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.
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