Latest / Mechanical Engineering Made Simple / (#102)Yield Strength Stress and Eccentric Joint Failure

Transcript

(#102)Yield Strength Stress and Eccentric Joint Failure · Mechanical Engineering Made Simple

• 0:00
  Welcome back, design junkies, to Mechanical Engineering Made
• 0:02
  Simple. Today we are undertaking a
• 0:05
  critical deep dive into really the foundation of any successful
• 0:09
  construction or machine design. We're talking about the
• 0:12
  principles of strength and materials and, just as
• 0:15
  important, engineering material selection.
• 0:18
  This is it. This is the knowledge that turns
• 0:20
  all those abstract concepts from a materials data sheet.
• 0:23
  You know, all those numbers like CI, pounds per square inch into
• 0:27
  a real practical structure. Something you can actually
• 0:30
  guarantee will not fail. Right.
• 0:31
  So our mission here is to understand not just what a
• 0:34
  material is, but how it behaves. Exactly how it behaves when you
• 0:38
  apply external forces, whether they're static, dynamic or
• 0:41
  cyclic, and what happens when it deforms.
• 0:44
  OK, let's start where every good design process has to begin with
• 0:47
  the vocabulary, the language of force and change.
• 0:50
  We're talking about stress and strain.
• 0:52
  Now we know stress is that internal force per unit area,
• 0:55
  but let's quickly clarify strain, because that's the
• 0:58
  fundamental measure of deformation, isn't it?
• 1:00
  It is strain is. It's simply the measure of
• 1:03
  dimensional change relative to its original size.
• 1:06
  It's a unit of deformation, so. It's a ratio.
• 1:08
  It's a ratio. If you're stretching A
• 1:10
  component, you just take the total length that changed by and
• 1:13
  you divide that by its initial original length.
• 1:15
  So for instance, if you stretch A6 inch bar by say 1/4 of an
• 1:19
  inch, the strain is just 0.25 / 6, which gives you about 0.042
• 1:26
  per inch. You're looking at relative
• 1:28
  movement, not the absolute change.
• 1:30
  And the beauty of most engineering materials, at least
• 1:33
  early on, is that this relationship is wonderfully
• 1:36
  linear. All thanks to hooks law.
• 1:38
  Precisely. Hooke's Law tells us that up to
• 1:40
  a certain point, we call it the proportional limit.
• 1:43
  The body deforms in direct proportion to the unit stress
• 1:46
  you put on it. That linearity is what makes
• 1:48
  predictable design even possible.
• 1:50
  You can see it perfectly in a simple mechanical spring.
• 1:53
  And when we quantify that specific linearity, we get the
• 1:56
  materials fingerprint of stiffness, the modulus of
• 2:00
  elasticity, or what most people call Young's modulus.
• 2:03
  Young's modulus, Yeah, it's the ratio of unit stress to unit
• 2:07
  strain, but only within that proportional zone.
• 2:10
  A high modulus means the material is incredibly stiff.
• 2:14
  It takes immense stress to get a tiny amount of strain.
• 2:17
  And a low modulus means it's more pliable.
• 2:20
  Right, it basically defines the materials resistance to elastic
• 2:23
  deformation. But I mean, designers spend most
• 2:26
  of their time thinking about what happens after that linear
• 2:29
  zone. That's where things get
• 2:31
  dangerous, where the material stops being predictable.
• 2:34
  That brings us to the elastic limit.
• 2:36
  This is the absolute maximum stress a material can handle and
• 2:40
  still. Snap back to its original shape.
• 2:42
  Exactly, and still fully returned to its original
• 2:44
  dimensions once you remove the load.
• 2:46
  For a lot of steels, we often just treat this as the same as
• 2:49
  the proportional limit, but the truly critical number for
• 2:52
  structural integrity is the yield strength.
• 2:55
  So why is yield strength so much more important than, say, the
• 2:58
  ultimate break point? Because yield strength is the
• 3:01
  maximum stress you can apply without causing permanent
• 3:03
  deformation. Think about it, if your bridge
• 3:06
  or your machine housing permanently bends even a little,
• 3:09
  it has failed. Even if it didn't snap into.
• 3:12
  Right. That permanent strain means your
• 3:13
  dimensional tolerances are gone, functionality is compromised,
• 3:17
  and the structure is now fundamentally rinker.
• 3:20
  It's over. I find it really interesting
• 3:22
  that for materials that don't have a nice clean yield point,
• 3:27
  like some alloys or plastics, we've had to sort of invent 1.
• 3:30
  We have. We use what's called the yield
• 3:33
  strength by offset method. It's just a standard way to draw
• 3:36
  a line on the stress strain curve, usually offset by a tiny
• 3:39
  percentage of strain, and that line defines the boundary where
• 3:43
  we say permanent deformation has officially begun.
• 3:46
  Now everyone knows ultimate strength, the tensile strength.
• 3:50
  That's the biggest number on the chart the absolute maximum
• 3:52
  stress material can take before it just fractures.
• 3:55
  Right. It's the very peak of the curve.
• 3:57
  But like you said, if you're designing against failure, you
• 3:59
  design against yield. If you hit the ultimate
• 4:01
  strength, it's already far, far too late.
• 4:05
  Let's shift gears just a little. Let's look at a couple pairs of
• 4:07
  material properties that define how we can actually use them.
• 4:10
  Yeah. First up, elasticity versus
• 4:13
  resilience. So we covered elasticity.
• 4:15
  That's the ability to snap back. Resilience, though, is a measure
• 4:20
  of the energy stored in the material while it's deforming.
• 4:23
  More importantly, it's the recoverable strain energy when
• 4:26
  the load is removed. OK, so like a bumper on a car A.
• 4:29
  Perfect example, You want it to absorb impact energy to form and
• 4:32
  then spring back without any permanent damage.
• 4:34
  That is resilience in action. And for manufacturing, we have
• 4:38
  ductility and malleability. They sound similar, but they're
• 4:41
  not. They both relate to formability,
• 4:43
  sure, but in totally different ways.
• 4:45
  Ductility is the ability to be drawn out into a long, thin
• 4:49
  wire. Think of copper power lines.
• 4:51
  Malleability, on the other hand, is the ability to be compressed
• 4:54
  or hammered or rolled into a thin sheet, like stamping out
• 4:57
  car doors or making aluminum foil.
• 4:59
  OK, let's connect this to our next segment, designing for real
• 5:02
  world failures. Because in the real world, you
• 5:05
  never, ever design a part to operate right up to its yield
• 5:08
  strength. You build in a factor of safety.
• 5:11
  The factor of safety or FS is a non negotiable mechanism to
• 5:16
  minimize risk. Historically, you'd take the
• 5:18
  yield strengths, let's call it S1, and you divide it by your
• 5:21
  chosen factor of safety FS to get your allowable working
• 5:25
  stress S. It gives you a.
• 5:27
  Buffer. A comfortable buffer.
• 5:28
  Although modern practice often defers to allowable design
• 5:32
  stresses that are already set by authorities like ASTM or AISC,
• 5:36
  it standardizes that risk tolerance across an entire
• 5:39
  industry. Now, the forces we deal with
• 5:42
  aren't always simple. Sometimes time itself is the
• 5:45
  enemy, which leads to some really interesting failure
• 5:47
  modes. Let's start with cold flow cold.
• 5:49
  Flow is a major headache. It's the gradual, permanent
• 5:52
  deformation of materials that aren't very elastic.
• 5:55
  We're talking about things like lead or certain plastics like
• 5:58
  Teflon. They're under a constant static
• 6:00
  load and they just slowly squeeze out of the way.
• 6:02
  So if I use a Teflon gasket in a flange, what's going to happen
• 6:05
  over a few months? That constant pressure will
• 6:08
  cause the Teflon to gradually creep or extrude out of the
• 6:11
  joint, and you'll lose your seal.
• 6:13
  If you're designing with these materials, you absolutely have
• 6:16
  to compensate, usually with spring loading or something that
• 6:19
  maintains continuous pressure as the material deforms.
• 6:22
  OK, so if a static load is 1 silent killer repeated varying
• 6:27
  loads or another, this is fatigue.
• 6:29
  Fatigue failure is a really complex phenomenon.
• 6:32
  It's caused by cyclical loading. Think of a rotating shaft or an
• 6:36
  airplane wing flexing over and over.
• 6:39
  And even if the stress never gets close to the yield
• 6:41
  strength, these microscopic cracks can form.
• 6:43
  And they just grow over time until.
• 6:45
  Well, until catastrophic failure.
• 6:48
  What's crucial here is understanding the fatigue
• 6:50
  endurance limit. This is the highest unit stress
• 6:53
  you can apply repeatedly indefinitely without causing
• 6:56
  failure. And that limit depends hugely on
• 6:58
  the material and how it's treated.
• 6:59
  Oh absolutely. For example, a medium carbon
• 7:02
  steel with a Brunel hardness between 1:50 and 200 might have
• 7:06
  an endurance limit somewhere between 42,000 and 50,000 size.
• 7:11
  Keep your operating stress below that, and in theory the part
• 7:14
  should never fail from fatigue. And there's also stress rupture
• 7:17
  failure. Right, that's common in some
• 7:19
  high performance aluminum alloys.
• 7:21
  The materials allowable ultimate strength actually goes down the
• 7:25
  longer a high load is applied. Time literally eats away at its
• 7:28
  strength. Let's pivot to the really
• 7:30
  dynamic stuff, impact and shock. If a heavy object hits a
• 7:35
  structure, that kinetic energy has to go somewhere.
• 7:37
  Where does it go? It gets dissipated through three
• 7:40
  main channels, deformation of the moving mass itself,
• 7:43
  deformation of the structure it hits, and conversion into heat.
• 7:46
  But what's truly surprising for most designers is the effect of
• 7:49
  a suddenly applied load, even if it's not a true high velocity
• 7:52
  impact. This is the key inside, isn't
• 7:54
  it? Tell us why applying a load
• 7:56
  quickly is so much worse than applying it slowly.
• 7:59
  The data is clear if you apply a load suddenly, and by that I
• 8:03
  mean almost instantaneously but without initial velocity, that
• 8:07
  load produces stress and deflection that is twice as
• 8:10
  great as the same exact load applied slowly.
• 8:12
  Twice the stress and twice the deflection.
• 8:15
  That's huge, and that's why we need tests that measure
• 8:17
  toughness under those conditions, like the Izod impact
• 8:20
  test. Precisely.
• 8:21
  The Izod test uses a weighted pendulum that swings down and
• 8:24
  smacks A carefully notched specimen.
• 8:27
  The energy it takes to fracture that specimen, measured in foot
• 8:30
  pounds or Newton meters, gives you a real number for its
• 8:33
  ability to absorb shock. All right, moving on, let's
• 8:36
  apply these concepts structurally.
• 8:38
  Let's talk beams and connections.
• 8:40
  When we analyze a beam, the first thing is always
• 8:43
  calculating the forces that the supports, which comes down to
• 8:46
  equilibrium, right? Two fundamental rules for any
• 8:48
  static beam. First, the sum of all your
• 8:51
  vertical forces has to be 0. Up forces have to balance the
• 8:54
  down forces. 2nd and this is the core of stability, the sum of
• 8:58
  the moments of all those vertical forces must also equal
• 9:01
  0. If the moments don't balance,
• 9:03
  the whole thing rotates and collapses.
• 9:05
  And once we have those reaction forces, we can map the internal
• 9:08
  bending moment along the beam, and that immediately reveals the
• 9:12
  structure's weak point. We call that the dangerous
• 9:14
  section. It's the cross section of the
• 9:16
  beam where that bending moment is at its absolute maximum.
• 9:20
  So for a simple beam with a load spread evenly across it, that's
• 9:23
  right in the middle. Exactly.
• 9:25
  But for a cantilever beam, one that's fixed at only one end,
• 9:28
  the moment is always always greatest right at the the fixed
• 9:32
  support. And we know the ultimate
• 9:34
  strength of a beam is tied directly to its geometry, its
• 9:37
  shape. It absolutely is.
• 9:39
  The formulas link the ultimate bending moment M to the ultimate
• 9:42
  tensile strength of the material FT and the beams section modulus
• 9:47
  S. For an I-beam, M is equal to FT
• 9:50
  times S, but for a square section it's 1.5 times FT times
• 9:55
  SA. 50% increase just for the shape.
• 9:57
  And for a solid circular section, it's 1.7 times FT times
• 10:01
  S The geometry dictates A staling factor for its strength.
• 10:04
  It's not just about the material.
• 10:06
  We also have parts that handle twisting instead of bending like
• 10:09
  Dr. shafts. That's torsion.
• 10:11
  Right when a member transmits torque, it's all about shear
• 10:14
  stress. We calculate the ultimate torque
• 10:17
  TU using the ultimate shear strength FS and a torsion
• 10:21
  constant TC, which depends on if the shaft is solid or hollow.
• 10:26
  The goal is just to make sure the maximum shear stress from
• 10:29
  that pork stays well below the materials shear yield strength.
• 10:33
  OK, let's tackle what might be the most complex analysis here.
• 10:36
  Eccentrically loaded shear joints.
• 10:39
  You've got a plate held on by a bunch of bolts, but the load is
• 10:41
  applied off center. This is a classic recipe for
• 10:44
  failure because the Bolts don't share the load equally.
• 10:47
  It's a huge challenge that uneven loading can cause just
• 10:50
  one or two fasteners to take almost all the load.
• 10:53
  And to analyze it right, you have to follow a critical five
• 10:56
  step process. It all starts with the geometry.
• 10:59
  So why is step one locating the centroid of the bolt pattern so
• 11:02
  foundational? Because the centroid is the
• 11:04
  geometric center point, it's the point that the entire group of
• 11:07
  bolts wants to rotate around when that off center load is
• 11:10
  applied. If you don't calculate your
• 11:11
  forces relative to that rotational center, your whole
• 11:13
  analysis is just wrong. OK, so once we have the center,
• 11:16
  what are the 2 main forces we're trying to combine?
• 11:19
  You've got the primary shear force, which is just the main
• 11:22
  load divided equally among all the bolts acting straight down.
• 11:25
  Then you have the reaction element force FN, created by
• 11:29
  that twisting action. It acts perpendicular to a line
• 11:32
  drawn from the centroid to each specific fastener.
• 11:36
  And that leads us to the most critical step, Step 4.
• 11:39
  That's where you have to combine those two forces victorially.
• 11:42
  You have to add the primary shear and the reaction moment
• 11:44
  force to find the true resultant force Fr on each bolt.
• 11:50
  They're almost never aligned, so you have to use trigonometry.
• 11:52
  The fastener with the highest resultant force is your weak
• 11:55
  link. That's the one that will fail
• 11:57
  first. And Step 5 is the final check.
• 11:59
  Computing the actual shear stress Tau on that most loaded
• 12:03
  fastener, you just divide that resultant force Fr by the
• 12:06
  cross-sectional area of the fastener AM.
• 12:09
  If that stress is higher than what's allowable for the
• 12:11
  material, the design is unsafe. Period.
• 12:13
  This is so important that analysis could show that the
• 12:16
  bolts on one side of a joint are carrying ten times the load of
• 12:20
  the bolts on the other. You have to know where that
• 12:21
  critical point is. Exactly.
• 12:24
  It turns what seems like complex physics into a predictable way
• 12:27
  to avoid failure. For our final segment, let's
• 12:30
  move into material selection, starting with the massive world
• 12:33
  of Steel and the AI Society designation system.
• 12:37
  That code gives you instant clues.
• 12:39
  The ASI system is designed to give you immediate design
• 12:42
  information, mainly based on carbon content.
• 12:45
  If you see a low carbon steel, say AI SI 1006 to 10:15, you
• 12:50
  know it's going to be highly formable, easy to Weld, and
• 12:53
  perfect for things like sheet metal where ductility is key.
• 12:55
  And as we add more carbon? We add strength and hardness,
• 12:58
  but we usually sacrifice some weldability and ductility.
• 13:01
  Medium carbon steels, like 10:30 to 10:52, those are the
• 13:04
  workhorses for automotive parts and forging.
• 13:06
  They can be hardened, then you jump to high carbon steels 1055
• 13:09
  to 1095. You basically give up on welding
• 13:12
  them, but you get incredible wear characteristics perfect for
• 13:15
  springs and tools. The power of selection really
• 13:18
  hits home when you compare a basic play steel to a highly
• 13:22
  treated alloy. The difference is just
• 13:24
  staggering. Take a common structural quality
• 13:27
  plate steel like ASTM A-36. Its yield strength is around
• 13:30
  what, 36 to 38,000 CSI? No.
• 13:33
  Take a high carbon steel ASI 1095, but instead of using it as
• 13:38
  is, you put it through a water quench heat treatment.
• 13:41
  That process boosts its yield strength all the way up to
• 13:44
  138,000 CSI. The heat treatment completely
• 13:47
  transforms its capabilities. For the engineer in the field,
• 13:51
  we have some neat identification tricks.
• 13:53
  Let's talk about the copper sulfate test.
• 13:55
  Yeah, this is a great quick check.
• 13:57
  It's a fast way to tell plain steel from stainless steel.
• 13:59
  You put a drop of copper sulfate solution on a clean spot.
• 14:03
  If it's regular carbon steel or iron, a metallic copper film
• 14:06
  immediately forms on the surface.
• 14:07
  If it's stainless steel, nothing happens.
• 14:10
  No copper deposit and. We can even tell different types
• 14:12
  of stainless steel apart with just a magnet.
• 14:14
  That's the second trick. The common 300 series stainless
• 14:18
  steels, the Austinitic grades they're non magnetic, but the
• 14:22
  high strength heat treatable 400 series the Martin Siddik grades,
• 14:27
  they are magnetic. And what about measuring
• 14:29
  hardness? The Brunel test.
• 14:31
  Right. The Brunel hardness test works
• 14:33
  by pressing A hardened steel ball of a known size, usually
• 14:37
  10mm, into the surface with a very specific load.
• 14:41
  You then measure the diameter of the little circular impression
• 14:44
  it leaves behind. The smaller the impression, the
• 14:46
  harder the material. It's a direct, quantifiable
• 14:48
  measure. Let's shift.
• 14:49
  Away from steels for a moment, aluminum alloys are just
• 14:52
  indispensable today. They offer an incredible
• 14:54
  strength to weight ratio. Modern aluminum alloys are
• 14:57
  strong, but they weigh about 2.8 times less than steel.
• 15:01
  That's why they dominate aerospace, high speed rail,
• 15:03
  performance cars. Anywhere that's saving mass is
• 15:06
  critical. And finally, let's touch on
• 15:08
  engineering plastics, where selection is driven by very
• 15:10
  specific functions. The properties are extremely
• 15:13
  specialized here. Take polycarbonate brand name
• 15:15
  Lexan. Its whole deal is being
• 15:17
  virtually unbreakable and optically clear.
• 15:19
  Perfect for safety, Shields, housings, things like that.
• 15:22
  Then you have plastics for mechanical parts for movement.
• 15:26
  Like a sedal, which you might know as delrin or silken, this
• 15:29
  stuff has a high modulus and a ridiculously low coefficient of
• 15:33
  friction. That's why you see it used for
• 15:35
  precision bearings and gears. And we come full circle back to
• 15:38
  failure modes with Teflon or PTFE.
• 15:41
  It's a perfect case study in trade-offs.
• 15:43
  Teflon is a miracle material in some ways.
• 15:46
  Unmatched chemical resistance, super low friction, great
• 15:49
  insulator. But.
• 15:49
  You have to remember cold flow. You absolutely must apply that
• 15:52
  lesson because Teflon has essentially 0 elasticity.
• 15:57
  Any constant pressure will cause it to creep and deform over
• 16:00
  time. If you design A Teflon seal
• 16:02
  without accounting for that creep, your otherwise perfect
• 16:05
  design will fail. It's just a matter of when.
• 16:07
  So we've covered the whole cycle from fundamental limits like
• 16:11
  Young's modulus and yield strength, to the complex
• 16:13
  analysis of off center joints, and finally to the specific
• 16:17
  quirks of materials like quench steel and PTFE.
• 16:21
  When you connect all the docks, successful mechanical design is
• 16:23
  really about integrating these different domains.
• 16:26
  You have to pick a material that can handle the specific type of
• 16:29
  load, static, dynamic, cyclic, and then you have to do the
• 16:32
  structural analysis to make sure the geometry distributes those
• 16:35
  stresses safely. It's not about finding the
• 16:38
  strongest material, it's about finding the most appropriate one
• 16:42
  that meets all the constraints without failing.
• 16:44
  So what does this all mean for you?
• 16:46
  Well, the next time you pick up some piece of hardware, maybe
• 16:49
  it's a complex plastic housing or a lightweight aluminum bike
• 16:52
  frame. Don't just see its shape.
• 16:55
  Think about the invisible forces governing its survival.
• 16:58
  Consider what property, like its ultimate shear strength, or
• 17:01
  maybe Poisson's ratio, which dictates how much it shrinks
• 17:04
  sideways when you stretch. It governs the flex and
• 17:06
  durability of that seemingly simple object you use everyday.
• 17:09
  Understanding those intrinsic properties is how you move from
• 17:12
  just building something to truly engineering it for the long
• 17:15
  term. This has been a true deep dive
• 17:18
  into the fundamentals of material integrity.
• 17:21
  If you haven't already, get over to our YouTube channel
• 17:24
  Mechanical Engineering Made Simple, where we post hands on
• 17:27
  how to videos, visual breakdowns, and ractical
• 17:29
  engineering walkthroughs you can actually use.
• 17:32
  A family that solves together stays together.