Cold stabilization is cycling the temperature - for example, immersing in a water:alcohol solution below room temperature, then immersing in boiling water, then repeat. This can remove residual stresses. No comment regarding fatigue - such a complex issue, it is impossible to generalize. I have no idea if there are Internet information sources.
The biggest reason to use T7 is for improved Stress Corrosion Cracking resistance.
T651 means that mechanical stress relief was used between quenching and artificially aging. Usually done on semi-materials (sheet, bar, etc.) with constant cross section, not on final parts.
Regards,
Cory
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