Totally broken iPhone serial number

If it is broken in pieces why do you need it?

If you have been syncing with iTunes on your computer you might find it there.

If it is literally in pieces Apple probably will not do an out-of-warranty replacement of your iPhone.

Find the serial number or IMEI on your iPhone, iPad, or iPod touch - Apple Support

If you don’t have the original box, or sales receipt, no can.