in Ultra-thin Fiber-Reinforced Composite Laminates

Micromechanical Models of Transverse Cracking

in Ultra-thin Fiber-Reinforced Composite Laminates

Luca Di Stasio ^{1 ,2} Zoubir Ayadi ¹ Janis Varna ²

1 Ecole Europ´eenne d’Ing´enieurs en G´enie des Mat´eriaux, Universit´e de Lorraine, Nancy, France ´

2 Avdelningen f¨ or materialvetenskap, Lule˚ a tekniska universitet, Lule˚ a, Sverige

Ultra-thin Fiber Reinforced Polymer Composite (FRPC) Laminates: an Introduction

Technological origins and applications

THIN PL Y LAMINA TE

TOW≈ 12/24k fibers

CONVENTIONAL LAMINA TE

Solar Impulse 2, from [1]. Nuon Solar team’s car, from [2].

Damage in FRPCs: a visual introduction

By Dr. R. Olsson, Swerea, SE.

By Prof. Dr. E. K. Gamstedt, KTH, SE.

The thin ply effect

1 2 3 4 5 6 7 8

40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

n [ −]

Y T [M P a]

In situ transverse lamina strength Y

T

as a function of thickness and ply orientation

[0

₂

/90

_n

]

_S

[ ±30/90

n

]

_S

[ ±60/90

n

]

_S

[90

8

]

_S

Measurements of in-situ transverse strength from Flaggs & Kural, 1982 [3].

Objectives & Approach

What do we want to achieve?

I Investigate the influence of volume fraction, material properties, thin ply thickness and bounding plies’

thicknesses on crack initiation

I G _∗c = G _∗c 

θ _debond , ∆θ _debond , E _{( ··)} , ν _{( ··)} , G ₍₎ , VF _f , t _ply , _t ^{t ply}

bounding plies



How do we want to achieve it?

I Design and categorization of several Representative Volume Elements (RVEs)

I Automated generation of RVEs geometry and FEM model

I Finite Element Simulations (in Abaqus)

Design & Analysis of Representative Volume Elements (RVEs)

x, i y, j

z, k

A⁰ A

0^◦

A A⁰

x, i z, k

RVE

LAMINA TE AS A 3D PLA TE 2D SECTION

X 2D space

X Linear elastic materials X Displacement control

X Dirichlet-type boundary conditions X Linear elastic fracture mechanics X Contact interaction

i, x k, z

O

Ωf Rf

Γ1

(0, Rf)

(−R^f, 0)

(0,−Rf)

(Rf, 0)

Ωm

C≡ (+l, +l) D≡ (−l, +l)

B≡ (+l, −l) A≡ (−l, −l)

l

l

l l

Γ3

θ

∆θ

∆θ

I L

H a Γ4

Γ2 w (x, l) = w (l, l)

w (x,−l) = w (l, −l)

u (l, z) = ¯ε· l

u (−l, z) = −¯ε^x· l

i, x k, z

O

Ωf Rf

Γ1

(0, Rf)

(−R^f, 0)

(0,−Rf)

(Rf, 0)

Ωm

C≡ (+l, +l) D≡ (−l, +l)

B≡ (+l, −l) A≡ (−l, −l)

l

l

l l

Γ3

θ

∆θ

∆θ

I L

H a Γ4

Γ2 (

u (x, l) = u (l, l)^x_l w (x, l) = w (l, l)

(

u (x,−l) = u (l, −l)^xl w (x,−l) = w (l, −l)

u (l, z)x= ¯ε· l

u (−l, z) = −¯ε^x· l

i, x k, z

l

l

l l

u (l, z) = ¯ε· l

u (−l, z) = −¯ε · l

C≡ (+l, +l) D≡ (−l, +l)

B≡ (+l, −l) A≡ (−l, −l)

G≡ (+l, +tratio· l) K≡ (−l, +tratio· l)

F≡ (+l, −tratio· l) E≡ (−l, −tratio· l)

(0, Rf)

(−Rf, 0)

(0,−Rf)

(Rf, 0)

Ωf

Ωm

Ω^u_[0◦]

Ω^b_[0◦] Rf

O

I L

H a

Γ1 Γ3

Γ4

Γ2

θ

∆θ

∆θ

i, x k, z

l

l

l l

u (l, z) = ¯ε· l u (−l, z) = −¯ε · l

C≡ (+l, +l) D≡ (−l, +l)

B≡ (+l, −l) A≡ (−l, −l)

(0, Rf)

(−Rf, 0)

(0,−Rf)

(Rf, 0) Ωf

Ωm

Rf

O I L

H a

Γ1

Γ3

Γ3

Γ2

θ

∆θ∆θ

x, i z, k

O

∆a

a ∆a

crack closed

∆a crack closed

∆uC

∆wC Z^u_C

Z^l_C X^l_C X^u_C

VCCT: G _I = ^Z _2B∆a ^{C ∆w C} G _II = ^X _2B∆a ^{C ∆u C}

x, i z, k

O

∆a

a ∆a

crack closed

∆a crack closed

n_i

Γ_i

n^num_i

Γ^num_i

J-Integral: J _i = lim _{ε →0} R

Γ _ε



W (Γ) n _i − n ^j σ jk ∂u _k (Γ,x _i )

∂x _i

 d Γ

Preliminary Results & Validation

∆θ = 15 ^◦ , δ = 0.4 ^◦ , VF f = 0.001, _R ^l

f ≈ 28

∆ θ = 100 ^◦ , δ = 0.4 ^◦ , VF f = 0 .001, _R ^l

f ≈ 28

−180−170−160−150−140−130−120−110−100 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 0

5 · 10

⁻²

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

∆θ [ ^◦ ] G (·· )

 J m

2



Energy release rate G ( ··) as a function of debond angular semi-aperture ∆θ

G I

G II

G T OT

δ = 0.4 ^◦ , VF f = 0.001, _R ^l

f ≈ 28

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

∆θ [ ^◦ ]

T ime [h ]

Simulation time as a function of debond angular semi-aperture ∆θ

Total CPU Time Wallclock Time

δ = 0.4 ^◦ , VF f = 0.001, _R ^l

f ≈ 28

Conclusions & Perspectives

What has been accomplished?

I 2D micromechanical models have been developed to investigate crack initiation in thin ply laminates

I A numerical procedure has been devised and implemented to automatize the creation of FEM models

I Validation for VF _f → 0 (matrix dominated RVE) with respect to previous literature [4, 5]

What’s next?

I Investigate the dependence on VF _f , t _ply , t _ply /t bounding plies and different material systems

I Study numerical performances with respect to model’s parameters

I Repeat for different RVEs and compare

Acknowledgements

The support of the European Commission through the Erasmus Mundus Programme is thankfully aknowledged.

References

[1] NTPT makes world’s thinnest prepeg even thinner. (2017, February 10). Retrieved from http://www.thinplytechnology.com/news-159-ntpta-makes-world-s-thinnest-prepreg-even-thinner [2] oXeon TECHNOLOGIES. (2017, February 10). Retrieved from http://oxeon.se/technologies/

[3] Donald L. Flaggs, Murat H. Kural; Experimental Determination of the In Situ Transverse Lamina Strength in Graphite/Epoxy Laminates. Journal of Composite Materials, 1982; 16(2).

[4] Toya, M.; A crack along the interface of a circular inclusion embedded in an infinite solid. Journal of the Mechanics and Physics of Solids, 1974; 22(5), pp. 325-348.

[5] Par´ıs, F., Cano, J., and Varna, J.; The fiber-matrix interface crack - a numerical analysis using boundary elements. Int. J. Fract., 1990; 82(1), pp. 11-29.

S´ eminaire de l’´ ecole doctorale EMMA 2017

May 4 ^th , 2017