Understanding Young’s Modulus

Welcome back to the Efficient Engineer channel everyone! In this video we’re going to talk about Young’s modulus, one of the three main elastic constants along with shear modulus and bulk modulus, which are used to describe how a material deforms under loading. Let’s introduce Young’s Modulus using the tensile test.

The tensile test is a very common mechanical test which takes a test piece and stretches it along its length. It is a uniaxial test meaning that it applies a load in one direction only, as shown here. During the test, the test machine measures the applied load and the change in length of the test piece. The main output from the tensile test is the stress-strain curve, which describes how much the material we’re testing will deform for different levels of applied stress. Watch how the stress strain curve evolves as we perform a tensile test on our test piece, which in this case is made of steel.

The test ends when the material fractures. We can observe that the stress-strain curve is split into two regions – the elastic region, where the curve is linear, and the plastic region. If the applied stress is low and we remain in the elastic region, the original dimensions of the component will be completely recovered when the applied load is removed. For larger stresses that take us into the plastic region, permanent plastic deformation will remain after the applied load is removed. In the elastic region the stress-strain curve is a straight line for most materials. This means the strain is proportional to the applied stress. Hookes law gives us the relationship between stress and strain in this linear elastic region. The ratio between stress and strain is Young’s modulus, also called the modulus of elasticity, which we denote with the letter E.

Understanding True Stress and True Strain

It has the same units as stress, so psi in US customary units and Pascals in SI units. We can also measure Young’s modulus as the gradient of the slope in the elastic region. Young’s modulus is essentially a measure of how stiff a material is. The higher the Young’s modulus, the stiffer of material and so the smaller the elastic deformations will be for a given applied load. If we perform tensile tests for a few different materials we will notice that the slope of the stress-strain curve is different for each of them. Different materials can have vastly different values for Young’s modulus.

For anisotropic materials like wood or composites such as carbon fiber the value of Young’s modulus will depend on the direction in which the load is applied. This graph shows the range of typical Young’s modulus values for polymers, metals and ceramics In general ceramics have higher values of Young’s modulus, metals have slightly lower values, and polymers have much lower values. Understanding what is happening at the atomic level can give us a better understanding of Young’s modulus.

On an atomic level a materials Young’s modulus is closely related to the strength of the bonds between its atoms. We can imagine these inter-atomic bonds as tiny springs connecting adjacent atoms. Elastic strain is the result of an increase in spacing between the atoms of the material, and is resisted by the strength of the inter-atomic bonds, or the stiffness of the little springs in our model. This is very different to the mechanism behind plastic deformation, which involves rearrangement of the position of the atoms.

Understanding Stress Transformation and Mohr's Circle

This is why elastic deformations are reversed when the load is removed but plastic deformations are not. I mentioned earlier that Young’s modulus is smaller for polymers than it is for ceramics and metals. This is because it is the weaker inter-molecular bonds in polymers that determine the material stiffness, rather than the stronger atomic bonds. Looking at things on the atomic level can also help explain why differences in Young’s modulus for alloyed metals tend to be small.

take the example of carbon steel. Mild steel and high carbon steel have quite different mechanical properties. Their yield strengths for example are very different. And yet they have very similar Young’s modulus values, which at first glance might seem surprising. We can explain it using our inter-atomic bonds model.

Mild steel has a carbon content of up to 0.25% and high carbon steels can have a carbon content of up to 0.95%. Adding such a small number of additional carbon atoms to the existing iron atoms isn’t enough to significantly affect the overall resistance to increasing the spacing between atoms, and so the Young’s modulus is very similar for mild steel and for high carbon steel, despite some of their other mechanical properties being very different. Young’s modulus is a crucially important material property when it comes to engineering. In engineering design, a common objective for many different applications is to keep elastic deformations as small as possible, which means that Young’s modulus is a key parameter that needs to be considered in the material selection process.

Understanding Torsion

Take the example of a bridge. If we construct a bridge from a material with a low Young’s modulus it will deflect a large amount when something crosses it, which is probably not the desired response. Selecting a high stiffness material would ensure that elastic deformations remain small for large loads. That concludes this brief introduction to Young’s modulus. If you have any interesting facts about Young’s modulus, let me know in the comments. And stay tuned for more videos!