Only in the as-welded condition. The "L" grade material is less likely to sensitize (form chromium carbides in the grain boundaries) and therefore less likely to suffer related corrosion issues (intergranular corrosion attack and higher sensitivity to chloride stress corrosion cracking).
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Rust never sleeps
Neither should your protection
I'm going to have to disagree with the previous post in that the only benefits are in the as-welded condition. The affects that lower carbon in the 304L has is based on the corrodent. This can be quite pronounced especially under highly oxidizing conditions.
In our case we have one process where we oxidize organics with HNO3 using 304L SS as the primary MOC. There is direct relationship between the general corrosion rate experienced and the %C in the base metal. Historically as the processing of SS has improved we have continually decreased the max. C when specifying 304L stainless steel from 0.030/0.035 to the present max. of 0.015.
This effect is most evident in our large 304L storage tanks. We map the location of each plate and compare the corrosion rate on each plate vs the chemistry.
In another process where we remove organic peroxides we again used 304L with with carbon as low as obtainable.
I'll disagree with myself also. In acid service (nitric usually) you can measure the effect of C down to low levels.
In most services though the reason that higher C material does not preform as well is that it is not annealed fully. If you use an electrochemical test for determining senitization you will be amazed (dismayed) at how badly annealed commercial product can be. Even 304L from mills often has trace amounts of carbides in grain boundaries.
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Rust never sleeps
Neither should your protection