D. J. Lekou Centre for Renewable Energy Sources (CRES) T. T. Assimakopoulou, T. P. Philippidis
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Transcript of D. J. Lekou Centre for Renewable Energy Sources (CRES) T. T. Assimakopoulou, T. P. Philippidis
Estimation of the Uncertainty in Measurement of Composite Material Mechanical Properties
during Static Testing
D. J. LekouCentre for Renewable Energy Sources (CRES)
T. T. Assimakopoulou, T. P. PhilippidisUniversity of Patras
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Blade Structural Design
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Lamina Characterization
y
x
1
2
θ
Standard Properties Fibre Direction
ISO 527-5 E1, 12, XT 0
ISO 527-5 E2, (21), YT 90
ISO 14129 G12, S ±45
ISO 14126 XC, (E1) 0
ISO 14126 YC, (E2) 90
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The uncertainty
Parameter associated with the result of a measurement Characterizing the dispersion of values,
reasonable attributed to the measurand e.g. standard deviation
Describes the level of knowledge of the measurand
Increases confidence in the validity of a measurement result
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The Tests
0 2500 5000 7500 10000 12500 15000 17500 20000 22500 25000
STRAIN ()
0
10
20
30
40
50
60
70
80
AP
PLI
ED
FO
RC
E (
kN)
GAUGE 1GAUGE 2
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The Measurands
Measurand Symbol Calculated by:
Cross Section A
Modulus of Elasticity E
Poisson Ratio xy
Stress (Strength) (F)
Strain @ failure F
Shear Modulus G12
Shear Strain (@ failure) (F)
FAE 1
WHA
xyxy
AF FF
yx FAG 2112
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Uncertainty analysis
Nx,...,x,xfy 21 Test instruments
Load Cell, Strain gauges, Micrometer
Specimen Dimensions, Shape &
Tolerances
Test procedure Zeroing, Sampling,
Alignment
Test environment Temperature, Humidity
1
1 1
1
2
2
2
2N
j
N
jkxxxx
kj
N
jx
jc
kjkj
j
ruux
f
x
f
ux
fyu
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Uncertainty of Coupon Strength
Cross-sectional area Instrument, Coupon shape
Load Load cell
Specimen alignment Manufacturing & Test procedure
Recording of Ultimate Stress Sample rate & Equipment
AF FF
22
A
u
F
uu AF
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Uncertainty of Coupon Elastic Property
Stress (measurand) Strain (measured)
k-factor, etc. Misalignment
Calculation procedure Range Linear regression Averaging
Test procedure Zeroing
-500 500 1500 2500
STRAIN ()
0
40
80
120
160
ST
RE
SS
(M
Pa
)
GAUGE 1GAUGE 2
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Uncertainty of Reported Properties
Arithmetic mean
Standard deviation
Correlated measurements Same equipment Coupons from same batch
n
iipn
p1
1
n
iip pp
ns
1
2
1
1
1
1 11
22
2 21 n
j
n
jkp,p
n
jp kjj
uun
pu
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Properties of UD on-axis
Unc. in Cross-Section uA = 0.84%
Unc. in Strength u = 1.10%
Unc. in Ult. Strain u = 0.90%
Unc. in E-modulus uE = 1.65%
5000 15000 25000STRAIN ()
0
100
200
300
400
500
600
700
800
ST
RE
SS
(M
Pa
)
GAUGE 1GAUGE 2
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Misalignment effects on properties
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0 0.5 1
Misalignment angle (deg)
Err
or
(%)
(Xp
-X)/
X
XT
YT
XC
-0.80
-0.70
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0 0.5 1
Misalignment angle (deg)E
rro
r (%
) (G
p-G
)/G
G12
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E-modulus
S.G. Range
Chord LS-1 LS-2
SG10.05-0.25 1.07 1.07 1.08
0.09-0.19 1.07 1.07
SG20.05-0.25 0.94 0.94 0.97
0.09-0.19 0.97 0.97
AVE0.05-0.25 1.00 1.00 1.02
0.09-0.19 1.02 1.02
0 1000 2000 3000 4000 5000STRAIN ()
0
10
20
30
40
50
60
ST
RE
SS
(M
Pa
)
GAUGE 1GAUGE 2E1 - FIT
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Mean value of E1
Experiments: 29 tests, Mean= 39.04 GPa, COV= 2.64%
Usual approach (95% conf. level): E1 = 39.04 ± 0.63 GPa (1.6%)
Current analysis: E1 = 39.04 ± 1.28 GPa (3.3%)
2% lower Stiffness (95% Conf.)
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Mean value of XT
Experiments: 29 tests, Mean= 776.50 MPa, COV= 4.65%
Usual approach: Rk,XT = 695.55 MPa (89.6% of mean value)
Current analysis: Rk,XT = 646.92 MPa (83.3% of mean value)
7% lower characteristic strength value
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Conclusions – Recommendations
Uncertainty in Measurements Distinguish between uncertainty in measurement and
inherent property variability
Report Uncertainty of measurements As input for designers & certification bodies For improvement on test procedures
Use Analysis on Uncertainty For estimation of number of tests
Extension of presented analysis Fatigue results
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Thank you for your attention