Elasticity (understanding elasticity from stress strain curve)

maheshshenoy

Hello .. I have problem understanding how to decide which material is more elastic based on stress strain curve.. my understanding is as follows
1)if a material has big youngs modulus.. then it is more stiff

2)a material with a big youngs modulus may be or may not be very elastic (elasticity is independent of youngs modulus.. it only tells how stiff something is)

3)if a material has a very big yield point.. then is it more elastic?? what if a material can deform more (so less youngs modulus) but has lesser yield point.. then is it more elastic??

maheshshenoy

This is a sample curve

Attached Thumbnails

 

afreiden

High yield value = strong
Large E = stiff
Large strain to failure = ductile

maheshshenoy

Well.. i got that.. but how do find which is more ELASTIC?

Chestermiller

Most people would quantity it by the maximum amount of recoverable tensile strain. But why do you feel compelled to have a definition of "more elastic?"

maheshshenoy

So you mean to say.. we don't have to really define which is more elastic ? its not relevant in the real world application?

Chestermiller

I guess it helps your intuitive mind set to be aware that elastomers/rubbers exhibit large recoverable strains, and metals and ceramics exhibit small recoverable strains. But I think you already knew that.

maheshshenoy

Yes.. and we still say steel is more elastic compared to those elastomers.. so basically elasticity is not just a measure of how much recoverable strain its can exhibit right?..
So thats what i wanted to know exactly when we say something is elastic.. what do we mean.. it must have high yield point and must exhibit high recoverable strains.. correct?

Studiot

Technically, elasticity is the property of a material to recover its strain after removal of stress.

Nothing more.

It does not imply that the strain be large or that any particular mathematical relationship exists between stress and strain or that all the strain be recovered. It does refer to all the stress induced strain that is recovered, however.

The stress - strain relationship may be linear or non linear.
The elastic relationship for steel is particularly linear over its elastic range which is why people say (loosely) that steel is 'more elastic' than a rubber band which does not have a linear stress-strain relationship.

Strain can also occur by other agencies eg thermal strain which can be stress free.

Elasticity may appear in conjunction with other effects such as hysteresis or plasticity.

In ordinary English elasticity is often mixed up with these other effects and the definition is not so precise. The ordinary English definition should not be used in technical forums.

maheshshenoy

So what I finally understand is.. elasticity is not something we can quantify.. so its not a physical quantity right?

Studiot

You are getting there.

No, even in technical English 'elasticity' is not mathematically quantifiable in general.

However for obvious reasons we have developed several definite mathematical (quatifiable) relationships, the most important being linear-elastic or hookean (which is a sub class).

Chestermiller

To me, as a guy with lots of experience in materials engineering, linearity of stress-strain behavior is not a requirement for a material to be considered very elastic. The key requirement, as I said before, is how much recoverable strain the material is capable of exhibiting. Elastomers display non-linear behavior from the get-go even over large deformations, but yet, they are capable of a high degree of recoverable strain. Where do we think the "elast" of elastomers comes from?

Studiot

That's almost exactly what I said so what is your angle?

The only difference is that I also said linear-elastic is the most important. This is simply because linear theory is still by far the most solvable in almost all disciplines and we try to linearise or create linear approximations wherever possible.

go well

Chestermiller

Thanks Studoit. In the case of polymeric materials, man-made fibers, and rubber products (e.g., automobile tires) which constitute a major part of my experience base, the deformations are typically large and the behavior is typically non-linear and often viscoelastic. So this is basically my angle.

Chet