Stress relieving intrumented steel bar

A little more information will help.

Bar material?
Prior thermal history?
Test conditions?

Likely you are noticing that material behavior at the small scale (as measured via strain gauges) can vary greatly and so large scale behavior becomes the "average" response of many small scale regions. The exercising can induce strain hardening and make the bar's properties more uniform over its entire area.

Regards,

Cory

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

It may be advisable to stress moderately the bar in a tensile testing machine before applying the strain gauges, in order to overcome the lack of sensitivity at zero.

The pre-conditioning must be done in the same mode as the application. If you are loading in torsion, then condition in torsion.
Cory is right on with this, concerning local behavior. At low loads there isn't a uniform stress pattern in the part. You haven't loaded it enough to overcome all of the minor local variations in strength and residual stress.
An example is when you want to take very accurated measurements of elastic modulus. You always load the sample in tension to about 1/2 of the yeild, tehn unload to about 10% of yeild, and then re-load. The values from the final loading are much more consistent and accurate.

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Corrosion never sleeps, but it can be managed.

I think Cory's solution is good, but is somewhat of a "workaround" required likely because of gage response. What type of gages are you using? What is their gage length? Using the longest practical gage length and using a gage that is well bonded to the bar (preferably welded)will also help to mitigate these issues. Adhesive bonded strain gages are susceptible to temperature, moisture, and other variations that might be affecting your low strain range.