# How to calculate % volume change due to wire drawing

I am currently doing some lab work involving wire drawing and trying to calculate the % volume change of the wire after wire drawing. I am using the geometrical data (length and diameter) of the wires before and after the drawing process for these calculations. From various sources online I have learned that the volume doesn't change for the wire drawing process.

However, my calculations don't seem to show this feature. I have calculated the volume of the wire (before and after the wire drawing process) using the formula:

Volume = $$\small\sf\pi {(radius^2)(length)}$$.

In my calculations the volume of the wire after each draw gradually decreased.

Can some tell me if this is correct or if there is another method to conduct this calculation. Any form of help would be greatly appreciated.

There are two causes of the change in shape.

One is plastic deformation, which takes place as constant volume.

The other is the elastic deformation caused by the stress that is "locked in" to the structure when you stretch the material. They usually do cause a change of volume, related to the value of Poisson's Ratio of the material. Try measuring the volume of your wire, then annealing it, then measure the volume again. If the wire is a "soft" material like brass or copper, you can anneal it by simply heating it up to red hot for a few seconds and letting it cool naturally in air.

Note that if you only measure the diameter at a few places along the length, the calculation for the volume will probably not be accurate because after drawing, the wire probably won't have a constant diameter. It might be more accurate to do something like make a coil of the wire, immerse it in a liquid, and measure the volume directly.

Assuming your wire is steel and the Poisson ratio 0.3, if you pull the wire such that you have 1% elongation then your radius shrinks by 0.033% so your ratio of the volume change is.

(0.997)2*1.01 = 1.0039

This means the volume has increased by a factor of 0.0039.

Approximately 4 thousands.