Two-dimensional problem of the deformation of a plate by a glancing detonation wave

Deribas, A. A.; Kuz'min, G. E.

doi:10.1007/bf01102698

Cited by 4 publications

(7 citation statements)

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“…It is noteworthy that in all the experiments, the detonation of the charges used was not idea/. It follows from Table 1 that the values of k from (11) can be calculated from formula (9). Here the ratio between Q and Ec is in the same limits as for highly brisant HE, for which the detonation is close to ideal detonation.…”

Section: (S)mentioning

confidence: 95%

“…2. Deribas and Kuz'min [9] gave the solution of the two-dimensi0nal stationary problem of acceleration of an incompressible plate that consists of elements not connected to one another. This problem was solved earlier by Taylor [10].…”

Section: (S)mentioning

confidence: 99%

“…(12), the initial acceleration velocity is V = 0.. We note that in deriving Eq. (11) in the formulation of the problem from [9], the plate to be accelerated was a set of incompressible elements that were not connected to one another, each element having a finite mass. The results of dedicated experiments, the technique of which was expounded in [14], showed that at the initial moment of acceleration, the angle/9 is different from zero and its value can be determined with sufficient accuracy if the compressibility of the plate material is taken into account and the (P-U) diagram of the accelerated material and the detonation-wave parameters of the accelerating charge are used.…”

Section: (S)mentioning

confidence: 99%

“…3, 7, and 9 (see Table 1), the quantity k was found by solving the two-dimensional problem of a plate accelerated by an HE laver [9]. 2.…”

Section: (S)mentioning

confidence: 99%

“…The Prandtl-Mayer centered rarefaction wave is at the point of intersection of the detonation wave with the free surface. Based on the analytical solution and the numerical calculations performed in [9], Kuz'min [11] proposed a formula that determines the position of the plate:…”

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confidence: 99%

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Acceleration of metal plates by a tangential detonation wave

Deribas¹

2000

J Appl Mech Tech Phys

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1. The Gurney scheme developed in the U.S.A. in the early 1940s is in widespread use for determining the acceleration velocity in explosions of flat, cylindrical, and spherical charges of different configuration [1]. The processes that accompany the acceleration are described within the framework of the instantaneousdetonation model, and the velocity distribution in the explosion products is assumed to be linear. Exact formulas for determination of the acceleration parameters for plates and shells of different geometry are obtained under these assumptions.Upon acceleration of a plate by an HE layer opened at one side (Fig. la), the Gurney formula for the velocity of the plate has the form [2] v= rE v/r 2 + 5r + 4"Here r is the ratio of the HE mass to the mass of the plate to be accelerated; the quantity EG is called the Gurney energy and is a portion of the energy Q, namely, the heat of explosion that converts to the kinetic energy of the explosion products. We give here the Gurney formulas describing the acceleration for the cases shown in Fig. 1. We use the notation adopted in the Western literature [1]. For acceleration of two plates of different mass by an HE layer (Fig. lb), we haveIn the symmetric case of acceleration of two identical plates (Fig. lb), Eq. (2) takes a simpler formUpon acceleration of a cylindrical shell by an inner charge (Fig. lc) packed closely in the internal hollow, we haveIn the spherical case (Fig. ld), the velocity formula takes the form V/ 2x,/~a = (M/C + 3/5) -a/2.Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090.

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Section: (S)mentioning

confidence: 95%

Section: (S)mentioning

confidence: 99%

Section: (S)mentioning

confidence: 99%

“…3, 7, and 9 (see Table 1), the quantity k was found by solving the two-dimensional problem of a plate accelerated by an HE laver [9]. 2.…”

Section: (S)mentioning

confidence: 99%

Section: (S)mentioning

confidence: 99%

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Acceleration of metal plates by a tangential detonation wave

Deribas¹

2000

J Appl Mech Tech Phys

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Effect of material strength on the rotation dynamics of a plate driven by sliding detonation of an explosive charge

Drennov

2010

Combust Explos Shock Waves

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Experiments revealed different rotation dynamics of plates driven by a sliding detonation wave if the plates were made of materials with close physical properties but different strength. By modifying the existing formula for the bending angle, it was possible to describe the experimental data in a unified manner. Accounting for the dynamic strength of metal allowed prediction of the formula for the bending angle for one material based on the known formula for another material with close physical properties.In many practically important cases, shock waves in solid and liquid media propagate in such a manner that their fronts are not parallel to the interfaces or not perpendicular to the velocity of the medium ahead of the front. A key parameter which characterizes such waves is the rotation angle of the material flow behind the front. In the frequently encountered case in practice where plates are driven by sliding detonation of a high explosive (HE) charge, this is the plate rotation angle.At the end of the acceleration, the plate acquires velocity w ∞ and rotates by angle β(∞), which is determined from a geometrical consideration of the scheme of the stationary rotation of the plate invoking the Garney formula [1-3]:Here D is detonation velocity of the HE charge, r is the ratio of the HE mass to the mass of the accelerated plate, E G is the Garney energy (part of the energy Qthe heat of explosion converted to the kinetic energy of explosion products). At present, one-and two-dimensional computational schemes have been developed to describe the acceleration of metal plates by a tangential detonation wave [1][2][3][4][5]. These schemes allow one to calculate not only the limiting angles of rotation of plates but also their acceleration dynamics. However, for practical problems, it is convenient to determine rotation angles β(∞) by relation (1).The initial (shock-wave) rotation angle β(0) is obtained from the intersection of the shock polars of the material of the accelerated plate and explosion products [6]. This is a rigorous definition of the angle β(0).For applied purposes, approximate methods are used. Drennov and Mikhailov [7] proposed a graphical method of determining the mass velocity in the plate material at the time of shock-wave arrival at the free surface u 0 = w 0 /2 from the intersection of a (p, u)-diagram of the plate material with the unloading isentrope of explosion products from the Jouguet point (p J , 0) -for sliding detonation in the y direction, the velocity of the explosion products is u = 0 (here w 0 is velocity of the plate at the time of shock-wave arrival at the free surface).In [8], similar considerations are presented in analytical formHere the left side is the shock adiabat of the plate material, and the right side is the pressure of the detonation products in the one-dimensional unloading wave, ρ 0 and

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