1st CoSACNet Meeting

Neil McCartney

NPL Materials Centre

National Physical Laboratory, UK

Southampton University , 30 January 2001

Design tools for composites

Definition of design ?

Selection of materials, geometry, loading modes and limits so that products meet specified performance criteria e.g.

deflections within specification failure loads in excess of maximum expected load during service avoidance of microstructural damage ( ply cracks / delaminations ) lifetimes ( cycles / time ) in excess of specification

Design is quantitative and based on mathematical models that adequately represent behaviour

semi-empirical / phenomenological relationships analytical formulae ( from Hooke’s law to complex analyses ) finite element or boundary element analysis

Modelling issues for composites

Reliable design procedures will be based on physical modelling

The availability of high performance computers will revolutionise the design of composite structures

Realistic complex models can be used for design of materials (Virtual Testing) and components

Models must be thoroughly validated and incorporated into easy-to-use design procedures

Life prediction, durability are exceedingly complex phenomena that are very difficult to model physically

Phenomenological approaches can be useful but are not usually reliable – e.g. failure criteria for composites

Conventional failure criteria

phenomenological in nature - no physics ! based on invariance requirements

applied to stress states for composite structures where no damage has been allowed for

not easily applied to environmentally or fatigue damaged composites

Tsai - Wu (1971)f F F Fi i i ij i j ijk i j k( ) 1

Physically based models are needed !

Design issues for composites

Materials design Fibre / matrix / volume fraction selection for UD laminates Orientation / thickness selection for plies in a laminate

Prediction of elastic constants Prediction of expansion coefficients ( thermal / moisture ) Types of loading

In-plane biaxial - through-thickness - shear Out-of-plane bending ( anticlastic bending )

Damage growth and property degradation Ply cracking – delamination – fibre fracture – interface debonding

Strength predictions Durability issues – fatigue – environmental exposure Delivery of design methods to users ( Software – Web )

Delivering design tools to users

Commercial systems LAP and CoDA

UK Composite Design Toolset ( DERA, AEAT, NPL, SER Systems Ltd )

Web-based design tools – E-mail communication

Smart design manuals

CoDA

for

Component and Composite Design AnalysisVersion 3

Graham D Sims and Bill Broughton

NPL Materials Centre

National Physical Laboratory, UK

CoDA

A commercially supported package

What does CoDA do ?

CoDA has four independent, but integrated, modules that have been validated experimentally

Panels, Beams, Laminates, Materials Synthesiser

Pre-preg laminates, chopped strand mat, sandwich panels

Implementation of failure criteria

CoDA can be used to undertake preliminary analysis of sub-components with Plate or Beam geometries

CoDA can also synthesise the properties of composite materials, laminates and sandwich structures, which can be used in a seamless manner within the design modules

CoDA

CoDA

CoDA

CoDA

CoDA

UK Composite Design Toolset

A collaboration between DERA, UKAEA & NPL

Integrated toolbox comprising modules that can exchange data & resultsPC008A/15A – DERA – Micromechanics, LPT, 2D/3DGENLAM – DERA – Non-linear LPT – thermal stresses

– scissoringCCSM – Cambridge, IC, DERA – Micromechanics + LPT

– unnotched & notched failurePREDICT – NPL – progressive damage modelling in laminatesLAMFAIL – UMIST, DERA progressive damage with empirical

model – nonlinear scissoring – complex load histories

A global data base of materials properties – links to other systems

PREDICT - Design objectives

Predict properties of UD composites from properties of fibre and matrix

Predict in-plane properties of general symmetric laminates

Predict initial formation of fully developed ply cracks in a general symmetric laminates subject to general in-plane loading and thermal residual stresses

( in fatigue loading designers will want to avoid damage )

Predict progressive degradation of thermo-elastic constants as a function of applied stress or strain ( strain softening rules needed for FEA analyses )

Predict effects on damage resistance of varying orientations and thicknesses of plies in a laminate

Predict effects of temperature changes on ply crack formation

( investigate thermal cracking during manufacture, or cooling )

Designing composites from fibre and matrix level

Predicting ply properties – validation

Predicting laminate properties

Delaying damage formation during loading

PREDICT

Ply geometry and location of ply cracks

2L

Ply 1Ply 2 Ply3Ply 4

- 45o 90o 0o0o 90o - 45o45o 45o

Quasi - isotropic laminates

Comparison of axial stress in crack plane (GRP)

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

x (mm)

Str

ess

(GP

a)

Model

FEA

FEA by Tong, Guild, Ogin & Smith (1997)

45o - 45o 90o 0o

Ply crack

Interfacial shear stress on 0o / 90o interface (GRP)

0

0.01

0.02

0.03

0.04

0 0.2 0.4 0.6 0.8 1y / L

Str

ess

(G

Pa)

Model

FEA

FEA by Tong, Guild, Ogin & Smith (1997)

0

5

10

15

20

25

30

0 0.5 1 1.5 2

Ply crack density (/mm)

Ax

ial

Yo

un

g's

mo

du

lus

(G

Pa

)

Experiment

Model

Experiment

Model

Experiment

Model

[02/902]s

[02/908]s

[02/904]s

GRP : Predicted from fibre/matrix properties

Experimental data : Lodiero & Broughton, NPL, 2000

T)()(E

)(

)(E)(E

)()( AT

A

A

At

A

a

T)()(E)(E

)(

)(E

)()( T

T

T

A

At

T

tT

Stress - strain relations for damaged laminate

is a label denoting the presence of some form of damage in thelaminate defined by a set of other parameters

Same form as those for an undamaged laminateValidity confirmed by accurate stress analysis

Degradation of properties of laminates

Damage parameter : 1)(E

E)(D

A

A1

k, k’ and k1 are easily calculated using CLT

Thermo-elastic constants for damaged laminates :

A

1

E

)(DQP)(P

11122

tTAT

t

A

a

A

A

tTA

k'kkkk'kk'kk'kk1:Q

EEEE

1

E

1

E

1:P

Continuum damage mechanics (CDM)

S

L

NMMM

O

QPPP

1 1 0

1 1 0

0 0 1 1

1

2

3

/ ( ) /

/ / ( )

/ ( )

E d E

E E d

d

A A A

A A T

A

Stress - strain relation = Swhere

Damage parameters d1, d2 and d3 are such that

0 1 1 2 3 d ii , ,

dE

Ed

E

EdA

A

T

T

A

A1 2 31 1 1

( ),

( ),

( )

Face view of crack growth using continuum model

0

1

2

3

4

5

0 5 10 15Normalised crack length

Nor

mal

ised

cra

ckin

g s

tres

s

Bridged crack theory

Long crack asymptote

Griffith crack

Master curve for ply cracking

Defect size

Str

ess

for

pro

pag

atio

n

Unstable growth

Stable growth

Design limit

Design limit is derived for long cracks

Design limit is exact if growth is stable

Design limit is a lower bound if growth is unstable

Predictions are pessimistic

Designs will be safe

Ply crack initiation criterion :

s

E E

s

A A

21 1 0

( )

( )

Criterion for progressive discrete ply crack formation :

s

E E

s i ni

i i

A i A i

21 1

11

1

0

( ) ( )

( ) ( )

...

Criteria for ply crack formation

( ) 0

s0 is value of s at ply crack closure

s k k

s k Tt T

o

o

'

1

Potential cracking sites

Ply crack locations

Potential cracking sites are evenly spaced

Ply cracks are non-uniformly spaced

Progressive cracking methodology

Allocation of fracture energies

0

0.01

0.02

0.03

0 50 100 150 200Fracture energy of potential cracking site

(J/m2)P

roba

bilit

y de

nsity

Mean fracture energy = 150 J/m2

Standard deviation = 15 J/m2

Master curve for triaxial loading

0

s s0

Gradient

E

DA

1( )

si s0

Inelasticstrain

Damage initiation stress Gradient of unloading line Enclosed area

Area

= 0

Key features :

Apply directly to other stressand temperature states

for which = 0 :

Tks

k'ks

1o

Tt

A popular approach of damage mechanics

HomogenisedCrackedlaminate

Homogeneousdamaged plyin laminate

Degraded properties modelled semi-empirically

Classical laminate analysis

Crackedlaminate

HomogenisedCrackedlaminate

Homogeneousdamaged plyin laminate

Approach of NPL model

Out - of - plane bending

Non-symmetrical laminates

Through-thickness thermal gradients

Major problem is dealing with anti-clastic bending

Model already exists for ply cracks subject to plane strain bending

Anti-clastic bending of UD ply

Plane strain bending of cracked [ 0 / 90 / 0 / 90 / 0 ] laminate

i = 1

i = 2

i = N+1

M M

0

90

0

90

0

x

y0

- Work in progress to predict ply crack formation -

Comparison of model with FEA

-8

-4

0

4

8

12

16

0 0.2 0.4 0.6 0.8 1 1.2

x (mm)

Axi

al s

tres

s (

GP

a)

FEA (Becker (1998)

Plane strain model

GRP laminate

Ply crack

90o ply0o ply 90o ply0o ply 0o ply

Modelling laminate failure

Physical modelling of damage modes

Cross-ply laminates subject to biaxial loading

Prediction of failure strain and strength

Biaxial loadingThermal stresses

Multiple plies

Modelling failure of cross-ply laminates

Effects of ply cracking alone on laminate properties are well understood

Ply cracking affects thermo-elastic properties (strain softening) but we need to address laminate failure issues

Tensile failure is determined principally by fibre fracture

Statistical nature of fibre failure must be included

Predicting the failure of cross-ply laminates is the first step

0o 90o 0o

Modelling failure of cross-ply laminates

Biaxial loadingThermal stresses

Static failure of

fibres

fibre/matrix debonding

frictional contact

shear yielding

Fibre matrix cellBiaxial stresses

Thermal stresses

0o 90o 0o

0

0.4

0.8

1.2

1.6

2

2.4

0 0.05 0.1 0.15Strain

Stre

ss (G

Pa)

0

20

40

60

80

100

120

0 0.05 0.1 0.15Strain

Mod

ulus

(GPa

)

0.88

0.92

0.96

1

1.04

0 0.05 0.1 0.15Strain

b / L

Mechanical behaviour of fibre / matrix cell

L - b is length of debond zone

Could substitute any other model

for which a look-up table can be constructed

Monte Carlo model for progressive failure in 0o plies

Parameters :

M, N, L Element length

Repeated runs ofa simulation to determine the statistical variabilityof performance

Critical fibre stress or strain ?

In fibre tests performance of fibre in tension can be characterised by : axial fibre stress at failure axial strain at failure f = Ef f

In a composite fibre subject to triaxial loading there are both loading & Poisson ratio effects on axial fibre strain

Assume fibre strength in a composite is governed by axial fibre failure strain consistent with concept of fibre axial strain controlling the stability

of fibre defects initiating tensile failure

Stress-strain behaviour

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5

Axial strain %

Axi

al s

tres

s (G

Pa)

No fibre fracture

Fibre fracture

Failure

Degradation of axial modulus

62

63

64

65

66

67

68

69

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Axial stress (GPa)

Axi

al m

odul

us (G

Pa)

No fibre fracture

Fibre fracture

Failure

Growth of ply cracks during axial loading

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Axial stress (GPa)

Cra

ck

de

ns

ity

(/m

m)

No fibre fracture

Fibre fracture

Failure

The effect of fibre fractureon properties

CFRP (Vf = 0.6)

Virtual testing is defined as the combination of high quality models, high performance computing and a user - friendly interface

Will replicate many aspects of physical mechanical testing so that engineers do not need to learn a new vocabulary

Will allow material properties to be derived from more fundamental properties, leading to inventive materials design

It will be more than just a simulation, because extensive validation and testing will have taken place, resulting in a reliable replacement for some physical testing

Virtual Testing

Virtual testing of composites over the Internet

Web site address http://materials.npl.co.uk/

Virtual testing : Composite laminates

Developed at NPL, the Internet based system enables a materials designer to ‘create’ an entirely new material and to test it

Image taken from NPL Internet Laminate Damage Simulation

The system simulates the damage caused by cracking

as load increases and predicts the subsequent degrading of

material properties

Composite Laminate Testing

The user can generate design data for damaged composite laminates

Results taken from NPL Internet version of Laminate Damage Simulation

The Future : The era of simulation

Conclusions

Reliable design methods for composite materials will be based on physical models of behaviour. Key to reliability is rigorous validation of design methods

Physical models are complex in nature and not usually amenable to simple design rules ( sometimes there is no alternative )

Damage models have good potential for application in construction sector

( e.g. bridge strengthening with CFRP )

The implementation of physically based design methods in design offices will usually involve the use of computer based techniques : Specific software packages – LAP, CoDA, Toolset Web-based access to specific design packages, NPL demonstrator Web-based access to distributed software – networking ? Integration of design, optimisation, prototype and production simulation in

virtual manufacturing