Welcome to our third and final lesson in our introduction to material elasticity course.
Today we're going to be focusing on how real world design is impacted by material
elasticity. If I'm thinking about elasticity or really any material property during design
I need to be thinking about how my material will perform once in service in the product and how
that relates back to my material properties. When talking about elastic behavior often
we're referring to stiffness which I defined both in our introduction and in lesson one.
Do I want a material that has high stiffness for example in a chair leg or do I want a
material that has low stiffness for example the cushion in that chair? Stiffness can be
both desirable or undesirable depending on the application. So how do I begin to think about this?
Let's take an example where I want a high degree of stiffness: a bridge. If we think about ancient
bridges, we're often thinking about the Romans. Romans were known for their bridge building skills,
building these stone bridges with these elegant arches. The pieces of stone used to construct
these bridges were quite large if we compare this bridge to a modern-day bridge, built out of steel.
We see that the pieces of steel are much thinner. Now both of these bridges serve to
facilitate the same function; get humans from one place to the other that they couldn't reach before-
perhaps across a body of water. But why can't we build stone bridges that look like steel bridges?
To think about why we pick one material over another in design we need a way to compare our
different material properties with one another. We could do this with sets of tables like the
ones shown here or we could take a more visual approach. Let's see the visual approach in action
This involves something called an Ashby property chart like the one shown here. This has taken the
values from that table and plotted them against one another. The small circles or bubbles represent
individual materials. The bubble showcases the range of values for that attribute.
Now there's a range because these materials might differ slightly, from the raw material itself to
its processing. The larger bubbles or envelopes represent general trends found with material
families. In today's lesson we'll be using these Ashby charts to compare different material
properties with one another. Let's look at an Ashby chart specifically plotted for our bridge example,
so we have stone-like materials and we have ferrous alloys from the iron carbon phase diagram
which encompasses our steel. I've plotted Young's modulus on the y-axis
This will be our elastic property of interest. Today I've plotted density on the x-axis because
often we're trying to design something that we want it to be both stiff and light.
We can see from this chart here that our stone and stone-like materials have a much
lower Young's modulus than our steels. What impact does this have when we're designing our bridge?
If we think of our equation for Young's modulus it's stress over strain. Now I don't really want
a high strain for a bridge. I don't want really any deflection at all, albeit elastic.
So we'll focus on stress which is force over some initial area Ao. If my stone bridge is to be
able to withstand the same force and have the same deflection as my steel bridge, based on my
Young's modulus I'll have to have a significantly larger cross-sectional area for my pieces of stone.
This is part of the reason that our bridges look different. Now this is one example of
how elastic behavior has impacted our design based on our material choice.
What's another example where I'm utilizing a different part of my elastic behavior? In lesson
two we learned that if I'm applying a force to my atomic bonds I'm stretching them and I'm imparting
some energy on my system. We can visualize this through a rubber band. As I apply a force and
stretch my rubber band, I'm imparting some elastic energy into my system. When the force is released?
The energy is also released and the rubber band is launched across the room.
Now we saw that different bonding types have different bond strengths which then means that
our materials behave differently elastically. This directly impacts not only their elastic
behavior but their ability to store this elastic energy. Now what's a way that we can utilize
this stored elastic energy that's more useful than me losing rubber bands around my office?
We can think of pole vaulting. The sport of pole vaulting
involves a person holding their vaulting pole running towards some bar set at a specific height.
When they get to the bar the pole will bend, we'll have elastic energy stored
in that vault pole, and that's then released allowing, the vaulter to vault over the bar.
I need that pole to be lightweight since the vaulter needs to run and gain speed
when running towards the bar and I also need the bar to be stiff and flexible-- a combination
of the two where the pole can bend so that I get some elastic energy stored but it doesn't break.
Now the first pole vaults were made out of wood; we used them to get across small streams.
Then when it became a sport we went from wood eventually to aluminum, which is a
lightweight metal, and finally we make these pole vaults mainly out of composite materials
sometimes with an aluminum core. Now why have we made these material choices over the years?
We can look at an Ashby chart again once again, plotting Young's modulus versus density.
But this time I'm comparing wood and wood-like materials to my composites and my aluminum alloys.
We can see from this chart that wood is quite lightweight but it has a significantly
lower Young's modulus than both my composites and my aluminum alloys.
If we're focusing on just the composites in aluminum why am I moving more towards composites
and away from aluminum? They have roughly the same Young's modulus. Well the composites, particularly
carbon fiber composites, are much lighter. That density is important; the pole needs to
be lightweight I'm going to carry it while running towards my bar. Another thing that we learned in lesson two
was about anisotropy and we mentioned composites in this discussion. We can control the arrangement
of my reinforcement in my matrix in my composite thus changing its anisotropy and also changing
its elastic behavior. This is something we can utilize and take advantage of in our design
to design that pole so that it has the correct balance of stiffness and flexibility while
maintaining that light weight so that I get my maximum energy stored to vault me over that bar
without my pole snapping. Now these are just two different examples of how my elastic behavior in
my material has impacted how I design a product and they were vastly different applications.
Can you think of something around your house where stiffness might be a key design criteria?
And with that, we've come to the end of our lesson and our course. Let's take a moment to summarize.
In our first lesson, we were focused on defining different terms, equations, and diagrams related to
material elasticity. We used our newfound knowledge of these equations in a short homework assignment
to calculate stress and strain values with relevant material information. Our second lesson
focused on the impact that atomic bonding has on our elastic behavior and our materials and why
different materials behave differently in the elastic region of my stress strain curve.
And in today's lesson we saw some real world examples of how a material's elastic behavior
directly impacts how we design our products and other things that we use in our day-to-day life
or maybe not in the case of the pole vault). Now I mentioned this multiple times, that elasticity is a
complex subject and we've only started to scratch the surface, but my hope is that with this course
and with the different equations diagrams and terminology you've learned you're able to start
using this knowledge in various ways. My name is Dr. Kaitlin Tyler and thanks for joining me