In accordance with dynamic impact experiments and macro-micro scopics observational approaches, such as high speed image processing technique and electron microscope technique etc., a study on dynamic initiation and propagation processes of the interface crack between the face and core for the sandwich composites are carried out. Employing micro-damage mechanics theory, a novel dynamic fracture mechanics analysis model considering geometrical and physical characters of the viscoelastic interface layer and a novel damage mechanics model reflecting the influence of the meso-scopic constitutional materials parameters along the front region of the  interface crack are established ,and the corresponding crack initiation and propagation criteria are also proposed. Adopting analytic singular integration equation method and meshless method on basis of local-global analysis principle, dynamic initiation and propagation processes of the interface crack are analyzed, respectively. By parametric discussing, the relationship between the influence factors (e.g., loading speed, physical and geometrical properties of material constitutions and strength of viscoelastic interface layer, etc.) upon the failure modes (e.g., initiation and propagation of interface crack, micro crack in core, etc.) are examined systemically, and dynamic failure mechanism of the materials is well provided, furthermore, a toughening design principle for sandwich composites is proposed. The research project is one of challenging academic work with engineering background and the achievements are believed to form some contributions for developing nonlinear dynamic fracture mechanics and promoting design and application of advanced sandwich composites and engineering structures in China, therefore it is of impotence in theory significance and engineering value.