A reinforced plastic sheet composite were fabricated with 70 vol % continuous gl

Question

A reinforced plastic sheet composite were fabricated with 70 vol % continuous glass fibre. The tensile strength of matrix is given as 60 MPa, while the tensile strength of matrix at fiber failure is at 40 MPa. The elastic modulus and tensile strength of glass fibre is 76 GPa and 2 GPa respectively.

a) If the composite has fibre-to-matrix modulus ratio of 25, estimate the longitudinal tensile strength and elastic modulus of the composite.

b) Determine the tensile strength of the composite If the same fraction of glass fibers is aligned and discontinuous inside the matrix. Given: - Length of glass fiber   = 15 mm - Diameter of glass fiber = 15 um - Strength of fiber-matrix bond = 4 MPa

Explanation / Answer

The tensile strength of matrix m' = 60 MPa

the tensile strength of matrix at fiber failure = 40 MPa

The elastic modulus of the fiber Ef = 76 GPa

tensile strength of glass fibre f = 2 GPa

(a) fibre-to-matrix modulus ratio Ff / Fm = 25

volume fraction of fibers Vf = 70 % = 0.7

The elastic modulus of the matrix can be obtained from, Ff / Fm = EfVf / EmVm = EfVf / Em(1-Vf)

25 = 76 GPa (0.7) / Em (1-0.7)

The elastic modulus of the matrix Em = 76 (0.7) / (0.3) 25 = 7.09 GPa

The elastic modulus of the composite Ecl = Em(1 Vf ) + Ef Vf = 7.09 GPa (0.3) + 76 (0.7)

= 55.327 GPa (upper bound)

The elastic modulus of the composite lower bound can be determined using

Ect = Em Ef / (EmVf +  Ef Vm ) = 19.4 GPa

The longitudinal tensile strength is determined using Equation

cl = m' (1 Vf ) + f Vf

   = 60 MPa (1-0.7) + 2 GPa (0.7) = 60 MPa (1-0.7) + 2 x 103 MPa (0.7)

cl   = 1418 MPa

(b)To compute the longitudinal strength, It is necessary to compute the value of the critical fiber length first.

Length of glass fiber l = 15 mm - Diameter of glass fiber d = 15 um - Strength of fiber-matrix bond c = 4 MPa

lc = f d / 2c = 2 GPa (15 x 10-6 m) / 2 (4 MPa) = 2 x 103 MPa (15 x 10-6 m) / 2 (4 MPa)

= 3.75 x 10-3 m = 3.75 mm

since given Length of glass fiber l = 15 mm > critical fiber length lc 3.75 mm, (not much greater difference)

thus, the tensile strength of the composite cd = f Vf (1 (lc/ 2l)) + m' (1 Vf )

= 2 x 10 3 MPa (0.7)(1-(3.75/30)) + 60 MPa (1-0.7)

   the tensile strength of the composite cd = 1225 + 18 = 1243 MPa

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