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).

Simulation of natural fragmentation of rings cut from warheads

Natural fragmentation of warheads that detonates causes the casing of the warhead to split into various sized fragments through shear or radial fractures depending on the toughness,density,and grain size of the material.The best known formula for the prediction of the size distribution is the Mott formulae,which is further examined by Grady and Kipp by investigating more carefully the statistical most random way of portioning a given area into a number of entities.We examine the fragmentation behavior of radially expanding steel rings cut from a 25 mm warhead by using an in house smooth particle hydrodynamic(SPH) simulation code called REGULUS.Experimental results were compared with numerical results applying varying particle size and stochastic fracture strain.The numerically obtained number of fragments was consistent with experimental results.Increasing expansion velocity of the rings increases the number of fragments.Statistical variation of the material parameters influences the fragment characteristics,especially for low expansion velocities.A least square regression fit to the cumulative number of fragments by applying a generalized Mott distribution shows that the shape parameter is around 4 for the rings,which is in contrast to the Mott distribution with a shape parameter of 1/2.For initially polar distributed particles,we see signs of a bimodal cumulative fragment distribution.Adding statistical variation in material parameters of the fracture model causes the velocity numerical solutions to become less sensitive to changes in resolution for Cartesian distributed particles.

Strain rate dependency and fragmentation pattern of expanding warheads

For the characterization of the behaviors of a metal material in events like expanding warheads, it is necessary to know its strength and ductility at high strain rates, around 104e105/s. The flyer plate impact testing produces the uniform stress and strain rates but the testing is expensive. The Taylor test is relatively inexpensive but produces non-uniform stress and strain fields, and the results are not so easily inferred for material modeling. In the split-Hopkinson bar(SHB), which may be used in compression, tension and torsion testing, the strain rates never exceeds 103/s. In the present work, we use the expanding ring test where the strain rate is 104e105/s. A streak camera is used to examine the expanding ring velocity, and a water tank is used to collect the fragments. The experimental results are compared with the numerical simulations using the hydrocodes AUTODYN, IMPETUS Afea and a regularized smooth particle(RSPH) software. The number of fragments increases with the increase in the expansion velocity of the rings. The number of fragments is similar to the experimental results. The RSPH software shows much the same results as the AUTODYN where the Lagrangian solver is used for the ring. The IMPETUS Afea solver shows a somewhat different fragmentation characteristic due to the node splitting algorithm that induces pronounced tensile splitting.