Composite Rule of Mixtures Calculator

Rule of Mixtures (ROM) The rule of mixtures predicts properties of fiber-reinforced composites from fiber and matrix properties. Valid when fibers are continuous, aligned, and well-bonded to the matrix.

Volume Fractions Vf + Vm = 1 (fiber + matrix = 100%) Typical Vf: unidirectional prepreg 0.55–0.65 | hand layup GFRP 0.30–0.45 | woven fabric 0.45–0.55

Longitudinal Modulus (along fibers: iso-strain assumption) E₁ = Ef × Vf + Em × Vm ← Voigt upper bound Both fiber and matrix experience the same strain → stiffnesses add in parallel.

Transverse Modulus (perpendicular to fibers: iso-stress assumption) 1/E₂ = Vf/Ef + Vm/Em ← Reuss lower bound Both fiber and matrix carry the same stress → compliances add in series.

Density ρc = ρf × Vf + ρm × Vm (linear rule of mixtures — exact for well-consolidated composite)

Longitudinal Tensile Strength σ₁* = σf* × Vf + σm’ × Vm Where σm’ = matrix stress at fiber failure strain. Requires Vf > Vcrit to achieve composite strengthening. Vcrit = (σm* − σm’)/(σf* − σm')

Transverse Strength and Other Properties Transverse strength is matrix-dominated — ROM is less accurate; use Tsai-Hill or Halpin-Tsai. Shear modulus (Halpin-Tsai): G₁₂ = Gm(1+ξηVf)/(1−ηVf), where η=(Gf−Gm)/(Gf+ξGm), ξ≈1

Typical Fiber Properties Carbon (AS4): Ef = 235 GPa, σf = 3930 MPa, ρ = 1.79 g/cm³ Glass (E-glass): Ef = 73 GPa, σf = 3450 MPa, ρ = 2.60 g/cm³ Aramid (Kevlar 49): Ef = 124 GPa, σf = 3600 MPa, ρ = 1.44 g/cm³

Typical Matrix Properties Epoxy: Em = 3.5 GPa, σm = 70 MPa, ρ = 1.25 g/cm³ Polyester: Em = 3.0 GPa, σm = 55 MPa, ρ = 1.20 g/cm³