Progressive Failure Modelling of Composite Laminates Containing

Tapered Holes

Chun Wanga, Andrew J. Gunnionb, and Adrian C. Orificib,c

aAir Vehicles Division, DSTO, AustraliabCRC-ACS, Melbourne, Australia

cRMIT University, Melbourne, Australia

4th International Conference onComposites Testing and Model Identification

2

OUTLINE

ObjectiveRecent developmentsExperimentsPredictive ModelsResults and DiscussionSummary

3

Objective

Strength Prediction capability for compositesPrediction of residual strength after damage Optimise damage cutoutDesign of conformal antenna slotsDesign and certification of repairs

Wire dipole

Slot in infinite x-z ground plane Callus (DSTO)

4

Some Examples of Recent Developments

Abaqus damage model (2006)Milestone: research→engineering

Lapczyk and Hurtado (2007): Camanho et al (2007): 38.5% accuracy for tension of bolted joint

Inherent-flaw fracture mechanicsIBOLT: method of choice at LM Aero (Eisenmann and Rousseau 2004)Empirical correction for countersunk holes

Continuum damage mechanics Camanho et al (2007): 10.5% accuracy for OHTBogert et al (2006): 21.4% accuracy for slits

Camanho et al (2007)

Fracture energy

5

Experiments

Three types of specimens subjected to tensionStraight through-hole (diameter=6.35mm)Straight through-hole (diameter=50mm)Scarfed hole (diameter=50→200mm)Stiff and soft laminates:

[40/40/20]%[20/40/40]%

Stacking sequencesPanel: [45/90/-45/02]3S

OHT coupons: [45/02/-45/90]3S

[-45/902/45/0]3S

6

Experiments

Scarfed hole

2R

α

2R+2t/tanα

7

Tensile strength of stiff laminates

0

20

40

60

80

100

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Crosshead displacement (inches)

Stre

ngth

(ks

i)

Room Temperature

2.0" hole in[45/90/-45/0/0]3S

Scarfed hole in[45/90/-45/0/0]3S

0.25" hole in[45/90/-45/0/0]3S

8

Failure modes

9

Strains in straight-hole panel

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8

Crosshead displacement (mm)

Load

(kN

)

0

5000

10000

15000

20000

25000

30000

35000

Stra

in (m

icro

stra

in)

Load

inside hole - right

inside hole - left

gauge 3

gauge 5

30-ply panel[45/90/-45/0/0]3S

Room Temperature50mm hole diameter500mm wide panel

Tested 28 May 2008

hole edge gauges 5mm from edgefarfield gauge 135 mm from hole

Some ductility

10

Strain in scarfed-hole panel

0

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500 600 700 800 900

Load (kN)

Stra

in (m

e)

Gauge 1Gauge 2Gauge 3Gauge 4Gauge 5

Tip failure (1st group of zeros) Failure of 2nd group of zeros Failure at edge of scarf

Suspected premature failure of strain gauges

11

Fracture Mechanics Model

Critical flaw determined from fracture energy and ply percentage

Predicted strength is identical to cohesive zone model predictionIndependent of actual bridging law or the softening behaviour

Reported to be hole-size dependent

0 0 45 45 90 902un notched

n G n G n GaCπσ −

+ +=

( / )un notched

notched f a Rσ

σ −=

12

Identification of Fracture Parameters

45 0 90 451 15 5

G G G G= =

45 0 90 451 15 5

G G G G= =

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

0 100 200 300 400 500

Fracture energy (kJ/m2)

Pred

icte

d st

reng

th (M

Pa)

Experimental data (stiff laminate)

Experimental data (soft laminate)

Stiff laminate

Soft laminate

0G

Assume:

13

Predictions

Open hole tension strength of quasi-isotropic laminateData by Mollenhauer et al (CompTest 2006)Model does not predict layup effects

Hole diameter (mm)

0 5 10 15

Tens

ile S

treng

th (

MP

a)

0

200

400

600

800

[45/0/-45/90]S (Mollenhauer et al)[0/45/90/-45]S (Mollenhauer et al)Fracture mechanics

14

Predictions

Large straight-hole and tapered holeSignificant under-prediction of strengthNeed greater critical flaw size

Hole diameter (mm)

0 50 100 150 200 250

Tens

ile s

treng

th (

MP

a)

0

200

400

600

800

Stiff laminate [40/40/20]%

Scarfed hole

Straight-hole

15

Abaqus Damage Model

Strain-softening model:Bazant’s crack band modelBest for square elements

Shell elements: all plies have identical strains at any time. Scarfed region is modelled as multi-stepped (one step per ply). No bending.

Issues:Mesh refinementIdentification of fracture energiesPredictions of through-thickness geometry variation

0

500

1000

1500

2000

2500

0 0.5 1 1.5 2

Strain

Stre

ss (

MPa

)

Element=0.1mmElement=0.4mmElement=0.6mm

16

Mesh refinement

0.0

250.0

500.0

750.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Element size (mm)

Pre

dict

ed O

HT

stre

ngth

(MPa

)

Abaqus/ExplicitExperimental value

Straight-hole of 6.35mm diameterRelative insensitivity to mesh refinement

Stiff laminate

17

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

0 50 100 150 200 250 300Ply fracture energy G0T (kJ/mm2)

Pre

dict

ed s

tren

gth

(MPa

)

Experimental data of stiff laminateExperimental data of soft laminateExplicitExplicitImplicitImplicit

Hole diameter=6.35mm (0.25")Smallest element=0.6mm

Stiff laminate

Soft laminate

Identification of Fracture Energies

0 00.8C TG G= 90 90 00.003T C TG G G= =

.

Ply fracture energies depend on solverConsistency between two stacking sequences

18

Explicit versus Implicit

Implicit code suffered convergence problems and required dampingExplicit code more robust, damping not required, but requires large time increments to avoid inertia effect

0 2T LEρ

=Fundamental resonant (in-plane) period

0 2T LN NT h≈

∆

T hEρ

∆ = L

• Independent of density • Element size h needs to be small fraction of critical flaw size (e.g., h = 0.1 a)• N=?

Time increment:

Total time: many times of the fundamental period

Number of increments:

19

Ratio of run time to fundamental period T/T0

0 20 40 60 80 100

Erro

r

0.00

0.02

0.04

0.06

0.08

Abaqus/Explicit

Abaqus/Explicit

Run time versus error due to inertia effectError less than 2% requires loading duration about 30 times the fundamental periodAny disturbance resulting from damage progression reverberates 60 times

20

Failure path

Straight hole

0 degree ply

Crack inclined at 26 degreesCrack inclined at 11 degrees

21

Failure path

Scarfed hole

90 degree ply45 degree ply

0 degree ply

Crack inclined at 11° Crack inclined at 22°

22

Hole diameter (mm)

0 50 100 150 200 250

Tens

ile s

treng

th (

MP

a)

0

200

400

600

800

Stiff laminate [40/40/20]%

Fracture mechanics prediction

Abaqus/explicit prediction

Scarfed and straight-hole panels

Abaqus model provided an improvement but under-predicted strength by 20% and the angle of fracture path.

23

Quasi-isotropic laminates

Over-prediction of strength for large holesUsing fracture energies “backed-out” from stiff laminate data

Stacking sequence effect not predicted

Hole=2.54mm (element=0.2mm)

Hole diameter (mm)

0 5 10 15

Tens

ile S

treng

th (

MP

a)

300

400

500

600

700

800

[45/0/-45/90]S (Mollenhauer et al)[0/45/90/-45]S (Mollenhauer et al)Abaqus/Explicit model

Quasi-isotropic laminate

±5% error band

24

Damage Initiation Model

Difference in fracture path due to incorrect damage initiation model?Need alternative failure criterion to model off-axis plies

45 deg ply 0 deg ply

Hole=12.7mm (G0t=160 kJ/m2)

(element=0.2mm) (element=0.2mm)

25

Alternative Failure Criteria

Modified strain-invariant (Wang, C.H., Chapter 8, Multi-scale Modelling of

Composite Material Systems, 2005)

Fibre tensile fracture (shear failure)

Fibre compression failure (micro-buckling)

Matrix shear failure

Matrix dilatation fracture

( ) ( )f fvM cε ε≥

( ) ( )1

f fcσ σ≤

26

Stress-invariant theory

Comparison with published data(Wang 2005)

σxx (MPa)

-1000 -500 0 500 1000

σ yy (

MP

a)

-1000

-500

0

500

1000Experimental dataInitial failureFinal failure

AS4/3501-6(0/90/45/-45)

Longitudinal Stress (MPa)

-1500 -1000 -500 0 500 1000 1500 2000

In-p

lane

She

ar S

tress

(M

Pa)

0

20

40

60

80

100

120

140DFVLR tensionDFVLR compressionMBB testPrediction

T300/BSL914C(00 unidirectional lamina)

σyy (MPa)

-200 -150 -100 -50 0 50

τ xy

(MP

a)

0

20

40

60

80

100

120

Experimental dataPrediction

E-Glass/LY556(00 unidirectional lamina)

27

Gross strain

0.000 0.002 0.004 0.006 0.008

Max

imum

stra

in a

t hol

e ed

ge

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Abaqus/ExplicitStrain gauge 1Strain gauge 2

Straight hole (50mm dia)

Damage Progression Model

Predicted maximum strain is less than measurementStress-softening law may need modification

28

Conclusions

Fracture mechanics (inherent-flaw) showed promises at dealing with stacking sequence, but failed to predict effects of hole size and through-thickness tapering.Abaqus damage model under-predicted strength of cutouts larger than those in calibration coupons.Comparison of prediction with experimental data suggests alternative damage initiation model and damage progression model.Optimisation techniques may be required to back-out material properties.Improved solution method needs to be developed to improve computational efficiency.