Chapter 10, Problem 21P

The stress fields near a crack tip of a linear elastic isotropic material for mode II loading are given by:

${\sigma }_{xx}=\frac{K_{II}}{\sqrt{2\pi r}}\sin \frac{\theta }{2}\left(2+\cos \frac{\theta }{2}\cos \frac{3\theta }{2}\right)$

${\sigma }_{yy}=\frac{K_{II}}{\sqrt{2\pi r}}\sin \frac{\theta }{2}\cos \frac{\theta }{2}\cos \frac{3\theta }{2}$

${\sigma }_{xy}=\frac{K_{II}}{\sqrt{2\pi r}}\sin \frac{\theta }{2}\left(1-\sin \frac{\theta }{2}\sin \frac{3\theta }{2}\right)$

For K_II= 300 ksi $\sqrt{in}$ . plot the stresses (each in a separate figure) in the domain $0\le \theta \le 90°$ and $0.02\le r\le 0.2$ in. Plot the coordinates x and y in the horizontal plane, and the stresses in the vertical direction.