Dear Abhinav,

Yield Point Phenomenon (YPP) is related to Lüders strain (Lüders Band propagation) and it seems that lot of parameters must be take into account such as dislocation density, but aslo temperature, strain rate, grain size, and carbon content in the case of steels.

The occurrence of YPP in High carbon steel is reduced probably due to the presence of carbides (cementite) that strongly influence dislocation motion, stress relief, etc. In addition, the higher is the carbon content, the more phases other than ferrite will be formed to fix the excess carbon, these phases influencing the YPP.

Please take a look on the oustanding work done by David H Johnson (Lüders bands in RPV steel, PhD Thesis, Cranfield University, 2012) that is available on the link below for more information. Your experimental observation is in accordance with his work and you can also find in addition to explicit physical and metallurgical explanations, a simple model that set the interactions bewteen Lüders band and precipitates.

https://www.google.be/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCsQFjABahUKEwis5ZSvs-_HAhWItRoKHUH-DVQ&url=https%3A%2F%2Fdspace.lib.cranfield.ac.uk%2Fbitstream%2F1826%2F8039%2F1%2FPhD_thesis.pdf&usg=AFQjCNEj4s8LwbqPEqPC7UQIbPEON8RSbQ&sig2=_ornIvuzrtmpH99d_c741Q&bvm=bv.102022582,bs.1,d.d24

To begin, Luders strain is not due to unlocking of dislocations, rather new dislocations are produced. To answer your questions, are you comparing ferritic microstructures in low-carbon steels to martensitic or tempered martensitic microstructures in high-carbon steels?  

Thankyou for the response to both of you. Prof. Krauss, I have annealed both the mild steel sample and a high carbon(0.61C-1.71Si-0.86Mn) sample before subjecting them to tensile test. In mild steel distinct yield point phenomenon was observed in the engineering stress train diagram while in the high carbon steel sample the yielding was continuous. 

There are probably some nice detailed studies are performed on this aspect, which have nailed the essential elements coming into play, sorry, but off the top I can not direct you to them. But you are probably thinking about this in the wrong way. Whether for this phenomenon you take the old theories, (dislocations breaking free from the locking interstitials), or the new theories, (the stress reaching a point where new dislocations are generated), the subsequent progress of those (new) dislocations in the case of say ultra low carbon steels is usually considered to be glide like through a soft single phase matrix. If that glide  process continues, then you can get highly extensive Luders bands, but in other situations that 'easy' deformation process is curtailed and you get more normal and general work hardening instead.  In high  carbon steels you will not have that simple matrix for the 'easy' flow/deformation (dislocation glide) hence no Luders bands, you'll be directly into general work hardening. It's dated now, but pages 235-252 of chapter 9 in the book "The Plastic Deformation of Metals", by the late prof. R.W.K. Honeycombe, pub Ed Arnold, 1975. and that book in general provides insights in the deformation processes, well worth a read. My picture might be wrong (in the light of any detailed investigations alluded to above) but it seems reasonable.

Dear Abhinav Varshney,

I think the above answers are worrthwile to be noticed. Nevertheless I will try to make an additional remark. In a low carbon common steel, let's say up to 0.1 weight % C, a significant part of the carbon atoms present is in solid ferrite solution, thereby enabling the interactions between interstitial solute (carbon) atoms and dislocations that are linked to yielding and Lüders-band formation. Increasing the carbon content inevitalbly results in the presence of carbides (e.g. in pearlite or as separate carbides), depending on the heat-treatment). The greater the role of these carbides, the larger the yield strength and the smaller the extent of yielding. 

Thankyou Butler and Mourik for your response.  I am quite satisfied by the reason mentioned by Butler. Increasing carbon will indeed restrict the motion of dislocations and will hence not allow  the dislocations to move as freely as in low carbon steels. This will lower the possibilty of yield point phenomenon to take place in high carbon steels.

 And of course as per Jerome and Mourik role of carbides in restricting the motion of dislocations can't be neglected which can additionally or in some cases dominantly contribute  to  the continuous yielding. 

Very simple explanation of the effect you observe could be the following.

In low carbon steel carbon atoms are dissolved in the matrix as interstitials, which are known to expand lattice around them. On the other hand, dislocations create tensile stresses below the half-plane. Therefore, highly mobile carbon atoms readily occupy these positions near dislocation core. The binding energy of carbon with dislocation is about 0.5 eV. So pinning of dislocation on carbon atoms trapped in the dislocation core explains high yield stress, which rapidly drops down to Peierls-Nabarro stress when dislocation is released.

In high carbon steel carbon segregates and forms carbides. Therefore its concentration in the matrix reduces and no yield point phenomena is observed.