In 1912, the Titanic set off for her maiden voyage across the Atlantic Ocean.

The ship’s builders were convinced that even in the most disastrous collision at sea, the ship could float for two to three days, enough time for nearby ships to come to its rescue. But on April 14th, the Titanic struck a massive iceberg and in just three short hours the ship had sunk.

The collision fractured the ship’s hull, cracking it like a china plate, as well as shearing off the rivets holding it in place. And as we all know, it was an absolute disaster. One of our most important tasks as engineers is to try and avert catastrophes like these.

You see, when it comes to structures, tools and equipment, we need to make sure they’re made of the right stuff. That means taking a closer look at the materials they’re made of. So this episode is really going to test your, uh mettle. [Theme Music] If a material exists, there’s a pretty good chance an engineer has thought about using it at some point.

As far back as two and a half million years ago, early humans were using the materials around them, primarily stone and wood, to build tools like hammers and axes. These days, we’ve developed totally new materials. There’s aerogel, for example, which is an ultra-light substance that can withstand high temperatures.

Not to mention graphene, a one-atom-thick sheet of carbon atoms that’s stronger than steel and superb at conducting heat and electricity. While those advanced materials might be used more widely in the future, today, most materials that engineers work with can be categorized into three groups. Metals and their alloys; ceramics and glass; and polymers.

Which material is best suited for a job depends on its properties, and how those properties affect it in practice. More specifically, whatever we’re using, it’s vital to know the material’s mechanical properties. Mechanical properties relate to how a material’s shape changes when a force is applied to it.

To make better sense of this, it helps to have a concrete example in mind. But we’re not actually going to use concrete. At least not yet.

Instead, we’ll consider a steel beam, like the kind widely used in civil engineering and construction. Of course, we could make beams out of all kinds of materials, and the resulting beams would have different properties. But no matter what you’re making them out of, there’s one important thing to know: no material is perfectly rigid.

As long as you apply a large enough force, a beam will deform and change shape, even if only internally. Some things you encounter in everyday life might seem totally rigid because the change in shape is so small. But when that stops being the case, it can have dramatic consequences.

Something that all engineers aim to avoid is failure . Not in the sense of whether or not you do things exactly right all the time. Even engineers aren’t perfect, and sometimes we get things a little wrong.

It’s all part of the learning process. When it comes to materials, the word ‘failure’ describes the point at which a material breaks. And unlike messing up a few problems on your math homework, this is the kind of failure that isn’t worth the learning opportunity!

In a system like a car, where everything depends on the structural integrity of the materials, the outcome could be fatal. So to prevent critically dangerous situations, engineers characterize a material’s mechanical properties so they can prevent it from failing. If you’re using a beam to construct a building, those properties are crucial for keeping the structure standing tall.

This is where stress comes in. We touched on what stress means in an engineering context when we looked at fluids: it’s the force applied over a particular area of the material. We can apply this type of stress to our beam in three distinct ways: There’s compressive stress, which pushes in on the ends of a material.

Then there’s tensile stress, which stretches and potentially elongates it. And finally, there’s shear stress, where you push sideways on a material in opposite directions. To measure the effects of this stress on our beam, we look at its strain.

Strain is how much the beam’s length changes in a particular direction. When we were discussing stresses on liquids, the level of deformity was linked to the liquid’s viscosity: how easily it flowed in response to pressure. In a materials context, the level of deformity is a little more complicated.

But like so many things in engineering, visualizing it as a graph can help. Let’s take the beam and put it in an extensometer, a piece of equipment with an awesome name that will apply tensile strength to the beam and measure its strain. To graph what’s happening, we’ll put the level of stress we’re applying, represented by the Greek letter ‘sigma,’ on the vertical axis.

Then we’ll put the strain on the horizontal axis. When the stress we’re applying is perpendicular to the ends of the beam, as in the extensometer, the resulting change in length is called the normal strain. That’s represented with the letter ‘epsilon.’ As we increase the stress on the object, the material will begin to display signs of strain, changing its length.

The amount of stress a material is subjected to before it undergoes a particular amount of strain – in other words, the slope of the line – is known as the modulus of elasticity. That quantity is a measure of how resistant our material is to bending and stretching. The closer the line is to vertical, the higher the modulus.

To make sense of the units here, stress is measured in gigapascals because it’s a force applied over an area, which gives it the same dimensions as pressure. Strain, meanwhile, is a ratio of two lengths, so it’s a dimensionless quantity – it has no units. Putting that all together, the modulus of elasticity has units of gigapascals.

But what does the modulus actually mean? Let’s compare beams made of two different materials: rubber and concrete. Rubber has a modulus of elasticity of just 0.01 gigapascals, while concrete has a modulus of 30.

That means for a given amount of stress applied to each material, the rubber will have a proportional change in length 3,000 times that of the concrete! That’s not surprising, right? We know it’s easier to stretch rubber than concrete.

So the modulus of elasticity, which you can measure from the stress-strain diagram, gives you an idea of how much the material resists a change in shape under an applied stress. For example, in units of gigapascals, the modulus of glass is around 50, while brass is around 100. Steel is higher still, at around 200, while diamond clocks in at a whopping 1,220 gigapascals!

So far, all the lines on the stress-strain diagram have been straight, with constant slopes. But as you apply even more stress, that relationship breaks down, and the material will begin to deform and stretch along its cross section as well as its length. We call that point the yield stress.

For example, apply enough tensile strength to a bar of clay and eventually it gets thinner in the middle as it stretches to meet the demands of high tensile stress. Finally, if we apply enough tensile stress, the material breaks apart entirely and undergoes failure. And the exact same thing can happen to our steel beam, too!

The stress-strain curve tells you about another important property for avoiding failure and determining a material’s suitability: its toughness. A material’s toughness is the amount of energy it can absorb before it undergoes failure. On our diagram, that’s represented by the total area under the curve for the material, from the origin to the failure point.

If you know a bit of calculus, you’ll recognise this as the integral of the stress-strain curve. Toughness isn’t the same as strength, though! A material might be very strong, with a very high modulus of elasticity, but break after only a small amount of strain.

On the other hand, a material might be able to strain a long distance without breaking, but have a very low modulus of elasticity, like Play-Doh. Toughness is a balance between the two. And while a tough material might be useful for making the foundations of a building, in other applications it might be something you want to avoid!

For example, by adding carbon to the steel beam, you can give it a greater yield stress. It barely deforms under a single impact, but that also makes it more brittle. Meanwhile, low carbon steel has a low modulus of elasticity, it will deform much more quickly because it has a low yield stress, but that makes it more ductile, so it’s more useful for shaping and welding.

But neither of those options maximizes the toughness of steel! Toughness would be finding the middle ground where you maximize the area under the curve, so the steel is able to absorb as much energy as possible before fracturing. A measurement that comes in handy for measuring this is the Charpy impact test, which tells us the toughness of our material by whacking it with a hammer.

No, seriously. The Charpy test measures toughness by taking a small sample of material and striking it with a hammer on a pendulum and trying to break it. The height you drop the hammer from and the height that the hammer swings up to after smashing through the material can determine how much energy the hammer lost breaking the sample.

And that tells you how tough the material is. While not all material tests are quite as fun to perform, there are lots of different mechanical properties to consider in materials that could make them totally great for the job at hand or just completely useless. For example, there’s hardness, which is how much your material deforms in a particular location – that is, how easily you can dent it.

Measuring hardness is simple enough: you use a device called an indenter to apply a localized load to your material and see how much it gets dented. Pretty straightforward! Another mechanical property which can be a good or a bad thing, depending on the situation, is creep strength.

Which thankfully has nothing to do with the Minecraft monster. Creep strength is how much a material resists deforming or, to use the engineering term, resists creep under long term stress or extreme temperatures. In some cases, a low creep is a good thing.

In the blades of a propeller, too much creep could elongate the blades and make them hit the casing, damaging them. But in a concrete structure, some amount of creep can be useful since it prevents the concrete from cracking outright. There’s also fatigue strength, which measures how many times a material can endure a certain amount of stress before it fails.

Sometimes even applying small loads of stress well below the yield stress still leaves tiny impacts, like microscopic cracks in the material. If that small amount of stress is applied repetitively, the cracks can deepen and spread in the material until they eventually cause fracture. As you’d expect, a material might be able handle lots of little bits of stress applied to it over time before it fractures.

But it might only survive failure under a few large stresses. The fatigue strength is the highest possible stress a material can withstand a given number of times before undergoing failure. Of course, hardness, creep strength, and fatigue strength are just some of a material’s mechanical properties.

We might also need to consider how the surface of our chosen material reacts with its environment, how much it costs to produce and obtain, and even what it looks like. And while all of those are important, it isn’t much use considering those other properties until you’re sure the material is mechanically up to the task of handling the stresses and strains the world is gonna throw its way. And knowing about the the strengths of the materials you use will add to your strengths as an engineer.

In this episode, we’ve started considering the materials that are used in engineering. We looked at mechanical properties of materials, which describe how much strain a material undergoes given a certain amount of stress. From stress-strain diagrams, we found useful properties that could be measured like the modulus of elasticity and toughness, and described other material properties like hardness, creep strength, and fatigue strength.

Next time, we’ll get into the real substance of things and discuss the materials themselves in a bit more depth, starting with what makes a metal a metal. Crash Course Engineering is produced in association with PBS Digital Studios.

If you have a couple minutes, we have some homework for you because PBS Digital Studios is conducting its annual survey, which gives us a chance to hear from you and helps us make some big decisions. Plus, 25 random people will win a PBSDS t-shirt. Head on over to the link in the description.

Crash Course is a Complexly production and this episode was filmed in the Doctor Cheryl C. Kinney Studio with the help of these wonderful people. And our amazing graphics team is Thought Cafe.