Resource giving has a limit (I think +1 or +2 relationship?), but each race can increase the maximum relationship gain from a particular resource (credits for TEC, crystal for Advent, metal for Vasari) after appropriate research.
Locked teams will automatically put you at 10 relationship points, and resource giving won't change that. The only way to go beyond 10 is through Envoys, as Ryat mentioned. For 17.5 relationship, you'll need to have Envoys at five different planets (putting more than one Envoy at a planet simply lets it gain relationship faster - the cap of 1.5 doesn't change).
You'll also have to go through the trouble of keeping those Envoys and the planet they're stationed at alive (losing the planet will cause you to instantly lose any relationship you gained from that planet, even if Envoys remain in the gravity well).
