Not a mayday, but on a partial engine failure off a runway with few land-ahead options I simply declared 'partial engine failure, returning to land immediate, 09L'. I couldn't hear the radio (despite the DC headset) due the misfiring engine, so just kept transmitting that in case someone else's transmission was blocking me.
The implied message was 'I'm in the sh1t and coming round for an immediate landing. It's MY runway, everyone else pi55 off'.
It must be added I only ever considered using the radio once I'd established we could (just) maintain height and had got the aeroplane low level close in downwind and stable for a '180 turn onto the numbers from maybe 250 feet' touchdown.
Aviate, navigate, communicate.
Off that same runway many years later another pilot (one I knew) had a total engine failure on take off. he 'communicated' (sent out a mayday) but didn't 'aviate' (i.e get the bleedin' nose down NOW).
He died and his passenger has life changing injuries. I wonder to this day why he pressed the xmit button rather than pushing the yoke forward to prevent the stall/spin that killed him. Not only did he 'stop flying the aeroplane', he did so in order to send a message which could not have been of any use whatsoever.
Maydays are great if you've first got the aeroplane stable (aviate navigate, communicate) and others may not be aware you might need rescuing from a wreck.