Effect of Wave Formation during Shock-Wave Compaction of Powders

Abstract

S. P. Kiselev and V. P. KiselevThe problem of shock-wave compaction of a metal powder enclosed in a metal container with a transverse partition is solved. A model of wave formation on the partition and in the compact adjacent to the partition is proposed; the model is based on the loss of strength in the powder due to collapsing of pores and to development of instability of the partition being compressed in the shock wave.Introduction. Shock-wave compaction of powders is widely used for obtaining materials with prescribed properties [1-3]. One of the drawbacks of this method is origination of various inhomogeneities in the compact. For instance, compaction of a powder with a "central body" leads to formation of a "cold" layer in the compact [3]; the reasons for origination of this layer were considered in [3][4][5].The experiments performed in [6] revealed a new type of inhomogeneities, which arise in shock-wave compaction of a copper powder in a cylindrical ampoule with transverse partitions made of transformer steel. The inhomogeneities were related to wave formation in transverse partitions and in adjacent layers of compacts. Additional experiments showed that the effect of wave formation after shock-wave loading was not observed if the ampoule was filled by a solid copper sample instead of the copper powder. The effect was not observed either if the transverse partitions were made of materials other than transformer steel (copper, aluminum, stainless steel, or steel St. 20). Results of numerical simulations of powder compaction in an ampoule with a transverse partition are described in the present paper; based on these results, an explanation for the wave-formation phenomenon is proposed.Formulation of the Problem. Figure 1 shows the schematic of powder compaction used in the experiment of [6], which was numerically simulated in the present work (in contrast to [6], only one partition is considered here, but this difference is not of principal importance). A cylindrical steel shell was filled by a copper powder (or by a mixture of copper and molybdenum powders), which was densely packed. Transverse partitions, which were thin circular plates, divided the powder into several portions for technological purposes. Powder compaction proceeded in a shock wave generated by a detonation wave excited by detonation of a high explosive (HE) on the shell surface. It turned out after compaction that wavy deformation of the partitions and adjacent compact was observed if the partitions were made of transformer steel (see Fig. 1).The effect of detonation products was simulated by pressure applied to the upper boundary of the shell P (x, t). The pressure at the detonation-wave front x = Dt was found from the Chapman-Jouguet condition [7] by the formula P H = (2/(γ + 1))ρ HE D 2 , where ρ HE is the density of the high explosive, D is the detonation velocity, and γ = 3. Behind the detonation-wave front, the pressure decreases in the centered expansion wave Dt/2 < x < Dt with an adjacent region 0 < x < Dt/2, where the pressure ...

Effect of the metal structure on the loss of stability of a thin plate separating a powder compressed by a shock wave

“…The density of dislocations on the partition surface is equal to zero; therefore, the wave length in Eqs. (2) is l x = 2h in the transverse direction and l y = 6h in the longitudinal direction. The maximum density of dislocations in Eqs.…”

“…The maximum density of dislocations in Eqs. (2) is A = 20 m −1 (n = 0.6 · 10 11 m −2 and b = 3.4 · 10 −10 m). Figure 6 shows the results of the numerical solution of Eqs.…”

“…It follows from here that powder compaction in the shock wave can be described by the model of a porous elastoplastic material, and the resultant compact can be described by the Prandtl-Reiss model. The equations that describe this process can be found in [2].…”

“…8b). Filling of voids is accompanied by the loss of stability in the micropowder [2] (S ij = 0). When the partition (plate) is compressed by the shock wave, the plate loses its stability.…”

“…The problem of shock-wave compaction of a metallic powder separated by a transverse partition was numerically solved in [2]. It was shown that wave formation was caused by the loss of stability of the plate compressed together with the powder, which loses its strength because of filling of voids.…”