What is Yield Stress? - Definition & Formula

What is Yield Stress? - Definition & Formula
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  • 0:03 How Objects React to…
  • 0:30 What Is Stress?
  • 1:08 What Is Strain?
  • 2:20 What Is Yield Stress?
  • 3:49 Calculation of Yield Stress
  • 5:25 Lesson Summary
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Lesson Transcript
Instructor: John Parsons

John has taught physics to both engineers and non-engineers, and has a master's degree in Civil and Environmental Engineering.

Yield stress is the amount of stress that an object needs to experience for it to be permanently deformed. This lesson will look at the definition of yield stress and how it relates to the strain the object experiences.

How Objects React to One Another

When you fold paper to create an origami crane, the paper will keep that new shape even after you release the paper. Whereas, if you stretch a rubber band, it will snap back when you let go. And some other objects will only partially restore to their original shape.

Things change when forces are applied to them, but not all items change the same, even if the same force is used. This lesson will look at why that happens, and how material science explains these phenomena.

What Is Stress?

Before looking at what causes these changes, there are a few concepts that need to be looked at first. Stress is the amount of forces (strength or energy) that is being exerted on an object, divided by its cross-sectional area to account for size.

Larger objects are able to withstand higher forces. By using stress instead of just force, we are able to use the same yield stress for the same material, regardless of how large the object actually is. To compute the amount of stress acting on the object, use the equation:

stress

What Is Strain?

Another important concept is strain, or how much an object deforms when forces are applied to it.

Most of the time this deformation will either cause the object to elongate or shorten, depending on how forces are applied. To compute strain, this change is divided by the object's original length, again to account for size.

Larger objects will have a greater change in length than smaller objects, even though they experience the same forces acting on them. To compute the amount of strain on an object, use the equation:

strain

There are two different types of deformation: elastic and plastic.

  • Elastic deformation will automatically reverse itself when external forces are removed. Imagine a rubber band - no matter how you stretch it, once you let go of one end it will 'snap' back to its original shape.

  • Plastic deformation is a permanent deformation. To reverse it, an additional external force needs to be applied to return the object to its original shape. When you squeeze the middle of a plastic bottle, it compresses and stays deformed even when you let go. You'd have to add pressure to the inside or squeeze the opposite direction to return it to normal.

What Is Yield Stress?

Stress and strain are directly related to each other: as one increases, the other increases as well. So, the more stress that an object experiences, the more it deforms until the object fails.

All objects will begin experiencing elastic deformation at first, but once the stress on the object exceeds a certain amount, it will experience plastic deformation. When that switch happens, the object has reached its yield stress.

Typically, every material has the same stress-strain relationship, though the size of each portion may be different. Elastic deformation is linear. The slope of the line is dependent on the material the object is made out of. Plastic deformation is not linear, making it more difficult to model.

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Take a look at this graph. The elastic deformation is in red and you can see that it's linear, while plastic deformation, which is in blue, is not.

Yield Point

Some material also has a yield point, a point where there is a sharp increase in the object's strain that does not correlate with an increase in stress. The yield point happens after an object has reached its yield stress.

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