Dear Oksana, you cannot refine the grains of any metal by heating unless you apply deformation first. If there is no prior deformation all you will get is coarser grains. And if you can apply deformation first, then the following annealing, which is recrystallization annealing, should be best designed in terms of temperature and time-length depending on the level of initial deformation. I am saying this so that you get the desired grain size effectively. Otherwise, following deformation, any heating given sufficient time wuld give you some degree of recrystallization.

Good luck.

Dear Oksana

maybe this book can help: P. Marshall: Austenitic stainless steel,

there are Phase equilibria systems.....

good luck. 

Ali Kaya's answer is correct you cannot refine the grain size without having a critical amount of cold-work (plastic strain) in the alloy.  This is required for recrystallization.  A good reference for recrystallization is chapter 3 of Paul Shewmon's book "Transformations in Metals" published by McGraw Hill.  Without cold-work/deformation you only get bigger grains from grain growth as Ali stated.

Daer Oksana Klok

The heat treatment process called  Annealing is suitable to decrease the grain size of 316L austenitic stainless steel.  

Ali and Larry`s answers are correct, the only way you have to decrease the grain size of a metal which does not undergo phase transformation at a certain temperature (this is the case of 316L, which is austenitic at all temperatures until liquidus) is by applying a sufficient degree of cold work prior to recrystallization annealing. You can calculate the amount of plastic work and the recrystallization temperature an time using some empirical formulas, which, I believe, are found in Shewmon's book, or by experimenting.

Probably. Surface Mechanical Attrition may prove to be an efficient method for reducing your grain size upto nano-level. 

by using cold working processes you can reduce the size of the grain.

Daer Oksana Klok

Could you inform the history process of your 316Li.e(casting or work hardening) please?. i need to know why 316 L coarsening?

Dear Oksana Klok,

Did you find a suitable treatment to get the finer grain size?

Best wishes,

Lu