Powerful Modelling Techniques in Abaqus to Simulate

Necking and Delamination of Laminated Composites

D. F. Zhang, K.M. Mao, Md. S. Islam, E. Andreasson, Nasir Mehmood,

S. Kao-Walter

Email: sharon.kao-walter@bth.se

SIMULIA 2015 Regional User Meeting, Copenhagen, Denmark12th October 2015

1.Dept. of Mech. Eng., Blekinge Institute of Technology, SE 371 79, Karlskrona, Sweden

2.Dassault Systemes SIMULIA Corp, West Lafayette, Indiana, USA

3.Fac. of Mech. & El. Eng., Shanghai Second Polytechnic Univ., 201209 Shanghai, China

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1. Motivation

2. Objectives

3. FEA Modelling

4. Simulation Results

5. Achievements

6. Perspectives

Contents

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1. Motivation

Various kinds of Packaging in our daily life

Microstructure illustration of PackagingEach layer has special function.Essential ConstituentAl-foil：prevent oxygen and light LDPE (Low Density Polyethylene )：avoid moist[from Eskil Andreasson]

Necking

Delamination

Micrographs of Necking and Delamination in Packaging Materials

[SEM microgaph by Nasir Mehmood, et al]

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to Develop 2-D FEM models based on present techniques in ABAQUS,

which can be used to simulate NECKING and interfacial DELAMINATION.

They will work as robust numerical analysis tools for our further research.

2. Objectives

Schematic diagram of the FEM model to be developed[by Eskil Andreasson]

LDPE

Al-foil

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Technique Framework

No. Necking in substrates/Al-foil, LDPE Interfacial Delamination

1

Elastic-Plastic

Progressive Damage Constitutive

VCCT

2 Cohesive Zone

3 XFEM

3.1 Technique Framework

3. FEA Modelling

5

3. FEA Modelling

(Failure Point)D=1b

Stiffness Degradation

E E (1‐D)E

Undamaged Response

(Damage Initiation Point)D=0a

ε

σ

Damaged Evolution ResponseSoftening and Necking

‐Dσ

Schematic diagram of our developed material constitutive

3.2 Modelling of Necking in Substrates

Necking

Stress

Concentration

Mat

eria

lS

ofte

ning

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3.2 Modelling of Necking in Substrates

3. FEA Modelling

Elastic-Plastic Progressive Damage Constitutive

Elastic Behavior Hooke’s Law

Plastic Behavior

Yield Criterion J2 Plasticity/Von Mises

Hardening Law Isotropic Hardening

Flow Rule Associated Flow

Damage Ductile Damage Model

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3. FEA Modelling

Ductile Damage Model

Ductile Damage Model-Void Nucleation, Growth, and Coalescence

We Find these phenomena from experiments.

So, Ductile Damage Model is used in our model.

3.2 Modelling of Necking in Substrates

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3.3 Modelling techniques of Interfacial Delamination

3. FEA Modelling

3.3.1 VCCT-Virtual Crack Closure Technique

Energy released to Open the crack = Energy to Close it

Schematic representation of VCCT for Mode I crack

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3. FEA Modelling

3.3.1 VCCT-Virtual Crack Closure Technique

δ1,6

LoadFv,2,5

5

2

4

3

1

6

y, v

x, u

LoadFv,2,5

Displacementδ2,5

Area=GIC×db

Fv,2,5crit

δ2,5crit

Calculation illustration of strain energy released for Mode I crack based on VCCT

Fracture Criterion for Mode I 12

, , , 11.0

Fracture Criterion for Mixed Mode 1.0

Power Law Model

3.3 Modelling techniques of Interfacial Delamination

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3. FEA Modelling

3.3.2 Cohesive Element

Cohesive Zone Technique: Surface-based, or Element-based, i.e. Cohesive Element

Cohesive Element-Traction-Separation Cohesive Law

Schematic diagram of Bi-linear Traction-Separation cohesive law

Separation

Traction

3.3 Modelling techniques of Interfacial Delamination

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3. FEA Modelling

3.3.2 Cohesive Element

Simplified, Bi-Linear Cohesive Law

Separation

Traction

Damage Initiation Criterion of Interfacial Delamination

Quadratic nominal strain criterion‐Quade1

Bi‐linear cohesive LawEvolution Criterion based on energy Power Law Model

∝ ∝ ∝

1

3.3 Modelling techniques of Interfacial Delamination

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3. FEA Modelling

3.3.3 XFEM

XFEM-eXtended Finite Element Method, is especially designed for treating Strong or

Weak discontinuities, e.g. Crack, Bi-material problem.

XFEM

Fracture

Bi-material InterfaceInterfacial Delamination

3.3 Modelling techniques of Interfacial Delamination

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3. FEA Modelling

3.3.3 XFEM

XFEM is extended by adding special enriched functions into generalized FEM.

3.3 Modelling techniques of Interfacial Delamination

displacement jump across Crack-surface

Crack-tip singularity

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3. FEA Modelling

3.3.3 XFEM

Illustration of normal and tangential coordinates for a smooth crack

1 ∗ ∙ 0, crack1 , crack

∝ sin 2 , cos 2 , sin sin 2, sin cos 2

In our model, Damage Initiation Criterion-Quade

Damage Evolution Criterion-Power Law based on EnergyVery similar to Cohesive Case

3.3 Modelling techniques of Interfacial Delamination

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3. FEA Modelling

3.4 FEM Models utilizing VCCT, Cohesive Element, XFEM

(a) It is realized by initial debonding part of Slave-Master

Contact Pair.

(b) It is the part without cohesive elements in interface.

(c) It is a pre-made horizontal crack in interface.

In the 3 models, CPE4 are used in substrates.

In (b), COH2D4 and SWEEP meshing technique should be

used in interface.

In (c), CPE4 are used in substrates and interface, but the

mesh in front of pre-made crack tips could be much finer.

A pre-made interfacial defect

A displacement boundary condition on the right side

All Degree Of Freedom on the left side are constrained

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4. Simulation Results

Necking and interfacial delamination are

achieved in all three models, as expected.

Deformation results of simulation and

theoretic analysis are very similar.

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5. Achievements

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6. Perspectives

These models will be used in our future research:(1) The model with VCCT will be used to get fracturemechanics parameters directly during necking anddelamination, such as fracture energy.(2) The model with Cohesive Element will be adopted to studythe influence mechanism of adhesion level or interfacestrength on necking and delamination.

A 1/4 uniaxial tension FEM model based on Cohesive Element is created because of symmetry

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These models will be used in our future research, such as:(3) The model with XFEM will be utilized to simulate propagationof multi-cracks in substrates and interface.(4) A 3D-FEM model suggested will be developed, and moreextensive research will be implemented, such as evolutionmechanism of interface debond in length and width direction.

6. Perspectives

Illustration of 3D FEM model from [Teng Li, Z. Suo, 2007]

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THANKS FOR YOUR ATTENTION!