In "Liners for Shaped Charges", Held uses a ranking of liner materials based on maximum jet speed times the square root of the liner density. He
further states that, as a rough approximation, max jet speed can be estimated as 2.34 times "bulk sound velocity" of the liner material.
Now, I'm not entirely certain of what he means by bulk sound velocity, but from the numbers in the table (table 1) it seems to be the speed of
longitudinal waves.
The speed of longitudinal waves can be calculated if shear and bulk moduli or Young modulus and Poisson ratio are known, but the interesting point is
that the formula features the square root of the density in the denominator.
In the ranking formula, this cancels out with the square root (density) factor.
This means that as a means of ranking liner materials, you can simply use the square root of (K+ 4G/3), where K is the bulk modulus and G is the shear
modulus. Or you could look up longitudinal sound velocity and multiply that with the square root of the density.
As an even simpler (and less accurate) method you could just use the square root of Youngs modulus.
There are probably many aberrations that would deviate from this ranking system (for instance, it rates steel higher than copper), but it accurately
predicts several well known phenomena such as the fact that lead is very poor, that aluminum is decent and so is glass.
|