Mechanical Properties Definitions {Texas A&M: Intro to Materials}


Howdy! The purpose of this video is to review some of the basic terminology that
you will encounter when talking about mechanical properties in materials. And we’re going to focus this all around stress-strain
diagram that’s one of the principal tools
that we use to interpret mechanical properties in
materials Now I am going to assume that you’ve already watched the video or read about stress and strain. as a quick
reminder, stress is defined as force per unit area and we typically
illustrate this on the vertical axis of a stress-strain diagram. Strain we show on the horizontal axis and thats defined as a change in length per
total length of material. Also this is engineering
stress and strain showing and we’re going to be talking about tensile stress strain diagrams which means that we are pulling, we’re pulling material along one axis. So that would be a tensile stress. you could create a stress-strain diagram
for compressive stress and strain as well. now we talked about stress and strain – the first thing i want to talk about is the
difference between elastic behavior and plastic behavior. so if you look at
stress-strain diagrams, typically we find fairly linear regions at low strains, and this is the elastic portion above the chart if I stress a
material, I have some deformation but if I remove
that stress, I come back along this same path. and that’s what makes it elastic – its recoverable. now somewhere out here we’ve gone off that linear path. so if I was to deform a material all the way out to here, I’m applying a lot of stress now, if I removed that stress, I have some irrecoverable strain. so that
would be the plastic deformation. so somewhere in here there’s a
distinction between this elastic and plastic deformation. so let’s look at
that in a little bit more detail. There are a couple terminology and points that one should
be familiar with. I’m going to draw a representative stress-strain diagram, and I see that the way I drew it, it looks pretty linear in here, but it starts to deviate from linearity at about this point. so this is called the proportional limit – the
proportional limit is defined as the point at which we’re no longer proportional. we’re deviating from linearity. If I was to extend that line, it would look something like that. now, oftentimes it’s very difficult to pinpoint
one distinctive stress at which this
proportional limit occurs so let me draw a second line, and we’ll make it a different color here, so if I was to draw a line that looked more like this, you know it’s very difficult to
say in there where exactly did I deviate from linearity. Was it here? was it here? So we use a convention to illustrate where we’re going from elastic to plastic transformation, and the way this convention works is that we
start off on the horizontal axis at 0.002 strain. This is just a number, it’s agreed upon and commonly used. Sometimes people use other numbers but we’ll use this
one. so that’s the same as 0.2% strain – some very small strain.
and the next thing I do is I’m going to draw a line with the same
slope as this line coming out the origin but
here I’m going to make it a perfect line so I could use a ruler I could use a graphing tool but I know that’s going to be a perfect line and at some point, at some point these two… at some point these two lines intersect and this is what is
commonly referred to you as a yield stress, yield point, or yield strength of a material
and the reason again that we use this convention is that it’s very difficult
sometimes to identify some specific point where it deviates from linearity. now that’s not always true, you know
some stress-strain diagrams might be very
distinct and then its easier to say yes your
yield stress is here but I would encourage you to use
this convention whenever possible. okay. one other thing that you should be aware
of is that certain steels exhibit a very interesting phenomenon
called yield point phenomenon. We can make a new axis here… what occurs is again we have elastic
behavior we start to exhibit plastic deformation but then there’s a drop and there’s a bit of a random stress that a material could withstand
and then it’ll continue to increase and plastically deform from
there. so I see this kind of behavior this is
usually called the upper yield point yield point and the lower yield point usually if I were to pick a yield
stress for this material I would pick that lower yield point
because once it goes past this upper yield point, this is now the new yield stress of the
material. so this is a behavior we don’t see in all materials but it is something I would like you to familiar with. One other thing that we should think
about is in this in this elastic region, again I have a nice linear region here, I can define
what’s called the elastic modulus, and this is a very
specific elastic modulus – this is Young’s elastic modulus sometimes it’s called the tensile elastic modulus (if I’m looking at a tensile stress-strain diagram) and so because its linear, we can describe… we can say that stress is proportional to strain, and they’re
proportional by some constant that we call Young’s
elastic modulus. If I were to rearrange this, I can see that the elastic modulus is just
given by the stress over the strain, which is just a slope,
right? Stress is on a vertical axis, strain is on
a horizontal axis. rise over run – I can find the elastic
modulus of a material just by looking at the slope of
that initial linear section. now remember, materials are not
always perfect and so in some cases we might have
something which is elastic it behaves elastically, so it’s totally
recoverable, but it’s not perfectly linear. So in
this case, if I applied some stress, I could come up here but I could still
recover all that strain upon removing the stress. so it’s not linear, so how do we
find the slope for it? There are two different things we can do. we could draw a line from – say I want the
elastic modulus at this point – I could draw a line from
the origin through that point and that’s what we
call the secant elastic modulus or I could look at the specific slope
of that line at that point and that’s what I would
call the tangent elastic modulus. So again, nature isn’t perfect. we try and make it
perfect by our models. but these are the terminologies that
you need to know to discuss elastic behavior in materials. okay so we talked about the elastic
portion so what’s going on down here what is some terminology you might need
for the other important points on this diagram?
so this label here Sigma_u, this is the ultimate stress or ultimate strength
of a material I should mention that this is kind
of a typical curve for a metal that we’re looking at. so usually, this
point is associated with necking, and we’ll talk
about necking at some future point but this is called the ultimate stress, that’s
the maximum of the stress-strain curve. finally, this is called the failure point, the failure stress, failure strength. This would be the
failure strain and this is when the material
actually breaks entirely on you. so this is a very important point in terms
of what is happening under extreme plastic deformation. one thing that we often talk about in materials is their ductility – how much can they deform before they break, and
so one measure of ductility is the percent elongation percent elongation at failure. and that he is exactly what the failure strain is, right? so percent
elongatio would be Delta L over L times 100. and strain again remember is just delta L over L. so that is ductility, one other thing that I wanted to talk about using the same graph we could talk about how much energy it
takes to either break a material, or how much
energy can be stored elastically and how we do that is by
integrating different areas of the stress-strain diagram so if I were to integrate stress strain curves from integrate stress d strain from 0 to the yield point, I would get this area here, and this is usually called the modulus of resilience. and so this tells us how
much energy can a material store elastically. if I were to integrate the entire area under the curve, so from 0 up to the failure sorry, that should be strain up to the failure strain again stress d strain, I get the area under that whole curve… that’s a measure of how much energy it
takes to break the material. now this would be a
kind of a static measure of that because these are usually captured by deforming a material very
slowly. There are other ways to measure this toughness so this
is the modulus of toughness – there are other ways to measure the toughness by a more dynamic experioment, so
essentially swinging down a heavyweight and breaking the material. And those two get related related toughness measures. Okay, so in review, we talked about definitions
we talk about stress and strain Proportional limit, yield stress, yield point, elastic limit. We talk about Young’s modulus, which is also referred to as Young’s tensile modulus, we talked about
ultimate stress and strain, failure stress, strength, which is also
defined as the rupture point sometimes. And we talked about ductility. And finally we talked about modulus of toughness, modulus of resilience.

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