For crystallite size vs. strength of polycrystalline materials, the Hall-Petch relation is a good place to start. Please see the attached review for a little more detail. Good luck!

http://tecdigital.tec.ac.cr/file/7266790/Materials_mechanical_size_effects_a_review.pdf

Thanks Martin

Dear Richard Chukwuma Meribe,

Assuming that your question regards metals and metal alloys I remark that:

1. after casting the grain size strongly relates to the cooling rate applied

2. after hot deformation the grain size is determined by the end temperature of the deformation process

3. after cold deformation the grain size is determined by the extent of the preceding deformation and the temperature of the recrystallization treatment applied

A brief introduction of the relations involved, including the Hall-Petch relation, can be found in the book

Materials Science in Design and Engineering (see link below). 

http://www.delftacademicpress.nl/m017.php

http://www.delftacademicpress.nl/m017.php

Thanks P. Van Mourik