Double lap joint finite element model Supported single lap joint finite element model

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an author's https://oatao.univ-toulouse.fr/24592

Montagne, Benoît and Lachaud, Frédéric and Paroissien, Eric and Martini, Dominique and Congourdeau, Fabrice Nonlinear finite element analysis of composite bolted lap joints: experimental vs numerical tests. (2019) In: The 22nd International Conference on Composite Materials (ICCM22), 11 August 2019 - 16 August 2019 (Melbourne, Australia).

Introduction and context

Double lap joint finite element model Supported single lap joint finite element model

Conclusions and perspectives

w

Nonlinear behavior of the composite material

• Double lap joint finite element model: good correlation between numerical and experimental tests thanks to the non linear composite behavior law

• Supported single lap joint finite element model: differences between numerical and

experimental stiffness, bolt modelling has to be improved because beam theory hypothesis not verified ^𝐿

𝜙 ~ 1

• Bolt tightening not taken into account because of shell finite element modelling

• Damage scenarios quite similar between double lap joint and supported single lap joints

Nonlinear finite element analysis of composite bolted lap joints: experimental vs numerical tests

B. Montagne

¹

, F. Lachaud

¹

, E. Paroissien

¹

, D. Martini

²

and F. Congourdeau

²

1

Institut Clément Ader (ICA), Université de Toulouse, ISAE-SUPAERO, INSA, IMT MINES ALBI, UTIII CNRS, 3 Rue Caroline Aigle 31400 Toulouse, France

2

DASSAULT Aviation, 78 Quai Marcel Dassault, 92210 Saint-Cloud, France

Falcon 7X: 250 000 fasteners

Rafale: 300 000 fasteners

Source NIAR

Aircraft composite content (% weight)

• Few composite parts on Falcon aircrafts

• Need to master composite bolted joint behavior to satisfy performance and safety requirements

Bearing Net section Cleavage Cleavage/ net section

Shearout

Failure modes of bolted joints

D

P

Bearing = preferential failure mode for the design of bolted

structures because of its progressive failure behavior

What are the physical phenomena leading to

bearing failure of composite bolted joints ?

• Interrupted tests on single lap joint specimens : validation of the damage scenarios using DIC

• Volume finite element modelling : bolt tightening taken into account, better modelling of the contact between the plates and the fastener, better modelling of the bolt, inter laminar

behavior could be studied Evolution laws

and coupling

•Brittle failure or not

•Relation between physical

phenomenon and properties to

degrade ? Degrading

mechanical properties

•In the different directions

•According to the load (tension,

compression, etc.)

Damage variables

•Correspond to the properties to degrade

Failure criteria

•At ply scale level

•One failure criterion f

_i

for one failure mode based on measured failure stresses

𝑑

₁

= 𝜙

₁

+ 𝜙

₂

𝑑

₂

= 𝑑

₄

= 𝜙

₄

𝑑

₂^𝑏

= 𝑑

₄^𝑏

= 𝜙

₄^𝑏

𝐸

₁₁

= 𝐸

₁₁⁰

1 − 𝑑

₁

𝐸

₂₂

= 𝐸

₂₂⁰

1 − 𝑑

₂

(1 − 𝑑

₂^𝑏

) 𝐺

₁₂

= 𝐺

₁₂⁰

1 − 𝑑

₄

(1 − 𝑑

₄^𝑏

)

0 500 1 000 1 500 2 000 2 500

0 0,01 0,02 0,03 0,04 0,05

σ

11

ε

₁₁

-1 600 -1 400 -1 200 -1 000 - 800 - 600 - 400 - 200 0

-0,03 -0,02 -0,01 0

σ

11

ε

₁₁

0 10 20 30 40 50 60

, 0,000 , 002,000 , 004,000 , 006,000

σ

22

(MP a)

ε

₂₂

- 350 - 300 - 250 - 200 - 150 - 100 - 50 0 50

- ,050 - ,030 - ,010

σ

22

(MP a)

ε

₂₂

0 20 40 60 80 100

0 0,01 0,02 0,03 0,04

τ

12

γ

₁₂

Longitudinal Transverse Shear

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

0 0,2 0,4 0,6 0,8 1 1,2

0 0,01 0,02 0,03 0,04

D a ma ge

τ

12

γ

₁₂

σ12 φ4b φ4

𝜙

_𝑛

= 1 − exp 1 − 𝑐

_𝑛^𝑚𝑛

𝑚

_𝑛

𝑐

_𝑛

= max( 𝑓

_𝑛

, 1)

𝑓

₁

=

^<𝜎_𝜎^11>+

11𝑅𝑇

2

+

^𝜎122_𝜎^+𝜎132

12𝑅𝑆

𝑓

₂

=

^<−𝜎_𝜎 ^11>+

11𝑅𝐶𝐶

2

𝑓

₄

= < 𝜎

₂₂

>

₊

𝜎

₂₂^𝑅𝑇

2

+ < −𝜎

₂₂

>

₊

𝜎

₂₂^𝑅𝐶

2

+ 𝜎

₁₂

𝜎

₁₂^𝑅

2

𝑓

₄^𝑏

= < 𝜎

₂₂

1 − 𝑑

₂

>

₊

𝜎

₂₂^𝑅𝑇

2

+ < −𝜎

₂₂

>

₊

𝜎

₂₂^𝑅𝐶

2

+ 𝜎

₁₂

1 − 𝑑

₄

𝜎

₁₂^𝑅

/𝑘

2

1 : 1

^st

fibers damage due to compression 2 : 1

^st

fibers damage due to tension

3 : tensile failure of 0° plies

1 : 1

^st

damage of the fibers due to

compression

2 et 3 : 1

^st

damage of the fibers due to

tension

4 : failure of 0° plies in tension -

divergence of the computation

Bolt modelled by contact elements Master node linked to a fixed spring

Composite plate meshed with laminated membrane elements

L o a d

Displacement measured by an extensometer 0 0

F

_max

Exp. Test 1 Exp. Test 2 Exp. Test 3 FEM

u

_max

Damage of

the matrix

Damage of the fibers in

compression 𝜙

₂

Damage of the fibers in tension 𝜙

₁

1

2

3 Ty=Tz=Rx=Ry=Rz=0

• Finite element models developped on SAMCEF® version 18.1

Composite plate meshed with laminated shell

elements

Aluminum plate Ty=Tz=Rx=Ry=Rz=0

Tx=Ty=Tz=Rx=Ry=Rz=0 Ty=Tz=Rx=Ry=Rz=0

• Bolt modelled with contact

elements – master nodes linked together by a beam with circular section in steel

• Initial stiffness higher than the experimental one

L o a d

Displacement measured by an extensometer 0 0

F

_max

u

_max

Damage of

the matrix

Damage of the fibers in

compression 𝜙

₂

Damage of the fibers in tension 𝜙

₁

1

2

3

2

2

2

3

3

3

4

4

4

FEM

Exp. Test