Energy deposition and microstructural modification in dynamically consolidated metal powders

A model is presented for the deposition of energy at powder particle surfaces during dynamic consolidation. The average energy flux incident on the surface of a powder particle is estimated to be E/tauA where E is the specific energy deposited by the shock, tau is the shock rise time, and A the measured powder specific surface area. This flux is assumed to be constant over the rise time of the shock, falling abruptly to zero for times longer than tau. Solution of the thermal transport equation subject to this boundary condition yields the thermal history within a powder particle having the area-equivalent diameter D = 6/rho0A, where rho0 is the solid density. The magnitude of the temperatures and the heating and cooling rates indicate likely material transformations. The penetration of a given isotherm provides an estimate of the volume fraction of material transformed. Good agreement is found between model calculations and measurements of the extent of local martensite formation in consolidated 4330V steel powder and of local melting in consolidated aluminum-6% silicon and copper powders. The general implications of the model are discussed