Figure - available via license: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Content may be subject to copyright.
Source publication
Historically, there has been little correlation between the material properties used in (1) empirical formulae, (2) analytical formulations, and (3) numerical models. The various regressions and models may each provide excellent agreement for the depth of penetration into semi-infinite targets. But the input parameters for the empirically based pro...
Citations
... Mechanical and Johnson-Cook parameters for the projectile[22] ...
This work is a part of a larger research effort to better understand the combined effect of the resulting blast wave and fragment impact following the detonation of a shrapnel bomb. The study presents insights into the establishment of a laboratory scale technique to generate a combined blast and projectile impact loading on a target using an explosive driven shock tube. The experiments are numerically simulated based on an Eulerian approach using the LS-DYNA finite element software. The main purpose of this paper is to enhance the numerical modelling of the proposed experimental setup. First, the numerical simulation aims to: (i) test the capability of the FE model to predict the projectile flight trajectory, (ii) predict the pressure profiles, the projectile velocity, the blast arrival time, and the different phases of the ball bearing flight. Second, the computational model is used for comparison ends with the experimental data. A good agreement was found between the experimental results and the numerical findings. Finally, the calibrated model serves to investigate other scenarios that were not performed experimentally.
... Density, elastic constants, and Johnson-Cook parameters for the RHA steel sphere[40]. ...
This work is a part of a larger research effort to better understand the combined effect of the blast wave and fragment impacts following the detonation of a shrapnel bomb. It is known that the time interval Δt, which represents the difference in arrival time between the blast wave front and the fragment at the position of a given target object, has a significant influence on its response mode. This paper presents insights into the establishment of a laboratory scale technique to generate a combined blast loading and single or multiple projectile impacts on a target. The objective of the setup is to control the time interval Δt to a certain extent so that the different response modes of the tested structures can be investigated. In order to reduce the complexity associated with the random nature of the shrapnel, steel ball bearings are used to simulate the projected fragments. They are embedded in a solid explosive charge, which is detonated at the entrance of an explosive driven shock tube. The experimental work demonstrates that it is possible to orient the path of a single projectile inside the tube when aiming at a target positioned at its exit. The setup guarantees the generation of a well-controlled planar blast wave characterized by its peak pressure, impulse and blast wave arrival time at the exit of the tube. The influence of the mass of the charge and the diameter of the projectile on its velocity study shows that for the same charge mass, the time interval increases with increasing projectile diameter. The experiments are numerically simulated based on an Eulerian approach using the LS-DYNA finite element software. The computational model allows to reveal details about the projectile flight characteristics inside the tube. Both the experimental and numerical data show the influence of the charge and projectile parameters on the time interval.
... In contrast, the present paper covers only models---analytical and numerical simulations---with experiments noted only in the context of description of the physical problems and validation of the analytical or numerical solutions. Thus, this paper is more concise and focused than these prior works, and it also includes coverage of more recent developments, particularly in areas of dimensional analysis [10,11,12,13] and modern hydrocode simulations [14,15,16]. The present description of constitutive models of (poly)crystalline solids, of which projectile and target are comprised, is also more sophisticated than those given in the above-mentioned prior works, accounting for geometric and material nonlinearity [17]. ...
... However, compressibility becomes more important in ceramic targets and concrete, for example, wherein initial porosity decreases with increasingly high compressive pressure, and where strength and pressure are coupled in the constitutive response due to frictional effects, for example [38,39,23]. Methods of dimensional analysis have been used to provide further insight into parameters and properties affecting the ballistic response of metallic [12,13] and ceramic [10,11] targets. The treatment in [11] is considered in further detail in what follows next. ...
Background: Methods for describing physics of impact and ballistics have been developed over a number of decades. These include analytical mathematical representations as well as modern computer simulations. Objective: Recent and historic developments towards modeling of impact phenomena pertinent to terminal ballistic events are summarized and compared. Two classes of physical problem are of focus: impact and penetration of metallic and/or ceramic targets by projectiles, and propagation of planar shock waves through solid material specimens induced by collision with flyer plates or by explosive loading. Method: The projectile-target problem is analyzed from perspectives of classical hydrodynamics, extensions accounting for strength, and fully resolved explicit dynamics simulations. The planar impact test is studied from perspectives of analytical solutions to Rankine-Hugoniot equations, steady wave analysis, and dynamic finite element simulations of shock waves in material microstructures. Key features of each approach are critically compared. Results: The two classes of physical problem are inherently related since material properties obtained from analysis of the latter experiments are typical input for models of the former problem involving ballistic penetration. Patents to computer methods and ballistic protection systems are noted. Conclusion: Reduced order models are shown to provide efficient, but often approximate, solutions giving insight into general trends. Modern, fully resolved calculations appear to be the only viable route to design and optimization of novel materials or structures with heterogeneous properties or complex geometries.
... Macroscopic constitutive models are used in hydrocodes for computing the response of protection systems subjected to impact, blast, and perforation. These models may be empirical [19][20][21][22][23] or based on micro-mechanical principles [24][25][26]. One-dimensional finite crystal mechanics models have also been developed for addressing planar shock experiments [27][28][29][30][31]. Finally, analytical penetration models based on a one-dimensional momentum balance and various simplifying assumptions have been invoked to describe mechanics of shaped charge jets [32][33][34] and long rods [35][36][37][38] piercing thick ductile metallic targets. ...
Principles of dimensional analysis are applied in a new interpretation of penetration of ceramic targets subjected to hypervelocity impact. The analysis results in a power series representation– in terms of inverse velocity–of normalized depth of penetration that reduces to the hydrodynamic solution at high impact velocities. Specifically considered are test data from four literature sources involving penetration of confined thick ceramic targets by tungsten long rod projectiles. The ceramics are AD-995 alumina, aluminum nitride, silicon carbide, and boron carbide. Test data can be accurately represented by the linear form of the power series, whereby the same value of a single fitting parameter applies remarkably well for all four ceramics. Comparison of the present model with others in the literature (e.g., Tate's theory) demonstrates a target resistance stress that depends on impact velocity, linearly in the limiting case. Comparison of the present analysis with recent research involving penetration of thin ceramic tiles at lower typical impact velocities confirms the importance of target properties related to fracture and shear strength at the Hugoniot Elastic Limit (HEL) only in the latter. In contrast, in the former (i.e., hypervelocity and thick target) experiments, the current analysis demonstrates dominant dependence of penetration depth only by target mass density. Such comparisons suggest transitions from microstructure-controlled to density-controlled penetration resistance with increasing impact velocity and ceramic target thickness.
This paper presents a spherical cavity expansion method based on the self-similar field considering dynamic hardening, which includes plastic strain, plastic strain rate, and temperature for an infinite compressible medium under J2 plasticity. This study proposes an approach based on the gradients of plastic strain and temperature under self-similarity transformation to deal with dynamic hardening models such as the Johnson-Cook (JC) and the modified Johnson-Cook (mJC) models. A theoretical model shows that the effective and radial stresses are reduced near the cavity surface and increased away from the cavity under the mutual influence of hardening and thermal softening. The JC hardening model is used to analyze the behavior of the cavity expansion for AISI 4340 steel. The proposed theoretical model was validated by comparing the result of the explicit finite element method (FEM). This study discusses the behavior of the expanding cavity problem for thermal softening and strain rate sensitivities. In addition, rigid penetration problems are simulated to analyze the application of the presented method. FEM and the proposed cavity expansion method were compared with the penetration depth of AA6061-T651 target using the mJC hardening model for a hemispherical-nosed penetrator. A comparison is made for the performance of the penetration depth with an ogive-nose projectile for AA7075-T651 and AA6061-T651 materials using the mJC hardening model. This study concludes that the proposed method can be applied without modifying the hardening models to spherical cavity expansion problems that involve dynamic hardening models dependent on strain, strain rate, and temperature under adiabatic heat.
In this study, two general solutions for the dynamic tensile load-carrying capacity of brittle materials subject to an arbitrary incident stress wave in the form of Fourier integral are derived. In order to verify the general solutions, we reduce them to three particular solutions, respectively, i.e., trapezoidal pulse, quadratic pulse and cubic pulse. It is found that all of them can well capture the experimental trends in the previous study. In between, the first two particular solutions can exactly accord with the two previous analytical solutions under the same boundary conditions, respectively. Therefore, for arbitrary tensile boundary pulses, the dynamic tensile strength of the brittle materials can be calculated from static parameters and characteristics of external loading. This study improves the credibility of the previous works that working on deriving the dynamic load-carrying capacity through analytical methods, and thus consolidate their theoretical foundation. Meanwhile, on basis of the general solution, the relation between the dynamic tensile load-carrying capacity and strain rate can be further deduced by combining static parameters, hence it could be inappropriate to claim the strain rate effect on tensile strength as an intrinsic material property anymore. In addition, we found that the process to obtain an explicit analytical solution becomes increasingly difficult with the increased complexity of wave form for an incident pulse, or even no explicit solution can be obtained.
The aim of this work is to demonstrate that one can derive the value of the dynamic resistive stress, which a given target exerts on a rigid projectile, by following the force needed to push a rigid indenter into the target in a static deep indentation test. In this study, we used a relatively soft target made of a lead-antimony alloy and a concrete target, representing ductile metals and brittle solids, respectively. For both targets, we followed the force–distance curves obtained by the deep indentations of hard punches, as they were slowly pushed in the targets by a loading frame. The effect of friction during these tests was taken into account in order to obtain the net axial resisting stresses, which were applied by the targets on these indenters. These static resisting stresses, at deep penetrations, were compared with the dynamic resisting stresses, which were inferred from the impacts of armor-piercing projectiles on these targets. The good agreement between the two sets of values strongly enhances the claim that one can use static indentation tests in order to estimate the ballistic resistance of various targets to rigid projectile penetration. The effect of strain rate sensitivity is highlighted by the test results for both the metallic and concrete targets. In addition, important insights concerning the cavitation phenomenon in the penetration of rigid projectiles are also highlighted in this work.
