Engineering Equations for Strength and Modulus of Particulate Reinforced Composite Materials

1. Engineering Equations for Strength and Modulus of Particulate Reinforced Composite Materials M.E. 7501 – Reinforced Composite Materials Lecture 3 – Part 2

2. Particulate Reinforcement Example: idealized cubic array of spherical particles

3. Experimental observations on effects of particulate reinforcement Experiments show that, for typical micron-sized particulate reinforcement, as the particle volume fraction increases, the modulus increases but strength and elongation decrease Flexural stress-strain curves for 30 µm glass bead-reinforced epoxy composites of various bead volume fractions. (From Sahu, S., and Broutman, L. J. 1972. Polymer Engineering and Science, 12(2), 91-100. With permission.)

4. Yield strength of particulate composites Nicolais-Narkis semi-empirical equation for case with no bonding between particles and matrix (6.65) where Syc is the yield strength of the composite Sym is the yield strength of the matrix material vp is the volume fraction of particles the coefficient 1.21 and the exponent 2/3 are selected so as to insure that Syc decreases with increasing vp, that Syc = Sym when vp=0, and that Syc=0 when vp=0.74 , the particle volume fraction corresponding to the maximum packing fraction for spherical particles of the same size in a hexagonal close packed arrangement

5. Liang – Li equation includes particle – matrix interfacial adhesion (6.66) where θ is the interfacial bonding angle, θ= 0o corresponds to good adhesion, and θ = 90o corresponds to poor adhesion

6. Finite element models for particulate composites development of axisymmetric RVE axisymmetric finite element models of RVE Finite element models for spherical particle reinforced composite. (From Cho, J., Joshi, M. S., and Sun, C. T. 2006. Composites Science and Technology, 66, 1941-1952. With permission)

7. Modulus of particulate composites Katz -Milewski and Nielsen-Landel generalizations of the Halpin-Tsai equations (6.67) where

8. and where is the Young’s modulus of the composite is the Young’s modulus of the particle is the Young’s modulus of the matrix is the Einstein coefficient is the particle volume fraction is the maximum particle packing fraction

9. Semi empirical Models Use empirical equations which have a theoretical basis in mechanics Halpin-Tsai Equations (3.63) Where (3.64)

10. And curve-fitting parameter 2 for E2 of square array of circular fibers 1 for G12 As Rule of Mixtures As Inverse Rule of Mixtures

11. Comparison of predicted and measured values of Young’s modulus for glass microsphere-reinforced polyester composites of various particle volume fractions.

12. Hybrid multiscale reinforcements Improvement of mechanical properties of conventional unidirectional E-glass/epoxy composites by using silica nanoparticle-enhanced epoxy matrix. (a) off-axis compressive strength. (b) transverse tensile strength and transverse modulus. (From Uddin, M. F., and Sun, C. T. 2008. Composites Science and Technology, 68(7-8), 1637-1643. With permission.)