ES 246 Project:
Effective Properties of Planar
Composites under Plastic
Deformation
Outline
1. Effective Properties of Composite Materials
2. Model Description
3. Model Validation
4. Effect of Inclusion Shapes
5. Isotropic/Kinematic Hardening
6. Conclusion and Future Work
1. Effective Properties of Composite Materials
Objective of the Research:
1. By introducing small amount of inclusion phase to improved the
bulk properties of the matrix.
(Boyce M. et al: rubber particles to improve
the toughness of the polymer)
(Evans A. : Low-dielectric high-stiffness
porous silica)
2. To formulate equations for accurate prediction of the effective
properties of composite materials.
Torquato S. et al: Mean Field Theory for Effective Modulus of Linear Elastic Composite
2. Model Description
-Composite Generation
Criteria for Inclusion Phase:
1. Random coordination
2. Random orientation
3. No overlap
Shape of Inclusion Phase:
1. Triangular
2. Square
3. Circular
1cm
Volume fraction of Inclusion Phase: 0.2
Inclusion number: 30
1cm
2. Model Description
-Materials Properties
Constitutive Law:
 E

    E  n
 Y0  0 
   Y 
   Y0
 
0
Y
Matrix
Inclusion
E
(GPa)
100
200
 Y0
(GPa)
2
4
n
(-)
0.5
0.5
14
Stress (GPa)
12
Inclusion
Matrix
10
8
6
4
2
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Strain
2. Model Description
-Finite Element Mesh
Triangular Inclusion
Rectangular Inclusion
Element Type:
4-Noded-Element Dominant
Element Size (Edge length):
~0.1 mm
Mesh Sensitivity:
Refined-mesh model gives
similar results.
Circular Inclusion
3. Model Validation
-Effective Modulus of the Composite
(Based on Mean Field Theory for Linear Elastic Material)
:shear modulus of the matrix and inclusion
:bulk modulus of the matrix and inclusion
:volume fraction of the inclusion phase
3. Model Validation
-Theoretical and Simulated Young’s Modulus
Theoretical:
E  113.08(GPa )
Simulated:
E  114(GPa)
4
3.5
Stress (GPa)
3
Inclusion
Matrix
Composite: Theoretical
Composite: Simulated
2.5
2
1.5
1
0.5
0
0
0.002 0.004 0.006 0.008 0.01
Strain (-)
0.012 0.014 0.016 0.018
3. Model Results
-Effects of Inclusion Shapes
Effective Electric Conductivity with High
Conductivity Inclusions:
Triangular > Square > Circle
(Both Experiments and Theory)
Effective Tangent Modulus with Stiffer
Inclusions:
Triangular > Square > Circle
Still True?
3. Model Results
-Effects of Inclusion Shapes
Effective Tangent Modulus
Triangular = Square = Circle
7
Stress (GPa)
6
5
4
3
Circular Inclusion
Triangular Inclusion
Rectangular Inclusion
Matrix
2
1
0
0
0.02 0.04 0.06 0.08 0.1
Strain (-)
0.12 0.14 0.16 0.18
3. Model Results
-Von Mises Stress Distribution
Triangular Inclusion
Rectangular Inclusion
Max: 9.629 GPa
Max: 12.605 GPa
Circular Inclusion
Max: 8.827 GPa
3. Model Results
- Isotropic or Kinematic Hardening (circular inclusion)
6
4
Stress
2
Matrix:Isotropic; Inclusion:Isotropic
Matrix:Kinematic; Inclusion:Kinematic
Matrix:Isotropic; Inclusion:Kinematic
Matrix:Kinematic; Inclusion:Isotropic
0
-2
-4
-6
-8
-0.15
-0.1
-0.05
0
0.05
Strain
(Bilinear constitutive relations assumed
for matrix and inclusion)
0.1
3. Model Results
- Isotropic or Kinematic Hardening (triangular inclusion)
6
4
Stress
2
Matrix:Isotropic; Inclusion:Isotropic
Matrix:Kinematic; Inclusion:Kinematic
Matrix:Isotropic; Inclusion:Kinematic
Matrix:Kinematic; Inclusion:Isotropic
0
-2
-4
-6
-8
-0.15
-0.1
-0.05
0
Strain
0.05
0.1
3. Model Results
- Isotropic or Kinematic Hardening (Effective Plastic Strain)
Conclusion
1. We calculate the effective elastoplastic properties of composite material
with an stiffer inclusion phase. The volume ratio of the inclusion is 0.2.
2. The shape of the inclusion phase has no effect on the effective tangent
modulus of the material.
3. The triangular inclusion phase gives the highest maximum Von Mises
stress in the matrix, and followed by the rectangular inclusion phase. The
circular inclusion phase gives the most uniform stress distribution.
4. The hardening type of the composite is dominant by the matrix phase.
4. Future Work
-3D Modeling is Possible