Don't understand what the problem wants.

Physics_wiz

This problem is from my Intermediate Mechanics of Materials class. Given are two tables for a specimen of medium-carbon steel with initial diameter 0.503 in and gauge length 2 in. The two tables are labeled "Elastic State" and "Plastic State".

The first table gives the Load vs. Elongation...Load ranging from 1,000 lbf to 9,200 lbf and Elongation ranging from 0.0004 in to 0.0089 in.

The second table gives load vs. Area. Load ranging from 8,800 lbf to 14,800 lbf and Area ranging from 0.1984 in^2 to 0.1077 in^2.

The question is to plot the engineering stress-strain diagram using two scales for the unit strain (epsilon), one from zero to about 0.02 in/in and the other from zero to maximum strain.

I don't understand what it means by the bold part. Also, how can I plot stress vs strain for the plastic part if I only have the change in area...I don't have the elongation so I can't find strain.

Any help would be appreciated.

Physics_wiz

OK, I got an idea. There's one data point overlap between the two tables at 9200 lbf. For this point, I know the elongation (from first table) and area (from second table) so I can find the lateral and longitudinal strain. From those, I can find poisson's ratio. After finding poisson's ratio, I can use it on the second table to get the longitudinal strain and have load (which can be changed to stress) vs. strain instead of load vs. area. From that I can plot the stress-strain diagram for the plastic area.

I really need to know if what I'm thinking about is right or wrong or if there's an easier way to do it because this would be a pain in the a$$ to do for all the data points and....I have to do it by hand on engineering paper and plot everything by hand too. Any advice would be appreciated.

Physics_wiz

After looking at the data again, I saw that there are two points that overlap. Poisson's ratio is different for both of them...should I use the one that's more in the elastic part or the one that's more in the plastic part?

Astronuc

In the purely elastic region, the strain is given by [itex]\epsilon = \sigma / E[/itex], and this begins before the 0.2% (strain) offset, where Yield strength is usually determined. The point where the stress-strain relationship departs the purely linear relationship is the proportional limit.

If one loads a tensile specimen to the point where stress = yield strength (as determine from the 0.2% offset, then there should be approximately 0.2% permanent (plastic) deformation (elongation) remaining when the specimen is unloaded (in a uniaxial test).

Going beyond yield, up to the ultimate tensile strength, the relationship between stress and strain is more complicated. At ultimate tensile strength, the uniform elongation is reached and that is when necking begins. Or course, this assumes a more or less ideal material.