The rise time of a strong shock wave propagating through a porous material is estimated by analyzing the finite deformation of an elastic/viscoplastic spherical shell under impulsive pressure loading. The analysis examines explicitly the effects of dynamic loading rate and initial temperature and explains the relatively large shock rise times observed in porous materials. Results of the analysis provide a consistent and realistic interpretation of available experimental data. Metallic and

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... c powders can be consolidated by the passage of a strong shock wave through an initially porous media. 1-4 Earlier investigations of shock wave phenomena in porous materials have focused primarily on the shock Hugoniot relationships and the minimum pressure required to produce a fully dense compact. 5, 6 In addition, the processes associated with shock consolidation have been investigated experimentally and theoretically. 7-9 A finite rise time of shock waves in porous materials has been observed 7,8 which was independent of pressure at high shock pressures. 8 The collapse of a spherical shell under an external impulsive pressure loading has been studied by Carroll and Holt 9 to model dynamic compaction of porous materials. The deformation of the matrix material was assumed to be rate independent, perfectly plastic. The finite rise time of the shock wave propagating through a porous material was found to be related to the time of pore collapse and it was shown that pore collapse is retarded by inertial effect. The dynamic consolidation process involves high strain rates in the range 10 5 to 10 7 s Ϫ1 . Experimental evidence indicates that flow strength of most metals is strongly rate dependent at these strain rates. 10,11 Tong and Ravichandran 12 have recently reexamined the dynamic pore collapse problem by considering the finite elastic/viscoplastic deformation of a spherical shell. Their results indicated that strain rate, strain hardening, thermal softening, dynamic loading rate, pore size, and initial relative density play a significant role in pore collapse. In particular, a viscoplastic material model including strain-rate sensitivity, strain hardening, and thermal softening is assumed to be of the form 10-12