The index n of the voltage-current characteristic of large superconductors is a crucial parameter to assess the allowed range for coil operation. In the tests of the Insert coils at the CSMC as well as in the short sample test in the SULTAN facility, it is observed that the index n dramatically decreases from the Nb3Sn strands extracted from cable-in-conduit provide the evidence of a permanent performance drop in the strands, likely due to the transverse load accumulation at the strand crossovers in the cable. This effect is not observed in NbTi conductors. The immediate implications for the Nb3Sn conductor design are discussed and layout modifications to mitigate the effect are proposed.