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The pertinents: 1968 convertible 327/300 HP automatic no mods.
The Situation: Took the car out this morning to a place for breakfast ~15 miles one way, no issues, ran like a dream, after a sausage omelet and a couple biscuits, hopped back in and headed home, again no issues, she ran great. Stopped for gas at a convenience store in the neighborhood (about a mile from home) Pumped 30 bucks in it while the Mrs went in and bought beer. Stowed the beer and went to start it, Nothing, no click, no nothing. pulled the battery cover open to find the positive connection melted off the battery, completely melted. No smoke, no foul odor, no warning, no nothing. Got the car back to the house and started inspecting. The insulation on the positive cable is fine no sign that anything went wrong other than the molten metal drops in the battery compartment and the end missing on the cable. I disconnected the cable from the starter and did a resistance check to ground and it was completely open. Not real sure where to go from here, except to the parts store.
The outside of the cable can look perfect on each end, but the copper strands inside the sheath can be coated with green oxide. Peeling the sheath back at least 6" from each end of the cable may show the oxide.
Also, if the sheath has been cut/gouged open where it runs along the tunnel can cause oxide.
FYI...I installed a replaceable inline fuse on my Harley to prevent a meltdown of the cable, battery, or starter.
Now that you guys bring it up, I have seen on older GM's where the Pos side terminal can get battery corrosion inside the cable end. It builds up under the jacket where the bolt goes and it's difficult to see on the side-terminal-style cable end ...but that could lead to a bad connection and maybe heat/spark's, etc. I don't know if I've ever seen one 'melt' though. Must have been only melting and not burning (or you'd definitely smell it).
Probably not any more than other classic cars. But point taken...
I rewired my car over the winter and many of the wire insulation were very brittle, some even cracked as I took them out.
That explains why I always had electrical gremlins for 10+ years.
I would inspect the starter. Many years ago on my 68, the ring in the Bendix gear broke. That caused the starter armature to hit the case. That melted the positive cable at the battery. After you fix the problem, consider adding a knife switch on the negative side of the battery. Jerry
consider adding a knife switch on the negative side of the battery. Jerry
This was literally the first thing I did when i bought my unrestored '71 a year ago. For the next couple years, until I do the full frame off and have personally inspected or replaced every wire, that knife switch gets opened every time the car sits for more than a few hours, and for sure every time it is inside the garage.