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: [email protected]SIMULIA 2015 Regional User Meeting, Copenhagen, Denmark 12th 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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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,
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
4
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
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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]