Strain hardening.

If you stretch the polythene you use daily then you will observe something different.
Firstly it will change its shape as you stretch it but then after some change it will need much more stretching force to deform.
This may look very normal but you will notice that how it happens that on deforming more,it needs more force.

This small thing is usual but has a great significance in field of materials which is called as strain hardening.

lattice

Now,before going to the concept of strain hardening and its affects,I will firstly brief you some basics of material and it's relation with forces applied.
Materials are made of atoms structured in such a way that they always try stabilize themselves by reducing their potential energy.

The structural arrangement of materials at atomic level,may contain some impurities ( other atoms) and change in external environment like radiation and temperature due to which defects arise in the material's structure .These defects cause dislocation of atomic structure system.It also leads to unbalanced forces and instability of structure.

Now,when you apply a load,after a certain limit plastic deformation occurs.This is because the number of dislocations increases.Gradually ,the dislocation density increases i.e., the distance between two dislocations also decreases.

Defects in lattice

Normally we will understand, the more the dislocations,the easier to deform but the beauty of nature lies here.Gradually,when dislocations come a  lot closer ,they together repel the forces.
Repel the forces?How's that?
It can be understood by man and drain analogy.
Suppose a man has to cross two open identical channels situated at certain distance by jumping.
Easy for him to do that,first one channel and then another.
What if there is one channel he has to cross of twice width of one channel?
It won't be that easy for him.His jump should be longer so that he don't find himself in water after leap.

Same happens with other dislocations who want to propagate through them.These two dislocations together act as wide channel for the other dislocations to jump through it.
This acts as hindrance and the movement of dislocation and thus strength increases.
It is just like two bully kids together hindering other bully.
They are not good for the whole class individually but acting as protector at this time.
This concept strain hardening is utilized in strengthening metals.
The material is deformed at the level of strain hardening and now the new stress to be induced to deform the material will be more.
The strain hardening not only strengthens material but has other effects too.

Strain hardening promotes corrosion.
The nail head is more vulnerable to corrosion than its shank cause while forging the nail by compression strain hardening occurs.
This is because of too much dislocations which cause instability and higher potential energy to make them react with corrosive elements.

Strain hardening increases resistivity to some extent. 
How?
The increased number of  dislocations reduce free carriers eletron as these  dislocations act as electron acceptor.So strain hardening decreases conductivity.But that change is not so significant in front of temperature and external impurities.


If we look at the mathematical form of strain hardening,then it follows,

σ =  K.𝞊^n

where 𝜎 is true stress

    K is constant

          𝛜 is true strain

          n is strain hardening exponent.

         𝛜 = ln(initial length/observed length)

The value of n is significant.The more the value of n,the more strain hardening for a given value of stress strain.

Note-The thing that is important to note that the calculation is based on true stress and true strain and not on engineering stress and strain.Both are different and follow different curves on stress strain diagram.The basic difference is that true strain follows instantaneous observations of cross sectional area.

Necking due to loading.A condition after strain hardening

Strain hardening is the stage after yield point and before the necking starts.
Necking is the point from where the deformation increases with significant cavity developments starts at minimum cross sectional area point followed by cracking of material.