zaist;
Typically, the higher the carbon content in steel, the higher the ductile-to-brittle transition temperature (DBTT). I would estimate that the DBTT @50% flat fracture for carbon steel with 0.50% carbon is about 100 deg F. This value is based on my picking off a data point from a graph of Charpy V-notch impact values versus test temperature for various plain carbon steels with varying carbon contents (0.11% to 0.67%).
The DBTT depends on heat treat condition and residual elements like S, P, As, Sb, Sn as well as the carbon content. I agree with metengrs estimate but it could be considerably greater. I would expect the range to be between 60F and 150F.
Depends on the heat treatment. Normalized or Q&T, and at what temperatures?
For a general idea look in the ASM Metals Handbook Vol.1 in the chapter on Notch Toughness of Steels.
Considering how low the toughness of this grade will be to start with you do need to be careful.
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Corrosion never sleeps, but it can be managed.
I believe this is your "pin" question from another forum- can you tell us a little more about the part - how big is it? what sort of service conditions does it see? etc You will probably get some advice on an appropriate material if 1050 is not the correct choice.