Dear Chen Ding this is a very interesting technical question. Unfortunately I'm not a proven expert in the field, as we work in the area of organometallic chemistry. However, I think that the attached rather old publication dated 1934 might give you some helpful hints. The paper is entitled:
EFFECT OF COLD-ROLLING ON THE INDENTATION HARDNESS OF COPPER
Oxygen-free copper—also known as OFC, Cu-OF, Cu-OFE, and oxygen-free, high-conductivity copper (OFHC is obtained by melting copper and combining it with carbon and carbonaceous gases.
Oxygen-free copper (OFC) or oxygen-free high thermal conductivity (OFHC) copper is a group of wrought high-conductivity copper alloys that have been electrolytically refined to reduce the level of oxygen to 0.001% or below.
High-electrical-conductivity coppers are distinct from coppers deoxidized by the addition of phosphorus in the smelting process. Oxygen-free phosphorus-containing copper (CuOFP) is typically used for structural and thermal applications where the copper material will be subject to temperatures high enough to cause hydrogen embrittlement or more exactly steam embrittlement. Examples include welding/brazing rods and heat exchanger tubing.