CompTest 2004

Analytical Models for Assessing Environmental Degradation of

Unidirectional and Cross-Ply Laminates

W R Broughton and M J LodeiroNational Physical Laboratory

Teddington, UK

23 September 2004

ContentsContents

Introduction

Materials

Moisture Diffusion – Temperature Dependence

Micromechanics + Classical Laminate Analysis

Shear Lag Theory

Empirical RelationshipsNon-Dimensional TemperatureKitagawa Power-Law RelationshipArrhenius Model

Concluding Remarks

IntroductionIntroduction

Mechanistic/physics based models are the preferred approach for determining the effect of environmental degradation on mechanical properties of PMCs

Analytical and semi- empirical models can be used to determine the degree of degradation of elastic and strength properties with the level of degrading agent, typically:

MoistureTemperatureMoisture + Temperature

Experimental evaluation carried out on unidirectional and cross-ply GRP and CFRP laminates

Models include input data obtained from conditioned resin samples

Laminate Property Predictive AnalysisLaminate Property Predictive Analysis

Layer or ply properties - micro-mechanics

Laminate properties - classical laminate analysis

Thermo-elastic and strength properties

Moisture diffusion (Fickian diffusion)

CoDA (Composite Design and Analysis) and PREDICT*

Empirical relationships ⇒ predict moisture/temperature effects

* NPL software packages

MaterialsMaterialsUnidirectional and cross-ply (0°/90°) laminates

E-glass/913 and E-glass/F922

HTA/F922

T300/914, T300/924 and T300/976

APC-2 (carbon/peek)

T300B/R23

XAS/914

Several cross-ply configurations were included in the assessment

[0°/90°]4S

[0°2/90°2]S

[0°2/90°4]S

[0°2/90°6]S

[0°2/90°8]S

Moisture DiffusionMoisture Diffusion

Diffusion coefficient D can be calculated using:

Moisture

h

Moisture

y

xz

M Moisture content (wt%)

M∞ Equilibrium moisture concentration

t Time

2

12

12

)tt(M)MM(h

16D

−

−π=

∞

FickianFickian DiffusionDiffusion

0 20 40 600

1

2

3

4

moisture equilibrium

Experimental Fickian Curve

Moi

stur

e C

onte

nt (w

t %)

Square Root of Time (hrs)1/2

0 20 40 600.0

0.2

0.4

0.6

0.8

1.0

moisture equilibrium

Experimental Fickian Curve

Moi

stur

e C

onte

nt (w

t %)

Square Root of Time (hrs)1/2

F922 Epoxy Unidirectional E-glass/F822

Diffusion Coefficients Diffusion Coefficients -- Anisotropic SolidsAnisotropic Solids

Diffusion coefficients parallel and perpendicular to the fibres may be estimated using:

Dm diffusivity of the matrixVf fibre volume fraction

Unidirectional E-glass/F922

)predicted(smm10x3.7D

)erimental(expsmm10x3.6D

smm10x3.8D

12822

12822

127m

−−

−−

−−

=

=

=

( ) mf

22mf11 DV21DDV1D

π−=−=

Diffusivity Diffusivity -- Temperature DependenceTemperature Dependence

0 20 40 60 800.0

0.5

1.0

1.5

2.0

2.5

3.0

25 oC 40 oC 60 oC

Moi

stur

e C

onte

nt (w

t %)

Square Root of Time (hrs)1/2

0 20 40 60 80.0

0.5

1.0

1.5

2.0

25 oC 40 oC 60 oC

Moi

stur

e C

onte

nt (w

t %)

Square Root of Time (hrs)1/2

Unidirectional E-glass/913 Unidirectional T300/924

0

Diffusivity Diffusivity -- Temperature DependenceTemperature DependenceArrheniusArrhenius RelationshipRelationship

D = Do exp-E/RT

Do - constant

E - activation energy

R - ideal gas constant

T - absolute temperature

Transverse Diffusivity Transverse Diffusivity -- Temperature DependenceTemperature Dependence

Arrhenius relationship:

D = Do exp-k/T

Note: Do and k are experimentally determined constants

Unidirectional T300/924 Unidirectional E-glass/913

3.0 3.1 3.2 3.3 3.410-8

10-7

D =1.711 exp-5532/T

Diff

usiv

ity, D

(mm

2 s-1)

1/T x 103 (1/K)3.0 3.1 3.2 3.3 3.4

10-8

10-7

10-6

D = 0.327 exp-4669/T

Diff

usiv

ity, D

(mm

2 s-1)

1/T x 103 (1/K)

Glass Transition Temperature Glass Transition Temperature vsvs Moisture ContentMoisture Content

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0400

450

500

550

600

Gla

ss T

rans

ition

Tem

pera

ture

(K)

Moisture Content (wt%)

25oC immersion 40oC immersion 60oC immersion line of best fit

F922 Epoxy Unidirectional E-glass/913

0.0 0.5 1.0 1.50

100

200

300

400

500

T300/924 E-Glass/913G

lass

Tra

nsiti

on T

empe

ratu

re (K

)

Moisture Content (wt%)

Tgwet = Tgdry – gM

g temperature shift (in K) per unit moisture absorbed

M moisture content (wt %)

Moisture Effects on Moisture Effects on ThermosetThermoset ResinsResins

Swelling, weight gain and cavity formation

PlasticisationReduction in glass transition temperatureLower operating temperaturesReduction in stiffness and strength properties

Chemical leachingLoss of fillers, catalysts, hardeners, pigments or fire retardants

Moisture Effects on EMoisture Effects on E--Glass FibresGlass Fibres

Leaching of alkali oxides (sodium + potassium) from the fibre surface

Formation of surface micro-cracks ⇒ stress concentrators

Glass fibres slowly decompose/dissolve

Permanent loss of strength (even after drying)

Process accelerated with increasing temperature and stress

Moisture +Temperature EffectsMoisture +Temperature EffectsUnidirectional and CrossUnidirectional and Cross--Ply LaminatesPly Laminates

Conditioned at 70°C/85% RH (1,000 hrs)

Micromechanics ⇒ lamina (layer) elastic and strength propertiesRule of mixtures, Halpin-Tsai, etc.

Classical analysis ⇒ laminate elastic and strength property predictionsLoss of integrity (i.e. ply failure) - ply discount theory All elastic properties (except E11) of failed 90° plies set to zero

CoDA ⇒ synthesise lamina and laminate properties

Tensile Properties for UD Laminates at AmbientTensile Properties for UD Laminates at Ambient(Measured/Predicted)(Measured/Predicted)

Material Tensile Strength (MPa)

Tensile Modulus (GPa)

Poisson’s Ratio

E-glass/913 (dry) Longitud inal Transverse

1215/ 1178 73.1/ 56.5

43.0/ 36.6 12.5/ 10.7

0.30/ 0.33

0.094/ 0.091 E-glass/F922 (dry) Longitud inal Transverse E-glass/F922 (wet) Longitud inal Transverse

1087/ 1479 58.6/ 52.9

797/ 1475 64.1/ 36.5

43.0/ 46.0 13.9/ 15.4

37.2/ 45.9 14.3/ 14.5

0.31/ 0.33

0.098/ 0.102

0.31/ 0.33 0.108/ 0.096

T300/924 (dry) Longitud inal Transverse

1723/ 2193 92.7/ 56.1

133 ± 2/ 136

8.5/ 8.7

0.34/ 0.29

0.020/ 0.021 HTA/F922 (dry) Longitud inal Transverse HTA/F922 (wet) Longitud inal Transverse

1684/ 2016 46.2/ 53.0

1728/ 2014 48.6/ 36.4

126/ 134 9.9/ 8.3

130/ 134 8.9/ 7.9

0.32/ 0.34

0.023/ 0.020

0.33/ 0.34 0.022/ 0.022

Strength of EStrength of E--glass/F922 and HTA/F922 Crossglass/F922 and HTA/F922 Cross--Ply Laminates Ply Laminates (Ambient Test Conditions)(Ambient Test Conditions)

Material First Ply Failure Stress (MPa) Tensile Strength (MPa) Measured Predicted Measured Predicted

E-glass/F922 (dry) [02/ 902]S [02/ 904]S [02/ 908]S

150 99 65

110 91 76

486 316 170

431 253 135

E-glass/F922 (wet) [02/ 902]S [02/ 904]S [02/ 908]S

178 134 98

80 65 54

340 282 159

312 181 98

HTA/F922 (dry) [02/ 902]S [02/ 904]S [02/ 906]S

360 135 149

455 322 255

814 516 407

972 649 484

HTA/F922 (wet) [02/ 902]S [02/ 904]S [02/ 906]S

399 267 189

455 322 182

864 569 413

972 649 454

Longitudinal Longitudinal ModuliModuli of Eof E--glass/F922 and HTA/F922 Crossglass/F922 and HTA/F922 Cross--Ply LaminatesPly Laminates(Ambient Test Conditions)(Ambient Test Conditions)

Material Initial Modulus (GPa) Final Modulus (GPa) Measured Predicted Measured Predicted

E-glass/F922 (dry) [02/ 902]S [02/ 904]S [02/ 908]S

29.4 26.2 20.2

28.6 23.1 16.8

23.5 16.1 9.4

22.1 14.5 8.5

E-glass/F922 (wet) [02/ 902]S [02/ 904]S [02/ 908]S

25.3 26.8 19.2

28.1 22.5 16.1

21.4 16.7 9.5

22.0 14.5 8.5

HTA/F922 (dry) [02/ 902]S [02/ 904]S [02/ 906]S

64.4 46.7 37.6

70.2 49.8 39.1

60.7 41.9 31.8

66.3 44.4 32.3

HTA/F922 (wet) [02/ 902]S [02/ 904]S [02/ 906]S

66.4 47.0 38.1

70.0 49.8 38.9

61.0 42.1 31.7

66.2 44.4 31.8

PoissonPoisson’’s Ratios of Es Ratios of E--glass/F922 and HTA/F922 Crossglass/F922 and HTA/F922 Cross--Ply LaminatesPly Laminates(Ambient Test Conditions)(Ambient Test Conditions)

Material Initial Poisson’s Ratio Final Poisson’s Ratio Measured Predicted Measured Predicted

E-glass/F922 (dry) [02/ 902]S [02/ 904]S [02/ 908]S

0.159 0.134 0.128

0.162 0.138 0.122

0.084 0.067 0.056

0.084 0.047 0.027

E-glass/F922 (wet) [02/ 902]S [02/ 904]S [02/ 908]S

0.155 0.133 0.119

0.154 0.130 0.115

0.105 0.060 0.038

0.080 0.044 0.026

HTA/F922 (dry) [02/ 902]S [02/ 904]S [02/ 906]S

0.042 0.042 0.041

0.040 0.031 0.028

0.040 0.027 0.022

0.019 0.010 0.007

HTA/F922 (wet) [02/ 902]S [02/ 904]S [02/ 906]S

0.049 0.042 0.039

0.038 0.031 0.027

0.038 0.028 0.021

0.019 0.010 0.007

Temperature Dependence Temperature Dependence -- Unidirectional T300/924Unidirectional T300/924

Property Temperature (°C) -40 20 120 Longitudinal tensile modulus, E11

T (GPa) Measured Pred icted

133 144

135 143

139 142

Transverse tensile modulus, E22T (GPa)

Measured Pred icted

10.8 13.3

10.5 10.5

8.2 8.4

Longitudinal shear modulus, G12 (GPa) Measured Pred icted

5.9 7.7

5.1 5.1

3.5 4.5

Longitudinal Poisson’s ratio, ν12 Measured Pred icted

0.37 0.40

0.40 0.40

0.39 0.39

Longitudinal tensile strength, S11T (MPa)

Measured Pred icted

1,750 2,211

1,683 2,195

1,550 2,186

Transverse tensile strength, S22T (MPa)

Measured Pred icted

63.6 48.9

60.8 44.1

56.1 24.7

Transverse CrackingTransverse CrackingEE--glass/F922 Crossglass/F922 Cross--Ply LaminatesPly Laminates

100 200 300 400 5000.0

0.5

1.0

1.5

2.0

2.5

Increasing 90o ply thickness

[02/908]S [02/904]S [02/902]S

Cra

ck D

ensi

ty (c

rack

s/m

m)

Applied Stress (MPa)

Shear Lag TheoryShear Lag Theory

Reduction in Exx as a function of average crack spacing, 2s, is given by:

EXX, EXX0, E11 and E22 are the longitudinal moduli of the cracked composite, uncracked composite, the longitudinal plies and the transverse plies, respectively.

( )1122

3XXO122

0XX

11

11

0XX0XX

XX

EbEdEdbG3

;

s)stanh(

EE

bdb

EE

1

1EE +

=λ

λλ

−

++

=

0° 90°

0°

↑ 2s ↓

b ←------→

2d ←--------------------------------→

b ←------→

Longitudinal Longitudinal ModuliModuli at Onset of Failure for Crossat Onset of Failure for Cross--Ply Laminates Ply Laminates EE--glass/F922 and HTA/F922 glass/F922 and HTA/F922 (Ambient Test Conditions)(Ambient Test Conditions)

Material Measured Laminate Analysis Shear Lag Theory E-glass/F922 [02/ 902]S [02/ 904]S [02/ 908]S

23.5 16.1 9.4

22.1 14.5 8.5

23.1 16.1 11.5

HTA/F922 [02/ 902]S [02/ 904]S [02/ 906]S

60.7 41.9 31.8

66.3 44.4 32.3

67.2 45.6 34.2

Empirical Approach Empirical Approach -- NonNon--Dimensional TemperatureDimensional TemperatureLaminate Property PredictionsLaminate Property Predictions

P Material property (e.g. longitudinal tensile strength)

PO Initial property value of the dry material at room or reference temperature To (296 K)

T Test temperature (K)

Tg Glass transition temperature of the material

g Temperature shift (in K) per unit moisture absorbed

M amount of moisture absorbed (wt %)

gMTTwhereTTTT

PP

gdrygwet

n

ogdry

gwet

o

−=

−

−=

Transverse PropertiesTransverse PropertiesUnidirectional EUnidirectional E--glass/913 Epoxyglass/913 Epoxy

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

modulus strength

P/P o

(Tgw - T)/(Tgd - To)

InIn--Plane Shear PropertiesPlane Shear PropertiesUnidirectional LaminatesUnidirectional Laminates

Shear Modulus Shear Strength

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

AS4/3501-6 XAS/914 T300B/R23 APC-2

P/P o

(Tgd-Topr)/(Tgd-Tr)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

AS4/3501-6 XAS/914 T300B/R23 APC-2

P/P o

(Tgd-Topr)/(Tgd-Tr)

Kitagawa PowerKitagawa Power--Law RelationshipLaw RelationshipShear PropertiesShear Properties

Kitagawa power-law relationship between shear yield stress, τ, and shear modulus, G, for glassy polymers is:

To Reference temperature (K) - generally room temperature (296K)

τo Shear yield stress at To

Go Shear modulus at To

n Constant

n

o

o

o

o

TGGT

TT

=

ττ

Kitagawa PowerKitagawa Power--Law Law –– InIn--Plane Shear PropertiesPlane Shear PropertiesUnidirectional CFRP LaminatesUnidirectional CFRP Laminates

AS4/3501-6 XAS/914 T300B/R23 APC-2 Victrex PEEK 0.85 1.00 1.10 0.89 1.07

Value of Exponent n

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

n = 1

-log

(T0τ

/Tτ 0)

-log (T0G/TG0)

AS4/3501-6 XAS/914 T300B/R23 APC-2

Kitagawa PowerKitagawa Power--Law RelationshipLaw RelationshipFlexural PropertiesFlexural Properties

Kitagawa power-law relationship between flexural strength, σf, and flexural modulus, Ef, for glassy polymers is:

To Reference temperature (K)

σfo Flexural strength at To

Efo Flexural modulus at To

n Constant

n

fo

fo

fo

fo

TEET

TT

=

σσ

Kitagawa PowerKitagawa Power--Law Law –– Flexural PropertiesFlexural PropertiesUnidirectional EUnidirectional E--glass/F922 and HTA/F922glass/F922 and HTA/F922

Longitudinal Flexure Transverse Flexure

n = 0.52 n = 1.35

0.01 0.1 10.01

0.1

1

T oE f/TE fo

Toσf/Tσfo

E-glass/F922 HTA/F922

1E-3 0.01 0.1 11E-3

0.01

0.1

1

T oE f/TE fo

Toσf/Tσfo

E-glass/F922 HTA/F922

Concluding RemarksConcluding Remarks

Micromechanics combined with laminate analysis proved satisfactory for predicting tensile properties of dry and moisture conditioned unidirectional and cross-ply laminates.

Using ply discount theory, it was possible to determine the elastic properties of damaged cross-ply laminates prior to final ply failure.

Shear-lag theory can be used to determine changes in laminate stiffness with transverse cracking – mechanistic/physics based models offer improved accuracy.

Kitagawa power-law + non-dimensional temperature analysis can be used to determine shear and flexural properties of unidirectional laminates as a function of temperature and moisture content.

ACKNOWLEDGEMENTSACKNOWLEDGEMENTS

This work forms part of the Measurements for Materials Systems (MMS) Programme funded by the United Kingdom Department of Trade and Industry (National Measurement System Directorate).

The authors would like to express their gratitude to the Industrial Advisory Group, and NPL colleagues Dr S Maudgal, Dr D Mulligan, Mr R Shaw, Mr S Gnaniah and Mr G Nunn, whose contributions and advice have made the work possible.