# 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.

SOOOOO CLEAR!!! i love using your lectures to reinforce what i am learning in class thank you for all your hard work.

helped me alot thanks!

really i need some doctors explaining dental stuffs like this doctor it's hard to me to studdy

thanks

Thank you sir…its very useful….

No words can express how I appreciate you for what you have done. Thank you so much!

hi tx for ur video.. i have question.regarding true plastic strain and stress up to which point we need to enter data for simulation in abaqus?is it fracture point or ultimate point?

Wow ! that's amazing

Awesome

THANKS PROFESSOR!!

thanks!!

In mathematics,we usually plot the known values in horizontal axis and plot their corresponding values vertical axis.why here in this diagram we do the opposite?

Nice presentation and lots of info. However surely (not blaming the prof as it is tradition but) elastic modulus E is a horrid name as it really represents stiffness. Rubber has very low E and concrete high E. Taking the reciprocal (1/E) is elasticity . Perhaps better to use symbol Y for young modulus or S for stiffness or whatever. This has been going on for hundreds of years, no wonder people get confused.