What is the maximum percentage of carbon allowed in stainless steel 202 so that it does not cause brittleness?
All standardised grades of alloys have definite limits of composition. If its common, then a quick search will find it. 0.15% is the specified limit for SS202.
Whether its brittle or not depends on what you mean by brittle and its thermal processing. Its a martensitic stainless steel so note the details in azom and that it will be more brittle when hardened as described.
Depends on the environment and mechanical stress (+ speed etc.) The brittleness of a piece of steel highly depends on it's composition (<10% Cr can make it super brittle, too) it's 'temperature history' (e.g. hardened, welded) and the temperature where it is exposed.
So this is found in table-works. You start with the temperature of your environment: (for details see charpy impact test)
Note that transition temperature. I guess, that's the line, your question refers to. So now you look up the table-works and find an adequate composition for your steel.
room temperature, welded/hardened → less than 0,25 % C (e.g. S235) are always fine; 0,25…0,5 % may work too
not welded/hardened → the same steel (0,25…0,5 C) can be ductile until -50°C
I couldn't find a reference in a quick search, but up to 0,8 % C shall be fine for most things you have in mind.
Type AISI 202 stainless is very tough regardless of carbon content ( in specification). It is an austenitic stainless with roughly half the nickel replaced by manganese. It becomes stronger with less ductility when it is cold worked , regardless of carbon . As an austenitic , it can not be hardened by heat-treatment. It is relatively uncommon so little data is available: However, the mechanical properties of 202 are similar to AISI 301 , a much more common grade.