Young's modulus is a fundamental elastic constant that quantifies a material's stiffness, representing the ratio of stress to strain in the elastic deformation region, and is crucial for engineering design to minimize unwanted deflections.
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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.
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.
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.
Let's 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.
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!
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