# Calculating Young's Modulus, Yield Stress, etc. from Force-Elongation Graph

• DuncanBain
In summary, the conversation is about deriving values from a Force vs. Elongation graph of an Aluminium specimen, specifically Young's Modulus, Yield Stress, Yield Strain, and Ultimate Tensile Strength. The person was initially confused by their calculations for UTS, which turned out to be around 695.7MPa. They later realized their mistake and clarified that the correct value for UTS should be around 400MPa. They also calculated Young's Modulus to be around 13GPa, which seemed low.
DuncanBain
Evening all,

I have a Force vs. Elongation graph of a specimen (Aluminium). From this I need to derive the values of Young's Modulus, Yield Stress, Yield Strain, Ultimate Tensile Strength and so forth.

I assumed this was fairly straight forward, but when I tried calculating the UTS, my answer was way way off of what it should roughly be.

The calculation I tried is as follows:

The maxima of the curve was 53.5kN and the A0 of the specimen was 76.9mm2.

UTS = F/A0 = 53500 / 76.9x10-6 = 695.7MPa

The answer should be around the 69GPa mark.

Any ideas where I'm going wrong? I get similar results when trying to calculate any other values from the graph.

Many thanks.

695.7MPa (~100 ksi) is about right for Al. That's pretty strong for Al.

69 GPa would be about right for the elastic (Young's) modulus.

Thanks for the reply. Made a mistake in my post in saying Young's Modulus should be around 69GPa rather than say that the UTS should be around 400MPa? So I guess it's really not that far off.

I also calculated Youngs Modulus but got around 13GPa which seems very low.

## 1. What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness or rigidity of a material. It is the ratio of stress (force per unit area) to strain (change in length per unit length) in a linear elastic material.

## 2. How do you calculate Young's Modulus from a force-elongation graph?

To calculate Young's Modulus from a force-elongation graph, you first need to calculate the slope of the linear portion of the graph, which represents the material's elastic deformation. The slope is equal to the stress divided by the strain. This value is equal to Young's Modulus.

## 3. What is yield stress?

Yield stress is the point on a stress-strain curve where a material starts to deform plastically, meaning it no longer returns to its original shape after the stress is removed. It is a measure of the maximum stress a material can withstand before it permanently deforms.

## 4. How do you calculate yield stress from a force-elongation graph?

To calculate yield stress from a force-elongation graph, you need to find the point on the graph where the material starts to deform plastically. This is usually indicated by a sudden change in the slope of the curve. The corresponding stress value at this point is the yield stress.

## 5. Can Young's Modulus and yield stress be calculated for all materials?

No, Young's Modulus and yield stress can only be calculated for materials that exhibit linear elastic behavior. Some materials, such as plastics, do not have a linear relationship between stress and strain, so these values cannot be accurately calculated for them.

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