Different samples of a material will stretch by different amounts - depending on their original length. Strain allows us to get a fair comparison between the amounts that they stretch. It is the relative increase in length of a sample. Or the extension per unit length.
Strain has no units because it is the ratio of two lengths. A wire that stretches by 10% will have a strain of 0.1.
What does strain mean?
Picture 4.4 Straining different wires.
Imagine two pieces of identical wire. Sample D is 3 times longer than sample C. They are both pulled with the same stress. Which one will stretch more? The longer piece - sample D. It will have three times the extension. You can think of it being made up of three shorter lengths, each of which stretches by the same amount as sample C.
Although sample D has three times the extension, its strain is the same. This is because it was three times longer to start with so its relative extension is the same. Both samples have a relative extension of about a seventh of their original length. Therefore they both have the same strain of about 0.15.
A stiff material is difficult to stretch or change shape. The Young's modulus is a measure of how difficult.
The formula for Young's modulus, E, is:
The Young's modulus is a measure of the stiffness of a material. It is what we call a bulk property - that is, it applies to the material not just a sample of that materioal. A stiff material will need a big stress to stretch it by a small amount (give it a small strain). The unit of Young's modulus is the pascal (Pa) though it is often measured in gigapascals (GPa). The Young's modulus of steel is typically around 190GPa.