Experimental and numerical study of the fragmentation of expanding warhead casings by using different numerical codes and solution techniques

There has been increasing interest in numerical simulations of fragmentation of expanding warheads in 3D.Accordingly there is a pressure on developers of leading commercial codes,such as LS-DYNA.AUTODYN and IMPETUS Afea.to implement the reliable fracture models and the efficient solution techniques.The applicability of the Johnson—Cook strength and fracture model is evaluated by comparing the fracture behaviour of an expanding steel casing of a warhead with experiments.The numerical codes and different numerical solution techniques,such as Eulerian,Lagrangian.Smooth particle hydrodynamics(SPH).and the corpuscular models recently implemented in IMPETUS Afea are compared.For the same solution techniques and material models we find that the codes give similar results.The SPH technique and the corpuscular technique are superior to the Eulerian technique and the Lagrangian technique(with erosion) when it is applied to materials that have fluid like behaviour such as the explosive and the tracer.The Eulerian technique gives much larger calculation time and both the Lagrangian and Eulerian techniques seem to give less agreement with our measurements.To more correctly simulate the fracture behaviours of the expanding steel casing,we applied that ductility decreases with strain rate.The phenomena may be explained by the realization of adiabatic shear bands.An implemented node splitting algorithm in IMPETUS Afea seems very promising.

On the study of ricochet and penetration in sand,water and gelatin by spheres,7.62 mm APM2,and 25 mm projectiles

We examine the ricochet and penetration behavior in sand, water and gelatin by steel spheres, 7.62 mm APM2 and 25 mm projectiles. A threshold impact angle(critical angle) exists beyond which ricochet cannot occur. The Autodyn simulation code with the smooth particle hydrodynamic(SPH) method and Impetus Afea Solver with the corpuscular model are used and the results are compared with experimental and analytical results. The resistance force in sand for spheres was proportional to a term quadratic in velocity plus a term linear in velocity. The drag coefficient for the quadratic term was 0.65. The Autodyn and Impetus Afea codes simulate too large penetration due to the lack of a linear velocity resistance force. Critical ricochet angles were consistent with analytical results in the literature. In ballistic gelatin at velocities of 50–850 m/s a drag coefficient of 0.30 fits the high speed camera recordings if a linear velocity resistance term is included. However, only a quadratic velocity resistance force with drag coefficient that varies with the Reynolds number also fits the measurements. The simulation of a sphere in water with Autodyn showed too large drag coefficient. The 7.62 mm APM2 core simulations in sand fit reasonable well for both codes. The 25 mm projectile ricochet simulations in sand show consistency with the high speed camera recordings. Computer time was reduced by one to two orders of magnitudes when applying the Impetus Afea Solver compared to Autodyn code due to the use of the graphics processing units(GPU).

Projected area and drag coefficient of high velocity irregular fragments that rotate or tumble

3 degrees of freedom(DOF)exterior ballistic computer models are used in fragment studies to calculate individual trajectories of each fragment based on drag coefficient and the projected(presented)area in the direction of velocity of center of mass.The expectation of a randomly distributed projected area is commonly used for fragments that tumble(random rotation)during flight.We forecast a model where the expected drag coefficient is dependent of shape and Mach number.Rotation or tumbling only affects the expected projected area.Models of projected areas during tumbling and rotation are presented.An examination of the data by Mc Cleskey(1988)indicates that the volume of the fragment to the power of2/3 is a better parameter to characterize the drag coefficient of the fragments than the maximum projected area.Hydrocode simulations are used to verify results and to study projected area and drag coefficient of fragments.