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The large currents in the cable-in-conduit conductors (CICC) destined for the high field magnets in the International Thermonuclear Experimental Reactor (ITER), cause huge transverse forces on the strands compressing the cable against one side of the conduit. This load causes transverse compressive strain in the strands at the crossovers contacts. Moreover, the strands are also subjected to bending and contact surfaces micro-sliding, which results into friction and anomalous contact resistance versus force behavior. Three Nb3Sn central solenoid model coil (CSMC) conductors were tested previously in the Twente Cryogenic Cable Press up to 40 cycles with a transverse peak load of 650 kN/m. This press can transmit a variable (cyclic) transverse force directly to a cable section of 400 mm length at a temperature of 4.2 K (or higher). To explore life-time cycling, we tested a CSMC Nb3Sn conductor up to 40,000 cycles. The coupling loss and the associated interstrand resistance between various strands and strand bundles are measured at various loads. The force on the cable and the displacement are monitored in order to determine the effective cable Young's modulus and the mechanical heat generation. Some aspects of strand deformation in CICC's are discussed. The test results are discussed in view of previous press results and data extracted from the ITER model coil tests.