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