## Materials Science and Engineering: An Introduction

$τ_{c} = 43.13 MPa$
Given: For a glass fiber–epoxy matrix combination, the critical ratio of fiber length to fiber diameter is 40. Required: fiber–matrix bond strength using data in Table 16.4 Solution: From Table 16.4, $σ^{*}_{f} = 3.45 GPa$ and $\frac{l_{c}}{d} = 40$; rearranging Equation 16.3: $τ_{c} = σ^{*}_{f} (\frac{d}{2l_{c}}) = (3.45 \times 10^{3} MPa)(\frac{1}{2})(\frac{1}{40}) = 43.13 MPa$