Fracture Mechanics and New Techniques and Criteria for the Design of Structural Components for Wind Turbines
Daniel Trias, Raquel Rojo, Iñaki Nuin, Esteban BelmonteAnalysis and Design of Aerogenerators – Wind Department
Index
INTRODUCTION Failure of composites: a matter of scale Failure criteria for fibre-reinforced composites
FRACTURE MECHANICS FOR ADHESIVE/DELAMINATION ASSESSEMENT: VCCT
Stresses in a single lap joint (Illustrative example) VCCT Implementation in a commercial FE code Application example
FRACTURE MECHANICS IN FAILURE CRITERIA: LaRC criteria (Short) Description Application example (only on article)
INTRODUCTION
Failure in composites: a matter of scale
Failure depends on phenomena (matrix and fibre cracking, debonding, kinking …) which take place at a scale of about 10um and which are nearly-brittle
Failure in composites: a matter of scale
46 m
Liberty Yao Ming
2.29 m
Blade
60 m5.000.000 : 1 scale relation with microscale (fibre diametre)
Failure criteria for fibre reinforced composites
MICROSCOPICAL CRITERIA
Failure of single constituents: fibre, matrix
May be used in multi-scale analysis
Computationally unaffordable for large structures
MACROSCOPICAL CRITERIA
Empirically obtained from global behaviour of laminae
Generally symmetrical “Black box” Ply level or laminate
level Tsai-Hill, Tsai-Wu, etc.
PHENOMENOLOGICAL CRITERIA
Bridge micro and macro behaviour by analyzing specific phenomena
Ply level Hashin, Hashin-Roten,
Puck, etc. Puck: Analyzes fracture
plane successfully spread since WWFE
Puck: Physically meaningless parameters
FRACTURE MECHANICS Theory 1900s. Application in
Computational Mechanics 1970s Introduce the effect of defects in
brittle behaviour, analyze kinking.
NASA: LaRC Criteria. Physically based parameters
Refine some failure criteria
Adhesive joints/ Delamination assessment:
- VCCT
- Decohesive elements
FRACTURE MECHANICS FOR ADHESIVE/DELAMINATION
ASSESSMENT: VCCT
Adhesive failure may happen…
Stresses in a single lap joint
Single lap joint
Stresses in a single lap joint
Single lap joint
Shear stresses
(Induced) Peel stresses
LARGE stress gradients!
Adhesive implementation in FE model: stress-based approach
2 nodes with same coordinates joined with a MPC/rigid link
2 nodes with same coordinates joined with a MPC/rigid link
Elastic spring element
Single slab joint
(FE model)
Adhesive
Stress dependence on mesh size
Peelin
g S
tress p
eak
+
-
Mesh
-siz
e
+
-
Fracture Mechanics approach
Based on crack propagation analysis:
Specially well-suited for cracked materials and brittle behaviour
Provides concepts and tools which allow the analysis of microscale phenomena and their application to component-scale situations.
Energy based analysis: stable solution for stress singularities
Mode IMode II Mode III
Combinations: mixed modes
Fracture Mechanics approach
GIc, GIIc, GIIIc are material properties. Usually: GIc < GIIc < GIIIc
Critical values of G are needed for each mode. Tests with a standard: Mode I : DCB test (ASTM, DIN, ISO) Mode II: ENF test (DIN) Mixed mode I/II: MMB test (ASTM) Mode III: some proposals
Failure criteria (Loss of adhesion / delamination) GI > GIc ? GII > GIIc ? GIII > GIIIc?
We need to compute GI, GII, GIII numerically: Virtual Crack Closure Technique (VCCT) Basic assumption: the energy needed to open a crack some Δa length is the same energy
needed to close it some Δa length
Fracture Mechanics approach : VCCT
Debonded region
Crack tipBonded region
Adhesive
G>Gc? : Would a potential crack propagate?
Crack tip: Local coordinate system
yL
xL
i x*k
Non-straight crack tip: Local coordinate system to be defined at each node of the crack tip
Debonded region
Crack tipBonded region
Need to find information on neighbor nodes and elements
Modified formulae: 3D non-regular meshes
Implementation with a commercial FE code
Model with defined adhesive zone (r.link)
Modification of adhesive model:
r.link spring + r.link
Model with non-rigid
adhesive zone
Stress solution
Initiation criteria
Definition of critical zones to crack
initiation
Computation of G (VCCT)
FE c
om
merc
ial so
ftw
are
(N
ast
ran, M
arc
)
Exte
rnal co
de (
MA
TLA
B)
USER INTERACTION
FE SOLUTION
Application to a Turbine Blade (1)
Application to a Turbine Blade (2)
Initiation criteria (stress) Detect zones where crack may appear
0.00001
0.0001
0.001
0.01
0.1
1
0 2000 4000 6000 8000 10000 12000
Length (mm)
Stress X
Stress Y
Stress Z
Stress norm
0
0.005
0.01
0.015
0.02
0.025
0 2000 4000 6000 8000 10000 12000
Length (mm)
Application to a Turbine Blade (2)
Need to solve again!
Crack “creation”: Adhesive is removed from those nodes showing larger value of the stress-based criteria
Application to a Turbine Blade (3)
GI, GII, GIII computed through VCCT formula, considering crack local coordinate system
Check adhesive failure criteria based on energy release rate
G analysis
0
0.000001
0.000002
0.000003
0.000004
0.000005
0.000006
0.000007
0.000008
1 2 3
Spring number
G (
N/m
m2) GI
GII
GIII
G/Gc analysis
0.000000001
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
1 2 3
Spring number
GI/GIc
GII/GIIc
GIII/GIIIc
G
Nearly the same methodology may be used for delamination
FRACTURE MECHANICS IN FAILURE CRITERIA: LaRC
criteria
Improvements achieved with LaRC
Fracture Mechanics employed for tensile matrix failure. In situ effects (dependence on ply thickness) are considered
Fibre kinking computed through Fracture Mechanics
Drawbacks:
Iteration required for the computation of fracture plane angles
Not (yet) spread in industry
Application to a component
σ11>0 and σ22>0
Failure Criteria: S11>0, S22>0
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0 500 1000 1500 2000Maximum Strength, Puck FF Larc04 #2 Matrix tractionPuck IFF Mode A Larc04 #3: Fibre failure
Application to a component
σ11<0 and σ22<0Failure Criteria S11<0, S22<0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0 500 1000 1500 2000
Larc04 #1: Matrix failurecompression
Larc04 #5: Biaxial compression
Puck Mode C
Failure Criteria S11<0, S22<0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0 500 1000 1500 2000
Maximum Strength, Puck FF
Larc04 #4: Kinking
Final Remarks and conclusions
Fracture Mechanics can be used successfully even in commercial finite element codes for adhesive assessment.
VCCT can be used for both adhesive and delamination assessment.
Fracture Mechanics has been used (NASA) to improve some failure criteria: Biaxial Compression Fibre Kinking
Future work: Compare with models with analytical solution (almost done!) Compare with tests on a substructure Fatigue model
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