PSI - Issue 28

Victor Kats et al. / Procedia Structural Integrity 28 (2020) 602–607

604

V. Kats, V. Morozov / Structural Integrity Procedia 00 (2020) 000–000

3

Table 1. Explosion chan nel radius,

Explosion chan nel volume,

Density of explo sion products,

Expansion coe ffi cient

Density of trans mitted energy

Pressure obtained in experiments,

Pressure calcu lated by provided model,

r , 10 − 3 m

V , 10 − 9 m

ρ, kg / m 3

6 J / kg

P , 10 9 Pa

P , 10 9 Pa

ε, 10

ρ

0 /ρ

0

0

0.15 0.12

59.5 74.4 89.3 99.2

13

1.463 1.035

1.53 1.07

0.2 0.4 0.5

3.14

11.5

12.56

0.1

10

0.75

0.746

19.625

0.09

8.5

0.574

0.59

10 9

1.6

1.4

1.2

1

P, Pa

0.8

0.6

0.4

55

60

65

70

75

80

85

90

95 100

/

0

Fig. 2. Dependence of the pressure provided by the explosion from the expansion coe ffi cient: obtained form experiments ( ♦ ) and calculated by provided model (line).

Figure 2 demonstrates the dependence of the pressure from ρ 0 /ρ in both the theoretical model and experimental study. Figures 3 and 4 provide dependence of the pressure from the volume to which the explosion products will expand and the radius of the explosion channel.

4. Circular stresses of the PMMA cylinder and aluminum shell

Formation and propagation of the shock wave is the main channel of energy transmission from the explosion products to the surrounding media (Bulgkov et al. (2009)). The following equation (Isakovich (1973)) describes the transmission of the pressure through the media boundary:

2 ρ 2 c 2 ρ 2 c 2 + ρ 1 c 1

P 2 =

P 1

(4)

Here ρ 1 , ρ 2 and c 1 , c 2 are densities and sound speeds of the exploding products (index 1) and PMMA (index 2). P 1 and P 2 are the pressure of the shock wave and pressure propagated inside the media respectively.