
384 Ballistics: Theory and Design of Guns and Ammunition
A
E
Y
I
n
=+
2
3
1
2
3
(15.67)
B =
(15.68)
where
I
x
x
dx
n
Y
E
=
−
−
−
∫
(ln)
1
1
3
2
(15.69)
In these expressions, E is Young’s modulus and n is the strain hardening exponent
(assumes power-law strain hardening). For an assumed incompressible 7075-T651 alumi-
num, Forrestal et al. [3] provide I = 3.896 and A = 4.609.
Empirically, curve-tting the stress–strain curves (thus including compressibility) for
7075-T651 yielded slightly different results with A = 4.418 and B = 1.068.
To approximate the normal stress on the ogive, we can replace the spherically symmetric
velocity, V in Equation 15.66 with ...