Distribution of Defects in Wind Turbine Blades
&
Reliability Assessment of Blades Containing Defects
Authors:
Henrik Stensgaard Toft, Aalborg University
Kim Branner, Risø-DTU
Peter Berring, Risø-DTU
John Dalsgaard Sørensen, Aalborg University / Risø-DTU
Contents
•
Introduction
•
Distribution of Defects in Wind Turbine Blades
•
Influence of Delaminations and Reliability Assessment
•
Non Destructive Inspection
•
Conclusion
•
Future Work
Introduction
Uncertainties in calculation of the load carrying capacity for wind
turbine blades.
1. Material properties
•
•
Physical uncertainty (Aleatory)
Statistical uncertainty (Epistemic)
Downwind side
Towards tip
Trailing edge
2. Finite Element calculation
• Model uncertainty (Epistemic)
Aerodynamic
shell
Leading edge
3. Failure criteria
• Model Uncertainty (Epistemic)
Upwind side
Main spar
(load carrying box)
Introduction
Uncertainties – captured by partial safety factors.
Local production defects are not taken into account !
•
•
Quality control of the production process
Non Destructive Inspection (NDI) of the blades
Stochastic models for the distribution of defects.
The models are set up on an empirical basis and have not yet been
calibrated against observations from blade manufacturing and testing.
Production Defects
Local production defects:
•
•
•
Delaminations
Wrinkles
Matrix cracks
Influence parameters:
•
•
•
Type of defect
Size of defect
Position of defect
Delaminations:
•
Areas of poor or no bonding
between adjacent plies.


Voids
Defects in glued joints
Distribution of Defects – Model 1
Defects are completely random distributed in the blade.
The blade can be considered as a 2-dimensional planar region A since
defects tend to occur in a layer or in the interface between two layers.
i)
The number of defects in the region A follows a Poisson distribution
ii) The distribution of defects is an independent random sample from a
uniform distribution
Distribution of Defects – Model 2
Defects occur in clusters which are randomly distributed in the blade.
i)
The “parent” defects follow model 1
ii) Each “parent” defect produces a number of “offsprings” following a
Poisson distribution
iii) The position of the “offspring” defects relative to their “parents” is
independently and identically distributed according to a bivariate
probability density function. (Normal distribution)
Distribution of Defects
Model 1
Completely Random Distribution
Model 2
Random Cluster Distribution
Load Carrying Capacity of Main Spar
Transverse strains in main spar – Failure defined according to:
•
•
Maximum Strain
First Ply Failure
Normalized strain [-]
4
3
Transverse xx
Longitudinal zz
First Ply Failure
2
1
0
-1
0
0.2
0.4
0.6
0.8
Normalized load [-]
1
1.2
Production Defects – Delaminations
• Size refers to percent of plate width
• Through thickness position 20%
Defect
Size
Longitudinal strain
(compression)
Transverse strain
(tension)
-
1.00
1.00
Delamination
30%
0.63
0.82*
-
40%
0.47
0.74*
-
50%
0.32*
0.66*
No defect
* The value is estimated.
Influence of Delaminations
Delamination at the most critical position in the main spar cap.
Size refers to percent of cap width.
Defect
Size
Load Carrying
Capacity
-
1.00
30%
0.91
-
40%
0.86
-
50%
0.81
No defect
Delamination
Influenced only by strength reduction in the transverse direction.
Buckling stability increased by the aerodynamic shell.
Reliability Assessment of Blades Containing Defects
Reliability of blade containing defects:
g  X R R  σ max , ε max , E, D   X L L
The limit state function cannot be used directly.
 factor characteristic load can be increased before blade failure
(characteristic material properties)
Influence of specific defects introduced by reduction factor on the load
carrying capacity.
g   

 intact
X R R  σ max , ε max , E   X L L
Reliability Assessment of Blades Containing Defects
Reliability of main spar with delamination at the most critical position.
  1  PF 
Target reliability index in IEC 61400-1,  = 3.09, PF = 10-3 per year.
Size
PF

-
1.910-3
2.90
30%
4.010-3
2.65
-
40%
6.210-3
2.50
-
50%
1.010-2
2.33
Defect
No defect
Delamination
Non Destructive Inspection
Probability of Detection (PoD)
Updated probability of failure:
PF|defect ,NDI  P  g  intact   0  P  | NDI  
P  g  defect   0  1  P  | NDI  
Cumulative Value [-]
1
0.8
0.6
0.4
0.2
PoD-curve
0
0
0.2
Defects are assumed perfect repaired.
PF

-
1.910-3
2.90
30%
2.210-3
2.85
-
40%
2.210-3
2.84
-
50%
2.310-3
2.84
No defect
Delamination | NDI
0.8
1
Delamination size without/with
NDI
1
Cumulative Value [-]
Size
Defect
0.4
0.6
Delamination size s [m]
0.8
0.6
0.4
0.2
0
Without NDI
With NDI
0
0.2
0.4
0.6
Delamination size s [m]
0.8
1
Conclusion
•
Probabilistic models for the distribution of defects have been proposed
and can be calibrated to observations.
•
Probability of failure increased by large delaminations.
(strength reduction in transverse direction is estimated)
•
Updating of PF by Non Destructive Inspection.
Future work
•
Quantify uncertainties in stochastic models for reliability.
•
Local defects influence on material properties in fatigue.
Distribution of Defects in Wind Turbine Blades
&
Reliability Assessment of Blades Containing Defects
Authors:
Henrik Stensgaard Toft, Aalborg University
Kim Branner, Risø-DTU
Peter Berring, Risø-DTU
John Dalsgaard Sørensen, Aalborg University / Risø-DTU