For the RVE in Figure 6.4, assume that the fiber length is greater than the ineffective length, and that the distribution of the fiber tensile normal stress is given by

\[\begin{gathered} \sigma_{\mathrm{f}}=\frac{4 \sigma_{\mathrm{fmax}} x\left(L_{\mathrm{i}}-x\right)}{L_{\mathrm{i}}^{2}} \text { for } 0 \leq x \leq \frac{L_{\mathrm{i}}}{2} \\ \sigma_{\mathrm{f}}=\sigma_{\mathrm{fmax}} \quad \text { for } \frac{L_{\mathrm{i}}}{2} \leq x \leq \frac{L}{2} \end{gathered}\]

a. Determine the expression for the fiber/matrix interfacial stress, \(\tau\), and plot its distribution along the fiber length.

b. Determine the magnitude and location of the maximum interfacial shear stress, \(\tau_{\max }\) and show it on the shear stress distribution from part (a).

Transcribed Image Text:

Of x dx FIGURE 6.4 Stresses acting on a differential element of fiber. Of + dof d D