D. J. Lekou Centre for Renewable Energy Sources (CRES) T. T. Assimakopoulou, T. P. Philippidis

17
Estimation of the Uncertainty in Measurement of Composite Material Mechanical Properties during Static Testing D. J. Lekou Centre for Renewable Energy Sources (CRES) T. T. Assimakopoulou, T. P. Philippidis University of Patras

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Estimation of the Uncertainty in Measurement of Composite Material Mechanical Properties during Static Testing. D. J. Lekou Centre for Renewable Energy Sources (CRES) T. T. Assimakopoulou, T. P. Philippidis University of Patras. Blade Structural Design. Lamina Characterization. - PowerPoint PPT Presentation

Transcript of D. J. Lekou Centre for Renewable Energy Sources (CRES) T. T. Assimakopoulou, T. P. Philippidis

Page 1: 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