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DEVELOPMENT OF CONSTITUTIVE MATERIAL MODEL FOR COMPOSITE WITH

NONLINEAR FIBERS AND MATRIX

Liva Pupure1, Roberts Joffe1,2 and Janis Varna1

1Luleå University of Technology, S-97187 Luleå, SWEDEN2Swerea SICOMP, S-94126 Piteå, SWEDEN

6th International Conference on Composites Testing and Model Identification,

April 22-24, 2013, Alborg, Denmark

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Outline

• Introduction

• Objectives

• Materials and Manufacturing

• Material model

• Damage

• Visco-plasticity

• Visco-elasticity

• Summary

• Acknowledgments

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Introduction

• Advantages: High specific properties, renewable, recyclable, good insulation and damping properties 0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7

Str

ess

(MP

a)

Strain (%)

Flax UD

Cordenka UD

• Disadvantages: Poor adhesion between fiber and matrix, limited fiber length, difficult to control fiber alignment and orientation, sensitivity to moisture and temperature, limited processing temperature, low impact strength, high non-linearity, variability of properties.

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Objectives

• Ultimate objective of my work:– Develop accurate models that can predict behavior of

whole bio-based structural composites, based on properties of constituents

• This work demonstrates methodology for identification of input parameters required time-dependent material model

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Materials and Manufacturing• Epobiox: epoxidized pine oil based resin ~75% bio-

based (Amroy Finland); curing agent Amroy Ca35Tghardener (mixing ratio 100:27)

• Regenerated cellulose fibers (RCF) used in this studywere Cordenka 700 Super 3

Manufacturing

• Fiber roving was winded on steel plates

using a filament winding machine (2 layers)

• The fiber preforms were impregnated

using vacuum infusion with resin heated

to 50˚C and afterwards cured for 2h at 80˚C

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Materials and manufacturing

Material E, GPa σmax, MPa εσmax, %

EpoBioX 3.6 56.8 1.8

RCF 22.6 654.4 8.9

RCF/EpoBioX 15.0 246.1 4.9

RH=41%

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Material model

max

0max

E

Ed

mm

mCS

exp1

t

a

dt

0

'

Damage Visco-elastic

Visco-plastic

td

d

gdSgd VP

t

,2

010max

mt

MVPVP dC

0

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Material modelVarna J, Rozite L, Joffe R and Pupurs A, Nonlinearbehavior of PLA based flax composites. Plast RubberCompos, 2012

Giannadakis K, Mannberg P, Joffe R and Varna J, Thesource of inelastic behavior of Glass Fibre /Vinilesternon-crimp fabric [±45]s laminates. J Reinf Plast Comp2011

Rozite L, Varna J, Joffe R and Pupurs A, Analysis of nonlinear behavior oflignin based flax composites, Mechanics of Composite Materials, 2012(accepted).

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Material model

Fibermodel

Matrixmodel Composite

model

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Damage

max

0max

E

Ed

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6

E m

od

ulu

s (G

Pa

)

Strain (%)

Normalized E modulus evolution in UD Cordenka

Load

Load, after 9 days

Unload

Unload, after 9 days

Ramp history of loading-unloading experiment to characterize damage

in fiber composite

Reversible or irreversible?

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Visco-plasticity

• By performing multiple step creep test at different stress levels

0

0,5

1

1,5

2

2,5

3

0 10000 20000 30000 40000 50000 60000

Str

ain

(%

)

Time (s)

RCF/EpoBioX

160 MPa140 MPa120 MPa100 MPa

mt

MVPVP dC

0

mMVP

m

VP CAt

tAconst 0*

)(.

No loading history and

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Visco-plasticity

mM

VP

m

VP

CAt

tA

const

0

*

)(

.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Str

ain

(%

)

Time t/t*

Plastic strain development RCF

Modeling250MPa200MPa150MPa100MPa

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Visco-plasticity

mM

VP

m

VP

CAt

tA

const

0

*

)(

.

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Visco-plasticity

• High scatter between samples from the same batch, material demanding test (large number of specimens required).

**2

*1

***2

2*1

1 ......t

t

t

t

t

t

t

t

t

t

t

t

t

tC nknnM

nnM

n

m

nMn

MMVPVP

Parameter Different samples

Onesample

m 0.26 0.26

M 14.1 14

CVP (%) 1.69·10-9 1.36·10-9

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Visco-elasticity

• By performing one step creep test at different stress levels (scatter between samples from one batch, sensitivity to moisture, tests in knee region)

• VP-strain can be removed from curve in order to obtain pure VE behavior

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Visco-elasticity

• Finding of the Cm and τm by mathematical fit for all samples separately

• Choosing reference sample and corresponding Cm and τm

1,1

2

,210

expexp1

exp1

tVPii i

irec

tVPi i

icreep

tt

a

tCg

a

tCgg

10

1

1

g

a

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creep

creep

creep

Stra

in (

%)

Stra

in (

%)

Stra

in (

%)

Time (sec)

Time (sec)

Time (sec)

creep

creep

creep

Stra

in (

%)

Stra

in (

%)

Stra

in (

%)

Time (sec)

Time (sec)

Time (sec)

Visco-elasticityREF: 100MPa REF: 120MPa

100

MP

a12

0 M

Pa

160

MP

a

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Visco-elasticity

• Finding master curve for aσ

EpoBioX RCF/EpoBioX

1a

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Visco-elasticity

• Finding master curve for aσ (RCF)1a

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Visco-elasticity

• Using reference sample and master curve for aσ

find functions g1 and g2

0

0.2

0.4

0.6

0.8

1

1.2

20 25 30 35 40 45 50

g2

Stress, MPa

g2

from fit of experimental data

fitting curve0

0.4

0.8

1.2

1.6

2

20 25 30 35 40 45 50

g1

Stress, MPa

g1

from fit of experimental data

fitting curve

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Summary

• Constitutive model to predict behavior of highly non-linearbio-based composite is in development. Main inputparameters are identified.

• Comprehensive experimental program has been carried outto characterize RCF and their composites. Results showedhigh scatter of data within one batch of specimens. Thisproblem can be solved by use of one specimen to identify allparameters.

• High sensitivity of these materials to moisture complicatesanalysis, since dependents of input parameters on moisturecontent should be accounted for.

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Summary

• It has been observed that Cm and τm obtained from fittingexperimental data from lowest or highest stress level showsunacceptable fit at different stress levels. Reference samplewith corresponding Cm and τm must be chosen fromintermediate stress levels, which showed best overall fit forall samples.

• The shape of master curve aσ can be seen from dataobtained using several samples as a reference sample. Aftermaster curve has been defined and reference samplechosen, parameters g1 and g2 can be identified by fitting.

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Acknowledgments

• Runar Långström, Birgitha Nyström and PeterMannberg (Swerea SICOMP) for supplyingmaterials

• Newsha Doroudgarian for help with experiments

• My studies has been financially supported byInterreg IV Nord project ANACOMPO (fundingby EU and local government)

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Thank you for your attention!