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Composite design Composite design procedure for racing procedure for racing

carscars

Mario SacconeStructural Analysis EngineerDallara Automobili

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AbstractIn this document few tested procedures to design composite parts for racing cars:

For both approaches a global or a ply-by-ply analysis is possible

Checking the Principal stresses and using failure criteria like Tsai-Wu or maximum strain

!Checking the Strain Energy !The strains!The deformations COMPOSITE PARTSCOMPOSITE PARTS

" Thickness" Shape" Material (Al, Fe, Mg,)" Adding or removing ribs

Possible modifications:

"thickness and angle of the single ply"materials, type of fiber, Tape or Fabric"shape "Use of different cores"special reinforcements into the lay-up

Possible modifications:

Checking the Von Mises Stresses < Yield stress

Checking the deformationsMETAL PARTSMETAL PARTS

DESIGN for STRENGTHDESIGN for STRENGTHDESIGN for DESIGN for STIFFNESSSTIFFNESS

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Introduction

Main differences with metals:! Composite materials are orthotropic and not isotropic! Tensile and compressive strength are different! The strengths along the fibers are different from those

transverse to them! Shear strength is also independent making a total of five

strengths instead of one! The elastic modulus changes drammatically according to the

material used, the angle, the kind of fiber and the type of prepreg (tape or fabric)

! Delamination problems! They dont have yield point so they completely work in the

linear field! Low properties for load out of plane and mainly depending

from the matrix system

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Composite common use at DallaraMonolithic structures

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Basic Composite Theory

Tension load σ = εE Flexural load

In a typical laminate ε remains constant but E changes it means we have different stresses through the thickness.

This effect determines the necessityto check the laminate ply by ply

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Basic Composite Theory

Angle influence on Elasticity Modulus of

Compositesvs.

aluminum

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DESIGN for STIFFNESSDESIGN for STIFFNESS

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Strain Energy concept Recall from mechanics of solids that for a linearly elastic

material the unit strain energy (strain energy per unit volume) is given by:

012

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T

x

y

zx y z xy xz yz

xy

xz

yz

εεε

σ σ σ τ τ τγγγ

Ω =

σ ε

=

( )u xε = ∂

( )( )( )

0 0

0 0

, ,0 0

, ,0 , ,

0

0

x

y

z

xy

xz

yz

x

y

u x y zz

v x y z

w x y zy x

z x

z y

ε

ε

ε

γ

γ

γ

∂

∂

∂

∂

∂

∂=

∂ ∂

∂ ∂

∂ ∂

∂ ∂

∂ ∂

∂ ∂

3D Strain definition

Low level study for quick response

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Strain Energy in FEM practical useInstead of a long ply by ply check we use the strain energy result as a quick quality value to reinforce composite structures in the first design step. For more accurate analysis we

later check the strain.

Dallara LMP900 for 24h of Le Mans TORSIONAL TEST

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FEA validationSP1 CHASSIS

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0 500 1000 1500

[mm]

[°]

FEM

Experimental test

Experimental TORSIONAL TEST

FEM TORSIONAL TEST

Gap between reality and FEA always < 10%

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DESIGN for DESIGN for STRENGTHSTRENGTH

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Failure Criteria

ZTL Hypothesis

aσx

2

Rm1t Rm1c⋅

σy2

Rm2t Rm2c⋅+

σxy2

Rm12 Rm12⋅+ 2 F12_Star⋅

1

Rm1t Rm1c⋅ Rm2t⋅ Rm2c⋅( )⋅ σx⋅ σy⋅+:=

b σx1

Rm1t

1Rm1c

−

⋅ σy1

Rm2t

1Rm2c

−

⋅+:=

a 0.013=

b 0.182=

c 1−:=

RFzfbb− b2 4 a⋅ c⋅−+

2 a⋅:= RFzfb 4.245=

Safety Factor FormulationSafety Factor FormulationInput data:

!X: Ultimate tensile strength 0°!X:Ultimate compressive strength 0°!Y: Ultimate tensile strength 90°!Y:Ultimate compressive strength 90°!S: In plane shear strength

But composite materials have different properties at 0° and 90°:

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Tsai-Wu Failure Criteria

Failure envelope of TSAI-WU Criterion

TSAI-WU Criterion for different composite materials

The formulation has an interaction term to keep in account if you are using a UD or a Fabric

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Failure Criteria Procedure

FIRST PLY FAILURE (F.P.F)FIRST PLY FAILURE (F.P.F)..

..

IteractiveIteractive ProcedureProcedure..

..

LAST PLY FAILURE (L.P.F)LAST PLY FAILURE (L.P.F)

Similitude with metal stress-strain curve

We work to stay far away from the We work to stay far away from the first ply failure like from the yield first ply failure like from the yield

stress for metalsstress for metals

Sorting ply by ply through the thicknessof the laminate we check:

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Carbon Monocoquehomologation tests

No failure on the chassisMax displacement: 50 mmFIA delegate must attend all the tests

Article 17 of FIA Roll structure testing

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FEA STRUCTURAL ANALYSIS

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PLY BOOKSIDE TESTSIDE TEST FRONT ROOL HOOPFRONT ROOL HOOP MAIN ROOL HOOPMAIN ROOL HOOP

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HOMOLOGATIONAfter all the calculations a real test has to be performed and passed successfully in order to homologate the car.

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Direct influenceon the Ply Book

IRL ROLL HOOP TESTReal pre-test Simulation model

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FEA benchmarkPRO/MECHANICA (release 22) NASTRAN (Femap release 7.0) HYPERMESH & OPTISTRUCT 5.1

In use at Dallara

P-element mesh H-element mesh

In order to verify the quality of our calculation procedure we made a benchmark with the reference software: NASTRAN

H-element mesh

Global discrepancy of the safety factor valueamong the 3 different softwares < 3%

In use at Dallara

Real test to homologate the car passed successfully

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CONCLUSION

! Composite materials work in the linear field as the major FEA codes so the results of the calculation could be quite realistic.

! On the other hand the parameters to play around are a lot and complex! Design for stiffness or for strength are two completely different approaches and the

second needs much more input data than the first one! The manufacturing problems (ignored in this discussion) had to be seriously kept in

account because a human is going to laminate most of the parts end FEM model could be quite different from the real one, in other words we should think composite and not any more metal during the analysis.

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REFERENCES

Structural Materials Handbook (ESA) Engineered materials handbook COMPOSITES (ASM) Theory of composites design (Stephen W. Tsai, Stanford

University) BOEING Procedures Advanced Composites Group procedures