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Supersonic Velocity of the Point of Contact O Technical Physics, Vol. 48, No. 8, 2003, pp. 1001–1008. Translated from Zhurnal TekhnicheskoÏ Fiziki, Vol. 73, No. 8, 2003, pp. 62–70. Original Russian Text Copyright © 2003 by Drennov, MikhaÏlov, Nizovtsev, RaevskiÏ. SOLIDS Perturbation Evolution at a Metal–Metal Interface Subjected to an Oblique Shock Wave: Supersonic Velocity of the Point of Contact O. B. Drennov, A. L. MikhaÏlov, P. N. Nizovtsev, and V. A. RaevskiÏ All-Russia Research Institute of Experimental Physics, Russian Federal Nuclear Center, Sarov, Nizhni Novgorod oblast, 607190 Russia e-mail: [email protected] Received December 30, 2002 Abstract—The perturbation evolution at the interface between identical metals (metal plates) that is exposed to high-speed oblique shock waves is observed experimentally for the first time (the waves are attached to the point of contact, so that a cumulative jet cannot form). The experiments are numerically simulated by the two- dimensional Lagrange method. An elastoplastic model where the dynamic yield strength is a function of mate- rial state parameters is employed. An analytical technique to treat instability development under given loading conditions is suggested. High strains produce a high-temperature zone near the interface (thermal softening zone). A short-lived shear flow with a high velocity gradient depending on the angle and velocity of plate col- lision is observed. In this zone, the shear modulus and the yield strength are appreciably lower than under nor- mal conditions, which favors instability development. © 2003 MAIK “Nauka/Interperiodica”. INTRODUCTION forms in the collision zone. With vc > vcr, attached High dynamic pressure in metals may be produced oblique shock waves set up at the point of contact. They turn the flows through angles that, taken together, add by oblique shock loading. Under these conditions, the γ specimen is subjected to the normal and tangential up to . The jet does not form in this case. It is believed components of stress and velocity [1, 2]. [1, 5] that perturbations at the metal–metal interface are also hardly probable in this situation, since their basic Oblique collision of metal layers (one way of load- source, a cumulative jet, is absent. ing by oblique shock waves) generates intense shear strains in the contact zone, heats up the surface layers The state of the interface under the supersonic load- of the metals considerably, and produces cumulative ing regime is little understood. jets [1, 3]. These effects distort the shape of the metal– metal interface, causing both regular and asymmetri- cally distorted waves to arise, and may even produce EXPERIMENTAL molten layers of mixed composition. In a number of Our experiments were carried out by the following cases, the specimens rigidly adhere to each other [1, 4]. scheme (Fig. 1). Plate 3 is rigidly mounted on massive To date, the subsonic conditions of oblique colli- steel support 4. Movable plate (striker) 2 is fixed over α sion, vc < C0 (where vc is the velocity of the point of plate 3 at an angle to it. The movable plate is set in contact and C0 is the sound velocity in a given mate- motion by explosion products of blasting explosive 1 rial), have been extensively studied. Under these load- (the pentaerythritol tetranitrate (PETN)–based plasti- ing conditions, a cumulative jet is continuously formed cized explosive with ρ = 1.51 g/cm3 and D = 7.8 mm/µs if the pressure near the collision point exceeds the metal or the octogen-based plasticized explosive with ρ = strength [1, 5]. 1.86 g/cm3 and D = 8.75 mm/µs), in which a plane glid- Collision at v > C is described in a way similar to ing detonation wave is generated. The minimal gap h c 0 between the plates is taken such that the movable plate a supersonic flow past a wedge [2]. If the angle of col- ≥ γ γ has a uniform velocity prior to collision: hmin (3– lision is constant ( = const, where is an analogue of δ δ 5) str, where str is the striker thickness [6]. To prevent the wedge angle), there exists a critical value vcr of the ≤ ≤ spalling in the striker, thin spacer 5 made of a low- velocity vc. When C0 vc vcr, detached oblique shock waves appear in the flow. In going through the wave acoustic-impedance material is inserted between the front, the supersonic flow becomes subsonic. Both striker and explosive. The spacer does not influence the flows arrive at the point of collision with a subsonic velocity and symmetry of the striker motion [7]. velocity (the fixed and movable plates are in the coordi- Oblique collision is characterized by the following nate system related to this point), and a cumulative jet parameters: D, the rate of explosive detonation; W, the 1063-7842/03/4808-1001 $24.00 © 2003 MAIK “Nauka/Interperiodica” 1002 DRENNOV et al. D a, mm 1 0.6 5 α 2 0.5 0.4 W min h a γ 0.3 v c 3 λ 0.2 4 0.1 Fig. 1. Experimental scheme. 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 M striker velocity; α, the initial inclination of the striker; Fig. 2. Perturbation amplitude a at the AMTs–AMTs inter- γ face vs. Mach number for γ ≈ 13.5° = const. , the angle at which the plates collide; vc, the velocity of the point of contact; and a and λ, the amplitude and wavelength of arising perturbations (Fig. 1). After dynamic loading, the plates were trapped by a porous layer. Fragments for preparing microsections were cut from the central parts of the plates (which typ- ically measure 100 × 60 × 4 mm). Figure 2 plots the perturbation amplitude a at the boundary between two AMTs å = 0.5, ×100 AMTs å = 1.2, ×75 contacting plates (made of AMTs aluminum alloy) vs. Mach number vc/C0 [8]. The perturbation amplitude a (rather than the perturbation wavelength λ) was taken as an independent variable, because, as a grows, the contact boundary may take the form of turbulently mixed melts of both materials (Fig. 3, AMTs layer). The value of λ becomes uncertain under these condi- AMTs å = 1.3, ×50 AMTs å = 1.4, ×50 tions. The choice of a as an independent variable pro- vides hydrodynamic similarity upon comparing the perturbation amplitudes at the interface between vari- ous (including dissimilar) metals. The ascending portion of the curve a = f(M) reflects the jet formation conditions at the point of contact (sub- AMTs å = 1.5, ×50 AMTs å = 1.7, ×50 sonic flow). The increase in the velocity vc causes the loading pressure and plastic shear strain rate in the con- tact zone to grow. A large shear of the metal is involved in the jet, and the perturbation amplitude increases. At ≈ vc vcr (the attachment of shock waves to the point of contact), when the jet formation regime changes to the jet-free regime of oblique collision, the perturbation M1 å = 0.6, ×100 M1 å = 1.6, ×50 amplitude reaches a maximum. The transition to the jet-free regime of plate colli- sion means the virtually instantaneous termination of the perturbation evolution (the basic source of perturba- tions disappears). Accordingly, the curve a = f(M) must terminate abruptly and fall to a = 0 at the point a = a . max M1 å = 1, ×100 M1 å = 1.5, ×50 However, in our experiments, the perturbation ampli- tude falls monotonically with a further increase in the Fig. 3. Micrographs of the contact boundary after fast velocity of the point of contact (vc > vcr). The drop from oblique collision. TECHNICAL PHYSICS Vol. 48 No. 8 2003 PERTURBATION EVOLUTION AT A METAL–METAL INTERFACE 1003 a = amax to a = 0 is observed in the Mach number inter- velocity in the upper half-space has the form [10] ≤ val 1.40 < M 1.75. Such behavior is observed for the ∂ ∂U U –1∂P first time. ---------x ++U ---------x ρ ------ = 0 ∂t 0 ∂x ∂x Similar experiments were carried out with another (1) ∂ pair of materials (copper and steel; Fig. 3), and they ∂U U –1∂P ---------y ++U ---------y ρ ------ = 0, gave similar results. In this case (the materials are sim- ∂t 0 ∂x ∂y ilar in physicochemical properties but differ in strength), the perturbation amplitude is greater for the where Ux and Uy are velocity perturbations related to softer material at the same Mach numbers, although the interface perturbations and P is pressure perturbation. Mach number range (∆M) of perturbation existence in Since the equations of motion in an elastic medium the supersonic regime (amax > a > 0) for the softer mate- are convenient to write for Lagrangean coordinates rial is narrower. instead of velocity, we will represent Eqs. (1) in terms Figure 3 shows the sections of the specimens when of perturbations of the coordinates X and Y. Small per- observed under a microscope. Here, perturbations at the turbations of coordinates are related to velocities as interface are apparently caused by development of ∂X ∂X Kelvin–Helmholtz instability due to the tangential dis- U = ------- + U ------- x ∂t 0 ∂x continuity of the velocities at the boundary between the (2) initially fixed and movable plates, which are in different ∂Y ∂Y U = ------ + U ------ . thermodynamic states. y ∂t 0 ∂x Behind the front of the oblique shock wave, the materials glide over each other. The temperature of the The Euler equations then take the form front grows. The relative gliding of the materials along ∂2 ∂2 ∂2 ∂ the interface results in intense shear strains, and the X X 2 X ρ–1 P ---------+++0 2 U0----------- U0--------- ------ = contacting surfaces melt.
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