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THEORY AND TECHNOLOGY OF THE COMPONENT FORMATION PROCESS GENERATION OF STRONG SHOCK WAVES IN THE HIGH-SPEED PRESSING OF METAL POWDERS L. A. Maksimenko, M. B. Shtern, I. D. Radomyselskii, and G. G. Serdyuk UDC 621.762.045 In the investigation of the high-speed (shock or explosive) compaction process of metal powders, it is important to establish whether strong shock waves are generated in the powders during their densifica- tions, as this necessitates a different approach to the quantitative description of the static and dynamic pressing processes. In continuum mechanics, the following definitions of a strong and a weak shock wave have been adopted. Values of any parameter characterizing a medium under consideration, such as density, pressure, velocity, or entropy, can be represented as values of some functions f(x), where x is the coordinate of the wave front path. For any point x = x 0, the value of such a function is ft=lim f(x)on the right and f2-lim f(x)on the left. xxo+ xxo- If fl f2, the point x 0, which characterizes the position of the shock wave front at a certain instant of time, is represented simultaneously by two values of the parameter under consideration. A stepwise change in the value of the parameter, sometimes referred to as a strong break, is observed; accordingly, the shock wave in such a case is termed a strong shock wave. If fl = f2 (but f/0x)l (af/0x)2), the value of the para- meter changes smoothly or shows only a slight break, and the shock wave in such a case is known as a weak shock wave. A strong shock wave appears when the rate of application of load exceeds the velocity of propagation of sound in the medium under examination. When the rate of loading is less than the velocity of sound, a weak shock wave is generated in the medium. In 1, on the basis of an analysis of the relationship p = p(h), where p is the compaction pressure and h the punch travel, it is concluded that only compression waves, i.e., weak shock waves, can exist in metal powders undergoing densifieation. In 2, on the other hand, a stepwise change in pressure was observed experimentally in the pressing of a steel powder in a closed cold die set with an initial velocity of 145 m/ sec, and consequently it was assumed that strong shock waves can occur in metal powder s. The present work was undertaken with the aim of demonstrating theoretically the possibility of strong shock waves being formed in metal powders. In the phenomenological approach to the investigation of the shock compaction process, the tool em- ployed is the theory of continua. According to this theory, the laws of the conservation of mass, impulse of force, and energy for the case of a one-dimensional flow of a medium can be expressed, as shown in 3, by the following equations: P o (u2.- D) = Pi (ul - D) = m; (1) P2 - P2 (U2 - D) 2 = Pl .4- P2 (ul - D) 2 = ; (2) T. G. Shevchenko Kiev State University. Institute of Materials Science, Academy of Sciences of the Ukrainian SSR, Translated from Poroshkovaya Metallurgiya, No. 4 (112), pp. 17-20, April, 1972. Original article submitted March 16, 1970. ?9 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00. 268 # Fig. 1. Shock adiabatic for metal powder. Fig. 2. Oscillogram of pressure buildup with time in shock pressing of iron powder. 92(u2_D)(e2_ P2 _t_(u2 D) ) ( +P-I-(u D) ) (3) Here p is the density, u the velocity, the energy of the medium, D the velocity of the shock wave front, calculated relative to the velocity u, and m, j, and e, respectively, are the mass, impulse, and energy fluxes through the shock wave front. The subscripts i and 2 denote parameters ahead of and behind the shock wave front, respectively. Equations (1)-(3) have been derived on the assumption that processes such as internal friction, diffusion, and heat conduction are absent in the medium. From Eqs. (I) and (2), we can obtain or 1 mZ=pl - 1 m2 m2 _ - Pl 0192 , (4) P2 - 91 The expression for m is valid irrespective of the type of waves (strong or weak) which densify the medium. In densification by weak shock waves, however, we always have m = 0, because the velocity of ap- plication of the load initiating a shock wave is close to the velocity of propagation of the latter, that is, uD. In the case of media densified by strong shock waves, m 0. Thus, to prove the existence of a strong shock wave in a metal powder, it is necessary to demonstrate that, when the latter is loaded at a velocity exceeding the velocity of propagation of sound in the powder, a mass flux travels across the wave front, i.e., m 0. Let us consider the shock adiabatic for a metal powder loaded at a velocity exceeding the velocity of propagation of sound in it. According to the experimental results obtained in 1, this adiabatic is approxi- mated by the curve illustrated in Fig. 1. Here h is the strain of the powder body and p the corresponding pressure. This curve is convex downward, and it can therefore be assumed that ap 02p 0h 0, Oh 2 O (5) since p = p(h) is capable of being differentiated. The density of the compact being pressed will be M p = S(ho_h) (6) 269 where M is the mass of the powder, S the cross-sectional area of the die in which the powder is being pressed, and h 0 the powder fill height. Since and from Eq, (6) it follows that we obtain, taking into account the expressions (5): Op _ dh Op ap ap Oh (7) dh d-5o, We can further write Hence o. (s) ap ( dh ) 2 apj a0 3 = ) Oh= ?9 (3) ula: asP. O. (10) 0p 2 As the function p = p(p) admits of being differentiated, it can be expanded according to Taylors form- P2 (P2) P (Pl) - (02 - Pl) + asp (P2 - Pl) Op z 2 ! + q (P2 - Pl) (11) Landau and Lifshits 4 have shown that lim q) (P2 - Pl) 2 0. Q-ef-o P2 - Pl Hence, considering only the first two terms of the expansion, we have P2 - Pl Op aSP (P2 - Pl) p2-Pl - Op t- Op 5 2 (12) Taking into account the expressions (8) and (10) and also the fact that, according to Zemplenrs theorem, P 2 P 1, we obtain We can therefore write Using Eq. (4), we obtain m 2 0, so that m 0. /)2 -Pl -0. P2- P P2 - Pl PJP2 0. P - Pl 270 Thus, in the shock densification of a metal powder, it is possible for the mass and wave velocities to have values at which the particle velocity exceeds the velocity of propagation of sound in the powder 1, and furthermore the inequality m 0 holds. These are the two necessary and sufficient conditions for the exist- ence of a strong shock wave. Using the apparatus described in 5, we were able to record pressure jumps in the shock pressing of PZh2M iron powder.* At initial pressing velocities in excess of 100 m/sec, the pressure buildup vs time oscillograms obtained were found to be similar to those reported in 2. However, pressure jumps were observed also at lower initial velocities. Figure 2 shows an oscillogram in which a nonuniform pressure gradient can be seen at an initial velocity of 75 m/sec. The slight diffusion of the pressure buildup front is linked with the finite width of the break. It is in this layer that dissipative effects associated with the pres- ence of internal friction, heat conduction, and the like are concentr