Analytical and numerical investigation of polyurea layered aluminium plates subjected to high velocity projectile impact

This paper discusses on the penetration of high velocity projectiles through aluminium–polyurea composite layered plate systems. An analytical model has been proposed to predict the residual velocity of aluminium–polyurea composite plates, and validated with both experimental and numerical investigations. Full metal jacket (FMJ) projectiles (5.56 mm × 45 mm), corresponding to NATO standard SS109, were fired at the aluminium–polyurea composite layered plate systems from a distance of 10.0 m at a fixed velocity of 945 m/s. Four different composite plate configurations were used with thicknesses varying from 16 to 34 mm. Each configuration consisted of six specimens. Residual velocities for each individual test were recorded. Numerical simulations of the penetration process have been performed using advanced finite element code LS-DYNA®. The well-established Johnson–Cook and Mooney–Rivlin material models were used to represent the stress–strain behaviour of aluminium and polyurea in the numerical analysis. The analytical and numerical models provided good approximations for the residual velocities measured during the experimental tests. Polyurea layers contributed positively towards the reduction of residual velocity of the projectile in composite plate systems. In addition, ballistic limit curves for different composite systems have been established based on the validated models. As the results showed that polyurea contributes positively towards the reduction of residual velocity of projectiles, the findings of this study can be effectively used for the similar applications in future armour industry.     

Identification of plasticity constants from orthogonal cutting and inverse analysis

The aim of this work is that from experimental determined cutting process parameters be able to predict the plasticity input constants to Finite Element Method (FEM) models. In the present study the Johnson–Cook constitutive model constants are determined on the basis of cutting process parameters in orthogonal cutting and by use of inverse analysis. Previously established links between Johnson–Cook constitutive model constants and cutting process parameters in the cutting process such as primary cutting force and chip compression ratio is used serve as a starting point in the inverse analysis. As a reference material AISI 4140 has been chosen in this study, which is a tempered steel. The Johnson–Cook constitutive model constants in the reference material are being changed within an interval of ±30%. The inverse analysis is performed using a Kalman filter. The material model for the reference material is validated on the basis of the experimental results in previous work. The model showed to predict the cutting process parameters with a high level of accuracy. The predicted Johnson–Cook constitutive model constants in the present study achieve an error between simulated- and experimental cutting process parameters of maximum 2%. The method described in this study is not limited to identify Johnson–Cook constitutive model constants, but the method can also be used for other constitutive models. The same applies to the process itself and the selected cutting process parameters, but orthogonal cutting has been used to illustrate and validate this method.     

The effects of strength models in numerical study of metal plate destruction by contact explosive charge

Based on a complete mathematical model, the authors set up a problem of metal plate destruction by contacting explosive charge in highly nonlinear dynamic software AUTODYN and solved in two cases using the Johnson–Cook and von Mises strength models. The numerical simulation results were compared with the experimental results and showed a good fit of numerical calculations versus experiments by using the von Mises strength model. The study also shows that the Johnson–Cook strength model, if applied unreasonably, will lead to large errors, which would help to avoid mistakes in the future high speed impact study.     

Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by blunt- and hemispherical-nosed projectiles

Experiments were conducted on aluminum plates of 1 mm thickness by using a gas gun and projectiles with blunt and hemispherical noses. Target plate was impacted with varying impact velocity. Impact and residual velocities of the projectile were measured. Ballistic limit velocity was found to be higher for hemispherical projectiles than that for blunt projectiles. Effect of nose shape on the deformation of the plate was also studied. Numerical simulations of the impact were conducted by using an explicit finite element code (ABAQUS). Johnson–Cook elasto-viscoplastic model available in the code was used to carryout the analysis. Material property tests were carried out with the help of smooth and notched tensile test specimens. Results obtained from finite element simulations were compared with those of experiments. Good correlation was found between the two. It was observed that the element size significantly affects the numerical results; therefore a sufficiently refined mesh was used. Adaptive meshing was found helpful especially in the case of impact by a hemispherical projectile.     

Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles – Calculations

The use of aluminium alloys in lightweight protective structures is increasing. Even so, the number of experimental and computational investigations that give detailed information on such problems is limited. In an earlier paper by some of the authors, perforation experiments were performed with 15–30 mm thick AA5083-H116 aluminium plates and 20 mm diameter, 98 mm long, HRC 53 conical-nose hardened steel projectiles. In all tests, initial and residual velocities of the projectile were measured and the ballistic limit velocity of each target plate was determined. In the present paper, an analytical perforation model based on the cylindrical cavity-expansion theory has been reformulated and used to calculate the ballistic perforation resistance of the aluminium plates. In addition, non-linear finite element simulations have been carried out. The target material was modeled with the Johnson–Cook constitutive relation using 2D axisymmetric elements with adaptive rezoning. To allow ductile hole growth, a pin-hole was introduced in the target. The analytical and numerical results have been compared to the experimental findings, and good agreement was in general obtained. A parametric study was also carried out to identify the importance of the different terms of the Johnson–Cook constitutive relation on the perforation resistance of the target. The results indicate that thermal softening cannot be neglected, so an alternative procedure for identification of the material constants in the power-law constitutive relation used in the cavity-expansion theory has been proposed.     

The modified temperature term on Johnson Cook model for AZ31 magnesium alloy

The quasi‐state and dynamic mechanism of AZ31 magnesium alloy at a strain rates range of 0.001 s^‐1–2500 s^‐1 under a temperature range of 20 °C–250 °C were researched by compression tests using the electronic universal testing machine and split Hopkinson pressure bar system. The true stress‐strain curves at different strain rates and evaluated temperatures were obtained. The result shows that the thermal soften effect of AZ31 magnesium alloy is significant. By modifying the temperature term of the original Johnson Cook model of AZ31 magnesium alloy, a modified Johnson Cook model of AZ31 magnesium alloy has been proposed to reveal thermal soften effect on the deformation behavior of AZ31 magnesium alloy more precisely. With the modified Johnson Cook model and fracture model, the finite element method simulation of AZ31 magnesium alloy hat shaped specimen under impacting was conducted. The numerical simulation result is consistent with the experimental result, which indicates that the modified Johnson Cook model and fracture model are greatly valid to predict the deformation and fracture behavior of the AZ31 magnesium alloy hat shaped specimen under impacting.     

The effect of target strength on the perforation of steel plates using three different projectile nose shapes

The effect of target strength on the perforation of steel plates is studied. Three structural steels are considered: Weldox 460 E, Weldox 700 E and Weldox 900 E. The effects of strain hardening, strain rate hardening, temperature softening and stress triaxiality on material strength and ductility are determined for these steel alloys by conducting three types of tensile tests: quasi-static tests with smooth and notched specimens, quasi-static tests at elevated temperatures and dynamic tests over a wide range of strain rates. The test data are used to determine material constants for the three different steels in a slightly modified version of the Johnson–Cook constitutive equation and fracture criterion.Using these three steel alloys, perforation tests are carried out on 12 mm-thick plates with blunt-, conical- and ogival-nosed projectiles. A compressed gas gun was used to launch projectiles within the velocity range from 150 to 350 m/s. The initial and residual velocities of the projectile were measured, while the perforation process was captured using a digital high-speed camera system. Based on the test data the ballistic limit velocity was obtained for the three steels for the different nose shapes. The experimental results indicate that for perforation with blunt projectiles the ballistic limit velocity decreases for increasing strength, while the opposite trend is found in tests with conical and ogival projectiles. The tests on Weldox 700 E and Weldox 900 E targets with conical-nosed projectiles resulted in shattering of the projectile nose tip during penetration.Finally, numerical simulations of some of the experimental tests are carried out using the non-linear finite element code LS-DYNA. It is found that the numerical code is able to describe the physical mechanisms in the perforation events with good accuracy. However, the experimental trend of a decrease in ballistic limit with an increase in target strength for blunt projectiles is not obtained with the numerical models used in this study.     

Influence of conical projectile diameter on perpendicular impact of thin steel plate

A numerical study of conical projectiles for perpendicular impact on a thin steel plate is reported. The target material considered, Weldox 460 E steel, is frequently used for this kind of application and several results of experiments are available in the international literature to verify numerical simulations. The Johnson-Cook constitutive relation coupled with the Johnson-Cook failure criterion have been applied to analyse penetration of the target and also the failure process. The analysis has been focussed on the influence of the projectile diameter on the perforation process, assuming the same projectile mass. The aim was to preserve the same initial kinetic energy and identical nose angle. The goal is to estimate the ballistic limit, the residual velocity, the plastic work, and the temperature levels produced during the penetration process. The analysis has shown a linear increase of the ballistic limit with the projectile diameter.     

Hypervelocity impact tests and simulations of single whipple bumper shield concepts at 10km/s

A series of experiments has been performed to evaluate the effectiveness of a Whipple bumper shield to orbital space debris at impact velocities of 10 km/s. Upon impact by a 19 mm (0.87 mm thick, L/D 0.5) flier plate, the thin aluminum bumper shield disintegrates into a debris cloud. The debris cloud front propagates axially at velocities of 14 km/s and expands radially at a velocity of 7 km/s. Subsequent loading by the debris on a 3.2 mm thick aluminum substructure placed 114 mm from the bumper penetrates the substructure completely. However, when the diameter of the flier plate is reduced to 12.7 mm, the substructure, although damaged is not perforated. Numerical simulations performed using the multi-dimensional hydrodynamics code CTH also predict complete perforation of the substructure by the subsequent debris cloud for the larger flier plate. The numerical simulation for a 12.7 mm flier plate, however, shows a strong dependence on assumed impact geometry, i. e., a spherical projectile impact geometry does not result in perforation of the substructure by the debris cloud, while the flat plate impact geometry results in perforation.     

Impact Deformation and Fracture Mechanisms of Plates of Brittle Materials

We have studied the deformation and fracture mechanisms of plates of brittle materials under impact loading. The paper presents the results of numerical simulation of impact interaction between a projectile and a multilayer plate with a brittle layer. Methods of compression and perforation testing of brittle materials have been elaborated. The results of numerical simulation are compared with the experimental data.     

Quasi-static perforation of thin aluminium plates

This paper presents an experimental and numerical investigation on the quasi-static perforation of aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical punch. A full factorial design was used to investigate the effects of varying plate thickness, boundary conditions, punch diameter and nose shape. Based on the results obtained, both the main and interaction effects on the maximum force, displacement at fracture and energy absorption until perforation were determined. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA. Simulations with axisymmetric elements, brick elements and shell elements were conducted. Quasi-static, isothermal versions of the Johnson–Cook constitutive relation and fracture criterion were used to model the material behaviour. Good qualitative agreement was in general found between the experimental results and the numerical simulations. However, some quantitative differences were observed, and the reasons for these are discussed.     

High velocity impact response of Kevlar-29/epoxy and 6061-T6 aluminum laminated panels

The high velocity impact response of composite laminated plates has been experimentally investigated using a nitrogen gas gun. Tests were undertaken on sandwich structures based on Kevlar-29 fiber/epoxy resin with different stacking sequence of 6061-T6 Al plates. Impact testing was conducted using cylindrical shape of 7.62 mm diameter steel projectile at a range of velocities (180–400 m/s) were investigated to achieve complete perforation of the target. The numerical parametric study of ballistic impact caused by same conditions in experimental work is undertaken to predict the ballistic limit velocity, energy absorbed by the target and comparison between simulation by using ANSYS Autodyn 3D v.12 software and experimental work and study the effects of shape of the projectile with different (4, 8 and 12 mm) thicknesses on ballistic limit velocity. The sequence of Al plate position (front, middle and back) inside laminate plates of composite specimen was also studied. The Al back stacking sequence plate for overall results obtained was the optimum structure to resist the impact loading.The results obtained hereby are in good agreement with the experimental (maximum error of 3.64%) data where it has been shown that these novel sandwich structures exhibit excellent energy absorbing characteristics under high velocity impact loading conditions. Hence it is considered suitable for applications of armor system.     

A new plasticity and failure model for ballistic application

Ballistic phenomena give rise to a plethora of failure modes that compete. Johnson–Cook (JC) plasticity and failure models have been extremely successful because, while being conceptually simple, they capture the essence of the operative mechanics and they provide reasonably good predictions for ballistic limits. Nevertheless, the Johnson–Cook models, due to their isotropic flow and failure surface, cannot reproduce certain failure modes commonly seen in quasistatic tests: cup and cone failure, slanted failure in tensile specimens, and slanted failure in compression specimens. This work shows that by introducing the third invariant (or Lode angle) in both the JC plasticity and damage models, cup and cone, and slanted failure modes arise naturally. After the model is presented it is exercised with a material taken from the literature to predict successfully Taylor anvil and ballistic penetration failure patterns.     

Perforation of a thick plate by rigid projectiles

Perforation of a thick plate by rigid projectiles with various geometrical characteristics is studied in the present paper. The rigid projectile is subjected to the resistant force from the surrounding medium, which is formulated by the dynamic cavity expansion theory. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. Simple and explicit formulae are obtained to predict the ballistic limit and residual velocity for the perforation of thick metallic plates, which agree with available experimental results with satisfactory accuracy.     

A comparative study on modified Johnson Cook,modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict the hot deformation behavior in 28CrMnMoV steel

The true stress-strain data from isothermal hot compression tests on Gleeble-3500 thermo mechanical simulator, in a wide range of temperatures (1173–1473 K) and strain rates (0.01–10 s⁻¹), were employed to establish the constitutive equations based on modified Johnson Cook, modified Zerilli–Armstrong, and strain-compensated Arrhenius-type models respectively to predict the high-temperature flow stress of 28CrMnMoV steel. Furthermore, a comparative study has been made on the capability of the three models to represent the elevated temperature flow behavior of this steel. Suitability of the three models were evaluated by comparing the accuracy of prediction of deformation behavior, correlation coefficient, average absolute relative error (AARE) and relative errors of prediction, the number of material constants, and the time needed to evaluate these constants. The results showed that the predicted values by the modified Johnson Cook and Zerilli–Armstrong models could agree well with the experimental values except under the strain rate of 0.01 s⁻¹. However, the strain-compensated Arrhenius-type model could track the deformation behavior more accurately throughout the entire temperature and strain rate range.     

An analytical model for composite sandwich panels with honeycomb core subjected to high-velocity impact

In this paper, an analytical model for perforation of composite sandwich panels with honeycomb core subjected to high-velocity impact has been developed. The sandwich panel consists of a aluminium honeycomb core sandwiched between two thin composite skins. The solution involves a three-stage, perforation process including perforation of the front composite skin, honeycomb core, and bottom composite skin. The strain and kinetic energy of the front and back-up composite skins and the absorbed energy of honeycomb core has been estimated. In addition, based on the energy balance and equation of motion the absorbed energy of sandwich panel, residual velocity of projectile, perforation time and projectile velocity have been obtained and compared with the available experimental tests and numerical model. Furthermore, effects of composite skins and aluminium honeycomb core on perforation resistance and ballistic performance of sandwich panels has been investigated.     

Material modelling for dynamic strain ageing phenomenon of alloy 20MnMoNi55

Dynamic strain ageing (DSA) is observed in the tensile behaviour of 20MnMoNi55. The DSA phenomenon contributes extra hardening for a certain combination of straining rate and temperature. At temperature ranging from 200°C to 400°C and a straining rate of 10^?4–10^?2?s^?1, alloy 20MnMoNi55 exhibits DSA. In the present work, DSA stresses are calibrated as a function of strain, strain-rate and temperature. Modification of the Johnson–Cook material model by incorporating DSA has been attempted. The modified flow stress model is used in finite element computation to simulate the material behaviour for a wide range of temperature and strain-rates including the DSA regime. The simulated results are in good agreement with the experimental results.     

Experimentation and modeling of inclined ballistic impact in thick polycarbonate plates

The penetration and perforation of a thick polycarbonate (PC) plate (one and 3 stacked) by an armor piercing 7.62 mm projectile is investigated experimentally and numerically. The characteristic structure of the projectile’s trajectory in the PC plates is studied. It is observed that the trajectory consist of a cavity and a circumferential cracked zone attached to it, which is fully embedded within a cylindrical plastic zone. The size of the plastic zone is approximately twice that of the cavity zone and can be clearly observed due to the change of the refractive properties of the material. Strong local recovery of the PC is shown as well.A 3D transient non-linear adiabatic finite element simulation is performed using the commercial software Abaqus 6.9-EF1. The numerical analyses include two combined failure criteria: “Ductile failure with damage evolution”, and tensile failure. The material properties are strain rate and temperature dependent. The numerical simulations are tested by comparing the numerical trajectory prediction to actual trajectories of inclined impacts of projectiles. It is found that the projectile perforates the plate at angles of inclinations of 30° and higher. The observed agreement between experiments and numerical modeling indicates that the combined effect of the two failure criteria (tensile vs. ductile failure) can reasonably well predict the projectile’s trajectory within a thick PC plate.The numerical analyses are further used to study the effect of the projectile impact velocity on the depth of penetration (DOP). It is found that the DOP scales slightly non-linear with the impact velocity. The core velocity during the penetration process is also slightly non-linear. The deceleration during penetration is almost a linear function of the penetration velocity and it is higher for higher penetration velocities.     

Energy absorption during projectile perforation of thin steel plates and the kinetic energy of ejected fragments

This paper concerns energy absorption in thin (0.4 mm) steel plates during perforation by spherical projectiles of hardened steel, at impact velocities between 200 and 600 m s⁻¹. Absorbed energies have been obtained from measured incident and emergent projectile velocities. These tests were simulated using ABAQUS/Explicit, using the Johnson and Cook plasticity model. A strain rate-dependent, critical plastic strain fracture criterion was employed to model fracture. Good agreement is obtained between simulations and experiment and the model successfully captures the transitions in failure mode as projectile velocity increases. At velocities close to the ballistic limit, the plates fail by dishing and discing. As the incident velocity is increased, there are two transitions in failure mode, firstly to shear plugging and secondly to fragmentation and petalling. The simulations also show that, during the latter mode of failure, the kinetic energy of ejected debris is significant, and failure to include this contribution in the energy balance leads to a substantial over-estimate of the energy absorbed within the sheet. Information is also presented relating to the strain rates at which plastic deformation occurs within the sample under different conditions. These range up to about 10⁵ s⁻¹, with the corresponding strain rate hardening effect being quite substantial (factor of 2–3 increase in stress).     

On the selection of constitutive equation for modeling the friction stir processes of twin roll cast wrought AZ31B

Proper numerical modeling of the Friction Stir Processes (FSPs) requires the identification of a suitable constitutive equation which accurately describes the stress-strain material behavior under an applicable range of strains, strain rates, and temperatures. While some such equations may be perfectly suitable to simulate processes characterized by low (or high) strains and temperatures, FSPs are widely recognized for their relatively moderate ranges of such state variables. In this work, a number of constitutive equations for describing flow stress in metals were screened for their suitability for modeling Friction Stir Processes of twin roll cast (TRC) wrought magnesium Mg–AL–Zn (AZ31B) alloy. Considered were 4 different reported variations of the popular Johnson–Cook equation and one Sellars–Tegart equation along with their literature–reported coefficients for fitting AZ31B stress–strain behavior. In addition, 6 variations of the (rarely used in FSPs simulations) Zerilli–Armstrong equation were also considered along with their literature–reported coefficients. The screening assessment was based on how well the considered constitutive equations fit experimental tensile stress–strain data of twin roll cast wrought AZ31B. Goodness of fit and residual sum of squares were the two statistical criteria utilized in the quantitative assessment whereas a ‘visual ’ measure was used as a qualitative measure. Initial screening resulted in the selection of one best fitting constitutive equation representing one of each of the Johnson–Cook, Sellars–Tegart, and Zerilli–Armstrong equations. An HCP–specific Zerilli–Armstrong constitutive equation (dubbed here as ZA₆ ) was found to have the best quantitative and qualitative fit results with an R² value of 0.967 compared to values of 0.934 and 0.826 for the Johnson–Cook and Sellars–Tegart constitutive equations, respectively. Additionally, a 3D thermo–mechanically coupled FEM model was built in DEFORM 3D to simulate the experimental tensile test from which the experimental load–deflection data was obtained. The three ‘finalist ’ equations were fed into the FEM simulations and were compared based on the 1) simulations’ running times and 2) goodness of fit of the simulation results to the experimental load–deflection data. It was found that the ZA₆ constitutive equation exhibited favorable run times even when contrasted against the simpler mathematical form of the Sellars–Tegart equation. On average, the ZA₆ equation showed improvements in solution time by 5.4% as compared with the Johnson–Cook equation and almost identical solution time (0.9% increase) with that of the ST equation. This result indicates that the proposed equation is not numerically expensive and can be safely adopted in such FEM simulations. Based on the favorable running times and goodness of fit, it was concluded that the HCP–specific Zerilli–Armstrong constitutive equation ZA₆ holds an advantage over all other considered equations and was, therefore, selected as most suitable for the numerical modeling of FSP of twin roll cast AZ31B.