Reaching breaking point: Materials, Stresses, and Toughness: Crash Course Engineering #18

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 propellor, 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.

About the author


  1. It's funny. I'm in college for ChemE and you guys always seem to release videos as I'm taking each course (just started a semester with Material Sciences)

  2. This just shows that no matter how strong something is, it always has a breaking point. I liked how you went into so much detail and taught me something new! Thanks for this video! I found it very interesting and I can't wait for the next video! DFTBA!

  3. Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application.

  4. She’s a lot skinnier than she was in the physics videos. Is she ok? Anyway, awesome series. I’ve always wanted to learn engineering. Thanks

  5. Fun fact: all substances are either metals or non-metals, and either organic or inorganic, and while there are no organic metals, there are inorganic non-metals, and those are the ceramics, including glass. Polymers, of course, are organic; so between them, metal, and ceramics, you've basically just said that "for now, the materials engineers work with are [exhaustive list of all possible materials]".

  6. I thought I knew this stuff (though it HAS been 46 years since I took a structures class in architecture school), but at 7:26, you say low carbon steel has a lower modulus of elasticity even though the slope on the stress-strain graph is identical to high carbon steel. It looks to me like what low carbon steel has is a lower elastic limit or yield point. Am I wrong?

  7. There's an old poem that comes to mind here. It was authored by Rudyard Kipling in 1935.

    THE careful text-books measure
    (Let all who build beware!)
    The load, the shock, the pressure
    Material can bear.
    So, when the buckled girder
    Lets down the grinding span,
    'The blame of loss, or murder,
    Is laid upon the man.
    Not on the Stuff—the Man!
    But in our daily dealing
    With stone and steel, we find
    The Gods have no such feeling
    Of justice toward mankind.
    To no set gauge they make us—
    For no laid course prepare—
    And presently o'ertake us
    With loads we cannot bear:
    Too merciless to bear.

    The prudent text-books give it
    In tables at the end
    'The stress that shears a rivet
    Or makes a tie-bar bend—
    'What traffic wrecks macadam—
    What concrete should endure—
    but we, poor Sons of Adam
    Have no such literature,
    To warn us or make sure!

    We hold all Earth to plunder—
    All Time and Space as well—
    Too wonder-stale to wonder
    At each new miracle;
    Till, in the mid-illusion
    Of Godhead 'neath our hand,
    Falls multiple confusion
    On all we did or planned—
    The mighty works we planned.

    We only of Creation
    (0h, luckier bridge and rail)
    Abide the twin damnation—
    To fail and know we fail.
    Yet we – by which sole token
    We know we once were Gods—
    Take shame in being broken
    However great the odds—
    The burden of the Odds.

    Oh, veiled and secret Power
    Whose paths we seek in vain,
    Be with us in our hour
    Of overthrow and pain;
    That we – by which sure token
    We know Thy ways are true—
    In spite of being broken,
    Because of being broken
    May rise and build anew
    Stand up and build anew.

  8. YES! I am dealing with this at work constantly. It felt like you were talking to me specifically. That really help me understand.

  9. I can't put into words how much I love this. I'm a hobbyist blacksmith, and far too often in this realm we see these termed used far too loosely. This is because most blacksmiths haven't had the material engineering that evolved out of what the historical blacksmiths came to learn. Giving these words like strength, toughness, and hardness formal definitions makes them all so much more useful, but only to those who have taken the time to learn their proper formalized meanings. Videos like this, make that understanding so very much easier. As a teen, I tried to learn this from things like Modern Marvels on cable TV, and they would almost always get at least one critical aspect almost completely wrong.

  10. i heard somewhere that there was a minor fire onboard a few days before the ship sank. it was put out, but the heat changes made the hull more brittle. anyone know if that's true?

  11. Your reason the Titantic went down was incorrect. It had nothing to do with the strength of the steel used. It had everything to do with the design of the ship.

  12. As a Materials Engineering student, I'll have to start sharing this video around whenever people ask me "so, what's that?"

  13. Very well presented. I did the test of communicability. In the whole length of 11 mins, I had to rewind only once to understand the term. Very well packaged and presented. Congratulations.

  14. Of coure, I am a good student too who is greatly interested in the subject, that makes the test a bit biased , nonetheless, my absorption rate is a a good indicator of the the communication strength of the video.

  15. Minor pedantry here, but…

    "Ep-SI-lon"? I am pretty sure it is supposed to be "EP-si-lon". Second syllable is said like "see", not "sigh".

    Minor linguist complain over. I do apologize.

  16. This channel is debatable in the topic of killing it as an act of mercy. Ever since they stopped making philosophy videos. The only reason I subscribed. It truly has been a fun ride. I learned so much about others and about myself. Thanks and goodbye

  17. In the harmonica world there are metal reeds. Historically they used bell brass. Today there are two main materials… bronze-phosphor and stainless steel (not sure what grade but it's magnetic but still good with moisture). There is a debate over which last longer. People fall into both camps, but I've noticed that the people who say steel lasts long self-describe themselves as hard players. My guess is that the stainless is staying under the fatigue stress levels with gentle players but more vulnerable at higher levels. I've read that under certain levels steel (and titanium) can undergo nearly infinite cycles without breaking. I also know when they are retuning reeds a lot of customizers prefer to polish to remove metal rather than just scratch the reeds because they are worried that scratches will create weak points that could lead to reed failure. (At $40 a pop for a harmonica, with 20 reeds per harp, with 12 harps in your set people worry about details like this!)

  18. 5:58–6:06
    “But as you apply even more stress… the material will begin to deform and stretch along its cross-section as well as its length”

    Just want to suggest adding in some detail here as the above sentence seems a bit ambiguous. Even in the elastic region of the stress-strain graph, all (normal) materials do experience deformation span/transverse-wise, and not just lengthwise before the yield point (see Poisson effect and/or Poisson’s ratio).

    In the elastic region, this effect is uniform across the material, as the cross-section area deforms uniformly across the entire length. At the yield point and beyond, this deformation begins to be non-uniform and is localized instead – hence the specimen necking/getting thinner in the middle before failure occurs there. (Also, I feel that defining the yield point as being the point beyond which the material can no longer return to its original shape to be a clearer explanation than the above).

    To summarize then, perhaps it would be better to phrase the above as “the material will begin to deform and stretch non-uniformly along its cross-section as well as its length” – or something along this tune?

    Still, thanks for summarizing a semester’s worth of introductory materials engineering so well! Wanted to add this to prevent any misconceptions of when transverse deformation occurs.

  19. Wow. What a needlessly convoluted and complicated way to explain this.
    Too Technical with too little Explanation.
    I actually learned such stuff and yet aside from terminology I hardly was able to comprehend any of what you said and basicly had to remember things from what I learned myself to realize what your Talking about….
    In Essence your Explaining what the Words mean but give it absolutely Zero Practical Knowledge to go with.

    For an Actual Engineer this might be understandable.
    But for those of us which are not Educated in Engineering especially even if we do have education in this field due to other Areas of Expertise this is really really hard to grasp.

    One example.
    Your actually using a Steel Beam as your first Example and then actually Show a Bridge.
    And you Explain that Materials will Bend and Break if a certain amount of Force is applied.
    Yet one of the most Importand Examples on Materials Qualities and one of the Reasons why Steel is such a Widely used Material for Bridges remains entirely unmentioned.

    One of the First things we Learned was about Permanent Deformation and Reversive Deformation (sorry if its not the correct Terminology in English I didnt learn it in English ^^)
    You are actually later on mentioning the effect of continues Stress and that smaller amounts of stress might reduce the breaking Point of the Material over time.
    Yet again in your explanation it basicly sounds like Material once it starts deforming is automaticly permanently damaged and will reduce its breaking point.
    Leaving out the Property of Materials being able to withstand certain repeated stress levels by deforming and then returning to Original form after the stress lets off.

    Or maybe you actually mentioned it but I didnt understand it 😛

    I think you should Redo this Video or maybe do a Second Video on it.
    I somehow dont think that many people without extensive prior knowledge in this field will actually be able to make sense of this right now ^^

  20. I had hoped you'd would have mentioned transition temperatures for them resulting in such things in the Space Shuttle Challenger failure and possibly an important variable in the Titanic sinking.

  21. The entirety of this engineering crash course(minus fluids) is taught in my a level classes like from 1-14 and from here to the semiconductor video is a level physics engineering or sumn lol

  22. There is no such thing as evolution nowhere in the Bible said that we evolved it was just a scientist MR Darwin thumb sucking

  23. The revitalization of the Old Town Drawbridge experienced another setback this week, as engineers determined that the furniture upholstery used to construct the bridge towers soaks up water and creates an unstable foundation. This week’s collapse was the third in as many months.

    Construction crews have tried building the bridge tower base supports from corrugated cardboard, non-dairy creamer, and ceramic bowls. Nothing has worked.

    Engineers are asking for help in determining how proper bridge towers are made. If you have any tips, please write them on notebook paper and mail them to

    Bridge Magic, LLC
    PO Box 616

    Do not use cursive or long words. Clearly labeled drawings are preferred.

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