delta S = far-field stress range (max stress - min stress)
a = crack length
beta = a geometry correction factor which depends on your geometry (to find the right one, see an appropriate testing standard, journal article, or a handbook, e.g. Tada/Paris/Irwin: http://www.ltas-cm3.ulg.ac.be/MECA0058-1/TheHandbookExcerpts.pdf)
Perhaps it would be useful for you to read a good textbook on fatigue crack growth phenomena? I can recommend the one by Professor Schijve: http://www.springer.com/gp/book/9781402068072, but I am sure there are (free) alternatives available on the internet.