Application of the Open Hole Tensile Test to the ...leriche/presentation_hole_on_plate.pdf ·...

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Département Mécanique et Mat ériaux

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Application of the Open Hole Tensile Test to theIdentification of the in-plane Characteristics of

Orthotropic Plates

J. Molimard, R. Le Riche, A. Vautrin, and J. R. Lee,-

GDR CNRS 2519,-

SMS/MeM, ENSM-SE, 158 Cours Fauriel, 42023 Saint Etienne, France

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Presentation summary

- Introduction

- Identification procedure

- First results

- Interaction between anisotropy and geometrical modelling errors

- Conclusion

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Orthotropic laminate

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Exx, vxy, Eyy , Gxy

Hypothesis :Uniform strain field

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90

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45

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0

�Load

Reference values

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��ε ��ε

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Introduction: global overview

I- Introduction

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√√√√��

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FEMAnalytical Model

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Hole on plate tensile test,T-shaped specimen,

Modified Iosipescu shear test,…

GIGSSS�

Minimization algorithm

Mechanicalproperties

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√√√√

√√√√ ( ) ( ) ( )��

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�� εεεεεε −+−+−=

��%

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�� =

��& �� '(� ��

��: number of measures R : residue vector

Lekhnitskii solution for a hole on infinite orthotropic plate (plane stress conditions)

Modified Levenverg-Marquardt algorithm

Introduction: identification strategy

I- Introduction

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Experimental technique: digital phase-shifting grating interferometry

-1θ

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Interference

resinspecimen grating

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πφ �� =⋅−=∆ − ��

)* !"

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=

−= −

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��Phase difference��

�� φφφ −=∆

spatialfilter

10mW-laser

lens1

Imag

ing

syst

em

Illumination system

toward PC

Toward piezo system

Tensile machine

Glass plate3 mirrors

lens 2

lens 3Rotating screen

CCD camera

x

z

II- Identification procedure

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φπ ∆=

+��


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•Specimen: NC2® reinforcement from Hexcel Composite+ Epoxy resin processed in a RTM moldStacking sequence [{0/90}3]s

Experimental technique: mechanical set-up and specimen


•Mechanical set-up:Table-top tensile deviceApplied stress 10 MPa

Studied field

32.5mm

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,&

256 mm

W = 26 mm

x

y

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Identification procedure: Unknown parameters


Position of the hole center (xc , yc)

Hole geometry (a, b)Covered field

ααααLoading axis

Material axis

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. /00. 1�0. ν�0

• Geometrical parameters:

• Material parameters:

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III- First results

First results: displacements and strains maps

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��ε ��ε

•Metrological aspects:Field: 779 by 917 pixelsSpatial resolution: 244 µmResolution: 6 µstrainsDerivation: least square (7 pixels)

-208.5 -148.9 -89.4 -29.8 29.8 89.4 148.9 208.5417nm/fringe +

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x

y

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4(4+�(2 15��2(� 15��-(� 15�Identified

values

4(4�(� 15��+ 15�+4 15�Reference

values

�+(� 6�(� 6(4 6(� 6Difference

ν�01�0/00/��

Identified values Differences between experimental and numerical strain maps

First identification results

III- First results

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#��ε �(� #�� ε ��

��#�#�

� �� εε −

� �� εε −��

� �� εε −��

E[ ]

= -0.6957 µε

s.d. [ ]

= 32.1672 µε

statistics

�� #��ε �(� #�� ε �� #�#� � �

�� εε −

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#��ε �(� #�� ε ��

��#�#�

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� �� εε −��

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E[ ]

= 0.4395 µε

s.d. [ ]

= 32.3187 µε

E[ ]

= 0.7691 µε

s.d. [ ]

= 58.9253 µε

statistics

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0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5

0

5

10

15

20

25

30

21.21%

Per

cent

err

or b

etw

een

FE

M w

ith fi

nite

witd

than

d an

alyt

ical

mod

el w

ith in

finite

wid

th (

%)

Specimen width (W) in FEM / hole diameter (D)

vxy

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7 & �+ ��

, & ��

Rel

ativ

e er

ror

betw

een

valu

es u

sed

in th

e F

inite

E

lem

ent s

imul

atio

n an

d th

e id

entif

ied

valu

es

usin

g th

e in

finite

ana

lytic

al m

ode

(%

)

Specimen width in FEM simulation (W)

Hole diameter (D)

W > 240 mm, D = 4 mm

W =26 mm, D < 0,43 mm

For Lekhnitskii Model

21.21%

0.96%

IV- geometrical errors

Study of geometrical modelling error

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• glass or carbon fibres• 2 epoxy resins• fibre volume fraction from 30 % to 60 %• [0] 4, [90] 4 or [0, 90] S stacking sequence

1st- Simulation of various material cases using a micro /macro approach

2nd- Calculation of the 3 required strain fields

3rd- Identification of the 9 parameters

4th- Results expressed as a ‘ratio’ vs. ‘anisotropy’

24 different casesAnisotropy ratio from 0.20 to 0.74

• with the normalized test geometry• using a FEM approach

• with the Lekhnitskii-based algorithm

Study of anisotropy vs geometrical modelling errors


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Study of anisotropy vs geometrical modelling errors

Poisson ratio ννννxy Transverse Young modulus ΕΕΕΕyy

Geometrical modelling errors grow with anisotropy

Use regression curves to correct identified materia l parameters


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An attempt to correct geometrical modelling errors

4(4�3(� 15�+�(� 15��-(3 15�Identified values

4(4�(� 15��+ 15�+4 15�Reference values

3�(+ 68-(� 68Mean error for all

studied cases

ν�01�0/00/��

Correction approach too simple and regression curve s unable to follow data scattering induce low confidence in corrected values.In particular, highest errors (up to 98%) for low P oisson’s ratio.

It is necessary to include the FEM within the identification procedure


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Final results using experimental maps and a FEM

(reference values from 3 classical tensile tests)


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ConclusionsFinally, identified mechanical parameters in agreement with classical tests (<6 %)

Necessity of using a FEM within the identification procedure

These identification studies show that extrapolating the normalized open hole tensile test to other geometries is questionable because of the anisotropy / geometry interaction.

PerspectivesExperimental techniques

Use of a simpler OFFM Technique (Speckle shearography)

Further results with other reference materials

V- Conclusion

Conclusions and Perspectives

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A hole subjected to uniform remote load at infinity

Γ

Solution for in-plane deformation in the case of plane stress state

traction-free boundaryconditionalong Γ

4=Γ

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−= ∞

∞

∞

∞

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σσ

σσ

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Under the conditionof the uniform stress

at infinity

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= ∞

∞

∞

∞∞

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εε

εε �

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−��

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= ∞

∞

∞

∞∞

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σσ

σσ

$�� σσ =∞

4== ∞∞�� σσ

Lekhnitskii’s solution in the case of the hole on a thin plate of which size are

considerably larger than the hole diameter

[ ] ∞−− += �!"#��

9� ς

[ ] ∞−− += !"" ��

9� ςSolution

Numerical simulation: Lekhnistskii’s analytical approach


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