# Mechanical properties of materials.

I'm going absolutely nuts over this chapter....ther seem to be millions of terms,which all seem to mean the same thing...could someone help me out??

Okay,the first set of questions I would like to get cleared is....
1. The proportional limit on a stress-strain curve is supposed to be the point upto which the strain obeys Hooke's law and perfect elasticity is exhibited...but then what is the elastic limit for?

2.I read that 'The nonlinearity in the stress-strain curve between the proportional limit and the elastic limit refers to strain hardening and plastic flow is induced here'...but I thought that plastic flow occurs only after the yield point.....please explain.

3.what happens beyond the yield point,when the wire elongates,even without the application of stress?(in terms of dislocations,slip,etc.)

4. In the purely plastic region of the curve,why does the curve first rise,and then go down again (till fracture)?

5.How do we differentiate creep,dislocation climb and strain hardening?

## Answers and Replies

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Mapes
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Gold Member
I'm going absolutely nuts over this chapter....ther seem to be millions of terms,which all seem to mean the same thing...could someone help me out??

Okay,the first set of questions I would like to get cleared is....
1. The proportional limit on a stress-strain curve is supposed to be the point upto which the strain obeys Hooke's law and perfect elasticity is exhibited...but then what is the elastic limit for?

2.I read that 'The nonlinearity in the stress-strain curve between the proportional limit and the elastic limit refers to strain hardening and plastic flow is induced here'...but I thought that plastic flow occurs only after the yield point.....please explain.

3.what happens beyond the yield point,when the wire elongates,even without the application of stress?(in terms of dislocations,slip,etc.)

4. In the purely plastic region of the curve,why does the curve first rise,and then go down again (till fracture)?

5.How do we differentiate creep,dislocation climb and strain hardening?
1. The elastic limit marks the onset of permanent deformation. This point lies at approximately the same point as the proportional limit for metals, but it's not necessarily the case for all materials. For example, elastomers can be deformed a large amount (to the extent that the stress-strain curve is nonlinear) without undergoing permanent deformation.
2. Plastic flow does mean that the material has yielded, but there are multiple definitions of "yield point" - you need to be more specific here.
3. It's not clear why the material is deforming in the absence of strain...

I'm not going to answer the rest because they are close to homework questions, which we don't just provide the answers for at PF. However, we will comment on your answers and provide feedback. So what are your thoughts?

I'm going absolutely nuts over this chapter....
One thing to beware of in this situation is.....it depends on the book.

As a material is stretched the sample gets thinner. When a test first starts the effect is hardly noticeable. But by end of the test the sample material is stretched right out and very thin.

This is significant as there is a huge change in cross section and the area of cross section during the test.

So when someone calculates the stress they can divide by different things to get different answers. There are two methods in common use

$$Engineering stress = \frac{{Force}}{{original area}}$$

This is used by, well, Engineers

$$Absolutestress = \frac{{Force}}{{actualarea}}$$

This is used by Physicists and Materials Scientists.

The stress strain curves produced look quite different so it is important to know which viewpoint is being adopted.

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1. The elastic limit marks the onset of permanent deformation. This point lies at approximately the same point as the proportional limit for metals, but it's not necessarily the case for all materials. For example, elastomers can be deformed a large amount (to the extent that the stress-strain curve is nonlinear) without undergoing permanent deformation.
Even in an elastormer,beyond the proprtional limit,something must have changed within the material to allow for permanent set....could this be dislocation?

2. Plastic flow does mean that the material has yielded, but there are multiple definitions of "yield point" - you need to be more specific here.
This is another point...in my book,they say that 'yield strength',ultimate strength',and 'breaking strength' all mean the same....however,on wikipedia, I found that they have slightly different definitions...what am I supposed to follow?

3. It's not clear why the material is deforming in the absence of strain...
Here,it seems that something called work hardening or strain hadening happens(it says so in my book)...are these 2 the same?
Does dislocation climb occur on work/strain hardening?

Also,as Studiot said,there are two types of stress-true and nominal.....is it true that in the stress-strain curve,the plastic region is always graphed astrue stress and the rest is in nominal stress?

Also,the question on 'creep' wasn't a homework question.....I honestly don't understand creep.....I read on websites that creep occurs in the form of dislocation climb...but then we could say that in plastic deformation,creep occurs...but we don't say that!!!

Mapes
Homework Helper
Gold Member
Even in an elastormer,beyond the proprtional limit,something must have changed within the material to allow for permanent set....could this be dislocation?
Dislocations don't occur in elastomers, which are amorphous (recall that dislocations are imperfections in crystals). The elastomer stress-strain curve can be nonlinear but elastic because the polymer chains straighten and become stiffer with increasing strain. Eventually, though, permanent deformation does occur when the polymer chains begin to slip past one another.

This is another point...in my book,they say that 'yield strength',ultimate strength',and 'breaking strength' all mean the same....however,on wikipedia, I found that they have slightly different definitions...what am I supposed to follow?
Check with your professor. In some materials science classes, different points are assumed to be approximately equal for simplicity.

Also,as Studiot said,there are two types of stress-true and nominal.....is it true that in the stress-strain curve,the plastic region is always graphed astrue stress and the rest is in nominal stress?
Yes, you can plot stress as true stress or engineering stress, but the curve doesn't switch from one to another (you have to choose one). The engineering stress decreases at a certain point in ductile materials, but this is just an artifact caused by division by the original cross-sectional area. The true stress continues to increase until the material fails.

On the creep question: creep is just time-dependent deformation from an applied load. Permanent (or plastic) strain consist of instantaneous strain, plus additional deformation over time due to creep. Yes, one of the mechanisms of creep is dislocation climb, but it may not be the dominant mechanism (other mechanisms are glide and viscous flow, and in general any thermally activated deformation processes).

Dislocations don't occu.....chains begin to slip past one another.
Thanks for pointing this out...I should have remembered! Concentrating on metals,I have this idea,ever since I was in high school, upto the proportional limit,the molecules in the material are pulling eachother,just like in an elastic band...then,beyond this point,there seems to be less stress rqd for a particular value of strain to be produced...but I can't seem to explain this in terms of my 'elastic band ' theory! What could it be beyond the proportional limit that causes the nonlinearity?

Also,I found on a website(sorry,I forgot which) where it said something about 'stress induced plastic flow' existing between the proportional limit and the elastic limit...I can't link all these pieces up!
The above statement also implies that there should be permanent strain at prop. limit...but the permanent deformation occurs only at the elastic limit,right?

PLease could someone also clear why there are two yield points...upper and lower...are they both points at which creep set in?(this sort of description is not found in any book,or website,so I have to get it cleared from Physicsforums.)

Mapes
Homework Helper
Gold Member
What could it be beyond the proportional limit that causes the nonlinearity?
I'm not sure which material you're talking about here. In an elastomer, the most likely reason for initial nonlinearity is straightening of the polymer chains. In a metal, the proportional limit and elastic limit are approximately the same, and the most likely reason for nonlinearity is slip (dislocation motion).

PLease could someone also clear why there are two yield points...upper and lower...are they both points at which creep set in?
It may be the case that an existing edge dislocation has some solute atoms sitting around it. These solute atoms will usually diffuse to minimize strain energy (that is, if they're too big (small) for the crystal, they'll move to locations near the dislocation where the stress is tensile (compressive)).

If the dislocation were to begin to move due to a load on the material, the solute atoms would need to move also, or the strain energy would go back up. The drag caused by these solute atoms (the so-called "Cottrell atmosphere") constitutes a strengthening effect.

But it's possible for the dislocation to rip away from these solute atoms and move more-or-less unimpeded. If this happens en masse, the material suddenly deforms more easily and the yield stress drops from an upper to a lower point.

(Creep is separate from this discussion. Creep occurs at stresses below the yield point; at stresses above the yield point, the material deforms instantaneously.)

Wiki has a pretty good spiel on the questions you are asking.

http://en.wikipedia.org/wiki/Proof_stress

A few pointers to remember.

Hookes law refers to the linear bit (strain proportional to stress)
A material may perform in a non linear manner, but still be elastic ie the strain is still recoverable on unloading.
The yield point (and after) is where all the strain is not recoverable on unloading. However the material still has strength reserves against further loading and will not fail at the yield stress.

Engineers generally use the proof stress.

There are many theories of yielding and failure, none acount fully for the observed phenomena but all have their usefulness in explaining and predicting some aspect.

These days there are many materials available to the designer with lots of properties. The test to destruction curves you are studying were developed a century ago when steel was the main material.
Most modern materials do not follow this curve.

Creep is a separate response from short term loading and can and does occur at any load (which is a particular problem with plastics materials).
The creep response is additional to any of the above and must be added to them

Thanks Studiot and Mapes.
I read through the wiki article on proof stress...not all of it was understandable(to me) but I think it has enlightened me on a few points.
By the way,I have a few questions left....

1.What is the relation between ductility and malleability...we read about it together usually...does it mean a material that has ductility also has to have malleability?

2.My thought about ductility till now was that is is an elastic change...we stretch the material into a wire...however,sources speak differently....I can't understand why is ductility a plastic chsnge and not elastic.

3. Also,I have a lingering question on my mind for many days.....the tensile and compressive strengths of a body should be equal...and the moduli measuring them should also be equal...afterall,they are basically the same process in opposite directions...why is it not so in reality?

Mapes
Homework Helper
Gold Member
Ductility, by definition, is ease of plastic deformation.

Tensile and compressive moduli are generally similar (I'm generalizing a bit here). Tensile and compressive strengths may be considerably different due to different relevant failure mechanisms (e.g., mode I fracture involves tension).

Malleable is the older word and stems from Latin. It means that the material can easily be pressed or hammered into other shapes, without a tendency to return to its original shape. The Romans coined the word to refer to a type of iron they could hammer into shape.
Plasticine is malleable.

Compare this with elastic, which does return to its original shape.

Ductile came from old French and in general English usage meant malleable or pliable (which can refer to a return to original shape).
When it was discovered that certain alloys could be drawn into long wires it was adopted to describe this behaviour.
Later engineers adopted an even narrower definition to distinguish the two main forms of failure of steel materials viz ductile and brittle.
A ductile failure is characterised by the material being drawn out to a long neck with a very large reduction of diameter at failure. the cross section at failure does not have a crystalline appearance. You get a long pre failure warning with ductile materials.

A brittle failure by contrast is a sudden failure with almost no warning. There is little reduction of diameter and the cross section has a very definite crystaline appearance.

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Simple theories of tension and compression failure do not allow for the true state of stress within a body due to the shape of the body. The squatness or fatness of a body affects its performance much more under compression than under tension. Don't forget that test samples try to determine uniaxial (one dimensional) parameters. We actually live in a three dimensional world.

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I keep referring to standard tests. That is because engineers require standardisation. They want a test which says " If I take many samples of standard size and shape of some material and subject it to a standard loading regime I can use the average result to compare future tests, conducted in the same manner, against."

Proof stress is one such test. The material is extended to a standard (say 0.1%) strain and the force (therefore the stress) required is measured. Experience will tell what range is acceptable for this stress so it can be used for quality control.

Malleable is the older word and stems from Latin. It means that the material can easily be pressed or hammered into other shapes, without a tendency to return to its original shape.

Ductile came from old French and in general English usage meant malleable or pliable (which can refer to a return to original shape).
Here,from the bolded part,it is very clear that malleability refers to plastic behaviour.
In the following description about ductility,however,you say that 'it means malleable/pliable(which can refer to a return in shape'...but that ductiliity can refer to malleability or pliability is self-contradictory...isn't it?

A ductile failure is characterised by the material being drawn out to a long neck with a very large reduction of diameter at failure. the cross section at failure does not have a crystalline appearance. You get a long pre failure warning with ductile materials.

A brittle failure by contrast is a sudden failure with almost no warning. There is little reduction of diameter and the cross section has a very definite crystaline appearance.
What is it that causes this characteristic difference between ductile and brittle fracture.
In other words,likr it says in my books,why is it that a brittle material if put back together,it fits exactly?
Also,in relation to thisiIt is said toughness is highest for brittle materials...

Yeas malleable behaviour is never elastic, but may not be exactly plastic either.

I did say that one meaning of ductile is malleable in general english usage. You will find this definition in the Oxford English Dictionary.

However I also said that engineers made a specific restricted definition, not including malleable, for ductile, which is the one we use in science and engineering.

You will find many words like this with a more general meaning in the english language than in scientific english.

Plastic behaviour by the way is another word that has a speciifc more restricted meaning in engineering terms.

What is it that causes this characteristic difference between ductile and brittle fracture.
This is a very good question that has exercised materials engineers and scientists for two centuries.
It is to do with differences in crystal structure. For example steel with a carbon content of less than 4% is ductile, but brittle with a greater carbon content. The crystal structure of steel chages dramtically at 4% carbon.

It is also the reason I mentioned that the none of various theories of failure fit all cases.

The maximum stress theory fits brittle failure best, whereas the Von Mises theory fits ductile failure best.

You should look these up.

An yes, you can often fit a brittle failed specimen back together. People often take advantage of this when they glue the broken (brittle failed) handle of a teacup back on.

Finally Toughness is another specially defined word in materials science and also 'Fracture Toughness'

An added difficulty is that materials such as steel which may be ductile in a uniaxial test may behave in a relatively brittle manner when subjected to bi- or triaxial stress states. Also the ductility along the drection of rolling may be quite different from that at right angles to it. These points are important in engineering practice.

Thanks for your answers...actually I'm in the middle of my mid-semester exams,so I'm a little late in looking them up.

I did say that one meaning of ductile is malleable in general english usage....You will find many words like this with a more general meaning in the english language than in scientific english.

Thanks for the clarification...these things often get people mixed up.

Plastic behaviour by the way is another word that has a speciifc more restricted meaning in engineering terms.

Just keeps on getting more complicated!

The maximum stress theory fits brittle failure best, whereas the Von Mises theory fits ductile failure best.

You should look these up.

I definitely will.

I find that there is a very wide variety in materials science...nothing seems to have a particular meaning or application.

Hi,
I don't have many more questions to ask..please bear with me for a little while longer.

Just a few more...

1.Please just tell me if hardness and impact strength are dependant on eachother.

2.Also,are the terms toughness,stiffness and resilience interrealated?

3. If I change the tensile strength of a material,will compressive strength,shear strength and torsional strength also change?

4.Bending strength is said to be measure of all the different kinds of strength...coukd you please explain this?