meca,
You need to specify the material, manufacturing method, and heat treating process with sufficient detail so that factors that affect brittle fracture are carefully controlled. There are a number of things that you need to consider:
1. Desired mechanical properties-- presumably you are investigating a nominal carbon composition because the shaft reqires a strong and/or hard surface. What is the strength and hardness reqirement?
2. Desired low temperature performance-- you may not have a design requirement for this, other than "shaft must not break at X temperature". Fracture toughness is one factor to consider, and fatigue strength is another.
3. Fracture toughness can be approximately understood using the conventional notched bar impact testing (usually Charpy). ASTM E 23 - 02 Standard Test Methods for Notched Bar Impact Testing of Metallic Materials is one standard that covers this test. This should probably be a requirement for the material to be certified for your application.
4. In addition to the standard chemical composition, you may need to place restrictions on the elements that are detrimental to fracture toughness: S, P, O, N, etc. S & P are usually specified to levels below 0.010 % (by weight) when fracture toughness is a requirement.
5. Cleanliness as determined by inclusion analysis (microscopic and macroscopic) is frequently specified for fracture-critical components. ASTM E 45 - 97Standard Test Methods for Determining the Inclusion Content of Steel is one method used, which categorizes inclusions by type (A = sulfides, B = oxides, C = silicates, & D = globular oxides), size, and distribution. Worst field views for thin and heavy series should be 0.5 maximum for all of these categories when low-temperature fracture toughness is needed. This may require that the material is produced using a degassing step before casting, or that the material be produced by a consumable electrode type process (VIM, ESR, VAR, etc.).
6. Heat treating process-- Is this part going to be through hardened? What is the section size? Hardenability needs to be appropriate when through hardening larger sections. The heat treating process must be carefully controlled so that no decarburization or internal oxidation occurs. Cracking after quenching is another defect that must be eliminated. Dye penetrant testing or magnetic particle inspection are commonly used to inspect heat treated parts for surface cracks.
These are some of the variables that you should consider when specifying the material for this application. Just writing "4340, HRC = 35" is not sufficient to guarantee adequate performance.