Repeat Problem 4.7 for an off-axis compression test.

Problem 4.7

An element of an orthotropic lamina having the properties given in Problem 4.3 is subjected to an off-axis tensile test, as shown in Figure 4.5. Using the maximum strain criterion, determine the values of \(\sigma_{x}\) at failure and the mode of failure for each of the following values of the angle \(\theta\) :

(a) \(2^{\circ}\),

(b) \(30^{\circ}\), and

(c) \(75^{\circ}\).

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:

• the maximum stress criterion,

• the maximum strain criterion, and

• the Tsai-Hill criterion.

2 A FIGURE 4.5 Off-axis uniaxial test of a unidirectional lamina specimen. x 0x