Daniel Trias, Raquel Rojo, Iñaki Nuin, Esteban Belmonte

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. 60 m Failure in composites: a matter of scale 5.000.000 : 1 scale relation with microscale (fibre diametre) 46 m 2.29 m Liberty Blade 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 Single lap joint

10. Stresses in a single lap joint 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 Adhesive Elastic spring element 2 nodes with same coordinates joined with a MPC/rigid link

12. - + Peeling Stress peak Mesh-size + - Stress dependence on mesh size

13. Combinations: mixed modes Mode I Mode III Mode II 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

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