ES 246 Project: Effective Properties of Planar Composites under Plastic

Deformation

1. Effective Properties of Composite Materials 2. Model Description3. Model Validation4. Effect of Inclusion Shapes5. Isotropic/Kinematic Hardening6. Conclusion and Future Work

Outline

1. Effective Properties of Composite MaterialsObjective of the Research:

2. To formulate equations for accurate prediction of the effective properties of composite materials.

(Boyce M. et al: rubber particles to improve the toughness of the polymer)

1. By introducing small amount of inclusion phase to improved the bulk properties of the matrix.

(Evans A. : Low-dielectric high-stiffness porous silica)

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 coordination2. Random orientation3. No overlap

Shape of Inclusion Phase:1. Triangular2. Square3. Circular

Volume fraction of Inclusion Phase: 0.2

Inclusion number: 30

1cm

1cm

0

00

0

Y

n

YY

Y

E

E

Matrix Inclusion

E (GPa) 100 200

(GPa) 2 4

n (-) 0.5 0.5

0Y

Constitutive Law:

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

2

4

6

8

10

12

14

Strain

Str

ess

(G

Pa

)

InclusionMatrix

2. Model Description -Materials Properties

2. Model Description -Finite Element Mesh

Triangular Inclusion Circular InclusionRectangular Inclusion

Element Type: 4-Noded-Element Dominant

Element Size (Edge length):~0.1 mm

Mesh Sensitivity:Refined-mesh model gives similar results.

:bulk modulus of the matrix and inclusion

:shear modulus of the matrix and inclusion

:volume fraction of the inclusion phase

3. Model Validation-Effective Modulus of the Composite

(Based on Mean Field Theory for Linear Elastic Material)

114(GPa)ESimulated:

Theoretical: )113.08(GPaE

3. Model Validation-Theoretical and Simulated Young’s Modulus

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.0180

0.5

1

1.5

2

2.5

3

3.5

4

Strain (-)

Str

ess

(GP

a)

InclusionMatrixComposite: TheoreticalComposite: Simulated

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

3. Model Results-Effects of Inclusion Shapes

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180

1

2

3

4

5

6

7

Strain (-)

Str

ess

(GP

a)

Circular InclusionTriangular InclusionRectangular InclusionMatrix

3. Model Results-Von Mises Stress Distribution

Circular Inclusion

Triangular Inclusion Rectangular Inclusion

Max: 12.605 GPa Max: 9.629 GPa

Max: 8.827 GPa

-0.15 -0.1 -0.05 0 0.05 0.1-8

-6

-4

-2

0

2

4

6

Strain

Str

ess

Matrix:Isotropic; Inclusion:IsotropicMatrix:Kinematic; Inclusion:KinematicMatrix:Isotropic; Inclusion:KinematicMatrix:Kinematic; Inclusion:Isotropic

3. Model Results- Isotropic or Kinematic Hardening (circular inclusion)

(Bilinear constitutive relations assumed for matrix and inclusion)

-0.15 -0.1 -0.05 0 0.05 0.1-8

-6

-4

-2

0

2

4

6

Strain

Str

ess

Matrix:Isotropic; Inclusion:IsotropicMatrix:Kinematic; Inclusion:KinematicMatrix:Isotropic; Inclusion:KinematicMatrix:Kinematic; Inclusion:Isotropic

3. Model Results- Isotropic or Kinematic Hardening (triangular inclusion)

3. Model Results- Isotropic or Kinematic Hardening (Effective Plastic Strain)

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.

Conclusion

4. Future Work-3D Modeling is Possible