I have a 99 dodge grand caravan that the cooling had quit on. I replaced the relay and two days later they quit again. I had the screws tight and relay nice and flat. I put high temp contact grease on the back, could a bad fan motor over work the relay and cause it to go bad again and how could I test the motor
You're right about the high current. If that's the problem, the fan should feel tight when you spin it by hand. Measuring the current won't really work. To vary the motor speed, the voltage is switched on and off rapidly and the percentage of on-time is increased to increase the motor speed. That's called pulse-width modulation. There is either full voltage across the relay and no current flow, or no voltage across the relay and full current. Either way, if you do the math, (volts x amps = power), one of those two will be zero, so in theory, no power is dissipated and no heat should be developed. That switching takes place hundreds of times per second. If you use a digital volt / ohm / amp meter, it takes a reading, analyzes it, displays it, then starts over again. It might take one reading when current is at 0 amps, and half a second later it could take the next reading when current is at maximum. The meter will not average the current reading like the older pointer-type meters. The display will bounce around in a confused meaningless state.
If the motor spins freely, there could be some other problem such as a wire to the motor is grounding out, or it's possible the new relay isn't even defective. Check for voltage on the 12 gauge gray wire at the relay, or you can jump that gray wire to the dark green wire and the fan should run wide open. That will prove the 12 volt feed and wiring are okay.
Many of these have two fan motors. Only one would have to be tight to draw excessive current. As a test, you could unplug one of them, then replace the 40 amp fuse with a 20 amp. The relay should hold up to the higher current of a single tight motor but the fuse will probably blow over time if that motor really is drawing heavy current. If it runs fine that way for a few days, unplug that fan and plug the other one in and try it again. If neither fan blows a 20 amp fuse, the pair shouldn't blow the 40 amp fuse. That would say they are drawing current well within the safety margin of the 40 amp fuse and the relay should be able to handle that.