Modeling delamination migration: quasi-static and … 2 Delamination Matrix-crack Impact M. McElroy et al. A numerical and experimental study of damage growth in a composite laminate

Modeling delamination migration: quasi-static and fatigue loading

S. T. Pinho, P.

BaizImperial College

London

B.Y. ChenImperial College London

National University of

Singapore

T. E. TayNational University

Singapore

J.G.

RatcliffeNASA Langley

N. V. De [email protected]

National Institute of Aerospace

https://ntrs.nasa.gov/search.jsp?R=20160006583 2018-07-02T03:13:11+00:00Z

mailto:[email protected]

Motivation

2

Delamination

Matrix-crack

Impact

M. McElroy et al. A numerical and

experimental study of damage growth in

a composite laminate. in proceedings of

the ASC 29th Technical Conference,

San Diego, CA, USA, 2014.

Migration: The process by which a propagating delamination

relocates to a new ply interface via matrix cracking

Delamination

Matrix-crack

R. Krueger et al. Fatigue Life

Methodology for Bonded Composite

Skin/Stringer Configurations.

NASA/TM-2001-210842, 2001.

Skin-stringer pull off

Contents

3

Summary

2 Modeling approach

3 Validation

4

1 Experiments

Contents

4

Summary

2 Modeling approach

3 Validation

4

1 Experiments: delamination migration test

Experiments: delamination migrationTest Setup - Premise

Delamination

(“positive” shear stress)

+

Migration

(“negative” shear stress)

-90o

0o

*adapted from Greenhalgh, 2009

*E.S. Greenhalgh, C. Rogers, P. Robinson. Fractographic observations on delamination growth and the subsequent migration

through the laminate. Composites Science and Technology, 69:2345-2351, 2009.

• Cross-ply laminate

• “2D” migration process

• Pre-crack (Teflon insert)

between 0o and 90o ply

• Variable load position (L)

All units in mm

12.7

Ls = 115

[0o]3

[90o]4

[0o]

[90o]4

Teflon

insert

a0=49

L12.7

Clamp

Clamp

[0o]2

6J.G. Ratcliffe, M.W. Czabaj and T.K. O’Brien. A test for characterizing delamination migration in carbon/epoxy tape laminates.

NASA/TM-2013-218028, 2014.

Experiments: delamination migration testTest setup

Experiments: delamination migration testTest setup - overview

L

Delamination

90o

0o

0o

90o4 +

Experiments: delamination migration testTest setup - overview

Migration

L

-

0o

90o4

L

Delamination

90o

0o

0o

90o4 +

9

0

5

10

15

20

25

1 1.1 1.2 1.3

Dm

mm

L/a0

L

Experiments: delamination migration testTest setup – validation data

Load - displacement Migration location

Damage morphology

Dm

0

100

200

300

400

0.0 0.5 1.0 1.5

Force,N

Displacement, mm

Contents

10

Summary

2 Modeling approach: Floating Node Method (FNM) and

Virtual Crack Closure Technique (VCCT)

3 Validation

4


Floating Node Method

X-FEMPhantom Node

Method (PNM)Floating Node

Method (FNM)Remeshing

Same solution Same solution

Same implementation

strategy suitable for standard

finite element architecture

B.Y. Chen, S.T. Pinho, N.V. De Carvalho, P.M. Baiz, T.E. Tay, A floating node method for the modelling of discontinuities in

composites, Engineering Fracture Mechanics, Vol. 127:104-134, 2014.

12

Real node

Floating node

Coordinates of

crack positions

Floating Node Method (FNM)

13


Real node

Floating node

Coordinates of

crack positions

14

T crack Intersecting cracks


• Floating Nodes are topologically related to each element with no initial position

assigned

• The position of the floating nodes is assigned only after the crack path is determined

• The floating nodes are used to form sub-elements within the original element and

accommodate crack networks

• Ideally suited to represent multiple cracks and their intersection

• Can be coupled with Virtual Crack Closure Technique (VCCT) and cohesive zone

crack formulations to model crack propagation

Key Characteristics:

projected crack path

Mode I

Mode II

Floating Node Method & Virtual Crack Closure Technique

Virtual Crack Closure Technique (VCCT):

FNM & VCCT applied to cross-ply laminates:

1 FNM Element

(multiple plies))

16

EE

I

Ω

Real node

Floating node (DoF)

Coordinates of crack

positionsN.V. De Carvalho et al, Modeling delamination migration in cross-ply tape laminates, Composites Part A: Applied Science and Manufacturing, 71, 192-203, 2015.

Laminate

Ω

90°

0°

0°

[0°/90°2/0°]


17

Real node

Floating node (DoF)


positions

Ω

EE

Laminate

Ω

[0°/90°2/0°]

I

90°

0°

0°

90°

0°

0°

[0°/90°2/0°]

1 FNM Element

18

• Mixed Mode exponential law:

• Fracture Criterion:

Quasi-static

Fatigue


0°

Delamination

E E

Real node

Floating node (DoF)


positions

90°

0°

I

19

Migration onset (delamination to matrix crack)

FNM & VCCT applied to cross-ply laminates: Migration onset

E E

90°

0°

0°

Real node

Floating node (DoF)


positions

I

Quasi-static

Fatigue

Material A

Material B

t

n

1

10

No growthNo growth

20

FNM & VCCT applied to cross-ply laminates: Migration onset – quasi-static

21

FNM & VCCT applied to cross-ply laminates: Migration onset – quasi-static

Material A

Material B

1

10

No growth

t

n

22

FNM & VCCT - application to composites: Migration onset - fatigue

t

nMaterial A

Material B0

Matrix Crack

Maximum tangential stress criterion:

Quasi-static

Fatigue

23


IE E

90°

0°

0°

θ

Real node

Floating node (DoF)


positions

FNM & VCCT - application to composites: migration matrix crack to delamination interaction

24

• Topological criterion

- local delamination is

onset when matrix crack

reaches interface 90°

0°

0°

Real node

Floating node (DoF)


positions

Migration (matrix crack to delamination)

I

E E

Fatigue algorithm

1

PROPAGATE THE CRACK

ACCUMULATE THE CYCLES

DETERMINE THE GROWTH

RATE FOR EACH CRACK

DETERMINE THE NUMBER OF

CYCLES NEEDED TO

PROPAGATE EACH CRACK BY

ONE ELEMENT, AND THE

CRACK WHICH PROPAGATES

IN FEWEST CYCLES

2

3

4

Verification – Static: DCB

26

0

10

20

30

40

50

60

70

0 1 2

Load,N

Displacement, mm

BENCHMARK

SIMULATION

* R. Krueger. An Approach to Assess Delamination Propagation Simulation Capabilities in Commercial Finite Element Codes. NASA/TM-2008-215123, 2008

*

30

31

32

33

34

35

36

37

1 100 10000 1000000

a, mm

N, Cycles

2D Benchmark

FNM - VCCT

27

Verification – Fatigue: DCB benchmark

BENCHMARK

* R. Krueger. Development of a Benchmark Example for Delamination Fatigue Growth Prediction. NASA/CR-2010-216723

*

SIMULATION

Contents

28

Summary



3 Validation: modeling delamination migration

4


Validation: Delamination migration testNumerical model

29

Dimensions (mm)

B* 2h C S a0

12.7 5.25 12.7 115 49

*B is the width of the specimen (out-of-the page);

90° - specimen width direction; 0° - specimen span direction

Model details

• Contact modeled between specimen and

clamps/baseplate

• Clamping force applied in a first static step

• Abaqus/Standard (Implicit) + UEL

• All material properties obtained using

standard/recommended test methods

a0

Clamp Clamp

Baseplate

Stacking sequence: [904/03/(90/0)2s/02/0/904/T/0/904/02/(90/0)2s/02/903/0/90]

Plies modeled within the FNM element

L

1

2 C

µ µ

µ 2h

u2=V

h

C S

ΩA

ΩB

ΩC

0°

90°

0°

1 FNM Element

4

30

Delamination Migration

1a0

L=a0 u2=V2

Validation: delamination migration testResults - migration process

Observations

• Correct sequence of events: delamination followed by migration

• Failure morphology well captured – including crack path

through-thickness

31

0

100

200

300

400

0.0 0.5 1.0 1.5

Load,N

Displacement (mm)

EXPERIMENTS

SIMULATIONS

MIGRATION

a0

L=1.0a0 u2=V

Migration

Validation: delamination migration testResults – load vs displacement

L=1.0a0:

Observations

• Max load: good agreement

• Delamination: unstable growth

followed by arrest and

subsequent unstable and stable

growth

• Migration: predicted before

delamination arrest

0

100

200

300

400

0.0 0.5 1.0 1.5

Load,N

Displacement, mm

EXPERIMENTS

SIMULATION

Migration

a0

u2=V

32


EXPERIMENTS

SIMULATION

MIGRATION

Observations


• Delamination: small region of

stable growth prior to main load-

drop

• Migration: predicted within the

main load drop

Migration

L=1.1a0:L=1.1a0

0

100

200

300

400

0.0 0.5 1.0 1.5

Load,N

Displacement, mm

EXPERIMENTS

SIMULATION

MIGRATION

Migration

33


L=1.2a0:

a0

L=1.2a0 u2=V

Observations


• Delamination: stable

delamination growth prior to

main load-drop


main load drop

0

100

200

300

400

0.0 0.5 1.0 1.5

Load,N

Displacement, mm

EXPERIMENTS

SIMULATION

MIGRATION

34

a0

u2=V

Observations


• Delamination: stable growth prior

to main load-drop


main load drop

L=1.3a0


Migration

0

5

10

15

20

25

30

1 1.1 1.2 1.3

EXPERIMENTS

SIMULATIONS

L/a0

ΔM,

mm

35

a0

L=a0 u2=V

ΔM

Observations

• Trend well captured

• Conservative predictions

Validation: delamination migration testResults – Migration location

Fatigue - Preliminary resultsDelamination growth and cycles to migration

36

0

5

10

15

20

25

0 50,000 100,000 150,000 200,000

N, Cycles

Series1

Series2

L=1.1a0

L=1.3a0

Δa,

mm

Migration

Observations

• Load-offset affects

fatigue life

Constant amplitude, R = 0.1 and f = 5 Hz:

Contents

37

Summary



3 Validation: modeling delamination migration

4


Summary

• Developed a finite element model based on the Floating Node Method combined with the Virtual Crack Closure Technique to capture the interaction between delamination and matrix-cracking

• Identified and applied migration criteria for both quasi-static and fatigue loading

• Compared simulations and experiments.– Good agreement observed for load-displacement, migration

location and path

• Validation of the fatigue simulations are in progress

38

N. V. De [email protected]

National Institute of Aerospace

Modeling delamination migration: quasi-static and fatigue loading

S. T. Pinho, P.

BaizImperial College

London

B.Y. ChenImperial College London

National University of

Singapore

T. E. TayNational University

Singapore

J.G.

RatcliffeNASA Langley

mailto:[email protected]

“Non-matching mesh”FNM

Backup Slides: cohesive zone elements

Ω Ω

…oror

Backup Slides: element integration

Backup Slides: Topological migration criterion, experimental evidence

Backup Slides: FNM vs PNM, convergence: KI

0%

2%

4%

6%

1.E+02 1.E+03 1.E+04 1.E+05

Phantom Node Method (PNM) (Abaqus)

FNM

Backup Slides: FNM vs PNM, accuracy: KI, KII

0

0.5

1

1.5

0 10 20 30 40 50

45

0

100

200

300

400

500

0 1 2 3

Load,N

Displacement, mm

BENCHMARK

SIMULATION

Backup slides: MMB benchmark

*R. Krueger. Development of and application of benchmark examples for mixed-mode I/II quasistatic delamination propagation predictions. NASA-CR-2012-217562, 2012.

*

Documents

Modeling delamination migration: quasi-static and … 2 Delamination Matrix-crack Impact M. McElroy et al. A numerical and experimental study of damage growth in a composite laminate