Why true strain is always smaller than nominal strain in tensile test?

In summary, nominal strain is always larger than true strain in a tensile test. This is because, while nominal stress is smaller than true stress due to the decrease in cross-sectional area, nominal strain is larger than true strain due to the increase in actual length being smaller than the theoretical length increase. This is related to the definition of strain, where nominal strain is based on the original length while true strain takes into account the actual length. This difference is not related to atomic forces and it is okay to upload questions on this forum.
  • #1
HongTechnology
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TL;DR Summary
Why true strain is always smaller than nominal strain in tensile test?

Is that mean that actual length increase is smaller than theoretical length increase?

Is it related to atomic forces?
Hi everyone.

I'm studying Mechanics of Materials and I got some question about 'nominal/true strain'.

First of all, I agree that in tensile test, nominal stress is always smaller than true stress

σt > σn

cause when the material specimen is being stretched, then the actual area of the specimen at the cross section would be decreased.

However, I wonder why nominal strain is always larger than true strain in tensile test. εt < εn

If I'm right, I guess that statement implies that actual length increase would be smaller than theoretical length increase.

cause ε=δ/L, am I right?

If I'm right, what factor is the main reason for that truth? Is it related to the atomic forces?

p.s. I just started to use this PhysicsForums, so I wonder if it is okay to upload questions here.

If I did wrong, I would appreciate if you tell me where should I upload questions. I'm not very good at english TT.

Anyway, thanks for reading my question.
 
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  • #2
Ah, I think I misunderstood the definition of each of them. It was a simple thing haha;
 
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FAQ: Why true strain is always smaller than nominal strain in tensile test?

1. Why is true strain always smaller than nominal strain in tensile test?

True strain takes into account the change in cross-sectional area of the material during the deformation process, while nominal strain only considers the original cross-sectional area. This means that true strain is a more accurate measure of the actual deformation of the material.

2. How is true strain calculated in a tensile test?

True strain is calculated by taking the natural logarithm of the ratio of the final length to the initial length of the material. This formula takes into account the change in length and cross-sectional area of the material.

3. Can true strain ever be larger than nominal strain?

No, true strain can never be larger than nominal strain. This is because true strain takes into account the decrease in cross-sectional area, which always results in a smaller value compared to nominal strain.

4. What is the significance of using true strain in a tensile test?

Using true strain allows for a more accurate measurement of the material's deformation and behavior under stress. It also takes into account any changes in the material's cross-sectional area, which can affect its overall strength and properties.

5. Are there any limitations to using true strain in a tensile test?

One limitation is that true strain can only be accurately calculated up to the point of necking, where the material begins to narrow and the cross-sectional area changes rapidly. Beyond this point, the calculation of true strain becomes more complex and may not accurately reflect the deformation of the material.

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