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What is the maximum percentage of carbon allowed in stainless steel 202 so that it does not cause brittleness?

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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.

http://www.azom.com/article.aspx?ArticleID=8209

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.

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The specified maximum carbon content in stainless steel 202 is 0.15 %.

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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) enter image description here

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.

An example:

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.

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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.

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