# Why is the Stress vs strain diagram preferable to the Load vs displacement diagram?

I’m really unsure what is the difference between stress vs. strain and load vs displacement graphs and why stress-strain is better.

I know that the units are different:

• stress is in MPa and the load is Force N
• and strain is no units and displacement/extension is units of length mm.

Can someone please me understand the differences and explain which one is better?

• Your post is missing said graphs – jko Mar 30 at 19:18
• This problem was addressed in the mid 1800s. A detailed exploration can be found by Bell's article in Handbuch der Physik (Bell, J. F. "Handbuch der Physik Band VIa/I." (1973)). Should be available at a university library. – Biswajit Banerjee Mar 30 at 21:16

The Load-Displacement (or Load Extension) and stress strain diagrams are two diagrams identical in shape. See below. The main visible difference is the values on axis (which are at first glance neglected).

So, it is natural when you first encounter them to question why do you want to learn about a stress and strain diagram which has obscure quantities (as in not directly measureable ), instead of the load-displacement diagram that has quantities that are directly measured and commonly understood.

The data you obtain from an tensile specimen experiment is the Load-Displacement curve. From the load-displacement you obtain the stress-strain by:

• stress is load over original cross-section A

$$\sigma= \frac{F}{A}$$

• strain is displacement over original length L

$$\epsilon = \frac{\Delta L}{L}$$

In both cases you divide with a constant quantity, so the shape does not change (as you can see in the image above).

## What's the difference.

Apart from the units there is a significant difference.

The stress-strain curve is relevant to all specimens made from this material

The Load-extension curve is relevant to specimens with only one combination of L and A.

So if you take a specimen with double the thickness, then the Force-extension diagram will change. (the force will double for the same displacement). However the stress vs. strain curve will remain exactly the same.

So the use of the stress-strain curve is that you can use it to predict the behaviour of (almost) any geometry even if you haven't tested it.