True Stress vs. True Strain
One thing that confuses a lot of people is that if you look at a stress-strain diagram, it will eventually begin to taper and then take a downward turn. This doesn't make sense as it would be that our strain is increasing as our stress decreases. However, you have to remember that a stress-strain curve measures how hard the machine is being pulled on, not how hard the object is being pulled. As the material begins to fail it necks, this reduces the area and reduces the force it is using to resist being stretched. The area, however, drops faster so the stress continues to increase up to failure.