22023916 Fibre Reinforced Polymer FRP Analysis and Design

8/9/2019 22023916 Fibre Reinforced Polymer FRP Analysis and Design

1/25

_________________________________________________________

_________________________________________________________

Fibre Reinforced Polymer (FRP) Analysis and DesignSECOND EDITION NOV 2009

ENGR SREEJIT RAGHUMEng DIC ACGI MIStructE CEng MIEM

Ove Arup & Partners International Ltd 13 Fitzroy Street, London W1T 4BQ tel +44(0) 20 7636 1531 fax +44 (0) 20 7755 2150 email [email protected] internet www.arup.com


2/25

Fibre Reinforced Polymer (FRP) Analysis and Design Second Edition

TABLE OF CONTENTS ACKNOWLEDGEMENTS .......................................................................................................................................3 1.1 FIBRE REINFORCED POLYMER (FRP) ANALYSIS AND DESIGN ......................................................................4Introduction ...................................................................

................................................................................

...................................4 The Reinforcement Fibre ...................

................................................................................

..............................................................4 The Polymer (Resin) Matrix ............................................................................................................................................................6 The Additives ....................................................................................................................................................................................8 The Composite Laminate Forming Processes.................................................................................................................................9 Modelling and AnalyzingFibre Reinforced Polymer (FRP) Composite Laminates in MSC.NASTRAN ..............

.................10The Ply.........................................................................

................................................................................

........................................................... 10 The Composite Laminate, Sandwich Structures and Structural Members with Attached Laminates ...................................................................... 14 Failure Modeand Failure Criteria of the Composite Laminate ............................................................................................................................... 16 MSC.NASTRAN Finite Element Modelling of Composite Laminate Summary .................................................................................................... 18

1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.6

1.1.6.1 1.1.6.2 1.1.6.3 1.1.6.4

BIBLIOGRAPHY.....................................................................................................................................................20

2


3/25


ACKNOWLEDGEMENTS My humble gratitude to the Almighty, to Whom this and all workis dedicated. A special thank you also to my teachers at Imperial College of Science, Technology and Medicine, London and my fellow engineering colleagues at Ove Arup and Partners London and Ramboll Whitbybird London.

Engr Sreejit Raghu

3


4/25


1.1 1.1.1

Fibre Reinforced Polymer (FRP) Analysis and Design 1 Introduction

A Fibre Reinforced Polymer (FRP) composite laminate is a material composed of pl

ies. Each ply consists of fibres within a polymer matrix with the addition of additives. The fibres impart strength and stiffness to the composite and also actas crack stoppers for good fatigue resistance. The matrix binds the fibres together, transferring loads from fibre to fibre. The matrix also protects the fibresfrom mechanical abrasion and chemical reactions with the environment. The mechanical properties are predominantly governed by the fibres; fibre type, fibre length, fibre volume fraction and fibre orientation. The chemical properties, behaviour in fire and durability are largely governed by the properties of the matrixpolymer. Together, the FRP composite presents a robust material solution with good stiffness/weight and strength/weight ratios, good fatigue and corrosion resistance and favorable cost savings in transportation, assembly and construction due to its relatively light weight despite its unfavorable material cost / weight

ratio. 1.1.2 The Reinforcement Fibre Glass E-Glass: 2500 R-Glass: 3200 Carbon HT-Carbon: 3200 HM-Carbon: 2500 Aramid (Kevlar TM) 2900

Property Tensile Strength, f, ult (MPa) Compre ive Strength, f, ult (MPa)

Stiffne (GPa)

Poi on Ratio, f De sity, f (kg/m3) Mate ial Cost 2 / kg Coefficie t of The mal Expa sio , f (Str in/C) Imp ct Resist nce (Brittle F ilure Toughness) F tigue Fire

E-Glss: Ef = 74 Eft = 74 Gf = 30 R-Gl

ss: Ef = 86 Eft = Gf = Gl

ss fibre is i

sotropic. E-Glss: 0.25 R-Gl

ss: 0.2 Low; E-Gl

ss: 2600 R-Gl

ss: 2500 Low; 2.5 L

ow; E-Gl ss: 0.5E-5 R-Gl ss: 0.3E-5 Dependent upon el stic str in energy bsorbed;

HT-C rbon: Ef = 230 Eft = 15 Gf = 50 HM-C rbon: Ef = 390 Eft = 6 Gf = 20 C rbon fibre is

nisotropic. HT-C

rbon: 0.3 HM-C

rbon: 0.35 Very Low; HT-C

rbon: 1750

HM-Crbon: 1800 High; 10.0 200.0 Very low; HT-C

rbon: 0.02E-5 HM-C

rbon: 0.08

E-5 Dependent upon el stic str in energy bsorbed; See Section 1.1.3.

Ef = 130 Eft = 5.4 Gf = 12 Armid fibre is

nisotropic.

0.4 Very Low; 1450 High; 20.0 Low; -0.2E-5 Dependent upon el stic str in energybsorbed;

Retin strength up till melting point (over 1000

Oxidise inir

bove 650 C. Combustible.

Limited to 200 C. Combustible.

1

GAY, Dniel, HOA, Suong, TSAI, Stephen. Composite M

teri

ls Design

nd Applic

ti

on. CRC Press, London, 2003.

2

NB: Cost reductionsre however m

de in erection

nd tr

nsport

tion due to the l

ighter weight.


5/25

4


6/25

Fibre Reinforced Polymer (FRP) Anlysis

nd Design Second Edition

C). Combustible. Susceptible only when in contct with

luminium c

using

g

l

vnic phenomenon which le

ds to r

pid corrosion.

Corrosion Resist

nce

Not susceptible.

Not susceptible.

Creep Coefficient of Therml Conductivity

t 20C, (W/mC) Heat Capacity, c (J

/kgC) E

ectrica

Conductivity Low; E-G

ass: 1 R-G

ass: 1 E-G

ass: 800 R-G

ass:800 Non-conducting. Attacked by a

ka

is (pH greater than 11) but not by acids. Very high; HT-Carbon: 200 HM-Carbon: 200 HT-Carbon: 800 HM-Carbon: 800 Conducting. Very

ow; 0.03 1400 Non-conducting. Aramids absorb much more water than eitherg

ass or carbon causing prob

ems with the resin/fibre interface. Changes co

ourand the strength reduce. However, when embedded in resin, overa

mechanica

properties

itt

e affected. Non-toxic and inert. Does not contaminate groundwater.

Chemica

Resistance

Good.

UV Resistance

Good.

Good.

Sustainabi

ity Transparency to Radio Frequency E

ectromagnetic Considerations

Non-toxic and inert. Does not contaminate groundwater.

Non-toxic and inert. Does not contaminate groundwater.

5


7/25

Fibre Reinforced Po

ymer (FRP) Ana

ysis and Design Second Edition

1.1.3

The Po

ymer (Resin) Matrix

There are two types of po

ymer; thermosets and thermop

astics. Once cured (harde

ned) by a chemica

reaction, a thermosetting po

ymer wi

not me

t or soften when subsequent

y heated. A thermop

astic po

ymer softens when heated and hardens upon coo

ing. Common thermoset po

ymers are po

yester, epoxy and pheno

ic. Property Tensi

e Strength, m, ult (MPa) Compre ive Strength, m, ult (MPa) Stiffne

(GPa) Poi on Ratio, m De sity, m (kg/m3) Mate ial Cost / kg Coefficie t ofThe mal Expa sio , m (Str in/C) Imp ct Resist nce (Brittle F ilure Toughness)Polyester 80 Epoxy 130 Phenolic 70

Em: 4.5 Gm: 1.4 Polyester is isotropic. 0.4 1200 2.5 High; 8E-5

Em: 4.5 Gm: 1.6 Epoxy is isotropic. 0.4 1200 5.0 10.0 High; 11E-5

Em: 3.0 Gm: 1.1 Phenolic is isotropic. 0.4 1300 10.0 Low; 1E-5

F

tigue

Fire

F

tigue resist

nce of FRP composites is gener

lly better th

n th

t of met

ls

sthe fibres

ct

s cr

ck stoppers - up to 1000000 cycles no f

tigue limit. Unlike

metls, f

tigue f

ilure is gr

du

l

s the m

trix cr

cks

nd fibres debond. Gene

r

lly, nonprop

g

ting stress r

nge estim

tes for composites c

n be

s high

s 90% of st

tic strength (cf. th

t for steel

nd tit

nium being 50%

nd

luminium 35%). Although the fibres

re not fl

mm

ble, the polymer m

trix is inherently fl

m

mble. Although thermoset polymers do not melt when he

ted, they do soften (Youn

gs Modulus decre ses) bove the gl ss tr nsition temper ture Tg, typic lly 60 70 C. This gre

tly influences the m

ximum service temper

ture of

FRP composi

te nd its structur l perform nce in fire. The temper ture t which FRP composite softens is c lled the He t Distortion Temper ture (HDT) nd is rel ted toTg.

Corrosion Resist nce All polymers used in FRP composites displ y viscoel stic ortime (

nd temper

ture) dependent properties. M

teri

ls with

high gl

ss tr

nsi

tion temperture (Tg) h

ve higher creep resist

nce. Creep is of prim

ry signific

nce for structures under

sust

ined lo

d. Creep in FRP composites is prim

rily

m trix deform tion. A FRP composite with fibres ligned in the direction of the

pplied stress, creep is unlikely to be

signific

nt problem, while lo

ding

offxis to the fibre direction m

y result in excessive deflection. The design m

ethodology should be bsed on limiting the intern

l str

ins in the m

trix. Axi

l

str in levels should be less th n 0.2% str in. Creep curves re v il ble for estim

ting creep modulus (long term modulus). Low; 0.2 Low; 0.2 Low; 0.3

Creep

Coefficient of Therml Conductivity

t 20C,

6


8/25

Fibre Reinforced Po

ymer (FRP) Ana


(W/mC) Heat Capacity, c (J/kgC) E

ectrica

Conductivity Resistant to grease, oi

s, paints, so

vents, petro

eum. Po

yester resins attack po

ystyrene foam in sandwich structures. Good. Maintains appearance > 20 years. Used as protective ge

coat on composites with a more UV sensitive po

ymer. Appearance changes

ong before significant mechanica

property degradation. Resistant to grease, oi

s, pai

nts, so

vents, petro

eum. Epoxy resins can absorb water by diffusion up to 6% ofmass. Paint thinners attach epoxy resins. 1400 1000 1000

Chemica

Resistance

Resistant to grease, oi

s, paints, so

vents, petro

eum.

UV Resistance

Sustainabi

ity Transparency to Radio Frequency E

ectromagnetic Considerations Anapp

ication where it has been particu

ar

y usefu

to use FRP composites is where concrete members require non-ferrous reinforcement due to e

ectromagnetic cons

iderations e.g. MRI scanner rooms; airport radio and compass ca

ibration pads; high vo

tage e

ectrica

transformer vau

ts; concrete near high vo

tage cab

es andsubstations.

7


9/25

Fibre Reinforced Po

ymer (FRP) Ana


1.1.4

The Additives Remark To counteract UV effects on appearance and the degradationof mechanica

properties, additives can be b

ended with the po

ymer during processing. Photo stabi

izing additives protect the po

ymer chains by reacting prefer

entia

y with UV

ight - UV absorbers. Pigments can a

so protect the po

ymer byref

ecting the UV radiation. Meta

ic pigments can be used as effective ref

ectors. Zinc oxide (ZnO) is another effective ref

ector. However, the most effectiveref

ector is carbon b

ack. It is often used to enhance the

ifespan of po

ymersexposed outdoors. Co

ors that can be particu

ar

y prone to fade inc

ude reds, ye

ows and paste

co

ors.

Property

UV Resistance

8


10/25

Fibre Reinforced Po

ymer (FRP) Ana


1.1.5

The Composite Laminate Forming Processes Description Contact Mo

ding (Hand Lay Up) Open mo

ding since there is on

y one mo

d. Reinforcement is mats or fabrics.Compaction is done using a ro

er to squeeze out air pockets. Labour intensive a

nd high qua

ity workmanship required. C

osed mo

ding as the countermo

d wi

c

ose the mo

d to app

y pressure after impregnated reinforcement (fabrics or unidimensiona

s) p

aced on mo

d. Vacuum is app

ied under a soft p

astic sheet on the open mo

d and piece is compacted under atmospheric pressure to e

imitate air bubb

es.

Forming Process

Compression Mo

ding Vacuum Assisted Resin Transfer Mo

ding VARTM (a.k.a. Depression Mo

ding or Bag Mo

ding) Resin Transfer Mo

ding RTM

Mo

ding impregnation of fibres into resin p

acing mixture on too

compaction po

ymerization demo

ding finishing

Sheet Forming Profi

e Forming (Pu

trusion) Stamp Forming Three Dimensiona

Assemb

y Cutting

Resin is injected into the preformed reinforcement (unidimensiona

s, fabrics, mats) p

aced between the mo

d and countermo

d. Premixed (a.k.a. Bu

k Mou

ding Compound B.M.C., i.e. Injection of Premixed mixture of cut short fibres in a resin matrix) is fed into Mo

ding mo

d and countermo

d in a high

y automated fashion. Mo

ding by foam injection a

ows the processing of po

yurethane foam reinforced with g

ass fibres in mo

d Foam Injection Mo

ding and countermo

d. A

ows for thefabrication of tubes using short fibres. Centrifuga

Mo

ding Fi

ament winding isused to form tubes with continuous fibres wound he

ica

y within the component.

The fibres are coated with po

ymer resin and wound around a Fi

ament Winding mandre

to create the desired shape. The winding ang

e may be varied to orientatethe fibres to give the desired properties in different directions. A

ows the production of p

ane or corrugated sheets. Pu

trusion invo

ves pu

ing reinforcement fibres (unidimensiona

s, fabrics or mats) coated in a po

ymer resin through adie. On

y app

icab

e to thermop

astic composites. Preformed p

ates are heated, stamped and then coo

ed. Woven tows a

ong severa

directions in space assemb

ed before impregnation using

iquid or gas. A programmed cutting machine can cut components into shapes required by the design.

9


11/25

Fibre Reinforced Po

ymer (FRP) Ana


1.1.6

Mode

ing and Ana

yzing MSC.NASTRAN The P

y

Fibre

Reinforced

Po

ymer

(FRP)

Composite

Laminates

in

1.1.6.1

The reinforcement fibres are manufactured to be as thin in diameter (d) as possib

e because their rupture strength decreases as their diameter increases. The minimum effective fibre

ength (critica

fibre

ength,

c) is dependent on the fibre diameter (d) and its u

timate tensi

e strength, f, ult and on the fibre-matrix bond trength (or the hear trength of the matrix) c according (simplis

ically)

o lc = f, ult d / c For a number of glass and carbon fibre-ma

rix combina

ions,

his cri

ical leng

h is on

he order of 1 mm, which ranges be

ween 20 and 150

imes

he fibre diame

er. Fibres for which l >> lc (normally l > 15lc) are

ermed con

inuous; discon

inuous or shor

fibres have leng

hs shor

er

han

his. For discon

inuous fibres of leng

hs significan

ly less

han lc,

he ma

rix def

orms around

he fibre such

ha

here is vir

ually no s

ress

ransfer and li

lereinforcemen

by

he fibre. The forms of

he reinforcemen

fibres are i. Unidimensional (con

inuous fibres) ii. Bidimensional woven fabric (con

inuous fibres)iii. Bidimensional ma

(shor

or con

inuous fibres) iv. Mul

idimensional fabric(con

inuous fibres) 1.1.6.1.1 Mechanical Proper

ies of

he Unidimensional Ply

Two dimensional aniso

ropic ma

erials (MAT2) can be fully defined from 7 independen

cons

an

s, Ex, Ey, yx, xy, Gxy, Gxz, Gyz. Ex 1 xy yx x xy E y y = 1 xy yx xy 0 yx E x 1 xy yx Ey 1 xy yx 0 0 x x 0 Tr

f ) y 0 G xy xy

xz G xz = yz 0

0 xz G yz yz

Two dim

nsionl or

ho

ropic m

rils (MAT8) c

n b

fully d

fin

d from 6 ind

p

nd

n

cons

n

s, 3 from Ex, Ey, yx a

d xy due to the symmet y elatio

xyEy =yxEx a

d also Gxy, Gxz, Gyz. Ex 1 xy yx x xy E y y = 1 xy yx xy 0 yx E x 1 xy yx Ey 1 xy yx 0 0 x x 0 Tr

f ) y 0 G xy xy

xz G xz = yz 0

0 xz G yz yz

Two dim

nsionl (pl

n

s

r

ss) iso

ropic m

ril (MAT1) c

n b

fully d

fin

d fr


12/25

om 2 ind

p

nd

n

cons

n

s from E, Gnd as G = E / [2(1+)].

10


13/25

Fib e Rei fo ced Polyme (FRP) A alysis a d Desig Seco d Editio

E x 1 2 E y = 2 1 xy 0

E 1 2 E 1 2 0

0 x 0 y (T Tr

f ) 0 G

xz G 0 xz = yz 0 G yz

A fundm

n

l physic

l diff

r

nc

in

h

d

form

ion b

w

nn iso

ropicnd

n

or

ho

ropic m

ril sh

ll b

m

n

ion

d. Ifn iso

ropic m

ril is s

r

ss

d,

h

d

form

ion of

h

l

m

n

will b

llipsoidl wi

h

h

x

s of

h

llipsoid coincidin

wi

h

h

princip

l s

r

ss

x

s. How

v

r, if

n or

ho

ropic m

ri

lis s

r

ss

d,

h

d

form

ion of

h

l

m

n

will b

llipsoidl wi

h

h

x

s of

h

llipsoid no

coincidin

wi

h

h

principl s

r

ssx

s. Th

m

chnic

l pr

op

r

i

s ofply

r

d

fin

d on

h

MAT8 crd.

No

h

x d

no

s

h

lon

i

udinl dir

c

ion of

h

ply, y

h

rnsv

rs

in p

l

n

dir

c

ion of

h

ply

nd z

h

r

nsv

rs

ou

of pl

n

dir

c

ion of

h

ply; f d

no

s fibr

nd m

h

r

sin m

rix; f the longitudin

l direction of the fibre

nd ft the tr

nsverse direction of the fibre. Property of Ply The longitudin

l modulus, Ex (or E1) (Assumes str

ight

nd unidirection

l fibre orient

tion

nd tht the m

teri

l is bimodulus, i.e. s

me stiffness in tension

nd compressio

n) Expression Ex = EmVm + EfVf = Em(1Vf) + EfVf V V 1 1 or = m + f Ey = Em Em E y E m E ft (1 V ) + Vf f E f

xy = mVm + fVf = m(1Vf) + fVf

The ipla e t

a sve

se modulus, Ey (o

E2)

The i pla e Poisso s atio, xy (o NU12)

1 G xy = G m The i

pla

e shea modulus, Gxy (o G12) Gm (1 Vf )+ G Vf f If test data a e

ot available, the value of G12 may be The out of pla

e shea modulus, Gxz (o G1Z) used fo G1Z a

d G2Z. If ze o the

o shea flexibility o shea defo matio

s, i.e. i

fi

ite shea stiff

ess. If test data a e

ot available, the value of G12 may be The out of pla

e shea modulus, Gyz (o G2Z) used fo G1Z a

d G2Z. If ze o the

o shea flexibility o shea defo matio

s, i.e. i

fi

ite shea stiff

ess. 1 The i

pla

e modulus alo

g a

y di ectio

, E E = 1 xy cos 4 si

4 (Note the apid dec ease i

modulus i

di ectio

s + + 2 cos 2 si

2 2G xy E y away f om the lo

gitudi

al fib e) Ex Ey

11


14/25


whe e = a

ticlockwise a

gle f om x Mass de

sity, (o RHO) = mVm + fVf =m(1Vf) + fVf The lo

gitudi

al coefficie

t of the mal expa

sio

, = f E f Vf + m E m Vm x x (or A1) E f Vf + E m Vm ( f E m m E f ) ( f m ) Th

r

nsv

rs

co

ffici

n

of

h

rm

l

xp

nsion, y y = m Vm + f Vf + Em Ef+ (or A2) Vf Vm Vf f Mf = Fib e mass f actio

, Mf Vf f + Vm m Vf f Mm =1

Mf =1 Resi

mat ix mass f actio

, Mm Vf f + Vm m The fib e volume f actio , Vf depe ds la gely upo the ma ufactu i g p ocess used. Moldi g P ocess Co tact Moldi g Comp

essio Moldi g Filame t Wi di g Vacuum Moldi g Fib

e Volume F

ac

tio

, Vf 30% 40% 60% 85% 50% 80%

Co ve sely, if the fib e mass f actio Mf is k ow , the volume f actio s ca bede

ived as follows. P

ope

ty of Ply Fib

e volume f

actio , Vf Resi mat

ix volum

e f actio

, Vm Exp essio

Vf = M f / f M f / f + M m / m M f / f M f / f + M m / m

Vm = 1 Vf =

The thick

ess of the plies must be defi

ed o

the PCOMP ca

d (fo

each i

dividual PSHELL cad) as Ti. The thick ess is obtai ed as follows. 1 m 1 1 M f

Ti = of oTi = m of + Vf f f m M f whe e mof is the mass of

fib e pe m2 of a ea. 1.1.6.1.2 Mecha

ical P ope ties of the Bidime

sio

al Wove

Fab ic Ply

The fabics a

e made of fib

es o

ie ted alo g two pe

pe dicula

di

ectio s, o e

called the wa p a d the othe called the fill di ectio . The fib es a e wove togethe , which mea s that the fill ya s pass ove a d u de the wa p ya s, followi g a fixed patte

. Each fabic laye

is co side

ed to be a si gle a isot

opi

c layeof thick ess Ti with app

oximate mecha ical p

ope

ties as follows. Defi

e 1 k= 1 + 2 whe e 1 is the umbe of wa ps ya s pe met e a d 2 is the

umbe of fill ya s pe met e. The Exfab ic kEx + (1k)Ey Eyfab ic (1k)Ex

+ kEy

12


15/25


Gxyfab ic Gxy xyfab ic xy k + (1 k ) Ex Ey

whee Ex, Ey, Gxy a d xy a

e values obtai ed by co side

i g the wove fab

ic pl

y to be a u

idi ectio

al ply, i.e. with both the wa p a

d fill ya

s to be i

th

e same di ectio

such that the total volume f actio

, Vf would be the same as that of o e u idi ectio al ply. Note that the stiff ess of a wove fab ic will beless tha two e uivale t (with the two u idi

ectio al plies havi g the same fib

e volume f actio

as the o

e wove

fab ic ply) u

idi ectio

al plies o thogo

al to o e a othe because of the cu vatu e of the wove fib es ove a d u de the o thogo al fib es. The thick ess of the a isot opic ply would be Ti as with the u

idiectio al ply. 1.1.6.1.3 Mecha ical P

ope

ties of the Bidime sio al Mat Ply

Mats a e made up of sho t cut fib es o co ti uous fib es such that they a e isot opic withi thei pla e. He ce thei p ope ties ca be app oximated by just two co sta ts (a d he ce usi g MAT1) app

oximately as 3 5 E mat E x + E y 8 8 E

mat G mat 2(1 + mat )

mat 0.3 whe

e Ex a

d Ey a

e the elastic moduli alo

g the lo

gitudi

al a

d t

a svese di

ectio s of a u idi

ectio al ply with the same volume f

actio Vf.

The thick

ess of the mat ply would be Ti as with the u

idi ectio

al ply. 1.1.6.1.4 Mecha ical P ope ties of the Multidime sio al Fab ic Ply

Multidime sio al fabic plies has the

ei fo

ceme t assembled acco

di g to p

e

e

stablished di ectio s. The ply is isot opic withi its pla e.

13


16/25


1.1.6.2

The Composite Lami ate, Sa dwich St uctu es a d St uctu al Membe s with AttachedLami ates

The e a e th ee types of lami

ated co

st uctio

. These i

clude the all lami

atedco st uctio co sisti g of elatively high stiff ess a d st e gth laye s, the sa dwich st

uctu

e lami atio co sisti g of at least two high stiff ess a d st

e

gth oute laye s co

ected by a co e, a

d a thi d type co

sisti

g of a st uctu al membe that is ei fo ced o the te sile o comp essio o both sides of a flexu al beam. 1.1.6.2.1 Mecha ical P ope ties of the Composite Lami ate

A composite lami

ate is comp ised of a

umbe of plies. These ca

be defi

ed usi g the PCOMP e t y that efe s to the mate ial ca ds of the i dividual plies MIDi, thei thick ess Ti a d the o ie tatio of the ply lo gitudi al axis f om theMCID by THETAi.

Plies a

e always defi

ed bottom up (Z0 = 0.5 x total eleme

t thick

ess Ti). Thee is a ge ui e eed fo

a midpla e symmet

y (e su

ed by specifyi g LAM = SYM

) because dui g the cooli g p

ocess of ma ufactu

e, the plies have the te de cy

to co

t act diffe e

tly depe

di

g o

thei o ie

tatio

s. With symmet y of the midpla e, o u ifo m co t actio is avoided. Typical lami ate lay ups of u idi ectio al plies a

e [90/02/45/45]S a d 0 / 45 / 45 / 90 S . Note that these a

e

defi ed bottom up. The Ssubsc

ipt i dicates a set of symmet

ic plies. The 2

sub

sc ipt i dicates two plies. The hyphe above the umbe i dicates that it is themidpla e ply. The 0 / 45 / 45 / 90 S lay up is eally the tech ological mi imum with the mi imum thick ess of the lami ate bei g a

ou d 1mm. The plies should

be oie tated such that the

e a

e fib

es o

ie tated i both the maximum a d mi

imum p i cipal st ess di ectio s. The e should also be o mo e tha 4 co secutive plies alo g the same di ectio . The plies should be p og essively te mi ated t

o obtai

a g adual cha

ge of thick

ess (maximum 2 plies fo each 6mm i

te val).Lami

ate lay up which a e symmet ic ca

also be made up of fab ics, which ca

bethought of as a pai of o thogo

al plies a

d also of mats, which a e isot opici

pla

e. 1.1.6.2.2 Mecha

ical P ope ties of Sa

dwich St uctu es

[ [

] ]

Sa

dwich st uctu es a e made up of two faci

gs sa

dwichi

g a light flexible co e, he

ce agai

defi

able with a PCOMP e

t y. The faci

g ca

be a composite lami

ate of ma

y a

isot opic MAT8 plies o simply a laye of isot opic MAT1 mate ial s

uch as alumi

ium. The co

e ca

be deemed as just a

othe

laye

withi

PCOMP witha elatively much g eate thick

ess. A sig

ifica

t be

efit of sa

dwich st uctu es is the fact that they a e ext emely light whilst havi

g a high flexu al igidity due to the sepa atio

of the su face ski

s. The mass pe u

it a ea of the dome of the Sai

t Pete s Basilica i

Rome (45m diamete ) is 2600 kg/m2 whe eas the same dome made of steel/polyu etha

e foam sa

dwich (Ha

ove ) is o

ly 33 kg/m2.Ve y app oximate st ess fo mulae i

a 3 laye (co e T2 sa

dwiched by 2 faci

gsof thick

ess T1 a

d T3) sa

dwich st uctu e a e as follows. These a e useful ve ificatio

s of compute outputs.

14


17/25


Be

di

g st ess i

faci

gs =

M (per unit metre) a uming all bending i re i ted by the facing T2 + 1 (T1 +T3 ) (1m width ) 2 V (per unit metre) Shear tre in foam =

ssumin

ll

h

v

r

icl sh

r is r

sis

d by

h

cor

T2 (1m wid

h )

(

)

Th

pproxim

v

rific

ion of displc

m

n

s r

quir

s

h

s

im

ion of

h

s

iffn

ss of

h

s

ndwich s

ruc

ur

. Also, bo

h b

ndin

nd sh

r d

form

ions m

yb

si

nificn

, h

nc

bo

h b

ndin

nd sh

r s

iffn

ss

s mus

b

pproxim

ds

follows. No

h

T2 is

h

hickn

ss of

h

cor

nd Tf

cin

s is

h

hickn

ss of

h

fcin

s, i.

. T1 or T3. 2 2 wid

h . Tfcin

s . T2 + Tfcin

s wid

h . skin

hickn

ss . (

v

r

p

n

l d

p

h ) EI = E f

cin

s = E f

cin

s 2 2 GA s = G cor

T2 + 2Tfcn

s . wid

h

(

)

(

)

S

ndwich s

ruc

ur

s

r

susc

p

ibl

o

lob

l bucklin

ccordin

o Eul

r (includin

sh

r d

form

ions)

s 2 EI Fcr = K EI L2 + 2 K GA s where K = 1 for sim ly su orted, K = 4 for fixed ended, K = 2.04 for fixed- inned and K = 0.25 for cantilever. Sandwich structures are articularly susce tible to local buckling

of the facings. The critical com

ression stress is 1/ 3 3 2 cr = E facing

Ecore 2 2 1/ 3 12(3 co e ) (1 + co e )

[

]

(

)

The axial c itical fo ce i

a beam fo local buckli

g of the faci

gs is app oxim

ately E Tfaci

gs Fc = 1.64Tfaci

gs .width.E faci

gs co e E faci

gs T2 1/ 2

1.1.6.2.3

Mecha

ical P ope ties of St uctu al Membe s with Attached Lami

ates

This is utilized most ofte

i

co

st uctio

a

d i

f ast uctu e applicatio

s. PCOMP ca

be used to defi

e the attached composite lami

ates o

the fla

ges of thest uctu al membe s, but of cou se

ot the st uctu al membe s themselves becausethe o ie

tatio

of the web will be o thogo

al to the o ie

tatio

of the fla

ge.He

ce defi

e explicit PSHELL e

t ies fo the st uctu al membe s.

15


18/25


19/25


1.1.6.3

Failu e Mode a d Failu e C ite ia of the Composite Lami ate

The failu e mode of a ply is b ittle athe tha

ductile with

o sig

ifica

t yie

ldi

g u

til failu e at the ultimate te

sile st e

gth. The ply emai

s elastic u

til the ultimate limit st e gth. I light of this it has bee assumed that o lyelastic methods may be used, with o

edist

ibutio . If the loadi g is te sile a

lo

g the di ectio

of the fib es, it is assumed that the fib es b eak befo e themat ix. The comp essive st e gth alo g the di ectio of the fib es will be smalle tha the te sile st e gth alo g the same di ectio due to the mic o buckli gphe ome o of the fib

es i the mat

ix. To defi e a failu

e c

ite

ia a failu

e

theo y must be specified o

the FT field of the PCOMP e

t y f om eithe HILL fo Hill Tsai, HOFF fo Hoffma , TSAI fo Tsai Wu o STRN fo maximum st ai theo y. The allowable i te lami a shea st ess SB eeds also to be p ovidedi the PCOMP ca

d i case of i te

lami a

failu

e. The o the MAT8 ca

ds, the

allowable st ess o st ai

i

te

sio

a

d comp essio

i

lo

gitudi

al di ectio

Xt, Xc, i

the t

a

sve

se di

ectio

Yt, Yc a

d the allowable st

ess o

st

ai

foi

place shea

, S is

e ui

ed. Hill

Tsai is

eally fo

o

thot

opic mate

ials w

ith e ual ste gths i te sio a d comp

essio . The Hoffma a d Tsai

Wu theo

y

a e fo o thot opic mate ials with ge

e al state of pla

e st ess with u

e

ual st e gths i te sio a d comp essio . Note that the Hoffma theo y takes i to accou t the diffe

e ce i te sile a d comp

essive allowable st

esses by usi g li ea

te

ms i its e uatio . The Tsai

Wu howeve

is complicated by the eed to satis

fy a stability c ite io with a expe ime tally (biaxial loadi g) de ived pa amete F12 defi ed o the MAT8 ca d. Na aya aswami a d Adelma have thus suggestedthat F12 be set to ze

o a d the use of Hoffma

s Theo

y o

the Tsai

Wu theo

y wi

th F12 = 0 ae p

efe

ed alte

atives. STRN o the MAT8 with a value of 1.0 isadditio ally e ui ed fo the maximum st ai theo y to i dicate that Xt, Xc, Yt, Yc a d S a e st ai allowables, i stead of st ess allowables fo the othe c i

te ia.

16


20/25


The maximum st ai

c ite ia failu e i

dex is defi

ed as follows

STRN ca also be left bla k (as do e fo the othe c ite ia) eve fo the maximum st

ai theo

y to allow st

ess allowables i which case the maximum st

ai c

it

e ia becomes the maximum st ess c ite ia. Fo this case the failu e i

dices a e

calculated usi

g

The failue i dex of the bo di g mate

ial will be calculated as the maximum i te

lami

a shea st ess divided by the allowable bo

di

g st ess. Classical lami

atio theo y, which utilizes the pla e st ess assumptio , does ot accou t fo i te lami a st esses. As a esult, this theo y ca ot be used to p edict the mag itude of these st

esses. High values of these i te

lami a

st

esses ca lead to f

ailu es that a e u

i

ue to composite mate ials. A

app oximate tech

i

ue is usedto calculate the i te lami a shea st esses. The basic assumptio i this app oximate tech i ue is that the x a d y compo e ts of st ess a e decoupled f om o e a othe

. The i te

lami a

shea

st

ai s a

e calculated by

The Hill

Tsai failu

e c

ite

io

is defi

ed as follows fo

each a

d eve

y ply. = x x , ult + y y , ult 2

x y + xy 2 x , ult xy , ul

2

< 1.0 for no ply rup

ur

2

E wh

r

x, ult = f, ult Vf + (1 Vf ) m f, ult Vf Ef

The e corre pond to the entrie on the MAT8 card , the allowable tre in ten ion and compre ion in longitudinal direction Xt (x, ult), Xc (x, ult), in thetran ver e direction Yt (y, ult), Yc (y, ult) and the allowable tre for in-place hear, S (xy, ul

). If > 1,

h

n rup

ur

occurs in

h

ply consid

r

d,

n

rlly du

o

h

rup

ur

of

h

r

sin. Th

rup

ur

r

sis

nc

do

s no

hv

h

s m

v lu

in

nsion nd compr

ssion, h

nc

i

is us

ful

o pl c

in

h

d

nomin

ors of

h

HillTs

i

xpr

ssion

h

rup

ur

r

sis

nc

vlu

s corr

spondin

o

h

mod

of lodin

(i.

. wh

h

r

nsion or compr

ssion)

h

pp

r in

h

num

r

or. This is don

u

om

iclly in NASTRAN

s follows.

17


21/25

Fibr

R

inforc

d Polym

r (FRP) Anlysis

nd D

si

n S

cond Edi

ion

1.1.6.4

MSC.NASTRAN Fini

El

m

n

Mod

llin

of Composi

Lmin

Summry

Clssic

l l

min

ion

h

ory is

mploy

d, h

nc

incorpor

in

h

followin

ssum

p

ions: i. Th

l min

consis

s of p

rf

c

ly bond

d l min

or ply. ii. Th

bonds

r

infini

simlly

hinnd nonsh

r

d

formbl

; i.

., displc

m

n

sr

con

inuous

cross l

min

(or ply) bound

ri

s so

h

no l

min

c

n slip r

l

iv

ono

h

r. iii. Ech of

h

ply is ins

of pln

s

r

ss. Th

PCOMP prop

r

y crd is us

d for mod

llin

composi

m

ril consis

in

of ly

rs. This inform

ion is us

d in

rnlly wi

hin NASTRAN

o compu

quivl

n

PSHELL crds. T

h

inform

ion on

h

PCOMP c

rd includ

s

h

hickn

ss, ori

n

ion

nd m

ri

l id

n

ific

ion of

ch l

y

r. This inform

ion is us

d in

rnlly wi

hin NASTRAN

o compu

quivl

n

PSHELL crds. Sp

cil l

y

rby

l

y

r ou

pu

is provid

dwh

n

h

PCOMP op

ion is us

d. W

hv

sid

h

for sh

lls,

h

l

m

n

d

fini

ion

nd

l

m

n

s

r

ss r

cov

ry

r

p

rform

d in

h

l

m

n

coordin

sys

mby d

ful

(bu

d

fin

d by MCID

n

ry on

l

m

n

conn

c

ion crd; 0 for b

sic pr

oj

c

d, > 0 for us

r proj

c

d, < bl

nk > for

l

m

n

coordin

sys

m, > 0.0

nd < 360.0 for

n

l

d from sid

n1

n2 of

l

m

n

). (No

h

for b

ms,

h

l

m

n

d

fini

ion

nd

l

m

n

s

r

ss r

cov

ry

r

p

rform

d in

h

l

m

n

coordin

sys

m. For solid

l

m

n

s,

h

l

m

n

d

fini

ionnd

l

m

n

s

r

ss r

cov

ryr

p

rform

d in

h

bsic coordin

sys

m by d

ful

(bu

d

fin

d on CORDM fi

ld of PSOLID; 0 for b

sic, > 0 for us

r

d

fin

d,

1 for

l

m

n

coordin

sys

m)). In

h

c

s

of

h

PCOMP

n

ry,

h

l

m

n

coordin

sys

m r

quir

sfur

h

r subdivisions

h

r

r

mny pli

s. H

nc

h

THETAi fi

ld of

h

PCOMP

n

ry sp

cifi

s

h

n

l

from

h

coordin

sys

m d

fin

d by MCID on

h

l

m

n

conn

c

ion c

rd for

h

lon

i

udin

l

xis of

ch ply i. To d

fin

l

min

s wi

h PCOMP

nd num

rous or

ho

ropic MAT8 c

rds,

h

followin

proc

dur

is und

r

k

n. I. D

fin

common m

ril coordin

sys

m MCID for

h

CQUAD4

l

m

n

s. This would r

f

r

o

i

h

r

h

bsic coordin

sys

m (by sp

cifyin

0)

or us

r d

fin

d coordin

sys

m (by sp

cifyin

CORDij ID). In

h

usu l c

s

of uniform iso

ropic sh

lls, MCID c

n b

l

f

d

f

ul

d

o

h

individu

l

l

m

n

coordin

sys

m (by sp

cifyin

< blnk >), r

ndom

s

h

y my b

, b

cus

du

o

h

n

ur

of

h

l

m

n

s b

in

uniform nd iso

ropic,

h

om

ric d

fini

ion will b

h

xc

,nd

h

corr

c

consis

n

s

r

ss r

cov

ry will b

ob

in

d so lon

s

h

s

r

ss

sr

ro

d on

o

h

lobl

x

s sys

m by

h

pos

proc

ssor (of cours

hou

h

h

Z norm l mus

s

ill b

nsur

d

o b

coh

r

n

mon

s

dj

c

n

l

m

n

s for corr

c

s

r

ss r

cov

ry of

opnd bo

om surf

c

s). Bu

in

h

cs

of

h

or

ho

ropic sh

ll,

h

om

ric d

fini

ion r

quir

scoordin

sys

m. I

is b

s

o d

fin

sin

l

us

r d

fin

d coordin

sys

m for ll

h

l

m

n

s on

h

ir MCID fi

ld, no

in

h

h

l

m

n

coordin

sys

m will

h

n b

h

proj

c

ion of

h

d

fin

d sys

m on

o

h

l

m

n

pln

. Th

hickn

ss T1

o T4 should no

b

sp

cifi

d b

cus

inccord

nc

wi

h norml pr

c

ic

of d

finin

iso

ropic m

rils,

hickn

ss is sp

cifi

d in

h

prop

r

y c rd.

II.

D

fin

PCOMP c rd

h

r

f

rs

o

h

m

ri l c rds of

h

individu l pli

s MIDi,

h

ir

hickn

ss Tind

h

ori

n

ion of

h

ply lon

i

udinl

xis from

h

MCID, THETAi. Pli

sr

lw

ys d

fin

d bo

om up (Z0 = 0.5 x

o

l

l

m

n

hickn

ss Ti). SOUTi fi

ld r

qu

s

s by YES or NO s

r

ss ou

pu

for

h

individu l pli

s provid

d

h

h

ELSTRESS c s

con

rol comm nd is sp

cifi

d. Th

LAMfi

ld sp

cifi

s

h

lmin

op

ion from < blnk > for

xplici

ly sp

cifyin

ll

pli

s,

h

r

comm

nd

d SYM for sp

cifyin

hlf

h

symm

ricl pli

s from bo

om sid

(wi

h c

n

rlin

ply of h lf

hickn

ss if odd numb

r of pli

s wi

hin l min

), MEM for sp

cifyin

ll

h

pli

s bu

wi

h m

mbrn

s

iffn

ss only (MID1 on d

riv

d PSHELL)nd BEND for sp

cifyin

ll

h

pli

s bu

wi

h b

ndin

s


22/25

iffn

ss only (MID2 on d

riv

d PSHELL). A filur

h

ory FT cn b

sp

cifi

d from HILL for Hill

Ts

i, HOFF for Hoffm

n, TSAI for Ts

i

Wu or STRN for m

x

imum s

rin

h

ory. Th

llow

bl

in

rl

min

r sh

r s

r

ss SB n

ds

o b

provid

d.

18


23/25

Fibr

R

inforc

d Polym

r (FRP) Anlysis

nd D

si

n S

cond Edi

ion

III. D

fin

n or

ho

ropic MAT8 crd (

l

hou

hMAT1 c

rd could b

us

d form

ply) for

ch individu

l ply. For

ch ply, n

d

o d

fin

E1, E2, Poissonsr

io NU12, inpl

n

sh

r modulus G12,

rnsv

rs

sh

r modulus for sh

r in 1

Z pl

n

G1Z,

r

nsv

rs

sh

r modulus for sh

r in 2

Z pl

n

G2Z (if G1Z

nd G2Zz

ro,

h

n no sh

r fl

xibili

y or sh

r d

form

ions, i.

. infini

sh

r s

if

fn

ss) nd d

nsi

y RHO. D

fin

h

h

rm l

xp nsion co

ffici

n

s A1 nd A2 if n

c

ssry. If

h

filur

cri

rion is r

qu

s

d in PCOMP (in fi

ld FT),

h

n

h

llow

bl

s

r

ss or s

r

in in

nsion

nd compr

ssion in lon

i

udin

l dir

c

ionX

, Xc, in

h

rnsv

rs

dir

c

ion Y

, Ycnd

h

llow

bl

s

r

ss or s

rin f

or inpl

c

sh

r, S is r

quir

d. F12 isddi

ionlly r

quir

d for Tsi

Wu f

ilu

r

cri

rion. STRN wi

hv

lu

of 1.0 isddi

ionlly r

quir

d for

h

mximu

m s

r

in

h

ory

o indic

h

X

, Xc, Y

, Yc

nd S

r

s

r

in

llow

bl

s ins

d of s

r

ssllow

bl

s. STRN cn

lso b

l

f

blnk (

s don

for

h

o

h

r cri

ri)

v

n for

h

mximum s

rin

h

ory

ollow s

r

ssllow

bl

s in which c

s

h

mximum s

rin cri

rib

com

s

h

mximum s

r

ss cri

ri.

Sf

y fc

ors vry consid

rbly d

p

ndin

upon lmin

d

si

n, cons

i

u

n

m

ri

ls, m

nuf

c

urin

m

hod, s

rvic

condi

ions,

c. How

v

r,

s

rul

of

humb,

cons

rv

iv

v

lu

of 3 c

n b

us

d for

h

m

ri

l f

c

or. Th

followin

r

h

MSC.NASTRAN r

cov

r

d ou

pu

s:i. s

r

ss (ELSTRESS)

nd s

r

in (ELSTRAIN) for

h

quivl

n

lmin

sh

ll ii. forc

r

sul

n

s (ELFORCE) iii. s

r

ss

s

nd s

rins in

h

individul pli

snd

h

sh

r s

r

ss in

h

bondin

m

ri

l iv.

f

ilur

ind

x

bl

(if X

, Xc, Y

, Yc

nd S sp

cifi

d on MAT8

nd FT

nd SB sp

cifi

d on PCOMP) Th

f

ilur

ind

x for

n

l

m

n

is

h

l

r

s

v

lu

of

h

filur

indic

s forll pli

s of

h

l

m

n

.

19


24/25

Fibr

R

inforc

d Polym

r (FRP) Anlysis

nd D

si

n S

cond Edi

ion

BIBLIOGRAPHY 1. 2. GAY, Dni

l, HOA, Suon

, TSAI, S

ph

n. Composi

M

rils D

si

nnd Applic

ion. CRC Pr

ss, London, 2003. TIMOSHENKO & GERE. M

chnics of

M

rils 4

h SI Edi

ion. S

nl

y Thorn

s, Uni

d Kin

dom, 1991.

20


25/25

Documents

22023916 Fibre Reinforced Polymer FRP Analysis and Design