Free-cutting copper alloy, and manufacturing method of free-cutting copper alloy

A free-cutting copper alloy comprising:

• higher than or equal to 59.5 mass % and lower than or equal to 64.5 mass % of Cu;
• higher than 0.50 mass % and lower than or equal to 1.20 mass % of Si;
• higher than or equal to 0.003 mass % and lower than 0.10 mass % of Pb;
• higher than or equal to 0.030 mass % and lower than 0.10 mass % of Bi;
• and
• higher than or equal to 0.010 mass % and lower than or equal to 0.14 mass % of P,
• with the balance being Zn and inevitable impurities,
• wherein among the inevitable impurities, a total content of Fe, Mn, Co, and Cr is lower than or equal to 0.35 mass % and a total content of Sn and Al is lower than or equal to 0.35 mass %,
• when a Cu content is represented by [Cu] mass %, a Si content is represented by [Si] mass %, a Pb content is represented by [Pb] mass %, a Bi content is represented by [Bi] mass %, and a P content is represented by [P] mass %, relationships of
• 56.8≤f1=[Cu]−4.7×[Si]+0.5×[Pb]+0.5×[Bi]−0.5×[P]≤59.0, and
• 0.04≤f2=[Pb]+[Bi]≤0.19
• are satisfied,
• a metallographic structure contains α phase and β phase,
• in constituent phases of the metallographic structure excluding non-metallic inclusions that are intermetallic compounds, precipitates, oxides, and sulfides, when an area ratio of α phase is represented by (α) %, an area ratio of γ phase is represented by (γ) %, and an area ratio of β phase is represented by (β) %, relationships of
• 30≤(α)≤75,
• 25≤(β)≤70,
• 0≤(γ)<3,
• 10.0≤([Bi]+[Pb]−0.002)1/2×10+([P]−0.001)1/2×5+((β)−7)1/2×([Si]−0.1)1/2×1.2+(γ)1/2×0.5≤14.0, and
• 1.2≤([Bi]+[Pb]−0.002)1/2×((β)−7)1/2×([Si]−0.1)1/2≤3.0
• are satisfied,
• a particle containing Bi is present in the α phase, and
• a compound containing P is present in the β phase.