Free-cutting copper alloy and method for producing free-cutting copper alloy

A free-cutting copper alloy comprising:

• higher than 77.0 mass % and lower than 81.0 mass % of Cu;
• higher than 3.4 mass % and lower than 4.1 mass % of Si;
• 0.07 mass % to 0.28 mass % of Sn;
• 0.06 mass % to 0.14 mass % of P;
• higher than 0.02 mass % and lower than 0.25 mass % of Pb;
• and
• a balance including Zn and inevitable impurities,
• wherein when a Cu content is represented by [Cu] mass %, a Si content is represented by [Si] mass %, a Sn content is represented by [Sn] mass %, a P content is represented by [P] mass %, and a Pb content is represented by [Pb] mass %, the relations of
• 1.0≤f0=100×[Sn]/([Cu]+[Si]+0.5×[Pb]+0.5×[P]−75.5)≤3.7,
• 78.5≤f1=[Cu]+0.8×[Si]−8.5×[Sn]+[P]+0.5×[Pb]≤83.0, and
• 61.8≤f2=[Cu]−4.2×[Si]−0.5×[Sn]−2×[P]≤63.7
• are satisfied,
• in constituent phases of metallographic structure, when an area ratio of α phase is represented by (α)%, an area ratio of β phase is represented by (β)%, an area ratio of γ phase is represented by (γ)%, an area ratio of κ phase is represented by (κ)%, and an area ratio of μ phase is represented by (μ)%, the relations of
• 36≤(κ)≤72,
• 0≤(γ)≤2.0,
• 0≤(β)≤0.5,
• 0≤(μ)≤2.0,
• 96.5≤f3=(α)+(κ),
• 99.4≤f4=(α)+00+(γ)+(μ),
• 0≤f5=(γ)+(μ)≤3.0, and
• 38≤f6=(κ)+6×(γ)1/2+0.5×(μ)≤80
• are satisfied,
• the length of the long side of γ phase is 50 μm or less, and
• the length of the long side of μ phase is 25 μm or less.