Combustion, Explosion, and Shock Waves, Vol. 35, No. 5, 1999

Shock-Wave Dispersion of Structural Materials

V. A. O g o r o d n i k o v , 1 A. G. Ivanov , 1 a n d N . I. K r y u k o v 1 UDC 539.04

Translated from Fizika Goreniya i Vzryva, Vol. 35, No. 5, pp. 122-126, September-October 1999. Original article submitted July 6, 1998.

R e s u l t s o f an e x p e r i m e n t a l s t u d y o f s h o c k - w a v e d i spe r s ion of c y l i n d r i c a l shells m a d e o f l ead , s tee l , a n d n a t u r a l u r a n i u m - 2 3 8 , w h i c h is caused by t h e p r e s e n c e o f va r ious m a c r o s c o p i c de fec t s , s t r u c t u r a l e l e m e n t s , a n d ad d i t i o n a l masses , a r e p r e s e n t e d a n d d i s c u s s e d

The process of dynamic dispersion of structural materials under the action of a shock-wave load is of great interest in practice, for example, from the view- point of evaluation of the formation and dispersion of the fine fraction of the fragments of nuclear-active materials in hypothetical emergency situations at nu- clear power stations. Nevertheless, this phenomenon has not been properly considered in the literature, ex- cept for some widely known events: multiple spalling, formation of a jet in a shaped charge and its sub- sequent destruction due to the longitudinal velocity gradient, and splitting of shells or compact bodies due to the accumulated amount of elastic energy or inertial forces.

This problem was part ly clarified by Ogorod- nikov et al. [1] who considered the outburst (ejection) of particles from a free surface (FS) of ferrous, cop- per, and lead samples, which is caused by the action of a shock wave (SW) of s trength about 70 GPa as one of the possible mechanisms of shock-wave disper- sion of s t ructural materials. It was shown that the ejection of metal particles is caused by inhomogeneity of the FS s t ructure (its roughness or smoothness) and has a microcumulative character. Depending on the quality of FS t reatment and SW strength, the ejected metal particles have dimensions 1-100 #m and travel faster than the FS; their velocity is 20-50% greater than the FS velocity. In addition, Ogorodnikov et al. [1] also noted that the dispersion of a shock-loaded material of a sample can be caused by other factors, for example, by the presence of defects, structural el- ements, or, as follows from [2, 3], additional masses. In the present paper, which is a continuation of [1], we consider these phenomena in more detail.

1Russian Federal Nuclear Center, Institute of Experimental Physics, Sarov 607190.

In many events impor tan t in practice, the shock- loaded object or sample of a structural material is made of several parts between which joint gaps can exist. The loaded object can be made as a two-layer sample with local cavities between the layers. In the course of exploitation of the objects, structural ma- terials are subjected to corrosion, which may cause the appearance of local corrosion defects of various sizes near the free and loaded surfaces of the samples or through corrosion defects. In addition, the sample accelerated by the shock-wave method can interact with various additional masses [2, 3]. In all these and other cases, the presence of defects, structural elements, or additional masses in the sample can be a source of ejection of metal particles or the reason for shock-wave dispersion of the material in the sample.

To reveal the qualitative pat tern of particle ejec- tion in the above cases and determine the amount of the ejected material depending on the size of de- fects and structural elements and the sample mate- rial, we conducted special experiments using a cylin- drical charge model and x-ray registration technique described in [1, 4]. We note tha t the number of points of detonation excitation on the surface of a cylin- drical high explosive charge was increased threefold as compared to experiments [4]. This ensured the outcome of a smoother front of the detonation wave to the surfaces of the cylindrical shells and allowed us to decrease the influence of the system of initi- ation of a high explosive (HE) charge on the phe- nomena under study. An aluminum shell served the same purpose. This shell had the same size as in [1, 4] and was located between the HE charge and the samples inspected. The la t ter were one-layer or two- layer cylindrical shells made of materials with sig- nificantly different physicomechanical characteristics:

576 0010-5082/99/3505-0576 $22.00 (~) 1999 Kluwer Academic/Plenum Publishers

S h o c k - W a v e D i s p e r s i o n o f S t r u c t u r a l M a t e r i a l s 577

Fig. 1 (beginning). Schemes of dispersion sources and x-ray patterns of the corresponding experi- ments: through defects (a), defects near the internal surface of the shell (b), joint gaps on the lower shell (c), and joint gaps on the second shell (d).

578 O g o r o d n i k o v , I v a n o v , a n d K r y u k o v

Fig. 1 (continued). Schemes of dispersion sources and x-ray patterns of the corresponding experi- ments: local cavity between the shells (e) and additional masses in the form of plates (f).

steel, lead, and natural uranium-238. The objective was a detailed study of the possible effect of material strength on the processes examined. Figure 1 shows characteristic types and dimensions (in mm) of the inspected structural elements or defects in shells and x-ray pat terns of the experiments. At the moment of x-ray photographing, the internal boundary of the shells converged to the relative radius r -~ 0.3RHE (RHE ---- 150 mm is the internal radius of the HE charge), its initial location is marked by a dashed curve in the figure.

Analysis of these and other experiments with similar s tructural elements or defects in shells made of different materials, which were conducted at dif- ferent times of x-ray photographing, allowed us to observe some regularities related to shock-wave dis- persion of the materials of the shells. The presence of through or corrosion defects on the internal bound- ary of the lower shells made of lead or uranium (the depth of the defects is half the shell thickness and their diameter varies between 2 and 10 mm) leads to ejection of the material (see Fig. l a and b), which has a cumulative character. The mass of the ejected material depends mainly on the defect volume and on the density of the shell material. Thus, for uranium shells with through defects of volume 3-80 mm 3 and defects on the internal surface of the shell of volume 1.5-40 mm 3, the amount of material ejected from the

shells is 0.5-8.0 and 0.1-3.0 g, respectively. The par- ticle material is partly captured by the shell as it converges. However, the particles reach the shell cen- terline when they approach the radius ,~0.1RHE. The presence of defects of comparable size on the exter- nal boundary of the shell does not lead to particle ejection.

The presence of joint gaps 0.2-1.0 mm wide near the internal shell leads to the formation of shaped jets of the metal (see Fig. lc) with specific mass m = (1-6) - 10 -2 g/cm, which reach the shell cen- terline approaching the radius ~0.3RHE. The pres- ence of joint gaps 0.2-1.0 mm wide near the exter- nal shell leads to a more complex mechanism of for- mation of metal jets (see Fig. ld) . This mechanism is related to extension and dispersion of a part of the lower shell located under the joint of the exter- nal shell and subsequent ejection of a metal jet from the joint, the amount of the ejected material being rasp = 0.1-0.7 g/cm. These particle reach the shell centerline approaching the radius ~0.1RHE.

The ejection has an even more complicated but again jet character in the presence of a local cavity in a two-layer shell (see Fig. le). The qualitative patterns almost coincide for steel and lead shells. It is of interest to note tha t the pat tern of shaped ejection of metal particles in the region of defects or joints is almost identical in all the above cases

S h o c k - W a v e D i s p e r s i o n o f S t r u c t u r a l M a t e r i a l s 579

TABLE 1

Target geometry Target size, Target material mm

5 x 40 Uranium

Plate

Rod

5 x 100 Uranium

5 x 40 St. 3

5 x 40 AMg-6

3x10 AMg-6

Uranium O5

03 Uranium

~5 St. 3

g5 AMg-6

O3 AMg-6

AL, Measurement radius mm (r/RHE)

13.5 0.15

13.9 0.27

22.0 0.15

38.3 0.15

37.3 0.15

11.7 0.15

11.7 0.27

19.2 0.15

33.4 0.15

29.0 0.27

with uranium and lead samples, despite the differ- ent initial s trength of the materials. The mass of metal particles in the jets ejected from the lead sam- ples is smaller by a factor of 1.5-2 than in the case of uranium shells, which approximately corresponds to the ratio of their densities. In determining the area of applicability of the hydrodynamic model of the medium to collision and jet-formation processes, the lower limit of velocities of the contact surfaces Wlo w is usually estimated; for these velocities, the influence of the medium strength can be ignored [5]. With account of the s t rength of the medium mate- rial, the magnitude of these velocities is determined by the expression Wlo w - 2(H/po) U2' where H is the dynamic strength of the material, which is close in value to the dynamic yield strength, and P0 is the density. For lead and uranium, for example, we have Wlo w -- 0.2 and 0.9 km/sec , which is significantly lower than the initial velocities of the shells W0 equal to 2.1 and 1.8 km/sec, respectively. These values can be used as the minimum velocities of the contact sur- faces part icipat ing in the jet-formation process. Both for lead and for steel we have W0 > Wlow; therefore, we should not expect a considerable effect of the den- sity of the shell material on the jet-formation process.

The jet formation in the case of interaction of a shock-loaded object with additional masses [2, 3] is of part icular interest; therefore, we consider it us- ing as an example the interaction of a uranium shell 3 m m thick with targets in the form of a rod 3 and 5 m m in diameter or a plate 3 and 5 mm thick (the plate thickness varied from 10 to 100 mm) made of steel (St. 3), aluminum (AMg-6), and natural ura- nium (see Fig. lf).

The results of x-ray studies indicate that the

Fig. 2. Dependence of the specific mass of a metal in the jet on the density of the material of the additional mass.

processes of plate or rod penetration into the shell are not much different and proceed with formation of a crater in the shell and ejection of a jet from this crater; this jet consists of the plate (rod) mate- rial (~80%) and the shell material. The material of the plate (rod) pressed out by the shell is distr ibuted between the shell and the plate (rod) with forma- tion of a cavity between them. When the plates (rods) penetrate into the shell, the initial angle of the jets increases with decreasing density of the tar- get materials. These angles are ~ = 13-17 ~ for ura- nium, ~ = 17-22 ~ for steel, and ~ = 25-40 ~ for alu- minum. The values of the consumption of the plate (rod) material or the decrease in their initial length AL = Lo - L, which were measured in special exper- iments, are listed in Table 1. An analysis of Table 1 shows that the consumption of the material of the

580 O g o r o d n i k o v , I v a n o v , an d K r y u k o v

plates (rods) depends weakly on their thickness and measurement radius and is mainly determined by the density of the target material; the dependence can be presented in the form AL = cons t / (p t ) 1/2. This has no qualitative contradictions with the hydrodynamic approximation according to which the length should decrease by A L = ~sh(Psh/Pt) 1/2 as a plate (rod) penetrates into a shell of thickness Psh and density ~ish. Figure 2 shows the specific mass of the metal calculated per 1 cm 2 of the plate or rod cross sec- tion, which is formed in the jet-formation process (m = p tAL) , as a function of the density of the plate (rod) material. This mass of the metal depends weakly on the target geometry and is determined by the density of the target-material for a given density of the shell material.

It is of interest to note tha t an indicator tanta- lum shell 0.05 mm thick was placed at the relative radius 0.2RHE in the experiment whose x-ray photo is shown in Fig. lfi The state of this shell demon- strated that the shell was loaded by metal particles ejected from the surface of a shock-loaded shell [1].

From the above considerations, it follows that, upon shock-wave loading of objects, there is a large set of mechanisms of fragmentation and dispersion of structural materials that should be taken into ac- count in constructing more realistic models of forma- tion and dispersion of the fine fraction of the frag- ments of s t ructural materials. The qualitative and quantitative results obtained can be used for devel- opment and verification of numerical methods of mul- tidimensional gas dynamics.

R E F E R E N C E S

1. V. A. Ogorodnikov, A. G. Ivanov, A. L. Mikhailov, et al., "Particle ejection from the shocked free surface of metals and diagnostic methods for these particles," Fiz. Goreniya Vzryva, 34, No. 6, 103-107 (1998).

2. A. G. Ivanov, L. I. Koehkin, V. A. Ogorodnikov, and E. S. Tyun'kin, "Characteristics of the acceleration of plates by a glancing detonation wave in the presence of an additional or concentrated mass," Fiz. Goreniya Vzryva, 26, No. 5, 127-129 (1990).

3. A. M. Buiko, A. G. Ivanov, Yu. D. Lavrovskii, et al., "Jet formation upon high-velocity impact of various targets on a thin shell," in: Abstracts of the Third Zababakhin Scientific Talks, Chelyabinsk-70 (1992).

4. A. G. Ivanov, Yu. D. Lavrovskii, and V. A. Ogorod- nikov, "Developing determinant perturbations in col- lapsing shells," Prikl. Mekh. Tekh. Fiz., 33, No. 5, 116-118 (1992).

5. N. A. Zlatin and A. A. Kozhushko, "Hydrodynamic model representations in the theory of high-velocity interaction of solids and the limits of their applicabil- ity," Zh. Teor. Fiz., 52, No. 2, 330-333 (1982).