Question

For some glass fiber-epoxy matrix combination, the critical fiber length-fiber diameter ratio is 33.2. Determine the fiber-matrix bond strength. Assume that the tensile strength for glass is 3.45 GPa (0.5 × 106 psi).

Answer 1

Answer:

The fiber-matrix bond strength is [b] 51.96MPa [/b]

Explanation:

We are given:

$l_c = 33.2$

$Tensile strength for glass (o_f) = 3.45GPa = 3.45*10^3MPa$

We take d=1

Therefore, to find the fiber-matrix bond strength we use the formula:

$t_c = o_f * ( d / 2l_c)$;

substituting figures in the equation, we have:

$t_c = 3.45*10^3MPa * [ 1 / (2 * 33.2)]$

= 33450 * 0.015

= 51.96 MPa

Therefore the fiber-matrix bond strength is 51.96MPa

Answer 2

Answer:

Fiber-matrix bond strength = 51.96 MPa

Explanation:

To calculate: Fiber-matrix bond strength

Critical fiber length diameter ratio, $\frac{R_{c}}{d} = 33.2$

Therefore, $\frac{d}{R_{c}} = \frac{1}{33.2}$

Tensile strength for glass, $\sigma = 3.45 GPa = 3.45 * 10^{9} Pa$

The formula for the fiber matrix bond strength is given by:

$\tau = \sigma (\frac{d}{2R_{c} }) \\\tau = 3.45 * 10^{9} (\frac{1}{2*33.2})\\ \tau = 3.45 * 10^{9} (\frac{1}{66.4})\\\tau = 0.052 * 10^{9} Pa\\\tau = 0.052 GPa\\\tau = 51.96 MPa$