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Future upgrades of the Large Hadron Collider (LHC) will require large aperture and high gradient quadrupoles. Nb3Sn is the most viable option for this application but is also known for its strain sensitivity. In high field magnets, with magnetic fields above 12 T, the Lorentz forces will generate mechanical stresses that may exceed 200 MPa in the windings. The existing measurements of critical current versus strain of Nb3Sn strands or cables are not easily applicable to magnets. In order to investigate the impact of high mechanical stress on the quench performance, a series of tests was carried out within a LBNL/CERN collaboration using the magnet TQS03 (a LHC Accelerator Research Program (LARP) 1-meter long, 90-mm aperture Nb3Sn quadrupole). The magnet was tested four times at CERN under various pre-stress conditions. The average mechanical compressive azimuthal pre-stress on the coil at 4.2 K ranged from 120 MPa to 200 MPa. This paper reports on the magnet performance during the four tests focusing on the relation between pre-stress conditions and the training plateau.