The Autodyn analyses designated by C

The Autodyn analyses designated by “C” and ”D” were made with JC parameters (Özel and Sattouf 2 in Table 4 and Fig. 6) that seemed extreme. By comparison to P/L values for the set of Autodyn analyses designated by “2”, the outcomes were, indeed, extreme.
Derivation of effective flow stress from experimental data By employing non-dimensional relationships, Riegel and Anderson illustrated a fit that brought together several sets of data for L/D = 10 tungsten and steel penetrators penetrating targets of several types of steel [2]. The fit had a familiar form, in particular YN = P/αL and α = (ρp/ρt)1/2. Here aN = −0.0567, bN = 1.16, cN = 1.86, dN = 1.96, and σt is the effective flow stress of the target. The suffix “N” stands for “non-dimensional.” Fig. 9 is a plot of Eq. (4), with the parameters from Ref. 2 for L/D = 10 penetrators. From Eq. (4), Finally, inverting Eq. (5), the effective flow stress for the target becomes a function of and XN By substituting P/L from Eq. (3), the four-parameter fit to most of the data in the Appendix, into Eq. (6), XN also becomes a function of . Fig. 10 is a plot of Eq. (7), given this GSK2126458 substitution. 1.16 GPa is an average of the flow stress values over the interval between 1000 and 2000 m/s. We used this value in the Autodyn hydrocode analysis above. Effective flow stresses for other target combinations will depend on the values of the coefficients in Eq. (3) or other fit, derived from a set of penetration experiments. Eq. (3) is a four-parameter fit, appropriate for the large set of Hohler–Stilp experiments listed in the Appendix. The EFS can be obtained not only from a fit but also from any set of repesentative tests. For example, by substituting a P/L datum from the table in the Appendix into Eq. (6), XN becomes a function of , and the effective flow stress can be computed by inserting the corresponding tabulated vP datum into Eq. (7). Effective flow stress values computed for all of the data in the Appendix is depicted in Fig. 11. The average flow stress for velocities between 1005 and 2046 m/s is 1.16 GPa, with a standard deviation of 0.04 GPa. By the same method, given the flatness of the data for velocities between 1000 and 2000 m/s, EFS effective flow stress values can be obtained for velocities in this range from a small number of tests of tungsten and steel L/D = 10 penetrators impacting steel targets of various types. Extension of this method to penetrators with other lengths, possibly penetrating non-ferrous targets, is the subject of future work.
Conclusions
Acknowledgement
Introduction Improvised explosive devices (IEDs) are today one of the most dangerous threats to military forces and their operational vehicles. IED threats cover a wide spectrum of scenarios ranging from explosive charges (military HE or homemade explosives) to projectile forming shells and HE filled munitions like grenades. The effects on a vehicle can be separated into local and global phenomena. There are local effects like penetration and perforation of fragments and projectiles, but there are also global effects connected with a high momentum transfer onto the vehicle and subsequent severe acceleration effects on the vehicle occupants [1,2]. During the time of more conventional military threat, protected vehicles were mostly exposed to effects from shallowly buried mines which showed well defined designs, burial conditions and charge masses (up to 10 kg). Most interest was focused on the mission kill of the vehicle and for heavy tanks on the destruction of the tank tracks. Global effects on the vehicle as a whole were not considered. This changed with the appearance of deeply buried IED charges deuterostomes contain significantly more HE which leads to high momentum transfer on the whole vehicle. The situation created the necessity for the analysis of the effects of buried charges on vehicle structures, especially for experimental and theoretical methods to predict the impulse transfer on the vehicle bottom. Experimental test methods were developed to measure and analyse the momentum transfer from unconfined and buried charges onto simplified generic structures, e.g. plates and cubes [3–7]. Of special importance are experimental results that include information about the spatial distribution of the specific momentum (Ref. 4 for buried charges and Ref. 5 for free charges including shape effects). Global momentum transfer and the influence of the embedding material is analysed in Ref. 3. A sand model including effects of moisture is presented in Ref. 6. The experiments were used to validate analytical and empirical models in the literature that were developed to quantify the impulse transferred from HE detonations [4,8]. On the other hand, numerical simulation models with detailed material descriptions for the embedding materials provided increasing knowledge about the details of the momentum transfer process, influence of embedding material and depth of burst. Adequate material and simulation models were necessary to describe correctly the load transfer from the detonation to the vehicle floor [2,6,7,9–11].