533
Prediction of Initial and Striking Velocity of Primary Fragments from Cased
Spherical Explosive inside Steel Cubical Structure
Prahalad Srinivas Joshi
*
and S.K. Panigrahi
Department of Mechanical Engineering, DIAT, Girinagar, Pune – 411 025, India
*
Email: prahjo20904@gmail.com
AbStrACt
Usually, energy generated from an explosive’s detonation is transferred partly in the form of the blast impulse
and some in the form of the kinetic energy of casing fragments. When detonation occurs in an explosive casing,
it breaks the casing into fragments of diferent weights with varying velocities. The extent of destruction by these
energized fragments depends upon the initial velocity they gain after an explosion. The momentum gained by the
fragments decides the capability to perforate a barrier or propagate an explosion. A three-dimensional non-linear FEA
method is used to model a box-shaped steel structure. This box-shaped structure is subjected to an internal cased
explosion for estimating the initial and striking velocities of primary fragments. The efect of varying charge weight
and the efect of the sacrifcial wall on the initial and striking velocity of fragments via numerical simulations are
also carried out. The initial and striking velocity values obtained through simulation are compared with the design
guidelines of the code-based approach, and a good agreement is reported.
Keywords: Explosive casing; Gurney equation; Initial velocity; Primary fragments; Striking velocity
Received : 25 March 2022, Revised : 02 July 2022
Accepted : 15 July 2022, Online published : 26 August 2022
Defence Science Journal, Vol. 72, No. 4, July 2022, pp. 533-542, DOI : 10.14429/dsj.72.18001
© 2022, DESIDOC
1. IntroduCtIon
Usually, the high explosives (HE) are enclosed in metal
casings while in service. Upon detonation, HE produces
exceptionally high pressure and hot gasses, which in turn
pressurizes the damaged inner walls of the metal casing to form
primary fragments. When they impact surrounding structures,
these primary fragments develop secondary fragments and
infuence the design of the armament and other protective
structures. Thus, studying the fragment velocity could beneft
design guidelines for the efectiveness of weapons consisting
of HE in a closed container like a warhead or bomb.
A mathematical model was developed by assuming an
infnitely long cylindrical casing, allowing only the radial
motion of fragments and nullifying the efect of detonation in
the longitudinal direction.
1
Based on this, initial velocities of
fragments due to the detonation of metal casings flled with HE
was calculated using Eqn. (1) and verifed with experimental
results.
2
The initial velocity of fragments is determined by the
equation given below:
0
2
1 0.5
β
=
+ β
v E
(1)
where v
0
is the initial velocity of fragments, √2E is Gurney
energy, E is contribution to the explosion’s kinetic energy due
to HE’s unit mass, and β is the ratio of casing mass to explosive
mass. Relation between stress state and thermo-plasticity
of cylindrical metal casings flled with HE with a slight
modifcation of Taylors
1
hypothesis of radial fracture mode was
proposed by Hoggatt and Recht.
3
It has been observed that the
walls of the metal casing accelerated radially outward due to
compressive hoop stress produced during the detonation of the
HE. It was also attempted to fnd speeds of metal layers after
detonation in the case of multi-layered warheads by Jones.
4
Jones-Wilkins-Lee equation
5-7
is widely used to study
the reaction processes of detonation of HE. Gas leakage in an
internal blast event was identifed, and the Gurney equation
was modifed by multiplying by a factor of 0.8 to overcome.
The factor accounted for the efect of gas leakage, which was
verifed by experimental results obtained by Charron.
8
The
material properties of the metal casings and HE characteristics
primarily afect the detonation outcome. Pearson
9
observed
that the behavior of fragments is not a separate event and can
infuence the total system. A series of aluminium and copper
cylinder expansion tests were carried out for a varied mass
of explosive to mass of cylinder ratio and explosives. These
were further verifed by performing the expansion tests for
evaluating and describing the acceleration characteristics
of the metal fragments by Bola, et al. and Kury, et al.
10-11
Subsequently, many researchers
12-14
calculated the fragment
velocities by modifying Gurney energy as mentioned in Eqn.
(2), given below.
G
D
2E
3.08
=
(2)
where, D is detonation velocity, and E
G
is Gurney energy.