ruptured duck, n. — Green’s Dictionary of Slang

ruptured duck n.

[orig. US Air Force jargon for a damaged aircraft; the ‘ruptured’ presumably indicates the fact that one wing of the eagle is underneath and extends beyond the circular design of the button]

(US milit.) the lapel pin or pocket insignia worn by an honourably discharged US serviceman; thus the honourable discharge itself.

1945		Time 29 Oct. 11/1: The design of the present discharge button is not popular (G.I.s know it as the ‘ruptured duck’).
1953		R. Chandler Long Good-Bye 202: He was wearing a British Army Service badge. Their version of the ruptured duck.
1965		L. Bruce How to Talk Dirty 31: He [...] wore a double-sized ruptured duck he had made especially for himself.