Post-buckling behavior of thin-walled damaged laminates under Compression-After-Impact loading

3DEXPERIENCE Conference Design, Modeling and Simulation

19 – 21 Nov. 2019

Post-buckling behavior of thin-walled damaged laminates under

Compression-After-Impact loading

Hamburg University of Applied Science (HAW Hamburg) Aurelio Jose Olivares-Ferrer, Markus Linke

1. Introduction

2. Problems

3. Solution approach

4. Results

5. Conclusions

OUTLINE

1. Introduction

2. Problems

3. Solution approach

4. Results

5. Conclusions

OUTLINE

Composites in the Aeronautical industry

Optimize structures by reducing weight:

Thin-walled laminates

Structural components mainly use:

Carbon Fiber Reinforced Polymers (CFRP)

Excellent mechanical properties, such as:

•

Specific strength

•

Specific stiffness

But, CFRP laminates have a main

drawback:

1. INTRODUCTION

Aircraft receive lots of impacts during their life

Mainly

low-energy impacts

caused by:

•

Ground operation (main cause)

•

Runway debris

Barely Visible Impact Damage (BVID)

1. INTRODUCTION

(Delaminations projected view)

X Y

The most widely used because:

•

Projected view of delaminations (2D)

•

In-airfield application

Internal damage detection

Non-Destructive Testing (NDT) techniques

Compression-After-Impact (CAI) tests

on laminated flat plates

1) Impact test

(damaging the samples at a controlled energy)

2) Inspection test

(dimensioning the damage size)

3) CAI test

(residual strength)

Check the

residual strength

of laminates with BVID

Simply Supported Clamped

OBJECTIVE:

Get more knowledge about failure mechanisms of CAI test of

thin-walled CFRP

laminates with BVID

By creating finite element models with Abaqus software

1. Introduction

2. Problems

3. Solution approach

4. Results

5. Conclusions

OUTLINE

The FE model of

CAI test

of

thin-walled laminates

must face:

Laminate

modeling

2.

PROBLEMS

Laminate modeling strategy and material definition

• Plies and interfaces.

• Damage initiation criteria for intra- and interlaminar failure modes.

• Damage evolution models for intra- and interlaminar failure modes (material non-linearities).

Laminate

modeling

buckling

Global

Y Z

2.

PROBLEMS

Post-buckling behavior

• In thin-plates, the buckling load is lower than the compression failure load of an ideal straight plate.

The FE model of

CAI test

of

thin-walled laminates

must face:

Z X

Laminate

modeling

buckling

Global

Initial

geometrical

imperfection

2.

PROBLEMS

Geometrical non-linearities

• Permanent deformations in the plate due to the previous impact.

• Influence the post-buckling behavior.

Laminate

modeling

buckling

Global

Initial

geometrical

imperfection

Internal

damage

2.

PROBLEMS

Modeling strategy of the initial damage

• Only a 2D projected view of the delaminated area known.

• Unknown damage pattern in the through-thickness

Z X

Laminate

modeling

buckling

Global

Initial

geometrical

imperfection

Internal

damage

2.

PROBLEMS

1. Introduction

2. Problems

3. Solution approach

4. Results

5. Conclusions

OUTLINE

Geometry and boundary conditions

a = 120mm

b = 90mm

Original CAI test

Simplification used in the

models

3. SOLUTION APPROACH

• Physical thickness is needed to model interfaces between layers.

Laminate modeling

Layers modeling strategy

Equivalent Single Layer (ESL) Cross-section Zoom-in Layers Interfaces Y Z Layer 1 Layer 2

.

.

.

.

.

.

3. SOLUTION APPROACH

Laminate modeling

Materia models

Layers

Interfaces

• Elastic behavior: Traction-separation law

• Damage initiation: Quadratic nominal stress criterion

• Damage evolution: Energy based

• Mixed mode: Benzeggagh-Kenane

• Laminate: [ 0w, 0, 90, 0, 90, 0, 90 ]s

• Layers: 12 unidirectional (UD) and 2 woven (W)

• Damage initiation: Hashin’s criteria

• Damage evolution: Energy based

• Softening: Linear

Post-buckling behavior

An initial perturbation is required to allow the geometrical non-linear behavior

Linear

buckling

Post-buckling

• Shapes of the buckling modes.

• The permanent deformation due to the impact is approximated by the first buckling mode.

• The perturbation is added by an initial geometrical imperfection.

3. SOLUTION APPROACH

Experimental

measurement approximationFE model

Source:

Olivares-Ferrer, A. J., et al (2019)

Initial geometrical imperfection

Y X

Y X

Initial damage modeling

Interfaces

Initially undamaged

Initially damaged

• Only initial delaminations are considered.

• Interfaces are divided into two zones.

• Damage idealization based on ultrasonic scans.

• Elliptical damage shape idealization.

X Y X Undamaged Damaged Interfaces

3. SOLUTION APPROACH

Simulation procedure

Solver

Static Riks

• Higher computation time.

• Lower computation time.

• But it has problems with delamination growth.

• Useful for verifying the explicit simulation without considering the interfaces (delaminations).

1. Introduction

2. Problems

3. Solution approach

4. Results

5. Conclusions

OUTLINE

Different through-thickness damage pattern idealization

Cylindrical pattern

y

z

Undamaged interfacePly

Conical pattern

4. RESULTS

Imp=0.1mm Imp=0.2mm Imp=0.4mm 269 215 267 219 264 228 0 50 100 150 200 250 300 Undamaged Damaged Failure S tress [Mpa]

Different magnitudes of the geometrical imperfection

4. RESULTS

Shape of the geometrical imperfection

4. RESULTS

b /2 b /2

Stress distribution comparison (𝛔𝛔_𝐏𝐏 = 𝟏𝟏𝟏𝟏𝟏𝟏 𝐌𝐌𝐏𝐏𝐌𝐌)

400 200 0 -200 Pl y St re ss , 𝛔𝛔𝟏𝟏𝟏𝟏 [ 𝐌𝐌 𝐏𝐏𝐌𝐌 ] -400 -600 -800 600 Y Coordinate, 𝐲𝐲[𝐦𝐦𝐦𝐦] -50-40-30-20-10 0 10 20 30 40 50 Damaged beff/2 beff/2 Undamaged

Interaction between global buckling and local delaminations

Middle

section

σ

1. Introduction

2. Problems

3. Solution approach

4. Results

5. Conclusions

OUTLINE

5. CONCLUSIONS

•

The creation of a finite element model that considers post-buckling behavior, initial geometrical

imperfection, initial damage and intra- and interlaminar damage evolution is feasible with ABAQUS

software.

•

A better understanding of the CAI test with thin-walled laminates is being possible through the investigation

of these models.

•

Further research still can be performed with the CAI models in order to improve the prediction of its

behavior.

1. Olivares-Ferrer, A. J., Linke, M., García-Manrique, J. A. (2019) Influence of geometric imperfections and

internal damage patterns of thin-walled laminates on failure in Compression-After-Impact testing,

Procedia Manufacturing.

REFERENCES

3DEXPERIENCE Conference Design, Modeling and Simulation 19 – 21 Nov. 2019

MANY THANKS

Questions?