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. 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.) Experiments show that, for typical micron-sized particulate reinforcement, as the particle volume fraction increases, the modulus increases but strength and elongation decrease Experimental observations on effects of particulate reinforcement

4. (6.65) Yield strength of particulate composites Nicolais-Narkis semi-empirical equation for case with no bonding between particles and matrix where S yc is the yield strength of the composite S ym is the yield strength of the matrix material v p is the volume fraction of particles the coefficient 1.21 and the exponent 2/3 are selected so as to insure that S yc decreases with increasing v p, that S yc = S ym when v p =0, and that S yc =0 when v p =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 = 0 o corresponds to good adhesion, and θ = 90 o corresponds to poor adhesion

6. Finite element models for particulate composites 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) development of axisymmetric RVE axisymmetric finite element models of RVE

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 E 2 of square array of circular fibers 1 for G 12 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. 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.) Hybrid multiscale reinforcements