Properties of Explosives and Their Application Part 1

This is the first part of a series on the properties and application of explosive materials. I suppose the first thing to do is define some terms. An explosive is any system, gas, liquid, or solid, that will propagate a supersonic wave front at a characteristic velocity that is supported by chemical reaction. A graphical relationship helps to show this.

One of the first aspects of explosive performance is the ability of the reacted material to move metal.  The Gurney Equations describe this well. R.W. Gurney did much of his initial work in Quantum Mechanics but later moved to the United States and was very productive in the field of metal motion due to gas dynamics from explosions. Gurney's equations could be considered near universal for many explosive systems. A copy of his original document is here in the Open PDF section of my Google Drive.

The following is the derivation of his equation for expansion of a tube filled with an explosive and detonated at one end.

Let C and M denote a unit length of the weight of the explosive charge and cylindrical tube. For a given explosive there is a characteristic energy per unit mass E associated with it's detonation and is highly dependent upon it's chemical formula and initial density. A metal tube of radius a filled with a gas of density rho which is expanding will expand according to:

Which collapses to:

For each case cylindrical, spherical, symmetrical planar and asymmetrical planar:

R is given by:

Where:

is known as the Gurney constant and is unique for each explosive material. To determine the Gurney constant, as well as other explosive parameters, an experiment known as a cylinder expansion test is done. The cylinder is a copper cylinder usually with wall thickness of 0.1" and an inside diameter of 1" filled with the explosive under test. Other diameters can also be tested. The sidewall velocity is measured usually near the halfway point of the cylinder to eliminate end effects. A video of a two dimensional model of the test is shown next.