegmund

CT SunCT Sun

2The Joint Advanced Materials and Structures Center of Excellence

Purdue UniversityPurdue University

Adhesively Bonded Composite Structures

• Motivation and Key Issues – Contribute to the development of reliability of

adhesively bonded structures• Objective

– Develop experimental and numerical methods to design and analyze design

• Approach– Nonlinear fracture mechanics methods (CTOA and

cohesive zone models)– Develop related educational and training material



FAA Sponsored Project Information

• Principal Investigators & Researchers– Thomas Siegmund (PI, School of Mechanical

Engineering)– CT Sun (Co-PI, School of Aeronautics and

Astronautics)• FAA Technical Monitor

– Curt Davies• Other FAA Personnel Involved

– No current• Industry Participation

– No current



Adhesively Bonded Composite Structures – CZM Approach

PI: Thomas Siegmund, Professor, School of Mechanical Engineering, [email protected]

Objective: Demonstrate the use of the cohesive zone model approach in the analysis of adhesively bonded structures

Approach: Employ previously developed data for Hysol EA9394 to typical structural joints



0

10

20

30

40

50

60

70

80

90

100

0 0.02 0.04 0.06

0.508mm1.524mm3.048mmcz law

Δn [mm]

T n [M

Pa]

0

10

20

30

40

50

60

70

80

90

100

0 0.02 0.04 0.06

0.508mm1.524mm3.048mmcz law

Δn [mm]

T n [M

Pa]

Cohesive Zone Model

Δ

T

T

Local Parameters:• Traction (T) – Separation (Δ)• H2O Concentration C(H2O)

C(H2O)• Load, Displacement• Environment• Time• Cycles

• Traction-Separation

• Damage

2

Adherent

Adhesive

CZ Elements

Finite element model withCohesive elementsF

F

Global Parameters:

COD



L-Joint

Feiha et al., International Journal of Adhesion and Adhesives, 2005, 47-59

Model entirely with continuum elementsAdhesive with

continuum elements & cohesive elements



L-Joint

Global Stresses

Stresses in Adhesive

Tractions in CZ



Joint Strength & Bondline Thickness

Structural (beam) elementsAdhesive with continuum elements & cohesive elements

Group A - Beam Elements

Group B – Cohesive Elements

Group C

Interface

Precrack / Cohesive Crack

CAD to FEM strategy:Define parts connected by

tie constraints to form assembly

Mesh parts independently



6.40E+03

6.60E+03

6.80E+03

7.00E+03

7.20E+03

7.40E+03

7.60E+03

7.80E+03

8.00E+03

8.20E+03

0 0.5 1 1.5 2 2.5 3 3.5

Hysol Thickness (mm)

Failu

re L

oad

(N)

Adhesive Cohesive --> Adhesive Cohesive Peel (adhesive)

Joint Strength & Bondline Thickness



Skin – Stiffener Joint: Effect of Flange Thickness

Structural (shell ) elements & Cohesive elements

J. F. Mandell et al., J. Solar Energy Engineering, 125, 2003, 522-530.



Skin – Stiffener Joint: Effect of Flange Thickness

tflange =4.5 mm tflange =1.0 mm

Delamination growth from flange free end

Delamination growth from flange center



Sandwich Panel Lap Joint

Solid elements for sandwich & Cohesive elements

Viscous Regularization of Damage in Cohesive Zone becomes essential in complex problems:

( ) ( ) 01 1v v vD D D T D Tμ

= − ⇒ = −&



Sandwich Panel Lap Joint

1st CZLast CZ

Computation w/o regularization

Computation with regularization may well predict complete joint failure in a modelConvenience of obtaining a numerically converging solution must not be considered as a real failure load,and can only be considered as an upper bound.

0.05

0.01

0.0005

0.047

0.0050.0001

μ=0.0001 μ varying



Education & Training

Course: “Computational Fracture Mechanics”(1) Review of classical fracture mechanics concepts for elastic materials;

(K, J)(2) Computational methods for classical fracture mechanics for elastic

materials; (singular elements etc.)(3) Computational methods of crack growth in elastic solids (including

modeling with cohesive zone models, model generation, analysis, convergence criteria, fracture and fatigue);

(4) Review of classical fracture mechanics concepts for nonlinear material; (J, deformation theory vs. plasticity)

(5) Computational methods for nonlinear fracture mechanics (cohesive zone model, R curves);

(6) Continuum damage mechanics concepts and computational aspects (void growth models, localization, ductile fracture).

Numerical examples (ABAQUS CAE, ABAQUS Standard) for all chapters.



Project I: Conclusion to Date

• Developed tools to measure cohesive zone properties• Explore various levels of model complexity• Explore capabilities of commercial software (ABAQUS)• Develop CAD to FEM modeling strategies

• Examples:– Bondline thickness dependence of joint strength

Solid model– Fillet radius influence on L-joint strength

Structural – solid model– Shell – stiffener structure

Structural model– Sandwich panel joint

Convergence of solution



Project I: A Look Forward

• Benefit to Aviation:– Response to increase in need for understanding

adhesive bonding processes and their reliability– Novel analysis approaches to aerospace structures– Address to fundamental issues in bonded structures– Provide related training and education material

• Future needs– Long term response of adhesively bonded structures:

fatigue & environment, variable amplitude loading– Further understanding of nonlinear failure processes



Project II: Prediction of Adhesive Lap Joint Strength Using CTOA

C.T. Sun, Professor [email protected], School of Aeronautics & Astronautics, Purdue University

Haiyang Qian, Ph.D. Student

Objective – Develop a CTOA fracture criterion to predict thickness-dependent adhesive lap joint strength

Approach – Conduct fracture experiments using DCB and single lap specimens of various adhesive thicknesses to validate the proposed CTOA approach and to determine the limitation on its applicability with finite element analyses of the experiments

mailto:[email protected]



Adhesive Thickness Effect on the Strength of Lap Joints

T

T

l

L

t

adhesvie

Adherend: Aluminum Alloy 7075

Adhesive: HYSOL EA9394

Surface Treatment: Semco Pasa-Jell 105 (etching method)

L=3in, l=1in, T=0.125int=0.008in, 0.01in, 0.02in, 0.06in

01

23

45

67

0 0.5 1 1.5

Bondline Thickness (mm)

Stre

ngth

of J

oint

s (k

N)

• Experimental result

• Joint strength increases as the bondlinethickness decreases up to 0.25 mm



Size of K-Dominance Zone in DCB

gularSinNonyy

Singularyy

Singularyy

−+=Λ

σσ

σ

x2K I

yy πσ =

Degree of K-Dominance

+ 0 (1)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 1 2 3 4Adhesive thickness (mm)

K-D

omin

ance

zon

e si

ze (m

m)

Steel Hinge

L

t

l

Wta



Plastic Zone Size in DCB Hysol EA9394

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50

0 0.01 0.02 0.03Strain

Stre

ss (M

Pa)

Dog-Bone Specimens Test DataSandia National Lab DataLinear ElasticExtended CurveAdhesive Thickness: 0.8 mm

Plastic Zone Size: 0.78 mm90% K-Dominance: 0.04 mm

0.78 mm

• Small scale yielding assumption is violated



Aluminum

114.3 mm (4.5 in)38.1 mm (1.5 in)

3.175 mm (0.125 in) Hysol EA-9394

Crack tip

P

DCB Test Result for Hysol EA9394 by LEFM

80

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130

140


Failu

re lo

ad (N

)

0

300

600

900


Ener

gy re

leas

e ra

te (J

/m^2

)



0.2 mm

d α

r0

1

2

3

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5

6

7

8

0 0.5 1 1.5 2

Adhesive thickness (mm)

CTO

A (D

egre

e)CTOA as Fracture Criterion in

DCB

Measured CTOA



Stress Decreasing

A

B

-100

0

100

200

300

400

500

600

0 5 10 15 20 25

Overlap (mm)

Nor

mal

Stre

ss (M

Pa)

Fracture Path in Single Lap Joint


Purdue UniversityPurdue UniversityPurdue Univeristy

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6

Adhesive thickness (mm)

Ener

gy R

elea

se R

ate

(J/m

)

GIGII

Embedded crack length: 0.3-0.7 mm

Location: 0.05 mm above the lower interface

Embedded Crack for Failure Prediction in Single Lap Joints

Mode I dominated



CTOA under Failure Load for Single Lap Joints

• CTOA is independent of adhesive thickness before failure mode change

0

1

2

3

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5

6

7

8

0 0.5 1 1.5 2

Adhesive Thickness (mm)

CTO

A (D

egre

e)



Project II: Conclusions to Date

• LEFM is not suitable for predicting fracture in DCB adhesive specimens because of large plastic zone relative to the K-dominance zone size

• A single CTOA value can be used to predict fracture in DCB specimens with different adhesive thicknesses.

• Failure loads of lap joints can be predicted using the CTOA measured with DCB specimens in conjunction with an assumed crack embedded near the adhesive/adherend interface.



Project II: A Look Forward

• Future Needs– results to date concentrated on adhesive using metal adherends – future work needed to

investigate other adherend (namely composite) and adhesive types and failure modes: interfacial (a.k.a. adhesion) and mixed interfacial/cohesive failure + composite failure

– investigate combined loading (simultaneous effects of temperature, humidity, cyclic loading) for range of bondline thickness and mode mix ratio

– establish mixed mode fracture criteria that accounts for bondline thickness– development of improved test specimen for constitutive curve measurement– account for localized failure evolution in modeling of shear tests – demonstrate

transferability to joints of generic configuration– use the developed fracture models to find optimized adhesive thicknesses for different

adhesives– develop a embedded crack concept in conjunction with the developed fracture models to

predict general bonded joint strength– Extend the CTOA fracture criterion to include bonded plates or shells under general

loading conditions– Conduct experiments to verify the proposed fracture criterion

Documents

Damage Tolerance and Durability of Adhesively Bonded ... · Durability of Adhesively Bonded Composite Structures Thomas Siegmund CT Sun. ... (ABAQUS CAE, ABAQUS Standard) for all