In the present work, we report on results of simulation-based study of mechanical response behavior and mechanisms of failure of a nanometer-scale polyimide adherent thin-film on a silicon substrate. A transition between adhesive and cohesive modes of failure with the strain rate was shown to occur in the system, subjected to high strain-rate tensile loadings. The physical mechanisms, leading to the bi-material failure, were identified for each failure mode. The study reveals that damage development and propagation are determined by a complex interplay between coupling across the interface and relaxation processes in the adherent layer. The two act in a synergistic manner to generate an instability, leading to either cohesive or adhesive failure.