Determine the longitudinal tensile strength of the hybrid carbon/aramid/ epoxy composite described in Problem 3.4 and Figure 3.10 of Chapter 3 if the fiber packing array is square with the closest possible packing.

Problem 4.3

An orthotropic lamina has the following properties:

\[E_{1}=160 \mathrm{GPa} \quad s_{\mathrm{L}}^{(+)}=1800 \mathrm{MPa}\]

\[\begin{aligned} & E_{2}=10 \mathrm{GPa} \quad s_{\mathrm{L}}^{(-)}=1400 \mathrm{MPa} \\ & v_{12}=0.3 \quad s_{\mathrm{T}}^{(+)}=40 \mathrm{MPa} \\ & G_{12}=7 \mathrm{GPa} \quad s_{\mathrm{T}}^{(-)}=230 \mathrm{MPa} \\ & s_{\mathrm{LT}}=100 \mathrm{MPa} \end{aligned}\]

Construct the failure surfaces in the \(\sigma_{1}-\sigma_{2}\) stress space for this material according to:

(a) the maximum stress criterion,

(b) the maximum strain criterion, and

(c) the Tsai-Hill criterion.

Transcribed Image Text:

Stress (GPa) 0.72 0.1 2.8 2.1 Carbon fiber Aramid fiber Epoxy matrix 0.0164 0.0054 0.021 0.033 Strain FIGURE 3.10 Stress-strain curves for fiber and matrix materials in a hybrid composite.