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Analysis oflaminates after initialfailure

Accounting forthemodification

ofstiffness inthefailed layers

Common

practice:

set

all

lamina

properties to

zero when failure occurs

(gives a

conservative

estimate of

the

load carrying capacity)

forthefailed ply

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2

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Example:5mmsymmetriccrossplyconstructed from 15identical laminae

p es

at an

p es

at ,

oa n

tract onN

x

Step 1:

Failure of

the

90 plies

x ens ona s ness ma x e o e a u e o e p y

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Step 2:failure ofthefirstply (maximumstrain theory)

Failure stresses

Calculation of

the

failure strains

Failure strains

The

90 ply will fail when x=0.00153

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The

load Nxleading tothefailure ofthe90 ply is solutionof

After thefailure ofthe90 ply,

90

Thefailure occurs for

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Flowchart for

laminate

strength analysis

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Shortfiber composites

onven en orcomp ex geome r es

Canbe mixedwith liquid resin andused ininjectionmolding(ininjectionmoulding,thefinalorientationofthefibers depends ontheflowinthemould)

Random oriented fibers arenearly isotropic

Notsuitable forcritical structures(less strength andstiffness),

butthis may changewith carbon nanotubes

Glassfiber reinforced nylon

with random fiber orientation

(Agarwall,Fig 4.11) 1

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Stresstransfer theory foraligned discontinuous fibers composites

Matrix shear deformation inarepresentative volume(Gibson)

Equilibrium alongz:

0

Thestressat the

fiber endis neglected

2

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We assumearigidplasticbehaviour ofthematrix.

(theinterfaceshear stressis constanty)

,

Andthemaximumoccurs at themiddleofthefiber

However,thefiber stresscannot exceed thestressthat

would occur inacontinuous fiber ,forwhich

Thiscorrespondsto

Theload transfer lengthis the

toreach this value

3

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Forafixed lengthl,ifoneincreases thecompositestressc fu

Thecritical fiber lengthis that which allows to

reachfu:

lcis also called

Ineffectivelength

4

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Numerical results:1.Elastic analysis

r

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Numerical results:2.Elasticplastic analysis

Interfacial shear stressnear fiber

endis notconstant,because of3D

yield stresscriterion is used.

6

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Modulus ofaligneddiscontinuous fiber composites

HalpinTsai (curve fitting on

numerical solutions)

(Same asfortransversemodulus ofcontinuous fibers with =2l/d)

(Same asfortransversemodulus ofcontinuous circular fibers :=2)

VariationofELofaligned shortfibers asafunction

oftheaspectratiol/d,fordiffernet valuesofEf/Em

7

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Asymptotic valueofELforlargel/d

(HalpinTsai convergestowards therule ofmixture)

Modulus ofshort

fiber composites

withrandomly oriented fibers

Empirical formulae:

WithELandETcorresponding toaligned shortfibers with

thesame aspectratiol/dandthesame volumefractionVf

Since thematerial is isotropic,

8

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1.Aligned shortfibers (HalpinTsai)

9

.

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Strengthofalignedshortfiber composites

Ifl>lc,thefibers will reach thefailure stressfu

Forvery small fiber volumefractions:thevalueforcontinuous fibers

is further lowered bylargestressconcentrations

Strengthofrandomlyoriented shortfibers

continuous laminate with thesame volumefractioncorrelate well with experiments.

Equivalentquasiisotropic laminate:

Analysis uptothefailure ofallplies

Maximumstrain theory

10

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Sandwichstructures

Plateswith similar flexural rigidityEI

11

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Simplified stressanalysis insandwichstructures

Bending stressesareintheskinonly,anduniform.Shear stressesareinthecore only,anduniform.

Thebending deflection is dependent onthetensile andcompressivemoduli intheskinmaterial.

12

.

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Sandwichpanelfailure modes(Hexcel composites)

13

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14http://www.hexcel.com/Resources/DataSheets/Brochure DataSheets/Honeycomb_Sandwich_Design_Technology.pdf