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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

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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)

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INTRODUCTION

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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

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

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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

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FRACTURE MECHANICS FOR ADHESIVE/DELAMINATION ASSESSMENT: VCCT

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Adhesive failure may happen…

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Stresses in a single lap joint Single lap joint

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

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

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

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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

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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

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

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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 tip Bonded region Need to find information on neighbor nodes and elements Modified formulae: 3D non- regular meshes

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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 commercial software (Nastran, Marc) External code (MATLAB) USER INTERACTION FE SOLUTION

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Application to a Turbine Blade (1)

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

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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

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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

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FRACTURE MECHANICS IN FAILURE CRITERIA: LaRC criteria

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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

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Application to a component σ11>0 and σ22>0

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Application to a component σ11<0 and σ22<0

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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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