In this study, a microscale interface consisting of amorphous polyethylene (PE) chains with the united-atom (UA) model and face-centered cubic (FCC) crystal copper as the substrate was established. Moving the copper layer with a given rate, the damage evolution of the interface during the tensile deformation was examined by molecular dynamics (MD) simulations. The stress-strain relationship was obtained to capture the evolution of tensile deformation. The distribution of the temperature field was adopted to predict the damage initiation and the failure mode. The phase diagram of the failure mode with respect to the thickness of the PE layer and the loading rate was provided. The results show that the PE layer with smaller thickness brings higher load-bearing capacity with larger yield strength. As for the rate-dependence, a rate hardening followed by a rate-softening of yield strength was observed. In addition, the failure modes evolves from cohesive failure to interfacial one as the loading rate of tension increases progressively. It can be assumed that the control parameter on the failure mode changes from pure material strength of PE to the bonding strength between PE and copper. Furthermore, a larger thickness of PE layer leads to the cohesive failure with higher probability under a narrow range of loading rate with small values. However, the thickness-dependence of failure mode attenuates gradually and diminishes ultimately under higher loading rate, which leads to the transformation from mixed mode to interfacial one.