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The penetration of shaped charge jets into targets at high velocities is significantly influenced by the compressibility effect, while at low velocities, the strength effect becomes predominant. In the latter regime, material strength dictates the resistance to plastic deformation and flow, a contrast to the shockwave-dominated interactions where compressibility is key. This paper presents a self-consistent compressible penetration theory that considers both the axial penetration and radial crater growth of shaped charge jets into targets. An integrated approach where the axial and radial dynamics are coupled has been proposed, influencing each other through shared physical principles rather than being treated as separate, empirically linked phenomena. The presented theory is rooted in the compressible Bernoulli equation and the linear Rankine–Hugoniot relation. These foundational equations are employed to accurately model the high-pressure shock state and subsequent material flow at the jet-target interface, providing a robust physical basis for the penetration model. Notably, it considers the target material's compressibility, which elevates the pressure at the jet-target interface beyond that observed with incompressible materials. This pressure increase is directly proportional to the target's degree of compressibility. As such, this model of compressible penetration reorients the analytical approach: rather than merely estimating penetration resistance, it determines this value from the target material's specific compressibility and yield strength. This shift from empirical correlations to a physics-based derivation of penetration resistance enhances the model's predictive power, particularly for novel target materials or engagement conditions outside established experimental datasets. This investigation establishes a quantitative link between the material's yield strength and its penetration resistance. The accuracy of this penetration resistance value is paramount, as it significantly influences the predicted crater diameter; indeed, the crater diameter's sensitivity to this resistance underscores the necessity for its precise determination. Ultimately, by integrating the yield strength of the target material, this framework enables the prediction of both the penetration depth and the resultant crater diameter from a shaped charge jet. The theory's validation involved two experimental sets: the first focused on shaped charge jet penetration into 45# steel at varied stand-offs, while the second utilized targets of high-to ultrahigh-strength steel-fiber reactive powder concrete (RPC) with differing strength characteristics. These experimental campaigns were specifically chosen to test the theory against both ductile metallic alloys, where plastic flow is significant, and advanced quasi-brittle cementitious composites, presenting a broad spectrum of material responses and penetration challenges. Resulting hole profiles derived from theoretical calculations demonstrated a strong correspondence with empirical measurements for both material types.

Reactive armour is a very efficient add-on armour against shaped charge threats. Explosive reactive armour consists of one or several plates that are accelerated by an explosive. Similar but less violent acceleration of plates can also be achieved in a completely inert reactive armour. To be efficient against elongated jets, the motion of the plates needs to be inclined against the jet such that a sliding contact between the jet and the plates is established. This sliding contact causes a deflection and thinning of the jet. Under certain circumstances, the contact will become unstable, leading to severe disturbances on the jet. These disturbances will drastically reduce the jet penetration performance and it is therefore of interest to study the conditions that leads to an unstable contact. Previous studies on the interaction between shaped charge jets and flyer plates have shown that it is mainly the forward moving plate in an explosive reactive armour that is effective in disturbing the jet. This is usually attributed to the higher plate-to-jet mass flux ratio involved in the collision of the forward moving plate compared to the backward moving plate. For slow moving plates, as occurs in inert reactive armour, the difference in mass flux for the forward and backward moving plate is much lesser, and it is therefore of interest to study if other factors than the mass flux influences on the protection capability. In this work, experiments have been performed where a plate is accelerated along its length, interacting with a shaped charge jet that is fired at an oblique angle to the plate’s normal, either against or along the plate’s velocity. The arrangement corresponds to a jet interacting with a flyer plate from a reactive armour, with the exception that the collision velocity is the same for both types of obliquities in these experiments. The experiments show that disturbances on the jet are different in the two cases even though the collision velocities are the same. Numerical simulations of the interaction support the observation. The difference is attributed to the character of the contact pressure in the interaction region. For a backward moving plate, the maximum contact pressure is obtained at the beginning of the interaction zone and the contact pressure is therefore higher upstream than downstream of the jet while the opposite is true for a forward moving plate. A negative interface pressure gradient with respect to the jet motion results in a more stable flow than a positive, which means that the jet-plate contact is more stable for a backward moving plate than for a forward moving plate. A forward moving plate is thus more effective in disturbing the jet than a backward moving plate, not only because of the higher jet to plate mass flux ratio but also because of the character of the contact with the jet.

To systematically characterize the post-target behavior of shaped charge jets under dynamic conditions, this study establishes a finite element model for jet penetration through finite-thickness moving targets, elucidating the evolutionary dynamics of jet interaction under lateral disturbances. By integrating virtual origin theory and dimensional analysis, a virtual source parameter is introduced to quantify post-target jet metrics. An engineering predictive model is further developed to describe the residual velocity and post-target diameter of jets under lateral perturbations. Static and dynamic penetration experiments validate the numerical simulations and theoretical framework. Results reveal that residual jet velocity decays exponentially with increasing lateral disturbance, while post-target diameter exhibits exponential growth. Strong agreement among numerical predictions, model outputs, and experimental data confirms the accuracy of the proposed framework. This work provides a validated methodology for assessing the post-target performance of shaped charges in dynamic scenarios.

Shaped charge has been widely used for penetrating concrete. However, due to the obvious difference between the propagation of shock waves and explosion products in water and air, the theory governing the formation of shaped charge jets in water as well as the underwater penetration effect of concrete need to be studied. In this paper, we introduced a modified forming theory of an underwater hemispherical shaped charge, and investigated the behavior of jet formation and concrete penetration in both air and water experimentally and numerically. The results show that the modified jet forming theory predicts the jet velocity of the hemispherical liner with an error of less than 10%. The underwater jets exhibit at least 3% faster and 11% longer than those in air. Concrete shows different failure modes after penetration in air and water. The depth of penetration deepens at least 18.75% after underwater penetration, accompanied by deeper crater with 65% smaller radius. Moreover, cracks throughout the entire target are formed, whereas cracks exist only near the penetration hole in air. This comprehensive study provides guidance for optimizing the structure of shaped charge and improves the understanding of the permeability effect of concrete in water. •A reliable modified theory for underwater hemispherical shaped charge jet formation is proposed.•Differences in jet velocity and shape formation between water and air are analyzed.•Post-penetration failure modes of holes and cracks in concrete differ in water and air.•Optimal standoff for underwater jets is shorter than in air, with more obvious shock wave effects.

The cavity characteristics in liquid-filled containers caused by high-velocity impacts represent an important area of research in hydrodynamic ram phenomena. The dynamic expansion of the cavity induces liquid pressure variations, potentially causing catastrophic damage to the container. Current studies mainly focus on non-deforming projectiles, such as fragments, with limited exploration of shaped charge jets. In this paper, a uniquely experimental system was designed to record cavity profiles in behind-armor liquid-filled containers subjected to shaped charge jet impacts. The impact process was then numerically reproduced using the explicit simulation program ANSYS LS-DYNA with the Structured Arbitrary Lagrangian-Eulerian (S-ALE) solver. The formation mechanism, along with the dimensional and shape evolution of the cavity was investigated. Additionally, the influence of the impact kinetic energy of the jet on the cavity characteristics was analyzed. The findings reveal that the cavity profile exhibits a conical shape, primarily driven by direct jet impact and inertial effects. The expansion rates of both cavity length and maximum radius increase with jet impact kinetic energy. When the impact kinetic energy is reduced to 28.2 kJ or below, the length-to-diameter ratio of the cavity ultimately stabilizes at approximately 7.

This paper presents the results of an experimental and numerical study conducted to investigate the mechanism of penetration of linear shaped charges (LSCs) into double layered targets. A type of LSC causing less collateral damage in terms of jet residues was studied. The LSC consisted of a linear liner and case with the depth to diameter aspect ratio of 2.0. Anti-theft doors and spaced steel plates were used to represent double layered targets. The anti-theft door and the equivalent targets were penetrated with little jet residues behind the exit crater. The experiments were simulated using the commercially available software AutoDYN as a 2-D planer symmetry FEM model of the LSC penetrating a double layered target. An Eulerian mesh was used to model the LSCs whilst the double layered target was modelled using a Lagrangian mesh. A fully coupled algorithm was used for two different meshes. The data from the experiments (the shape of the breach and jet residues) were used to validate the numerical model. The validated numerical model was used to gain insights into the penetrating mechanisms of the LSC. The numerical results indicated that the penetration mechanisms of the two layers target were different. The first layer was penetrated by a continuous jet typical of a high-speed jet whereas the second layer was perforated by both a jet tip and slug characterized by a low-impact velocity projectile (slug).

During the PTFE/Al reactive shaped charge jet formation, the burst wave generated by the explosion of the explosive is sufficient to achieve the ignition conditions of the reactive materials (RMS). As a result, the RMS will react, resulting in an energy loss from the reactive jet. In order to research the forming features of PTFE/Al reactive jet and the energy loss during the jet formation, a PTFE/Al reactive liner with a diameter of 74 mm was prepared and an X-ray pulses photography experiment was performed on the jet formation. And the parameters of Johnson-Cook constitutive model of RMS were obtained through quasi-static experiments and Hopkinson pressure bar experiments. The jet formation were simulated, and the AUTODYN secondary development technology was used. The results show that the secondary development technology can intuitively show the reaction of the active material during the jet formation. The PTFE/Al reactive jet is less cohesive, its jet diameter is thicker, and the morphology is divergent. The reactive materials reacted during the PTFE/Al reactive shaped charge jet formation. And during the reactive jet formation, the inner layer of the liner collided. Therefore, most of the chemical reactions occur inside the reactive jet.

Analyses presented in the article were carried out in order to characterize the main parameters of the shaped charge jet formed due to detonation of the PG-7VM warhead. As opposed to the previously published studies in which rolled homogeneous armored steel was mainly used as a target, in the current work the warhead penetration capability was determined against more contemporary high-hardness (500 HB) ARMSTAL 30PM steel armor with precisely determined mechanical properties. The research included experimental depth of penetration tests and their numerical reproduction in the LS-Dyna software. Special attention was paid to factors that could perturbate the shaped charge jet formation process and under- or overestimate its penetration capability. For this reason, warheads were X-ray inspected for structural discrepancies (voids or air inclusions in explosive, misalignment between the body, explosive, and liner, or lack of contact between the explosive and the liner) and properties of materials (explosive, targets, and most important warhead components) were analyzed before the experiments. The numerical model of the warhead was defined more accurately than in previously published studies, since it was based on the real grenade dimensions and its technical documentation. Thanks to this, the depth of penetration of the target made of ARMSTAL 30PM armored steel plates by the shaped charge jet formed from the PG-7VM warhead obtained by numerical simulation was consistent with the experimental results and equaled 278 mm and 280 mm, respectively. The difference between the experimental and numerical value was smaller than 1%, which confirms that the developed methodology of modeling allows users to properly reproduce the PG-7VM shaped charge jet formation and target penetration processes. A verified numerical model of the shaped charge jet penetration into a steel target was used to determine depth of penetration in function of stand-off distance for the PG-7VM warhead. A maximum depth of penetration of about 317 mm was obtained for the stand-off distance of 360 mm, which may indicate the potential direction of modernization of warheads.

An analysis of the interaction mechanisms between a Shaped Charge Jet (SCJ) and a single Moving Plate (MP) is proposed in this article using both experimental and numerical approaches. First, an experimental set-up is presented. Four collision tests have been performed: two tests in Backward Moving Plate (BMP) configuration, where the plate moves in opposition to jet, and two tests in Forward Moving Plate (FMP) configuration, where the plate moves alongside the jet. Based on the virtual origin approximation, a methodology (the Virtual Origin Method, VOM) is developed to extract quantities from the X-ray images, which serve as comparative data. γSPH simulations are carried out to complete the analysis, as they well capture the disturbance dynamics observed in the experiments. Based on these complementary experimental and numerical results, a new physical description is proposed through a detailed analysis of the interaction. It is shown that the SCJ/MP interaction is driven at first order by the contact geometry. Thus, BMP and FMP configurations do not generate the same disturbances because their local flow geometries are different. In the collision point frame of reference, the BMP flows in the same direction as the jet, causing its overall deflection. On the contrary, the FMP flow opposes that of the jet leading to an alternative creation of fragments and ligaments. An in-depth study, using the VOM shows that deflection angles, fragment-ligament creation frequencies, and deflection velocities evolve as the interaction progresses through slower jet elements.

In-situ stress and delay time in shaped charge jet blasting (SCJB) have significant effects on rock damage. In this study, the stress distribution pattern and damage mechanism of rock around the blast hole under coupled in-situ stress and blast loading are studied using theoretical analysis and numerical simulation. The effect of SCJB on rock crushed zone, jet erosion length and crack propagation characteristics under in-situ stress was explored. The results show that the SCJB method achieves directional crack extension and increases the crack extension length. Under equibiaxial in-situ stress condition, the crushed zone is circular, and the radius of the crushed zone, jet erosion length and crack length decrease with increasing in-situ stress level. Under an anisotropic pressure condition, on the other hand, the crushed zone is elliptical; the greater the difference between horizontal and vertical pressure, the more pronounced the anisotropy of the crushed zone. As the lateral pressure coefficient k decreases, the horizontal crack length tends to decrease whereas the vertical crack length increases. The vertical crack length of the delay blast hole increases with the increase of the delay time.