If you're concerned about braking a nail with simple lumber raised beds, you'd better take out nail insurance for tire (I'm in the U.S., so use ing the correct spelling) damage. Problem is, you'll either have to cut the tires in half making two equal halves (like slicing a bagel) and the depth for dirt on each half will be about 4 inches... not enough for most vegetables. Or... you could cut sections out of the arc of the tire, setting them with the tread side slightly buried in the garden. This will give you perhaps 6 inches of depth... again, not much for most vegetables... certainly not enough for root crops like potatoes, carrots or beets. Not only that but if you try to cut the "bead" part of the tire (the part that fits into the steel wheel, you'll need a hack saw and about 14 blades since the steel inside that area is made of several strands of cable...
In about two years when you're sick and tired of the tires (they won't hold the paint you desire... it'll peel off) if you were here in the U.S. you'd have to get a special permit from the government to dispose of them and then only at a regional recycling center... Go for the occasional broken nail and 2 X 8 inch lumber...