The Composites Centre - UPpaginas.fe.up.pt/~comptest/proc/files/presentations/PaulRobinson.pdf · The Composites Centre for research, modelling, testing and training in advanced composites

The Composites Centrefor research, modelling, testing and training in advanced composites

DELAMINATION RESEARCH: PROGRESS IN THE LAST TWO DECADES AND THE CHALLENGES AHEAD

COMPTEST’06, 11 April 2006

Paul RobinsonThe Composites CentreAeronautics Department

© Imperial College London

Introduction: An example The Composites Centre, Imperial College London

Data from Ei Engineering Village 2‘delamination’ AND ‘composites’

⇒7794 hits!

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The Composites Centre, Imperial College London

How to cover this? See the review papers: Delamination-a damage mode in composite structures, Garg, A.C. (Dept. of Aeronaut. Eng., Indian Inst. of Technol., Bombay, India), Engineering Fracture Mechanics, v 29, n 5, 1988, p 557-84

Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001Tay, T.E. (Dept. of Mech. Eng., Nat. Univ. of Singapore, Singapore), Applied Mechanics Review, v 56, n 1, Jan. 2003, p 1-32

Characterisation

Materials development

Modelling

Courtesy of D Cartie, Cranfield University


CharacterisationCrack Growth ModesDelamination growth in laminated composites can occur in Mode I, Mode II, Mode III and combinations of these modes.

This is because the fibre reinforcement in the plies above and below the delamination can act to constrain the delamination to remain at the interface.


Mode IDCB test: JIS K7086 (1993), ASTM D5528-01 ( first published 1994) and ISO 15024 (2001)

Mode II Many methods proposed : Stabilised ENF test JIS K7086 (1993) , no international standard

Clip gauge

Characterisation – current statusCharacterisation

Mode III ECT test has been investigated by ASTM; no standard has been established

?


MMB test (1988) : ASTM D6671/D6671M-04e1 (first published 2001)

Mode I/II

?

•Geometric non-linearity

From Sun & Davidson, Eng Frac Mech (2006)

Mode II Characterisation: problems?

•Difficulty in measuring

crack tip position

Courtesy of B Blackman, Imperial College

•Friction

Courtesy of B Blackman, Imperial College

+ others! - fixture compliance, precracking, ply waviness


Mode II recent research -

•Geometric non-linearity

•Fixture compliance

•Friction

Davidson and colleagues*

* Davidson & Sun, ‘Effects of friction, geometry and fixture compliance ….’, J Reinf Plast Compos 2005;24(15:1611-28

Sun & Davidson, ‘Numerical Evaluation of the effects of friction and geometric nonlinearities….’, Eng Frac Mech (2006)

Davidson, Sun & Vinciquerra, ‘Influences of friction, geometrical nonlinearities and fixture compliance ….’, submitted to J Compos Mater

ENF & 4ENF

Reduction in lever arm of vertical force components

Additional moment due to horizontal force components


Davidson et al: Results

• Friction and geometric non-linearities with rigid fixture produce small changes in perceived toughness – but larger for 4ENF

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

0 0.3 0.5

coefficient of friction

Perc

eive

d to

ughn

ess

/ Tru

e to

ughn

ess

3ENF4ENF

• More recent work (yet to be published) indicates the above in combination with fixture compliance and load range for compliance calibration can give large errors – again larger for 4ENF. (Expt’l results for 4ENF typically 9-60% higher than for 3ENF.)

• ASTM likely to produce a test standard for 3ENF (i.e. initiation toughness only)


Mode II recent research -

* Blackman, Brunner & Williams, ‘Mode II fracture testing of composites: a new look at an old problem’, accepted for publication in Eng Fract Mech

ESIS TC4 have conducted round robin evaluations of various Mode II test specimens. Recent work has focused on two particular aspects of the ELS specimen.

• difficult in measuring crack length accurately

• variability induced by clamping arrangement

ESIS TC4 *The Composites Centre, Imperial College London

CBT Data Reduction (from TC4 protocol)

( ) ( )N

EbhLa

C clampII ⋅Δ++Δ+

=1

3

33

23

( ) FEhb

aPG IIIIC ⋅Δ+=

132

22

49

Corrected Beam Theory

a

L

in which ΔII was obtained using 0.42ΔI obtained from a Mode I dcb test:

crack length (a)0Δ

(C/N

)1/3

=X-axis interceptΔ

VIS



Comparison of data reduction methods

Compliance calibration(using measured crack lengths)

New method (using calculated crack lengths)

A recent numerical study has confirmed the effectiveness of the proposed appoach*.* De Moura & de Morais, ‘Equivalent crack-based analyses of ENF and ELS tests’, EUROMECH Colloquium 473 Fracture of Composite Materials, 2005, Porto

Compliance calibration(using measured crack lengths)

New method (using calculated crack lengths)

Nesting in unidirectional laminates

Nominal pre-cure state

fibre direction

Post-cure state


Nesting: In two adjacent plies, fibres from one ply ‘nest’ in valleys in the other ply

cure

Upper and lower half profiles do not match causing opening if crack is to continue propagating

Profiles match in the unloaded state

Effect on Mode II delamination growth:

Film starter method

Natural starter crack


Mode II load-displacement plots (4ENF)

GIIc results

0200400600800

100012001400

.

Starter Method

GIIc

(J/m

2 )

Film Foil Spray Natural

Initiation values

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200

400

600

800

1000

1200

.

Starter Method

GIIc

(J/m

2 )

Film Foil Spray Natural

Propagation values


Materials developmentResin system improvement : rubber toughening (GIc)

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800

Epoxy 9% rubber

Frac

ture

Ene

rgy,

J/m

2

Single-Component (1K) ‘Hybrid’Anhydride/Epoxy + CTBN Rubber

‘The effect of silica nano particles and rubber particles on the toughness of multiphase thermosetting epoxy polymers’Journal of materials science [0022-2461] Kinloch yr:2005 vol:40 iss:18 pg:5083 -5086


How tough?

GIc for ‘Sellotape’

= 110J/m2


Rubber Toughening Mechanisms - Fracture Surface

• The rubbery-phase particle does not debond under the triaxial stress field in the vicinity of the crack tip but instead internally cavitates.

• This internal void allows plastic void expansion in the epoxy polymer to occur.

Materials development

Courtesy of AJ Kinloch, Imperial College


Nano-Silica Composites (SiO2 particles are formed ‘In-situ’ during a sol-gel manufacturing process)

Materials development : nano reinforcement of resin

TEM of a cured nano-silica/epoxy.


‘Added’ Nano-Particles << Kinloch & Taylor, J. Materials Sci., 37, 433, 2002 >>

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Epoxy 4% nano 8% nano 11% nano 15% nano 20% nano

Frac

ture

Ene

rgy,

J/m

2 But why do the nano-silica particles increase the toughness ?

‘The effect of silica nano particles and rubber particles on the toughness of multiphase thermosetting epoxy polymers’Journal of materials science [0022-2461] Kinloch yr:2005 vol:40 iss:18 pg:5083 -5086

Materials development : nano reinforcement of resin (GIc)

Single-Component (‘1K’) Epoxy/Anhydride with Nano-SiO2 (wt.%)


From FEG SEM Studies Courtesy Dr. I.A. Kinloch (Univ. Cambridge)

100 nm_____

Materials development : nano reinforcement of resinThe Composites Centre, Imperial College London

Materials development : composite reinforcement through-thickness

1cm

Many forms : stitching, weaving, tufting, z-pins, …..

‘Z-pinned composites: Pin testing and interlaminar toughness data reduction strategies’,Paul Robinson, Shumit Das & Marcin Fert, presented at 4th Int Conf on Fract of Polymers, Composites and Adhesives, Les Diablerets, Sept 2005.


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0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12crack length a (m)

Tru

e G

IC

True

GIc

(J/m

2 )Crack length (m)

Bridged zone

Developed bridged zone

Modelling development

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

−=∴

−=

2

3IIc

32

22

II

ν1EhG

38π

cP

Eh64πν19P

G

Simple formulae

Axisymmetric isotropic circular plate containing mid-plane circular delamination

Davies, G.A.O. and Robinson, P. "Predicting Failure By Debonding/ Delamination", Debonding/Delamination Of Composites, AGARD : 74th Structures & Materials Meeting, (AGARD_CP_530), Patras, Greece, May 1992.

Davies, G.A.O., Robinson, P., Robson J. and Eady D.“Shear driven delamination propagation in two dimensions", Composites Part A, 28A, 1997, 757-765.


Computational modelling development: Direct application of fracture mechanics

Determine FzA and Fz

B the vertical stress resultants acting at node 3 due to elements A and B

Determine w3 and w4, the vertical displacements of nodes 3 and 4

Similarly for Mode II:

So, for Mode I:

Detail of VCC* for 2-D mesh

*Rybicki and Kanninen “ A Finite Element Calculation of stress intensity factor by modified crack closure integral”, Engng Fract Mech, 9, 931-938, 1977.

Step 1. Calculate the energy available to drive the delamination growth


Step 2. The energy release rate is tested against a growth criterion, which involves the experimentally determined critical energy release rates (GIc, GIIc etc).

Step 3. The delamination front is advanced where the growth criterion is satisfied.

- Move mesh

- Disconnect nodes

Direct application of fracture mechanics (cont.)


Advancing crack front by moving mesh – example

Direct application of fracture mechanics (cont.)The Composites Centre, Imperial College London

Hitchings D, Robinson, P. and Javidrad, F., “ A Finite Element Model for Delamination Propogation in Composites”, Computers and Structures, Vol. 60, No 6, pp 1093-1104, 1996.

Nillson F.K. and Giannakopoulos A.E., “Finite Element Simulation of Delamination Growth”, 1st Int Conf on Computer-Aided Assessment and Control of Localized Damage, 1990, 299-313

Rinderknecht S. and Kroplin B. “A Finite Element Model for the Delamination in Composites Plates”, Mechanics of Composites and Structures, V1, No2, 1994 …………….

Advancing crack front by moving mesh -problems


Meshing problems as delamination fronts approach each other. How do delaminations merge?


Advancing crack front by disconnecting nodes

Problems : mesh only approximates the mesh front in a ‘stepped’fashion. Calculation of accurate energy release rates for stepped front very difficult


Ko A.W.L. “An investigation in the use of a stationary mesh approach to simulate delamination growth in composite laminates”, PhD Thesis, Imperial College, London, 2002

Kutlu Z. and Chang F.K. “ Composite Panels containing multiple through-the-width delaminations and subjected to compression. Part I”, Composite Structures, 31, pp 273-296, 1995.

Zie D and Biggers S.B. jr. “ Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique Part I: Formulation and validation”, Eng Fract Mech, Volume 73, Issue 6, April 2006, p 771-785 .


Direct application of fracture mechanics (cont.)ABAQUS implementation of VCCT


Computational modelling development: Indirect application of fracture mechanics

Step 1. A finite element model is constructed in which ‘interface’ elements are embedded between the layers of elements which are likely to delaminate.

(Often called the interface element approach or Cohesive Zone Model approach*.)

*Numerical simulation of free edge delamination in graphite-epoxy laminates under uniaxial tensionSchellekens, J.C.J. (Delft Univ of Technology); De Borst, R. , International Conference on Composite Structures, 1991, p 647

Interlaminar interface modelling for the prediction of delamination, Allix, O. (Lab. de Mecanique et Technol., GRECO/GIS Calcul des Structures, Cachan, France); Ladeveze, P. , Composite Structures, v 22, n 4, 1992, p 235-42


interface elements

cG

Indirect application of fracture mechanics (cont.)Step 2. A non-linear finite element analysis is performed.

Example

Progressive delamination using interface elementsMi, Y. (Imperial Coll); Crisfield, M.A.; Davies, G.A.O.; Hellweg, H.-B., Journal of Composite Materials, v 32, n 14, 1998, p 1246-1272


zone in a ‘softened’ state*

( )2/σcEG≈

*An Engineering Solution for using Coarse Meshes in the Simulation of Delamination with Cohesive Zone Model, Turon A, Davila CG, CamanhoPP & Costa J, NASA/TM-2005-213547, March 2005

Indirect application of fracture mechanics (cont.)

The softened zone can be made artificially larger by reducing the ‘strength’ σ of the interface element but this will alter the initiation of the delamination growth process.

Influence of mesh refinement on load – displacement plot

Progressive delamination using interface elementsMi, Y. (Imperial Coll); Crisfield, M.A.; Davies, G.A.O.; Hellweg, H.-B., Journal of Composite Materials, v 32, n 14, 1998, p 1246-1272


Circular plate with centralCircular plate with centralpoint loadpoint load

Interface elements Interface elements at the midat the mid--planeplane

Modelling Validation: Centre-loaded plateThe Composites Centre, Imperial College London

0

5

0 0.5displ. (mm)

Analyt ical

All numericalcurves

P (kN)

Courtesy of S Pinho, Imperial College

Modelling Validation: double crack dcb test

Delamination growth prediction using a finite element approachRobinson, P., Besant, T. Hitchings, D., 2nd ESIS TC4 Conference on Polymers and Composites, Les Diablerets, 1999, p135-147.

Implanted delaminations


( )310−×

ABAQUS Benchmark case

Influence of interface strength to1

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

to1= 66MPa

to1=110 MPa

to1=33MPa

Reaction force [N]

Displacement [mm]

to1=3.3 MPa

Experiment0 3.3It MPa=

S.Z.

S.Z.S.Z.

0 33.0It MPa=S.Z.

S.Z.S.Z.

0 ItIσ

Iδ

,I cδIcG

0Iδ

Grey interface: G = GIc fully broken

Modelling Validation: double crack dcb test

ELRIPS WP7 ‘Composite Bonded Repairs: Static and Fatigue Performance’, B. G. Falzon & R. T. Tenchev, Progress presentation, Imperial College, 19 October 2005


Blue interface:0 < G < ½GIc

Red interface:½GIc < G < GIc

Axisymmetric isotropic circular plate subjected to uniform pressure, p

Modelling Validation: pressure-loaded plate

τ

τ0GIIc

Predicting delamination and debonding in modern aerospace composite structures Davies, G.A.O.; Hitchings, D.; Ankersen, J. , Composites Science and Technology, v 66, n 6, May, 2006, Advances in Statics and Dynamics of Delamination, p 846-854

Shear driven delamination propagation in two dimensions,Davies, G.A.O.; Robinson, P.; Robson, J.; Eady, D., Composites - Part A: Applied Science and Manufacturing, v 28, n 8, 1997, p 757-765


annular mid-plane delamination of width l ( ) ( )llR

EtGp IIc

−⎥⎦

⎤⎢⎣

⎡−

=2

11

234

2

3

υ

Challenges ahead

ModellingRobust methods for selection of interface element parameters, extension of the techniqueAlternative modelling approaches? Address the reality of practical delamination growth – multiple delamination, migration ….

Characterisation

Mode III, test standards for non 0°/0° interfaces, tests for new materials (NCFs, 3-D woven preforms …), fatigue


Complete Mode II development (initiation test standard soon?, propagation….?)

Thank you


DAMAGE ZONE

CRACK MIGRATION

Schematic of crack path in a Mode I DCB test at a 0°/90° interface

Micrograph of the crack path in a mode II ELS test at a 0°/90° interface

TRANSVERSE σ

NESTING

Microscope stage testing in mode II

2000μm

2000μm

Film starter crack propagation

Natural starter crack propagation


Crack Opening Profile

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20

40

60

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180

0 2000 4000 6000 8000 10000

Hor. distance from crack tip, (μm)

Cra

ck O

peni

ng , μm

Film Foil Natural Spray


BAE TESTING

OTHER MODELS

Mesh-independent discrete numerical representations of cohesive-zone modelsRene de Borst, Remmers, J.J.C.; Needleman, A. Source: Engineering Fracture Mechanics, v 73, n 2, Jan. 2006, p 160-77

FATIGUE

Fatigue damage model for the interface element

In continuum damage mechanics the damage rate can be expressed as:

Peerling’s law – exponential law:

αεε~)~,( DCeDg=

is an equivalent positive strain measureε~

.εε βλ ~~DCe

dtdD =

Modified Peerling’s law:αεε~)~,( DCeDg=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=cc

DCedtdD

δδ

δδ

β

λ

(Note: even if the initial damage is zero, the damage starts to accumulate)

DCDCB

Z PINS

Materials development : composite reinforcement through-thickness

1cm

Longitudinal cracks in z-pin

Many forms : stitching, weaving, tufting, z-pins, …..

‘Z-pinned composites: Pin testing and interlaminar toughness data reduction strategies’,Paul Robinson, Shumit Das & Marcin Fert, presented at 4th Int Conf on Fract of Polymers, Composites and Adhesives, Les Diablerets, Sept 2005.


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The Composites Centre - UPpaginas.fe.up.pt/~comptest/proc/files/presentations/PaulRobinson.pdf · The Composites Centre for research, modelling, testing and training in advanced composites