Metals 101-8 Engineering Stress vs. True Stress

Video Transcript:

Let’s look at the difference between engineering stress and true stress.  

When we performed the tensile test in the last video, we only measured the test specimen cross-sectional area one time. As we pulled the specimen apart, its cross-section changed, but we didn’t take any additional measurements.  The reason for this is that we were interested in engineering stress and not true stress.

When you only measure the cross-sectional area at the beginning of the test, and you use that value for all your stress calculations, you are calculating what is called “engineering stress.”  

In contrast, when you re-measure the cross-section for each stress measurement your are finding ‘true stress.”  Now, finding true stress is more trouble than finding engineering stress, and it seems like it might be better, but it’s actually a terrible idea.

Let me explain.  We do a tensile test to determine how strong a material is.  For instance, we might test an aluminum part to evaluate it’s ultimate tensile strength (that is where the stress peaks on our diagram).  We see here that according to this ASTM Standard, the aluminum we are testing has a minimum tensile strength of 38.0 ksi.

And here, our test results show a tensile strength is above that minimum.  Our aluminum could withstand 39.2 ksi. This diagram shows that our material is as strong as it should be.  Now, let’s look at what our diagram would look like if we used true stress.

Stress is force divided by area.  With true stress we measure the area for each reading.  Our area gets smaller and smaller as it is stretched. Do you see what that does to the true stress level?  It keeps increasing as the part necks down and gets smaller. The diagram of true stress looks like this. Now it looks like our part is a lot stronger than the minimum.  It looks like our part could support 45 ksi. But nothing could be further from the truth!

We use engineering stress because it tells us how much force a workpiece can support with its original cross-sectional area.

You will see different symbols for engineering stress and true stress, but in this series we will only be using engineering stress, so we will just keep using the lower case sigma.