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(#92) The Invisible Forces That Break Machines · Mechanical Engineering Made Simple

• 0:00
  Welcome back to mechanical engineering made simple.
• 0:02
  It's great to be here. You know, I had a bit of a
• 0:04
  moment this morning. I was driving over that massive
• 0:07
  suspension branch, the one I take every day to get to the
• 0:09
  studio. And usually I'm just, you know,
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  listening to the radio, drinking my coffee, not thinking about
• 0:15
  much. But today, I found myself
• 0:17
  gripping the steering wheel a little tighter.
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  I was looking up at those huge cables, you know, the ones as
• 0:23
  thick as my body, and then looking down at the concrete
• 0:26
  Piers. And instead of thinking, wow,
• 0:28
  what a marvel of engineering, I was thinking, my God, look at
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  the millions of ways this thing could kill me.
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  That is a very, very common side effect of reading the material
• 0:37
  we've covered for today. I bet you start to see the world
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  not as a collection of solid objects, but as a collection of
• 0:45
  invisible forces all trying to tear those objects apart.
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  Exactly. It's like I've taken the red
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  pill. Because we aren't just talking
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  about how to build things today, are we?
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  We're talking about the dark side of engineering, the study
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  of failure. It is the burden of the engineer
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  in a way. You know, people think
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  engineering is about creation, and it is, of course it is.
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  But more than that, it's about prediction.
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  Prediction. It's the study of limits.
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  How much can a material take before it stretches?
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  How much before twists? When will it corrode?
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  And you know the ultimate question exactly when and how
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  will it snap? And that's really the mission
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  for this deep dive. We've gone through two absolute
• 1:24
  tomes of technical literature, specifically looking at stress
• 1:28
  analysis from one source and failure considerations from
• 1:31
  another. Two massive texts, yeah.
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  And my goal today is to bridge that gap, pun fully intended,
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  between the abstract math, all the Greek letters, the formulas
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  on the page, and the real world consequences.
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  We're talking about preventing planes from falling out of the
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  sky. We're talking about why a bolt
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  on my lawnmower snaps when I barely feel like I've touched
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  it. And it is a fascinating journey
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  because whether you are designing a a high pressure jet
• 1:56
  engine, turbine blade or just, I don't know, building a deck in
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  your backyard, the physics are exactly the same.
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  It's all the same rules. Understanding how forces flow
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  through matter, where they concentrate.
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  That's the difference between a working machine in a pile of
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  scrap. OK, so let's unpack this.
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  We have to start with the vocabulary, the language of
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  load. If we're going to talk about
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  things breaking, we have to talk about stress and strain for
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  fundamentals. Now, in normal English, if I say
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  I'm under a lot of stress or I'm under a lot of stress, I
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  basically mean the same thing. I mean, I need a vacation,
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  right? But in your world, these are
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  totally different concepts, aren't they?
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  Completely different. They are cause and effect and
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  confusing them is probably the first mistake most people make
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  when they get into this field. So where do we start?
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  Stress. Let's start with stress.
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  Imagine you have a bar of steel just hanging from the ceiling
• 2:49
  and you attach a weight to the bottom of it.
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  You are pulling on it. That pulling force is the load.
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  OK, the weight. Right, but stress isn't just the
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  load. Stress is the load divided by
• 2:59
  the area it's acting on. Right, I saw the formula in the
• 3:01
  text. It's written as the Greek letter
• 3:03
  Sigma equals P / A. Correct, Sigma is the unit
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  stress, P is the force the load and a is the cross-sectional
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  area. Now, why do we do this and why
• 3:15
  bother dividing by the area? I assume it's to make it fair to
• 3:18
  like compare apples to apples. Precisely.
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  That's a perfect way to put it. Think about it this way.
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  If I put 1000 lbs of force on a massive thick steel column like
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  the kind holding up a building. Column doesn't even notice.
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  It's negligible, but if I put that same 1000 lbs of force on a
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  thin piano wire. Snap.
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  It's gone. Immediate failure.
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  Right, the force the P was the same in both cases, but the
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  result was totally different. So force by itself is actually a
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  bad way to predict failure. Stress normalizes that force.
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  It tells us the intensity of the load.
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  I love the analogy of the snowshoe versus the stiletto
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  heel. That is the classic example,
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  isn't it? You can have a 200 LB person
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  wearing snowshoes walking across soft snow.
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  They don't sink. Why?
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  Big area. Because a 200 lbs is distributed
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  over a huge area. The P is 200 but the A is
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  massive, so the stress, the pressure on the snow is really
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  low. But put that same person in a
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  stiletto heel. And all 200 lbs is focused on a
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  tiny, tiny point. The area A is minuscule, so the
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  stress skyrockets and the heel just punctures the snow or your
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  hardwood floor. Right.
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  Or my floor. OK, so stress is the intensity
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  of the force. And you mentioned there are
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  three pillars of stress 3 flavors.
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  Yes, the way the force is applied matters a lot.
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  First, there's tension. This is pulling.
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  Imagine a tug of war rope. You were literally trying to
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  pull the atoms in the rope apart from each other.
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  OK, pulling. Got it. 2nd is compression.
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  This is the opposite. It's crushing.
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  Think of the concrete pillars holding up that bridge you drove
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  over. Gravity is pushing down on the
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  road, the ground is pushing up and the pillar is being squeezed
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  in the middle. Forcing the atoms closer
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  together. Forcing them closer, yes, yeah.
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  And the third one. This is the one that always gets
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  me sheer. Sheer it's the tricky 1.
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  Tension and compression act along the line of the object.
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  Sheer acts across it. The the best way to think of it
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  is a deck of cards. You put the deck on a table.
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  You put your hand on the top of the deck and slide it forward.
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  While the table holds the bottom of the deck.
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  Still, the cards slide over each other.
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  That sliding action is sheer. That is sheer stress.
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  Scissors work on sheer stress. That's why they're sometimes
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  called sheers. One blade goes up, one blade
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  goes down, and the paper in the middle experiences A sliding
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  failure. It doesn't stretch, it slices.
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  OK. So that's stress.
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  That is what we are doing to the material, the Causeway.
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  Now let's talk about strain. This is the effect.
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  Yes, strain is the response. It's denoted by the Greek letter
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  epsilon, and technically it's defined as the deformation per
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  unit length. Deformation per unit length, So
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  how much it's stretched divided by how long it was to start with
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  is that. It that's it exactly.
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  If you have a 10 inch rubber band and you stretch it by 1
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  inch, the total deformation is 1 inch.
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  The strain is 1 / 10.1. It's a dimensionless measure of
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  the geometric change in the material.
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  So if stress is the cause, the invisible force field inside the
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  metal strain is the effect, the actual physical movement that we
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  can see and measure. That is a perfect way to
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  visualize it. And for centuries, engineers and
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  scientists, you know, they've tried to figure out exactly how
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  these two relate. If I pull twice as hard, does it
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  stretch twice as much? And the answer is yes, for a
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  while at least. For a while, yes.
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  This brings us to the brilliant Robert Hook and Hook's Law.
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  Back in the 17th century, Hook discovered that for most
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  structural materials, steel, aluminum, wood, bone even, there
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  is a beautiful linear relationship.
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  Linear, meaning a straight line on a graph.
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  A perfect straight line. If 100 LB stretches at 1mm, then
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  200 lbs stretches at 2 millimeters, 300 pounds, 3mm.
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  It is perfectly predictable. We call this the proportional
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  limit. And the slope of that line, that
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  magic number that defines the relationship for a given
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  material. That is the modulus of
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  elasticity. We often call it Young's modulus
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  or just capital. EI always struggled with this
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  concept in school. Is E just how strong the
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  material is? No, and that is a crucial,
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  crucial distinction. E is not strength, E is
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  stiffness. OK, what's the difference?
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  Think of a rubber band and a piece of steel wire there, both
• 7:19
  the same size. You can stretch the rubber band
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  easily, right? It has a low modulus, it's
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  flexible, floppy. The steel wire is incredibly
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  hard to stretch. It resists deformation.
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  It has a very high modulus. It is stiff, but strength is
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  about when it breaks. You can have a material that is
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  very stiff but breaks easily, like glass, or material that is
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  floppy but very hard to break, like a bungee cord.
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  Young's modulus just tells you how much it will stretch for a
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  given load within that elastic region.
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  Got it. So steel is stiff, rubber is
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  flexible, diamond is incredibly stiff.
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  Correct. And there's another layer of
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  nuance here that I just find fascinating.
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  Poissons ratio, the Greek letter nu.
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  This is the 3D part of the puzzle, right?
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  It is because nothing happens in isolation.
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  When you stretch that rubber band, you are pulling it longer.
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  That's the longitudinal strain. But look closely at the middle
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  of the band. What happens to its width?
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  It gets skinnier and next down in the middle.
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  Exactly. To get longer, it has to get
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  thinner. Nature tends to conserve volume.
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  Poisson's ratio is simply the ratio of that sideways shrinking
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  to the lengthwise stretching the lateral strain to the
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  longitudinal strain. I saw in the notes that for
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  steel it's about .3 and for concrete it's like .1.
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  Right. Which tells us something,
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  doesn't it? It says that steel is much more
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  cooperative in rearranging its shape than concrete is.
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  Concrete just kind of sits there and resists.
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  It doesn't like to get skinny. OK, so we're pulling on this bar
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  of steel. We're measuring the stress,
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  we're measuring the strain. We can plot this on a graph, the
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  famous stress strain diagram. The biography of the material.
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  It really looks like a medical chart.
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  It tells you the story of the materials life from beginning to
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  end. It really does.
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  It tells you everything you need to know about its personality.
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  Let's walk through the life of a piece of, say, structural steel,
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  like the kind in your bridge. OK, so we start at 0 stress,
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  zero strain, we apply load. We are climbing up that straight
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  line Hook's law is in effect. We are in the elastic range.
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  This is the safe zone for design a happy place.
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  If you take the load off right now, the steel snaps back to its
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  original shape perfectly. No harm, no foul.
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  The atoms were just pulled apart slightly, like they're on tiny
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  springs, and then they just sprang back.
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  Perfect. Analogy.
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  Yeah, but then we hit a point where the line stops being
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  perfectly straight, the proportional limit.
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  The end of hooks law. Yes, the relationship gets a
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  little fuzzy here, but we are still elastic.
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  We can go a tiny bit further to the elastic limit.
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  This is the absolute point of no return the.
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  Point of no return. That sounds ominous.
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  It is because once you cross the elastic limit, you hit the yield
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  point and this is where the magic or the damage happens.
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  The material yields. Yields as in It it gives up, it
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  surrenders. Sort of.
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  It stops acting like a spring and starts acting like taffy or
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  clay. It begins to flow.
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  This is plastic deformation. Plastic deformation permanent.
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  Permanent. The crystal layers inside the
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  metal are actually sliding over each other, we call them slip
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  lanes and getting stuck in new positions.
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  If you take the load off now, it won't go back to its original
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  length. It is permanently stretched.
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  You have bent the paper clip. But it haven't snapped yet.
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  Not even close. No.
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  In fact, steel does something incredible here.
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  After it yields, it actually gets stronger.
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  It's called strain hardening. How does that work?
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  As those crystal layers slide and tangle up, they create a
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  mess of dislocations that block further movement.
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  It's like a traffic jam on the atomic level.
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  So you have to pull even harder to get it to stretch more.
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  The curve actually goes up again.
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  It fights back. It fights back hard until it
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  hits the peak of the curve. The ultimate tensile strength,
• 10:54
  the. Highest stress it can ever serve
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  all the. Absolute maximum.
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  Once you pass that peak, the game is over.
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  The material starts to neck down visibly.
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  You can see get very thin in one spot and then POW.
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  Rupture. Rupture, the breaking strength.
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  The end of the story. Now, the distance on that graph,
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  the amount of stretch between that yield point and the final
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  snap seems really, really important.
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  It is absolutely critical that amount of plastic deformation
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  defines whether a material is ductile or brittle.
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  And ductile is the taffy, the stretchy stuff.
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  Structural steel, aluminum, copper, gold.
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  They stretch a lot. Before they break, they give you
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  a warning. A warning.
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  If a steel beam in a building is overloaded, it will sag, It will
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  bend visibly. You can see it and say we need
• 11:41
  to get out of here. And brittle.
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  Brittle is glass, cast iron, ceramics.
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  You pull on them, they stretch a tiny, tiny bit in that elastic
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  range, and then they just shatter.
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  No warning, no sagging, just a sudden, catastrophic explosion
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  of energy. So for a bridge we definitely
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  want ductile for everything basic.
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  For almost everything structural, yes, we want
• 12:01
  toughness. And an engineering toughness has
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  a very specific definition. It's the total area under that
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  stress strain curve. It's the ability to absorb
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  energy before fracturing. So it's not just about being a
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  strong. No.
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  A tough material is strong. It takes a lot of force, a high
• 12:17
  curve, but it's also ductile. It stretches a lot, a long
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  curve. That combination allows it to
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  absorb the energy of a truck hitting a pothole or an
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  earthquake shaking the ground without just snapping.
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  OK, so we've got the material science down.
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  We understand the personality of the steel.
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  Now let's look at the shapes we build with it.
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  Beams, shafts and columns. The building blocks of the
• 12:39
  mechanical world. Let's start with beams.
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  This is bending one O 1 and there is a concept here that I
• 12:44
  found really trippy. The neutral axis.
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  It sounds like something from Star Trek, but it's real
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  physics. It is the magical line.
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  It's very real. Think about a simple beam
• 12:55
  spanning across a room. You hang a heavy chandelier in
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  the middle. The beam bends down in a :)
• 13:00
  shape. Right, it's Sags.
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  Now think about what the wood or steel fibers are doing inside
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  that beam. The top surface of the beam is
• 13:07
  getting shorter. It's being crushed together.
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  It's in compression. The bottom surface of the beam
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  is getting longer. It's being pulled apart,
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  stretched. It's in tension.
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  So if the top is squished and the bottom is stretched
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  somewhere in the middle, there has to be a place where nothing
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  is happening. Somewhere in the middle there is
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  a single layer of fibers that is doing absolutely nothing.
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  It isn't getting shorter and it isn't getting longer.
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  The stress there is zero. That is the neutral axis.
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  That is wild. You have these huge forces,
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  tension and compression at the top and bottom and then just
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  dead palm right in the center. And that single insight leads to
• 13:44
  perhaps the most famous and useful formula in all of beam
• 13:48
  design, the flexor formula. Yes, Sigma equals M * C all
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  divided by I. That's the one.
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  Let's decode that. OK, Sigma is our old friend's
• 13:56
  stress. M is the bending moment, which
• 13:59
  is basically a measure of how hard we are trying to bend the
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  beam. Correct, and C is the distance
• 14:04
  from that neutral axis. So C tells us that the stress
• 14:07
  gets bigger the farther you get from the center.
• 14:09
  Exactly. The top skin and the bottom skin
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  are taking the worst beating. The stress is at its absolute
• 14:14
  maximum at the outer surfaces. OK, that makes sense.
• 14:17
  And then we have this capital I on the bottom of the fractions,
• 14:21
  the moment of inertia. Now, honestly, in high school
• 14:24
  physics, this was the concept that always, always tripped me
• 14:27
  up. Is it mass?
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  Is it weight? What is it?
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  It's neither really, and that's why it's confusing.
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  Think of I as a measure of geometrical stiffness.
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  It has nothing to do with the material itself.
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  It's not about how much steel you have, it's strictly about
• 14:43
  exactly where that steel is located relative to the neutral
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  axis. OK, help me visualize that.
• 14:49
  I need an analogy. The best 1 is a standard 2 by 4
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  wooden plank. If you lay it flat on 2 cinder
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  blocks, the wide weight like a bridge, right?
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  And you stand in the middle. It bells quite a bit, doesn't
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  it? It's bouncing.
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  I can picture that. Now take that exact same 2 by 4.
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  You haven't changed anything about it.
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  OK, but this time you turn it on its side so it's tall and
• 15:08
  skinny. Stand on it now.
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  It's incredibly stiff, it barely moves at all.
• 15:12
  Exactly. You haven't changed the
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  material, you haven't changed the mass or the weight.
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  It is the exact same amount of wood, but you change the
• 15:19
  distribution of the area relative to the axis of bending.
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  By moving the wood vertically far away from the center, you
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  have exponentially increased I and.
• 15:28
  Since I is in the denominator of the stress equation, a huge I
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  means a tiny stress. A tiny stress and this explains
• 15:37
  the i-beam. It's not just a letter of the
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  alphabet, it's a genius level strategy.
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  It's a strategy to cheat gravity.
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  It is. You take all the steel out of
• 15:45
  the middle near the neutral axis where it's doing almost nothing,
• 15:47
  and you push it out to the top and batum flanges the extremes.
• 15:51
  You're putting the soldiers on the front lines where the war is
• 15:53
  being fought. That makes so much sense now.
• 15:55
  OK, so moving from bending to twisting torsion shafts like the
• 16:01
  drive shaft in a car? A very common application, yes.
• 16:04
  Here we aren't dealing with tension and compression so much
• 16:06
  as we're dealing with sheer You are twisting the bar and
• 16:10
  justice. Like with bending, the
• 16:12
  distribution of the material matters enormously.
• 16:15
  Where do you think the stress is in a twisting rod?
• 16:18
  Well, based on the beam logic, I'm going to guess it's zero in
• 16:22
  the very center and it's at a maximum on the outside surface.
• 16:25
  Spot on. The absolute center of a
• 16:28
  spinning shaft carries 0 torsional load.
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  It's just along for the ride. The outer skin is doing all the
• 16:34
  work, experiencing the maximum shear stress.
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  Which explains why so many Dr. shafts and axles and even light
• 16:41
  poles are hollow tubes. Precisely why pay for the heavy,
• 16:45
  expensive steel in the middle if it isn't doing anything?
• 16:48
  A hollow tube can handle nearly the same amount of torque as a
• 16:51
  solid rod of the same diameter, but at a fraction of the weight
• 16:54
  and cost. Nature, or I guess engineering
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  is lazy or efficient. Efficient.
• 16:59
  Always efficient. OK, last one in this section,
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  Columns. This is where things get a
• 17:03
  little sketchy because columns fail in a really weird way.
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  Buckling. Buckling is terrifying to
• 17:08
  engineers because it's an instability failure.
• 17:11
  It's not about strength. What do you mean by that?
• 17:14
  Well, if you have a short stubby block of steel, like a little
• 17:17
  cube, you have to literally crush it to make it fail.
• 17:20
  That takes millions and millions of pounds.
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  But if you take that same steel and make it into a long skinny
• 17:26
  rod. Like a yardstick.
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  Exactly like a yardstick. You push on the ends with just a
• 17:30
  little force and suddenly POP. It bows out sideways, it kicks
• 17:35
  out. You didn't crush the wood, you
• 17:36
  didn't even get close to the yield strength of the material.
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  It just gave up. It became unstable.
• 17:41
  And there's a famous formula for this, right?
• 17:43
  The Euler formula. Leonhard Euler.
• 17:45
  He figured out that the critical load, the load at which it
• 17:48
  buckles, depends very, very heavily on the length.
• 17:51
  In fact, it depends on the length squared in the
• 17:53
  denominator. Whoa, squared.
• 17:54
  So if you double the length of a column, you make it 4 times
• 17:58
  weaker against buckling. Four times weaker.
• 18:01
  It's a huge penalty and that's why you see all that cross
• 18:04
  bracing and scaffolding or radio towers.
• 18:06
  They are trying to shorten the effect of length of the columns
• 18:09
  to prevent that sudden buckling snap.
• 18:11
  The source material also mentions the second formula.
• 18:15
  It says Euler's formula assumes everything is perfect.
• 18:18
  Which of course, never happens in real life, right?
• 18:20
  In the real world, the column is never perfectly straight.
• 18:23
  The load is always a little tiny bit off center.
• 18:26
  We call that eccentricity. The secant formula is a much
• 18:30
  more complex but more realistic formula that accounts for that
• 18:34
  initial imperfection, that wobble.
• 18:36
  It's the real world version of the math that tells you things
• 18:40
  are going to fail even sooner than the perfect Euler case
• 18:42
  predicted. Comforting.
• 18:45
  Now, Speaking of the real world, real parts rarely see just one
• 18:48
  type of load. This brings us to combined
• 18:51
  stresses. A real part doesn't just get
• 18:54
  pulled or just get twisted. It gets everything at once.
• 18:57
  Oh absolutely. Imagine a crankshaft in a high
• 19:00
  performance race car. It's spinning at 8000 RPM.
• 19:04
  The explosions in the cylinders are banging down on it.
• 19:06
  That's bending. The resistance from the wheels
• 19:08
  is trying to stop it from spinning.
• 19:10
  That's torsion. The whole thing is incredibly
• 19:12
  hot, so it's trying to expand. Thermal stress.
• 19:14
  Exactly. It's a chaotic storm of forces
• 19:17
  acting in every direction simultaneously.
• 19:19
  So how on earth do we even begin to calculate?
• 19:22
  Will it break if the forces are pointing in 10 different
• 19:25
  directions? We use a clever mathematical
• 19:28
  technique to find what we call the principal stresses.
• 19:32
  Basically we take a tiny imaginary cube of material
• 19:34
  anywhere inside the part and we use math, basically
• 19:38
  trigonometry, to rotate that cube in our minds.
• 19:41
  We spin it around till we find the one specific angle where the
• 19:45
  pulling stress, the tension is at its absolute maximum and the
• 19:49
  shear stress is 0. So we're looking for the worst
• 19:51
  case scenario angle. We are finding the absolute
• 19:54
  worst case tension and the worst case shear at that point, and
• 19:57
  there's a graphical tool for this called Moore's Circle.
• 19:59
  I saw that it looks like something from a geometry.
• 20:02
  It is, but it's a brilliant way to visualize this complex 3D
• 20:06
  stress state. In 2D, you plot your known
• 20:09
  stresses on a graph, draw a circle, and the edges of the
• 20:12
  circle instantly tell you your maximum principal stress and
• 20:15
  your maximum shear stress. If the circle gets too big and
• 20:18
  touches the failure line, you're in trouble.
• 20:20
  But trouble is subjective, isn't it?
• 20:23
  This brings us to the theories of failure.
• 20:25
  I was honestly surprised by this.
• 20:27
  I thought there was just one rule, if the stress is bigger
• 20:30
  than the strength it breaks, but it's not that simple.
• 20:33
  No, it's not, because strength depends on how you attack the
• 20:37
  material. Is it ductile?
• 20:39
  Is it brittle? How is it loaded?
• 20:41
  So we have different theories for different materials and
• 20:43
  situations. OK, let's breakdown the big
• 20:45
  three mentioned in the text. First, the maximum stress
• 20:49
  theory, also called rankers theory.
• 20:51
  This is the simplest one. It's the weakest link theory.
• 20:54
  It says I don't care about the complex combination of stresses.
• 20:58
  If the pulling force in any any One Direction hits the breaking
• 21:01
  point of the material, the whole thing snaps.
• 21:03
  And this works for brittle stuff like glass.
• 21:05
  Exactly. Think of a piece of chalk.
• 21:08
  If you twist it, it doesn't shear flat, it snaps on a clean
• 21:10
  45° angle. Why?
• 21:12
  Because that's the angle where the tension was highest.
• 21:15
  Rankine works great for chalk, glass and cast iron.
• 21:18
  But it's dangerous for steel. Very dangerous.
• 21:21
  Steel is ductile. It doesn't care that much about
• 21:24
  being pulled. It cares about sliding.
• 21:26
  It fails and shear. So for steel ranking might
• 21:30
  predict you're safe when you're actually about to yield.
• 21:33
  For steel, a better, more conservative choice is the
• 21:36
  maximum shear theory or guests theory.
• 21:39
  And that one just says that failure happens when those
• 21:41
  sliding layers, the shear stress hits its limit.
• 21:44
  Correct. It says yielding begins when the
• 21:46
  maximum shear stress in the part equals the shear stress that
• 21:50
  would cause yielding in a simple tension test.
• 21:52
  It's a safer bet for ductile metals.
• 21:54
  But then there's the third one, the one the text calls the gold
• 21:57
  standard, the distortion energy theory, also known as von Mises
• 22:01
  stress. Von Mises.
• 22:03
  This is what every single computer simulation, every
• 22:06
  finite element analysis program uses today.
• 22:09
  It's a bit more abstract, but it's incredibly accurate.
• 22:11
  Yeah, I struggled with this one. Distortion energy.
• 22:14
  What does that actually mean? OK, think about a balloon filled
• 22:17
  with water. If you take that balloon and you
• 22:19
  lower it deep into the ocean, the water pressure is immense,
• 22:22
  right? It's crushing the balloon from
• 22:24
  every equally. OK.
• 22:25
  That's called hydrostatic pressure.
• 22:27
  Right now, does the balloon change shape?
• 22:30
  No, it just gets smaller. It shrinks, but it stays a
• 22:34
  sphere. Exactly.
• 22:35
  It changes the volume, but it does not distort.
• 22:37
  And it turns out that materials, especially ductile ones, can
• 22:41
  withstand enormous amounts of hydrostatic pressure without
• 22:44
  yielding. What breaks things is not the
• 22:47
  pressure itself, but the distortion, the energy that goes
• 22:51
  into changing the shape from a sphere to, say, an egg.
• 22:55
  So von Mises calculates only that bad energy, the shape
• 22:58
  changing energy. Precisely.
• 23:00
  It cleverly subtracts out all the safe hydrostatic pressure
• 23:04
  and calculates only the energy stored in the material from
• 23:06
  being distorted. And it says the material will
• 23:08
  yield when that distortion energy hits a critical limit.
• 23:11
  It is the most accurate predictor we have for when steel
• 23:14
  will actually yield. So if I see one of those
• 23:16
  colorful engineering stress maps on a computer, the red danger
• 23:19
  zone is showing me high von Mis stress. 99% of the time, yes,
• 23:23
  that's what you're looking at. Before we leave this, we have to
• 23:25
  talk about stress concentration. The text used a force flow
• 23:28
  analogy that really clicked for me.
• 23:30
  This is one of the most important and often overlooked
• 23:33
  concepts in design. We tend to think stress is
• 23:36
  spread out evenly, like butter on toast, but it's not.
• 23:40
  Stress flows more like water in a river.
• 23:42
  So if the river is wide and straight and smooth, the water
• 23:46
  is calm. It flows evenly.
• 23:49
  But what happens if you stick a giant sharp edged boulder in the
• 23:51
  middle of that river? The water has to rush around it.
• 23:54
  It speeds up. It gets all turbulent right at
• 23:56
  the edges of the rock. Exactly.
• 23:59
  In a material, that boulder is a hole or sharp notch or sudden
• 24:04
  change in diameter. The lines of force can't go
• 24:06
  through the hole, so they have to crowd together to get around
• 24:09
  the edges. And that crowding means the
• 24:10
  local stress is higher right there.
• 24:12
  Much much higher. We have a term for it, the
• 24:14
  stress concentration factor or K sub T for a nice smooth plate in
• 24:18
  tension. The stress is let's say 10,000
• 24:21
  PSI if you drill a simple circular hole in the middle of
• 24:24
  that plate. The stress goes up.
• 24:26
  The stress right at the top and bottom edge of that hole jumps
• 24:29
  to 30,000 PSI. It triples just because of a
• 24:32
  simple hole. It triples.
• 24:34
  And This is why engineers are absolutely obsessed with
• 24:36
  fillets. Those nice smooth rounded
• 24:39
  corners you see on machine parts?
• 24:41
  Sharp 90° corners are death. They are massive stress
• 24:45
  concentrators. A rounded corner let's that
• 24:48
  river of force flow smoothly around the bend instead of
• 24:51
  crashing into a wall. That is a perfect segue into our
• 24:54
  next section because those little stress concentrations,
• 24:57
  those little notches and scratches are usually where the
• 25:00
  silent killer begins its work Fatigue.
• 25:02
  Fatigue. Yes, this is the big one.
• 25:05
  This accounts for the vast, vast majority of mechanical failures
• 25:08
  in history, and it is in many ways the most frightening type
• 25:12
  of failure because it feels like a betrayal by the material.
• 25:15
  OK, I have to stop you there because this sounds like a
• 25:16
  complete contradiction. We just spent 20 minutes
• 25:19
  establishing that steel has a yield strength and an ultimate
• 25:22
  strength. The whole point of the stress
• 25:24
  strain curve is that if I stay below those numbers, if I'm in
• 25:27
  the safe elastic zone, the math says the part shouldn't break.
• 25:32
  The static math says that the math for a one time poll.
• 25:36
  So you're telling me I can follow all the rules?
• 25:38
  I can design my part so the stress is way way down in the
• 25:40
  safe zone where Hook's law says everything just springs back
• 25:43
  perfectly and the part will still fail?
• 25:46
  That feels like the material is cheating.
• 25:48
  It feels that way, doesn't it? Yeah, It's the difference
• 25:50
  between lifting a heavy box one time and bending a simple paper
• 25:54
  clip back and forth 100 times. The force to bend the paper clip
• 25:57
  is tiny. You aren't overloading it in the
• 25:59
  traditional sense at all, but what are you doing to the
• 26:02
  crystal structure every time you bend it?
• 26:04
  I'm wiggling, I'm working it back and.
• 26:05
  Forth, you are introducing microscopic cumulative damage.
• 26:11
  Every single time you bend it, a tiny dislocation, a flaw in the
• 26:14
  crystal lattice moves a little bit.
• 26:16
  You do it once, it's fine. 10 times it's fine, but a million
• 26:19
  times those tiny dislocations start to punch out.
• 26:22
  They form a micro crack and then on cycle #1,000,001.
• 26:28
  Snap and this happens well below the yield. .0 way below it can
• 26:31
  happen at half the yield strength or even less depending
• 26:34
  on the conditions. That is fatigue failure under a
• 26:37
  fluctuating or cyclic load. We visualize this with something
• 26:40
  called the SN curve. The SN curve.
• 26:43
  It's the cornerstone of fatigue analysis.
• 26:46
  You plot stress the S on the vertical axis against the number
• 26:50
  of cycles to failure the N on the horizontal axis, which is
• 26:53
  usually a logarithmic scale. And it slopes down right.
• 26:56
  Higher stress, fewer cycles. Generally, yes.
• 26:59
  The lower the stress you apply in each cycle, the more cycles
• 27:02
  the park can survive. It's a downward sloping curve.
• 27:04
  But there's a really weird and important quirk here, especially
• 27:08
  between steel and aluminum, something called the endurance
• 27:11
  limit. This is one of the miracle
• 27:13
  properties of steel and one of the reasons we build bridges and
• 27:16
  engine blocks out of it. For steel and other ferrous
• 27:19
  alloys, that downward SN curve eventually flattens out.
• 27:23
  It becomes horizontal. It hits a floor.
• 27:26
  We call that the endurance limit or fatigue limit.
• 27:28
  It means if you design your part so the cyclic stress is below
• 27:31
  that floor, the steel will theoretically last forever.
• 27:34
  Infinite life. You can cycle it a billion a
• 27:37
  trillion times and it just won't fail from fatigue.
• 27:40
  That's incredibly reassuring, but not for aluminum.
• 27:43
  Aluminum is different. Non ferrous metals like
• 27:46
  aluminum, magnesium, copper, their SN curve never flattens
• 27:50
  out, it just keeps going down and down and down, getting
• 27:55
  closer and closer to 0. So you're saying aluminum will
• 27:57
  eventually fail no matter how gentle you are with it?
• 28:00
  Given enough cycles, yes, even at very tiny stress levels,
• 28:04
  there is no infinite life stress for aluminum.
• 28:07
  And that is why aircraft, which are mostly made of aluminum,
• 28:10
  have very strict mandatory life stands.
• 28:13
  We count the cycles. Every take off and landing is a
• 28:16
  cycle. It's a major pressurization
• 28:17
  cycle on the fuselage. Yes.
• 28:19
  When a plane hits its designated cycle limit, it's done.
• 28:22
  We have to retire it or do a major structural overhaul
• 28:25
  because we know the fatigue cracks are statistically
• 28:28
  inevitable. That is slightly terrifying to
• 28:29
  think about next time I'm in a window seat looking at the wing
• 28:32
  flexing. It shouldn't be terrifying.
• 28:33
  It should be reassuring. It means we know the limit, we
• 28:36
  account for it, and we apply massive safety factors to stop
• 28:40
  well before we get there. OK.
• 28:42
  Now there are a lot of factors that can make fatigue even
• 28:44
  worse. The text highlighted surface
• 28:46
  finish as a big one. Oh, a huge factor.
• 28:48
  Remember our stress concentration discussion.
• 28:50
  Yeah, the notches and holes. Well, if you have a rough
• 28:53
  surface finish from machining or grinding, or even just
• 28:57
  scratches, each one of those tiny scratches is a microscopic
• 29:01
  notch, a tiny stress concentrator.
• 29:04
  It's a premade starting point for a fatigue crack.
• 29:08
  So olishing a critical part isn't just for making it look
• 29:10
  pretty. Not at all.
• 29:11
  It's for survival. A polished mirror finish.
• 29:14
  Remove all those potential starter cracks.
• 29:17
  It can easily double or triple the fatigue life of a component.
• 29:20
  What about the size of the part? The text mentioned a size
• 29:23
  effect. This is a weird statistical
• 29:25
  reality that trips a lot of people up.
• 29:27
  All other things being equal, bigger parts are weaker and
• 29:30
  fatigued than small parts. Wait.
• 29:31
  Weaker. That seems backwards.
• 29:33
  I know if I make a small pencil size steel rod and tested in the
• 29:37
  lab, it might last 1,000,000 cycles at a certain stress.
• 29:40
  If I build a giant propeller shaft out of the exact same
• 29:43
  steel, it might fail at only 500,000 cycles of that same
• 29:47
  stress level. It's a game of statistics and
• 29:50
  volume. A bigger part simply has more
• 29:53
  atoms. More volume means a higher
• 29:55
  statistical probability that there is a microscopic floss
• 29:59
  somewhere in that metal from the manufacturing process, a tiny
• 30:02
  piece of slag and inclusion A microscopic void.
• 30:06
  The bigger the haystack, the more likely you are to find the
• 30:08
  one needle that will start to crack.
• 30:10
  And of course, the environment, we have to talk about corrosion.
• 30:13
  Corrosion is a killer. If you are cycling a part in a
• 30:16
  salty or acidic environment. The corrosion creates pits in
• 30:20
  the surface. Each one of those pits is a
• 30:22
  perfect sharp bottom stress razor.
• 30:24
  It's like drilling thousands of tiny holes all over your part.
• 30:28
  It accelerates the fatigue process dramatically.
• 30:30
  The devastating 1-2 punch. OK, so we've got fatigue, which
• 30:34
  is the process of a crack starting and growing slowly.
• 30:37
  But what happens when that crack gets big enough?
• 30:39
  This brings us to Section 5, fracture mechanics.
• 30:42
  The text calls this a paradigm shift.
• 30:44
  It was a massive, massive shift in engineering thinking, really
• 30:47
  starting around world 4/2 and solidifying in the 50s and 60s.
• 30:51
  Before this, the design philosophy was based on the
• 30:54
  stress strain curve. We assumed materials were
• 30:56
  perfect continuous solids. Fraction mechanics starts with a
• 31:00
  much darker, more realistic assumption.
• 31:01
  It says the material is already cracked.
• 31:04
  They're already flaws from manufacturing.
• 31:06
  We can't see them, but they're there.
• 31:08
  Now what? That completely changes the
• 31:10
  question from Will it break to how fast is the existing crack
• 31:15
  growing and when does it become critical?
• 31:18
  Precisely. We stopped talking about average
• 31:20
  stress, and we start talking about the stress at the tip of a
• 31:22
  crack and we introduce a new variable.
• 31:25
  We talked about K sub D before the stress concentration factor.
• 31:29
  Now we talk about capital K, the stress intensity factor.
• 31:32
  The symbols are confusingly similar.
• 31:34
  They are, which is unfortunate, but the concept is very
• 31:36
  different. K describes the intensity of the
• 31:38
  stress field right at the sharp tip of a crack right, and the
• 31:42
  basic formula for it as a really scary term in it, it's that K is
• 31:46
  proportional to the stress times the square root of.
• 31:48
  A and a is the length of the crack.
• 31:50
  Yes, the square root of the crack length.
• 31:52
  This is huge. This means that as the crack
• 31:55
  grows, as A gets bigger, the stress intensity K gets bigger,
• 31:59
  and as K gets bigger, it drives the crack to grow even faster,
• 32:03
  which makes it even bigger still.
• 32:05
  It's a runaway positive feedback loop.
• 32:07
  It is an exponential runaway process.
• 32:09
  A crack might grow at a microscopic stable rate for
• 32:12
  years for 99% of the parts life. Then as it gets longer it starts
• 32:16
  growing inches per week, then feet per second.
• 32:19
  And there's a Cliff edge, a point of no return fracture
• 32:22
  toughness. K Subic.
• 32:24
  That is the Cliff edge. K so big is a fundamental
• 32:27
  property of a material. Just like yield strength, it's a
• 32:30
  measure of its resistance to a crack running wild.
• 32:32
  If the stress intensity factor K at the tip of your crack hits
• 32:36
  that critical value, case of bake game over.
• 32:39
  The crack becomes unstable. Meaning.
• 32:42
  Meaning it no longer needs any more cyclic load to grow, it is
• 32:45
  stored enough strain energy to tear itself apart.
• 32:49
  It unzips through the material literally at the speed of sound
• 32:53
  in that metal. That's when the wing falls off
• 32:55
  the plane. That's when the ship slits in
• 32:58
  two. In a cold sea, it happens faster
• 33:00
  than you can blink. So how do we design for this?
• 33:03
  We can't make everything perfect.
• 33:05
  The text mentions A philosophy called Leak before Break.
• 33:08
  This is a brilliant and life saving design philosophy,
• 33:11
  especially for things like pressure vessels, pipelines,
• 33:14
  rocket fuel tanks. So how does it work?
• 33:16
  You choose a material with a very high fracture toughness,
• 33:19
  and you design the wall thickness such that the critical
• 33:22
  crack length they needed for that final fast fracture is
• 33:26
  larger than the wall thickness of the vessel.
• 33:28
  OK, translate that for me. It means you design it so the
• 33:30
  crack will have to grow all the way through the wall and cause a
• 33:33
  leak before it gets long enough to cause the whole tank to
• 33:36
  explode. So the leak is the warning
• 33:37
  alarm, the puddle on the floor. The leak is the alarm.
• 33:40
  Exactly. If you see a jet of fluid
• 33:42
  shooting out, you shut down the system.
• 33:45
  It's a failure, yes, but it's a safe, detectable failure.
• 33:48
  If you don't have a leak before brake design, your first and
• 33:52
  only warning is the catastrophic explosion.
• 33:54
  I think I prefer the puddle. You all prefer the puddle.
• 33:57
  Moving on, there are other slower ways for things to fail.
• 34:01
  Section 6 talks about creep. This sounds like a slow motion
• 34:04
  horror movie. It is slow motion Creep is the
• 34:07
  tendency of a material to slowly move or deform permanently over
• 34:11
  time when it's under a constant load.
• 34:13
  Wait, the load doesn't change, but the part just keeps
• 34:15
  stretching by itself? Yes, usually this is a high
• 34:19
  temperature phenomenon. The classic example is a turbine
• 34:22
  blade in a jet engine. It's spinning incredibly fast,
• 34:25
  so centrifugal force is constantly pulling on it, and
• 34:27
  it's sitting in a gas stream that say 2000°F.
• 34:31
  Even though the stress from the spinning is well within the safe
• 34:34
  zone, the atoms are vibrating so violently from the heat that
• 34:38
  they can slowly slide past each other over hundreds of hours.
• 34:41
  So the blade physically gets longer.
• 34:43
  It grows like a glacier moving, and if you don't account for
• 34:47
  this in your design, the blade tip will eventually grow so long
• 34:50
  that it hits the outer casing of the engine and that's that's a
• 34:54
  very bad day. The text mentions 3 stages of
• 34:57
  creep. Right.
• 34:58
  There's primary creep, where the rate of stretching starts fast
• 35:01
  and then slows down as the material strain hardens a bit
• 35:04
  than their secondary or steady state creep.
• 35:07
  This is the long slow constant rate stretching where the part
• 35:10
  spends most of its life. And finally there's tertiary
• 35:13
  creep, the end game. The end game, the material
• 35:16
  starts to develop voids and micro cracks internally.
• 35:19
  The stretching accelerates rapidly and then rupture.
• 35:22
  And different materials have very different temperature
• 35:24
  thresholds for this. Hugely different.
• 35:27
  A soft metal like lead will creep significantly at room
• 35:29
  temperature. That's why ancient lead roofs on
• 35:32
  European cathedrals have often sagged and flowed downhill over
• 35:35
  the centuries. Steel needs to get up around 650
• 35:38
  or 700°F to start creeping noticeably.
• 35:41
  The nickel based super alloys we use in jet engines can resist
• 35:44
  creep up to 2000° or more. And what happens when you mix
• 35:48
  creep and fatigue like in that turbine blade which is hot and
• 35:52
  vibrating? You get a nightmare.
• 35:54
  It's a synergistic effect where they make each other worse.
• 35:57
  The vibration from fatigue creates cracks.
• 36:00
  The high temperature from creep causes voids to form at the
• 36:04
  grain boundaries. The voids then link up, giving
• 36:07
  the fatigue cracks an easy path to travel.
• 36:10
  It drastically, drastically reduces the lifespan of the part
• 36:13
  compared to either one acting alone.
• 36:15
  Let's talk more about the environment, Section 7.
• 36:18
  We touched on corrosion, but there is a specific type of
• 36:20
  failure here that honestly just terrified me fretting.
• 36:24
  Fretting the hidden enemy. It's so insidious because it
• 36:27
  happens in places you think are solid and safe, like a bolted or
• 36:30
  riveted joint. So nothing is visibly moving.
• 36:33
  Nothing you can see, but imagine 2 plates bolted together in a
• 36:36
  machine that vibrates their clan tight, but because of the
• 36:39
  vibration there is microscopic relative motion between the two
• 36:43
  surfaces. They're slipping back and forth
• 36:45
  by just a few micrometers. And that tiny little rubbing
• 36:48
  motion is the problem. It's a huge problem.
• 36:50
  It acts like a sub microscopic sandpaper.
• 36:52
  It rubs off the protective oxide layer on the metal, exposing
• 36:56
  fresh metal, which then instantly oxidizes and that gets
• 36:59
  rubbed off. It grinds the metal into a very
• 37:01
  fine powder, usually a black or reddish brown dust.
• 37:05
  In the aviation world, we call it Cocoa.
• 37:07
  And that dust. That cocoa is abrasive and the
• 37:10
  process creates tiny pits in the surface.
• 37:13
  And what are pits? Stress concentrations.
• 37:15
  Exactly. Which then become the initiation
• 37:17
  sites for fatigue cracks. And the truly scary part is this
• 37:21
  is all happening inside the joint where you can't see it.
• 37:24
  The mechanic looks at the bolt head and it looks perfectly
• 37:27
  fine, but inside the joint is bleeding metal dust and growing
• 37:30
  a crack that's about to cause failure.
• 37:32
  The other environmental killer mentioned was stress corrosion
• 37:35
  cracking, or SCC. This felt like a chemical
• 37:38
  detective story. It is.
• 37:40
  SCC is the perfect storm of material failure.
• 37:42
  You need three things to happen at the same time.
• 37:44
  If you only have two, you're fine.
• 37:46
  OK, what's the deadly trio? First, you need a susceptible
• 37:49
  material. Second, you need a specific,
• 37:51
  often seemingly harmless, corrosive environment.
• 37:54
  And 3rd, you need a sustained tensile stress.
• 37:58
  If you have all three. Disaster a sudden, brittle like
• 38:02
  failure in a normally ductile material.
• 38:04
  The classic historical example is the season cracking of brass
• 38:08
  ammunition cartridges used by the British Army in India.
• 38:12
  They store their ammunition in horse stables.
• 38:15
  The horse urine in the stables create ammonia fumes in the air.
• 38:18
  Well, it turns out the brass is highly susceptible to ammonia.
• 38:21
  So that's two susceptible brass corrosive ammonia.
• 38:24
  And the third, the bullet casing was under a constant tensile
• 38:27
  stress from the manufacturing process where it was crimped
• 38:30
  around the bullet. The perfect storm.
• 38:32
  Perfect storm. The cartridges were just split
• 38:34
  and crack open while sitting inertly in the boxes.
• 38:37
  The chemical attacks the grain boundaries in the metal,
• 38:39
  weakening them, and the stress just pulls them apart.
• 38:42
  It can cause a stainless steel pipe in a chemical plant to
• 38:45
  shatter like glass if just a trace amount of the wrong
• 38:48
  chloride is present. We've covered a lot of ways
• 38:50
  things can die today, which brings us to our last section,
• 38:53
  Failure analysis. This is the CSI portion of the
• 38:56
  show. It is forensics for machines.
• 38:59
  When a bridge falls or a plane crashes, the NTSB or engineering
• 39:02
  team goes in. We don't just ask did it break,
• 39:05
  we ask what was the failure mode and more importantly, what was
• 39:10
  the root cause. What's the difference between
• 39:12
  those two? The failure mode is the physical
• 39:14
  process. It failed by high cycle fatigue
• 39:17
  or it failed by ductile overload.
• 39:20
  The root cause is the human error behind it.
• 39:23
  It failed by fatigue because the designer specified a sharp
• 39:26
  corner in a high stress area or because the mechanic used the
• 39:29
  wrong bolt. And you can tell all that just
• 39:31
  by looking at the broken pieces. The fracture surface tells the
• 39:33
  truth. It's the black box recorder, the
• 39:35
  failure. We look for things like beach
• 39:36
  marks. Beach marks, like at the ocean.
• 39:39
  Exactly. In fatigue, the crack grows a
• 39:41
  little bit with these cycle or block of cycles.
• 39:44
  Every time the machine stops and starts, it can leave a tiny
• 39:47
  curved Ridge on the crack face. They look just like the ripples
• 39:50
  in the sand on a beach or like tree rings.
• 39:53
  By looking at them under a microscope we can literally see
• 39:56
  the cracks history and tell how long it was growing.
• 39:58
  This crack started three months ago right here at The Scratch.
• 40:01
  Exactly. If the surface is dull and
• 40:03
  cyberus with a lot of distortion, it was a ductile
• 40:06
  overload. It was ripped apart slowly.
• 40:08
  If it's shiny and granular and flat, it was a sudden brittle
• 40:11
  fracture. It snapped cleanly.
• 40:13
  The evidence is always there. And the goal of all this isn't
• 40:16
  just to assign blame for a lawsuit.
• 40:18
  No, not at all. The primary goal is
• 40:20
  retrospective design. Every time something fails, we
• 40:23
  learn a profound lesson. We rewrite the textbooks, we
• 40:27
  update the building codes and design standards.
• 40:29
  We change the safety factors. The formulas we discussed today,
• 40:32
  Euler von Mises, all of fracture mechanics.
• 40:35
  Many of them were refined or even created because of past
• 40:38
  disasters that forced us to understand why they happened.
• 40:42
  That is a very sobering thought. The engineering code book is
• 40:45
  written in blood. In many ways it is, but it is
• 40:48
  also hopeful because we learn we don't make the same mistake
• 40:51
  twice. Or at least we try very, very
• 40:53
  hard not to. You know, we started this deep
• 40:56
  dive talking about a bridge and my anxiety about driving over it
• 41:00
  this morning. But honestly, after unpacking
• 41:02
  all this, after staring into the abyss of failure for an hour, I
• 41:07
  think I actually feel better. Why is that?
• 41:09
  That seems counterintuitive. Because I realize it's not
• 41:12
  magic. It's not just luck holding that
• 41:13
  bridge up. It's math It's testing.
• 41:16
  It's a deep, obsessive, and honestly humbling understanding
• 41:19
  of stress, fatigue, fracture, and creep.
• 41:22
  It's knowing all the ways it can fail that allows us to build it
• 41:25
  so it won't. That's it.
• 41:26
  Engineering is a battle. A battle against the elements,
• 41:29
  against time and against the fundamental forces of nature.
• 41:32
  And by understanding the enemy, by studying and respecting the
• 41:35
  failure modes, we can win that battle.
• 41:38
  We can build a safer, more reliable world.
• 41:40
  So what does this all mean for you, the listener?
• 41:43
  Well, next time you are on a plane, or mowing a lawn, or just
• 41:46
  crossing that bridge, take a second to look at the metal.
• 41:48
  Think about the invisible war going on inside the atomic
• 41:52
  lattice, the constant tug of war of stress, the slow creeping
• 41:56
  glacier of high temperature, the silent cumulative memory of
• 42:00
  fatigue counting every single vibration.
• 42:04
  And appreciate that someone, somewhere did the math to make
• 42:07
  sure that working machine didn't become a pile of scrap.
• 42:10
  Well said, A deep respect for the materials.
• 42:13
  If you haven't already, get over to our YouTube channel
• 42:15
  Mechanical Engineering Made Simple, where we post hands on
• 42:18
  how to videos, visual breakdowns, and practical
• 42:21
  engineering walkthroughs. You can actually use a family
• 42:24
  that solves together, stays together.