The bonding between copper (Cu) and iron (Fe) to form a bi-layer composite using explosive welding is investigated through molecular dynamics simulation. Three stages in the joining process, including loading, unloading and cooling, are sequentially considered in modelling the formation of the bonding interface. The results demonstrate that three types of bonding interfaces can be obtained, based on whether melting happens. The morphologies and the atomic structures of the three types bonding interfaces in each stage are analyzed. The formation of nanograins near the bonding interface is mainly due to the melting and subsequent cooling process. Atomic simulations of tensile tests reveal that melting is not a necessary factor to form the bonding interface. What's more, depending on whether melting occurs, the joining mechanism can be regarded as pressure welding or fusion-diffusion welding.