I've been using a full wheatstone bridge (4 strain gauges) to read stress on a steel bar, through a circuit mounted on an arduino breadboard. This seemed alright. I later used two strain gauges of similar (but not same) properties and similar size for a half bridge. As soon as I completed the circuit, one of the strain gauges' foil darkened but the other one was fine. Could this happen if I use the wrong resistances in the other half of the bridge?
The power dissipated in strain gauge elements should always be far less than the power level at which you can do them any harm. Even connecting the "excitation voltage" across a single bridge element should do it no harm, eve though this would not be a useful thing to do. The implications are that you have done something which is fundamentally incorrect. The voltage used must be substantially greater than the rated voltage for the damaged part.
One possible reason for one only gauge being damaged is that the output is grounded or connected to v+ or to some other voltage so that theundamaged gauge "sees" little or no voltage.
Do you have a data sheet