Chapter 2 Answers.

Since the first chapter is historical, the second chapter is where we will start with answers. I’ll put up on a day this week.
1) On the curve in Figure 2.7a, mark the region of interest and explain what is happening there and why we would want to know.
Referring to the figure on the left, where X is strain and Y is stress and we are testing in tension.

A marks the linear region. In this area, we can calculate the modulus from the slope of the curve. In addition, we can see the limit of elasticity, where we can get 100% recovery. In some cases, you may see a small hump or toe at the start of the curve. This toe affect has pretty much been proven to be an instrument artifact. This linear region, particularly the elastic part of it is what we want to design to.

B indicates the nonlinear region of behavior. At this point, the material is distorting. As we enter into this region, the material deforms and at some point starts “necking” (C). The is where the material starts to flow and draw out, often to a thin filament. At some point, it breaks, giving us the ultimate strength of the material (D). Of course this is an idealized plastic and real materials may differ greatly.

2) Given a choice between nominal and true stress-strain data, explain the pros and cons of each.  Why would you expect the true strain curve to deviate from the ideal at some point?

Nominal stress strain data is what we can from the experiment itself. True strain data is calculated by tracking the size change of the sample as it distorts or necks and using that value for the calculation, instead of the original geometry used in nominal strain. This straightens the line out, but as the sample draws out, its not usual for the distort to exceed what is measured. Measuring this change can be down with strain gauges or optically with cameras. For most user, the nominal test is more useful as the information is more closely related to actual performance.