Powerful Modelling Techniques in Abaqus to Simulate
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1 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 1. Dept. of Mech. Eng., Blekinge Institute of Technology, SE , Karlskrona, Sweden 2. Dassault Systemes SIMULIA Corp, West Lafayette, Indiana, USA 3. Fac. of Mech. & El. Eng., Shanghai Second Polytechnic Univ., Shanghai, China SIMULIA 2015 Regional User Meeting, Copenhagen, Denmark 12th October 2015
2 Contents 1. Motivation 2. Objectives 4. Simulation Results 5. Achievements 6. Perspectives 1
3 1. Motivation Various kinds of Packaging in our daily life Microstructure illustration of Packaging Each layer has special function. Essential Constituent Al-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] 2
4 2. Objectives 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. Al-foil LDPE Schematic diagram of the FEM model to be developed [by Eskil Andreasson] 3
5 3.1 Technique Framework Technique Framework No. Necking in substrates/al-foil, LDPE Interfacial Delamination 1 VCCT 2 Elastic-Plastic Progressive Damage Constitutive Cohesive Zone 3 XFEM 4
6 3.2 Modelling of Necking in Substrates Necking σ (Damage Initiation Point) D=0 a Undamaged Response Dσ Stress Concentration Material Softening Stiffness Degradation E E (1 D)E Damaged Evolution Response Softening and Necking (Failure Point) D=1 b ε Schematic diagram of our developed material constitutive 5
7 3.2 Modelling of Necking in Substrates Elastic-Plastic Progressive Damage Constitutive Elastic Behavior Hooke s Law Yield Criterion J2 Plasticity/Von Mises Plastic Behavior Hardening Law Isotropic Hardening Flow Rule Associated Flow Damage Ductile Damage Model 6
8 3.2 Modelling of Necking in Substrates 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. 7
9 3.3 Modelling techniques of Interfacial Delamination VCCT-Virtual Crack Closure Technique Energy released to Open the crack = Energy to Close it Schematic representation of VCCT for Mode I crack 8
10 3.3 Modelling techniques of Interfacial Delamination VCCT-Virtual Crack Closure Technique y, v 6 5 Load F v,2,5 4 Load F v,2,5 F v,2,5 crit δ 1,6 2 3 δ 2,5 crit x, u 1 Area=G IC db Displacement δ2,5 Calculation illustration of strain energy released for Mode I crack based on VCCT Fracture Criterion for Mode I 1 2,,, Fracture Criterion for Mixed Mode 1.0 Power Law Model 9
11 3.3 Modelling techniques of Interfacial Delamination Cohesive Element Cohesive Zone Technique: Surface-based, or Element-based, i.e. Cohesive Element Cohesive Element-Traction-Separation Cohesive Law Traction Separation Schematic diagram of Bi-linear Traction-Separation cohesive law 10
12 3.3 Modelling techniques of Interfacial Delamination Cohesive Element Traction Simplified, Bi-Linear Cohesive Law Separation Damage Initiation Criterion of Interfacial Delamination Quadratic nominal strain criterion Quade Evolution Criterion based on energy Power Law Model 1 1 Bi linear cohesive Law 11
13 3.3 Modelling techniques of Interfacial Delamination XFEM XFEM-eXtended Finite Element Method, is especially designed for treating Strong or Weak discontinuities, e.g. Crack, Bi-material problem. Interfacial Delamination Fracture Bi-material Interface XFEM 12
14 3.3 Modelling techniques of Interfacial Delamination XFEM XFEM is extended by adding special enriched functions into generalized FEM. displacement jump across Crack-surface 13 Crack-tip singularity
15 3.3 Modelling techniques of Interfacial Delamination XFEM Illustration of normal and tangential coordinates for a smooth crack 1 0, crack 1, crack sin 2, cos 2, sin sin 2, sincos 2 In our model, Damage Initiation Criterion-Quade Damage Evolution Criterion-Power Law based on Energy Very similar to Cohesive Case 14
16 3.4 FEM Models utilizing VCCT, Cohesive Element, XFEM A pre-made interfacial defect A displacement boundary condition on the right side All Degree Of Freedom on the left side are constrained (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. 15
17 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. 16
18 5. Achievements 17
19 6. Perspectives These models will be used in our future research: (1) The model with VCCT will be used to get fracture mechanics parameters directly during necking and delamination, such as fracture energy. (2) The model with Cohesive Element will be adopted to study the influence mechanism of adhesion level or interface strength on necking and delamination. A 1/4 uniaxial tension FEM model based on Cohesive Element is created because of symmetry 18
20 6. Perspectives These models will be used in our future research, such as: (3) The model with XFEM will be utilized to simulate propagation of multi-cracks in substrates and interface. (4) A 3D-FEM model suggested will be developed, and more extensive research will be implemented, such as evolution mechanism of interface debond in length and width direction. Illustration of 3D FEM model from [Teng Li, Z. Suo, 2007] 19
21 THANKS FOR YOUR ATTENTION! 20
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