Using results from Exercises 3.19 and 8.43, show that the mode I crack tip von Mises stress is given by:

Next solve this equation for the radial coordinate and make a polar plot for a typical von Mises stress contour (σ_e = constant) about the crack tip. Result should look like the following figure, and represents the shape of the plastic zone size for the plane stress mode I crack problem.

Data from exercise 3.19

For the two-dimensional plane stress case (see Exercise 3.5), show that the relationship between the maximum shear stress and von Mises stress is given by:

Equation 8.43

Transcribed Image Text:

+- (27 sin 0 + 36 cos (2)) A 4r