Imam al-Shafi'i (may Allah have mercy on him) said: "The rational basis of the view of Ata' (may Allah have mercy on him) on this is that he held that there is neither making up nor expiation owed by him."
Imam al-Shafi'i (may Allah have mercy on him) said: "Allah Almighty declared the vow regarding the bahirah and the sa'ibah (animals) void only because it is disobedience, and He did not mention any expiation for it, and the Sunnah has come in accordance with this."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الأيمان / Q20056