Problem 14.1

  1. Use the equation $$e = \frac{l_1-l_0}{l_0}$$ where \(l_0\) is measured from Subfigure a and \(l_1\) is measured from Subfigure b, both along the hinge line
  2. Use the equation $$\gamma = \tan \Psi$$ to determine the angular shear and the shear strain. Measured the change in angle \(\Psi \)of the line that was originally perpendicular to the hinge line.

Problem 14.2

For each subfigure, except the first one (a), measure the dimensions of the grains, the long and short axes. Try to take 5 measurements of the long axis and 5 measurement of the short axis if possible.

Calculate the mean of the long and short values and take the ratio of these means to get $$1 + e_1 : 1 + e_2$$. For reference, use Figure 14.3 as a example. There is no need to add \(1\) to the mean values.

Finally, draw an example deformed grain in the box provided below the images.

Problem 14.8

Just as in 14.2, measure the long and short axes of a collection of grains; write those values in the lines provided

Take the mean of the long and short axes. That goes in the \(\bar{x}\) line.

Deterine the ratios $$1+e_2 : 1+e_3$$ and $$1+e_1 : 1+e_3$$ Remember, it is not necessary to add \(1\) to these values

Combine those ratios to determine $$1+e_1 : 1+e_2 : 1+e_3$$ using the following relationship: $$\frac{1+e_1}{1+e_2} = \frac{1+e_1}{1+e_3}\frac{1+e_3}{1+e_2}$$ Make sure the value of \(1+e_3 = 1.0\)

Plot those ratios on the graph provided