Determine maximum stress and modulus of elasticity:

 A composite of glass fibres and epoxy has all of fibres laid along the length and is needed to carry a stress of 12 MPa. The limiting stress carried by fibre & epoxy are respectively, σ_f = 2400 MPa, and σ_m = 80 MPa. The volume ratios and modulii of elasticity are explained below :

V _f  = 0.7,  V_m = 0.3,  E _f  = 72 MPa,         E_m = 3 MPa

Determine maximum stress the composite might carry in the direction of fibres & the modulus of elasticity.

Solution

The stress that composite can carry

σ_c = V _f  σ _f + V_m σ_m

= 0.7 × 2400 + 0.3 × 80

= 1680 + 24 = 1704 MPa

Modulus of elasticity of composite

E = V _f E _f  + V_m  E_m

= 0.7 × 72 + 0.3 × 3

= 50.4 + 0.9 = 51.3 MPa