Question

A new set of fiber-reinforced composite is designed to support the body function. Compute the longitudinal tensile strength of this fiber–epoxy matrix biocomposite in which the average fiber diameter and length are 0.018 mm and 2.2 mm, respectively, and the volume fraction of fibers is 0.35. Assume that the fiber–matrix bond strength is 122 MPa, the fracture strength of the fibers is 3800 MPa, and the matrix stress at composite failure is 5.9 MPa.

Answer 1

given

_f = 3800 MPa

= 3800 x 10⁶ Pa

d = 0.018 x 10^-3 m

_c = 122 x 10⁶ Pa

L = 2.2 x 10^-3 m

V_f = 0.35

_m = 5.9 MPa

= 5.9 x 10⁶ Pa

the critical fiber length is L_c = _f d / 2 _c

= 3800 x 10⁶ x 0.018 x 10^-3 / 2 x 122 x 10⁶

= 3800 x 0.018 x 10^-3 / 2 x 122

= 1900 x 0.018 x 10^-3 / 122

L_c = 0.2803 x 10^-3 m

or

L_c = 0.2803 mm

now

= _f V_f ( 1 - L_c / 2 L ) + _m ( 1 - V_f )

= 3800 x 0.35 x ( 1 - 0.2803 x 10^-3 / 2 x 2.2 x 10^-3 ) + 5.9 x ( 1 - 0.35 )

= 3800 x 0.35 x ( 1 - 0.2803 / 2 x 2.2 ) + 5.9 x ( 1 - 0.35 )

= 3800 x 0.35 x 0.936 + 5.9 x 0.65

= 1244.88 + 3.835

= 1248.715 MPa

the longitudinal tensile strength of this fiber–epoxy matrix bio composite

in which the average fiber diameter and length are 0.018 mm and 2.2 mm is = 1248.715 MPa