Dynamic Equilibrium Constitutive Relations of Copper Powder Within Dies Subjected to Mutliple Shock Compactions

An approximate dynamic equilibrium pressure p-specific volume V relation exists for porous materials of a simple type undergoing mutliple shock compaction processes. A copper powder medium in dies is assumed to be of such a type, and the relation is constructed when the medium is compacted by a punch. It is given by an expression in the form of p=(V−V_i)/[b{V_i(1−a)−V}], where V_i, a and b are the material constants. These constants are estimated by matching the computational and experimental results obtained for the mean green density of the medium. Similarly, a dynamic equilibrium lateral pressure p₁-specific volume V relation is also estimated for the medium after being given by p₁=αp²+βp for ρ<3430 kg/m³, where α and β are the material constants and ρ is the density, while p₁=0.5(V_solid/V)^νp+c for ρ≧3430 kg/m³, where V_solid is the specific volume of solid copper, ν the material constant, and the contant c continuously connects the lateral pressures of the above two equations at ρ=3430 kg/m³. The compaction processes analyzed using the estimated relations agree favorably with the powder particle movement and shock wave front paths from experiments, suggesting the validity of the simple type assumption and that of the estimated relationships.