1. Fracture Mechanics and New Techniques and Criteria for the Design of Structural Components for Wind Turbines
Daniel Trias, Raquel Rojo, Iñaki Nuin, Esteban Belmonte
Analysis and Design of Aerogenerators – Wind Department

2. 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)

3. INTRODUCTION

4. 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

5. Failure in composites: a matter of scale
: 1 scale relation with microscale (fibre diametre)
60 m
46 m
2.29 m
Blade
Liberty
Yao Ming

6. Failure criteria for fibre reinforced composites
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
MICROSCOPICAL CRITERIA
Failure of single constituents: fibre, matrix
May be used in multi-scale analysis
Computationally unaffordable for large structures
Refine some failure criteria
Adhesive joints/ Delamination assessment:
- VCCT
- Decohesive elements
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

7. FRACTURE MECHANICS FOR ADHESIVE/DELAMINATION ASSESSMENT: VCCT

8. Adhesive failure may happen…

9. Stresses in a single lap joint

10. Stresses in a single lap joint
LARGE stress gradients!
Shear stresses
(Induced) Peel stresses

11. Adhesive implementation in FE model: stress-based approach
Single slab joint
(FE model)
2 nodes with same coordinates joined with a MPC/rigid link
Elastic spring element
Adhesive
2 nodes with same coordinates joined with a MPC/rigid link

12. Stress dependence on mesh size
Peeling Stress peak + -
Mesh-size + -
Falta incluir perfil de tensiones analítico

13. 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 I
Mode II
Mode III
Combinations: mixed modes

14. 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

15. Fracture Mechanics approach : VCCT
Debonded region
Bonded region
Crack tip
Adhesive
G>Gc? : Would a potential crack propagate?

16. Crack tip: Local coordinate system
Non-straight crack tip: Local coordinate system to be defined at each node of the crack tip
Bonded region yL
Need to find information on neighbor nodes and elements
Modified formulae: 3D non-regular meshes
Debonded region xL i k x*

17. Implementation with a commercial FE code
Modification of adhesive model:
r.link  spring + r.link
Model with defined adhesive zone (r.link)
Model with non-rigid adhesive zone
FE commercial software (Nastran, Marc)
FE SOLUTION
External code (MATLAB)
Stress solution
USER INTERACTION
Initiation criteria
Definition of critical zones to crack initiation
Computation of G (VCCT)

18. Application to a Turbine Blade (1)

19. Application to a Turbine Blade (2)
Initiation criteria (stress)  Detect zones where crack may appear

20. Application to a Turbine Blade (2)
Crack “creation”: Adhesive is removed from those nodes showing larger value of the stress-based criteria
Need to solve again!

21. 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
Nearly the same methodology may be used for delamination

22. FRACTURE MECHANICS IN FAILURE CRITERIA: LaRC criteria

23. 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

24. Application to a component
σ11>0 and σ22>0

25. Application to a component
σ11<0 and σ22<0

26. 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