I've seen some formulas for crack length in the Wikipedia article "Compact tension specimen". Maybe you could find more information about this in books about fracture mechanics (like those by D. Broek, E.E. Gdoutos, J.F. Knott, B. Lawn, T.L. Anderson, A.T. Zehnder or other authors) and in research papers. CT specimen is very common and basic so it should be described in detail in literature.