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Papers by Sumita Dey

Research paper thumbnail of Experimental Tests and Numerical Simulations on the Ballistic Impact Response of a Highly Inhomogeneous Aluminium Foam

Materials

A sandwich structure is a composite material consisting of thin skins encapsulating a cellular co... more A sandwich structure is a composite material consisting of thin skins encapsulating a cellular core. Such structures have proven to be excellent energy absorbents and are frequently found in various types of protection. Even so, few studies exist in the open literature on the response of the core material itself under extreme loadings such as blast and impact. Since a blast load is usually accompanied by numerous fragments, it is important to understand and be able to predict the ballistic impact resistance of the often highly inhomogeneous cellular core materials in design. In this study, the ballistic impact response of an aluminium foam with a complex cell structure has been investigated both experimentally and numerically. First, an extensive material test program involving compression tests on cubic specimens loaded in the thickness direction of the foam was carried out to reveal the mechanical properties of the material. In addition, several of the specimens were scanned befor...

Research paper thumbnail of Ballistic perforation resistance of thin concrete slabs impacted by ogive-nose steel projectiles

International Journal of Impact Engineering, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Research paper thumbnail of Constitutive Relation And Failure Criterion For Three Structural Steels At High Strain Rates

Sustainability, 2002

The effects of strain rate, temperature and stress triaxiality on strength and ductility are stud... more The effects of strain rate, temperature and stress triaxiality on strength and ductility are studied for the three structural steels Weidox 460 E, Weldox 700 E and Weldox 900 E. The material properties are obtained from 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 constitutive relations and fracture criteria for the three steels.

Research paper thumbnail of Ballistic impact on concrete slabs: An experimental and numerical study

EPJ Web of Conferences, 2021

The ballistic perforation resistance of 50 mm thick concrete slabs impacted by 20 mm diameter ogi... more The ballistic perforation resistance of 50 mm thick concrete slabs impacted by 20 mm diameter ogive-nose steel projectiles is investigated experimentally and numerically. Three commercially produced concretes with nominal unconfined compressive strengths of 35, 75 and 110 MPa were used to cast material test specimens and slabs. After curing, ballistic impact tests were carried out to determine the ballistic limit curve and velocity for each slab quality. Material tests instrumented with digital image correlation (DIC) were conducted along the ballistic impact tests. DIC measurements were used to establish engineering stress-strain curves for calibration of a modified version of the Holmquist-Johnson-Cook concrete model. Finite element simulations of the impact tests gave good conservative predictions.

Research paper thumbnail of On the Dynamic Response of Laminated Glass Exposed to Impact Before Blast Loading

Experimental Mechanics, 2019

In this study, the effect of fragment or bullet impact before blast loading on laminated glass is... more In this study, the effect of fragment or bullet impact before blast loading on laminated glass is studied experimentally. First, laminated windows consisting of two 3.8 mm thick annealed float glass plates and a 1.52 mm thick PVB interlayer were blast loaded in a shock tube with various pressures as a reference. In these tests, the blast loading was successively increased until fracture occurred not only in the glass plates but also in the PVB interlayer. Second, a diamond drill was used to make a 5 mm diameter centrally placed hole in some windows before they were blast loaded with the same pressures as those used for the undamaged windows. Third, windows were impacted by 7.62 mm AP bullets, both with and without the brass jacket, before they were blast loaded. Such bullets may have similar mass and velocity to typical primary fragments from an explosive detonation. The results are finally compared with each other and discussed with respect to the blast protection offered. It is found that the capacity is significantly reduced if the laminated glass is perforated by a fragment or a bullet before it is blast loaded and that such impacts should be considered in the design of blast-resistant windows.

Research paper thumbnail of On the ballistic resistance of double-layered steel plates: An experimental and numerical investigation

International Journal of Solids and Structures, 2007

Civil and military ballistic protection systems often consist of thin, high-strength steel plates... more Civil and military ballistic protection systems often consist of thin, high-strength steel plates. Such plates may either be monolithic or layered with or without spacing. The idea of using layered plates instead of a monolithic one in order to increase the ballistic perforation resistance is not new, and the effect of using targets made up of several thinner plates has been investigated in the literature for a long time. However, results by various authors are contradicting and detailed experimental and numerical work is still required. In the present study, the ballistic perforation resistance of double-layered steel plates impacted by blunt and ogival projectiles was investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) targets of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocity, and the ballistic limit velocity of the different target combinations was obtained. In general, good agreement was obtained between the numerical simulations and the experimental results. It was found that in the case of blunt projectiles a large gain in the ballistic limit is offered by double-layered systems. These advantages seem to disappear when ogival projectiles are used. However, the main conclusion from both the experimental and numerical studies is that the overall protection level, i.e. the minimum ballistic limit velocity obtained independently of projectile nose shape, seems to increase significantly by double-layering the target.

Research paper thumbnail of Influence of the constitutive relation in numerical simulations of the perforation of steel plates

WIT Transactions on State of the Art in Science and Engineering, 2014

In the present study, the influence of the constitutive relation in numerical simulations of the ... more In the present study, the influence of the constitutive relation in numerical simulations of the perforation of steel plates has been studied using the nonlinear finite element code LS-DYNA. Two well-known constitutive relations found in the literature are combined with a fracture criterion, and these models have been used in the simulations. The different models have been calibrated and validated for the target material Weldox 460 E using experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Numerical simulations of the perforation process indicate that the physical mechanisms can be qualitatively well predicted independently of the chosen constitutive relation, but quantitatively more severe differences appear.

Research paper thumbnail of On the main mechanisms in ballistic perforation of steel plates at sub-ordnance impact velocities

Predictive Modeling of Dynamic Processes, 2009

This review is a summary of earlier published work carried out by CRISIMLab during the last decad... more This review is a summary of earlier published work carried out by CRISIMLab during the last decade on the ballistic perforation of steel plates at subordnance impact velocities. The reason for carrying out these studies was twofold. First, we wanted to increase our understanding of the many physical phenomena taking place during structural impact by studying some of the main parameters affecting the ballistic perforation resistance of steel plates in the sub-ordnance velocity regime. Second, we wanted to generate high-precision experimental data for the validation of computational tools to be used in the design of protective structures. The main focus in this summary has been on the experimental part. Since several parameters in the experimental studies are similar, such as the velocity regime, the projectile material and mass, and the target material and geometry, the comparison between the various experimental results are both easier and more reliable. The experimental set-up and the various experimental programmes are first presented in brief. Then some main experimental results from five different experimental studies are presented and discussed in some detail. A material model used for numerical simulations of the impact event, together with a short description of the material tests and identification of material constants, are described next. Finally, a selection of results from non-linear finite element simulations of the experimental tests is presented, before some concluding remarks are given.

Research paper thumbnail of Penetration of granular materials by small-arms bullets

International Journal of Impact Engineering, 2015

This paper presents an experimental and numerical study on the penetration of granular materials ... more This paper presents an experimental and numerical study on the penetration of granular materials by small-arms bullets. In the experimental tests, five different types of granular material (0-2 mm wet sand, 0-2 mm dry sand, 2-8 mm gravel, 8-16 mm crushed stone and 16-22 mm crushed rock) were impacted by four different types of smallarms bullets (7.62 mm Ball with a soft lead core, 7.62 mm AP with a hard steel core, 12.7 mm Ball with a soft steel core and 12.7 mm AP with a tungsten carbide core). The tests were carried out using different rifles to fire the projectiles, while the granular materials were randomly packed in a 320 mm diameter specially-designed steel tube. In all tests, the initial projectile velocity and the depth of penetration in the granular material were measured for each bullet type. In the numerical simulations, a discrete particle-based approach was used to model the behaviour of sand during bullet impact. The method works with discrete particles that transfer forces between each other through contact and elastic collisions, allowing for a simple and robust treatment of the interaction between the sand particles and the bullet which is represented by finite elements. An important observation from the study is that the penetration depth in dry sand is strongly influenced by deviation of the bullet from its original trajectory. Good agreement between the available experimental results and the numerical predictions is also in general obtained.

Research paper thumbnail of Ballistic Penetration and Perforation of Layered Steel Plates: An Experimental and Numerical Investigation

In this study, the response to normal impact of hardened ogival steel projectiles on layered stee... more In this study, the response to normal impact of hardened ogival steel projectiles on layered steel plates has been investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) plates of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocities and the ballistic limit of the different target combinations were obtained. Numerical simulations of the perforation processes were carried out using LS-DYNA. Both qualitatively and quantitatively good agreements were found between experimental and numerical results.

Research paper thumbnail of Localised shear banding in Weldox steel plates impacted by projectiles

Mechanics of Materials, 2007

Results from metallurgical investigations of Weldox 460 E, 700 E and 900 E steel plates impacted ... more Results from metallurgical investigations of Weldox 460 E, 700 E and 900 E steel plates impacted by hardened steel projectiles are presented. The strength is considerable higher for Weldox 700 E and 900 E than for Weldox 460 E, while the opposite is true regarding ductility. Penetration tests on the different alloys using blunt projectiles have shown that the ballistic

Research paper thumbnail of Protection performance of double-layered metal shields against projectile impact

Journal of Mechanics of Materials and Structures, 2007

This paper critically evaluates the protection performance of double-layered shields against proj... more This paper critically evaluates the protection performance of double-layered shields against projectile impact at the subordnance velocity using finite element methods. Four types of projectiles of different weight and nose shape are considered, representing various fragments generated from Improvised Explosive Devices (IEDs). It is found that the double-layer configuration is able to improve the ballistic resistance by 8.0%-25.0% for the flat-nose projectile, compared to the monolithic plate of the same weight. The upgrade is due to the transition of the failure mode from less energy dissipating shear plugging to more energy dissipating tensile tearing. Under impact by the conical-nose projectile, the double-layered target is almost as capable as the monolithic plate. The present research helps resolve the long outstanding issue of the protection effectiveness of the double-layer configuration.

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

International Journal of Impact Engineering, 2004

The effect of target strength on the perforation of steel plates is studied. Three structural ste... more 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 ogivalnosed 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.

Research paper thumbnail of Normal and oblique impact of small arms bullets on AA6082-T4 aluminium protective plates

International Journal of Impact Engineering, 2011

Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimental... more Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimentally and numerically. Two types of small arms bullets were used in the ballistic tests, namely the 7.62 Â 63 mm NATO Ball (with a soft lead core) and the 7.62 Â 63 mm APM2 (with a hard steel core), fired from a long smooth-bore Mauser rifle. The targets were struck at 0 , 15 , 30 , 45 and 60 obliquity, and the impact velocity was about 830 m/s in all tests. During testing, the initial and residual bullet velocities were measured by various laser-based optical devices, and high-speed video cameras were used to photograph the penetration process. Of special interest is the critical oblique angle at which the penetration process changes from perforation to embedment or ricochet. The results show that the critical oblique angle was less than 60 for both bullet types. A material test programme was also conducted for the AA6082-T4 plate to calibrate a modified JohnsoneCook constitutive relation and the Cockcroft eLatham failure criterion, while material data for the bullets mainly were taken from the literature. 3D non-linear FE simulations with detailed models of the bullets were finally run. Good agreement between the FE simulations and the experimental results for the APM2 bullets was in general obtained, while it was more difficult to get reliable FE results for the soft core Ball bullets.

Research paper thumbnail of Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles

International Journal of Impact Engineering, 2009

Thin plates of high-strength steel are frequently being used both in civil and military ballistic... more Thin plates of high-strength steel are frequently being used both in civil and military ballistic protection systems. The choice of alloy is then a function of application, ballistic performance, weight and price. In this study the perforation resistance of five different high-strength steels has been determined and compared against each other. The considered alloys are Weldox 500E, Weldox 700E, Hardox 400, Domex Protect 500 and Armox 560T. The yield stress for Armox 560T is about three times the yield stress for Weldox 500E, while the opposite yields for the ductility. To certify the perforation resistance of the various targets, two different ballistic protection classes according to the European norm EN1063 have been considered. These are BR6 (7.62 mm Ball ammunition) and BR7 (7.62 mm AP ammunition), where the impact velocity of the bullet is about 830 m/s in both. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit of the various steels. In the tests, a target thickness of 6 mm and 6 þ 6 ¼ 12 mm was used for protection class BR6 and BR7, respectively. A material test programme was conducted for all steels to calibrate a modified Johnson-Cook constitutive relation and the Cockcroft-Latham fracture criterion, while material data for the bullets mainly were taken from the literature. Finally, results from 2D non-linear FE simulations with detailed models of the bullets are presented and the different findings are compared against each other. As will be shown, good agreement between the FE simulations and experimental data for the AP bullets is in general obtained, while it was difficult to get reliable FE results using the Lagrangian formulation of LS-DYNA for the soft core Ball bullet.

Research paper thumbnail of On the influence of constitutive relation in projectile impact of steel plates

International Journal of Impact Engineering, 2007

In this paper the influence of constitutive relation has been studied in numerical simulations of... more In this paper the influence of constitutive relation has been studied in numerical simulations of the perforation of 12-mm thick Weldox 460 E steel plates impacted by blunt-nosed projectiles in the sub-ordinance velocity regime. A modified version of the well-known and much used constitutive relation proposed by Johnson-Cook and both the bcc-and hcpversion of the Zerilli-Armstrong constitutive relation were combined with the Johnson-Cook fracture criterion. These models were implemented as user-defined material models in the non-linear finite element code LS-DYNA. Identification procedures have been proposed, and the different models were calibrated and validated for the target material using available experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Perforation tests carried out in a compressed gas gun on 12-mm-thick circular Weldox 460 E steel plates were then used as base in a validation study of plate perforation using LS-DYNA and the proposed constitutive relations. The numerical study indicated that the physical mechanisms during perforation can be qualitatively well predicted by all constitutive relations, but quantitatively more severe differences appear. The reasons for this are discussed in some detail. It was concluded that for practical applications, the Johnson-Cook constitutive relation and fracture criterion seems to be a good choice for this particular problem and excellent agreement with the experimental results of projectile impact on steel plates were obtained under the conditions investigated.

Research paper thumbnail of A preliminary study on the perforation resistance of high-strength steel plates

Journal de Physique IV (Proceedings), 2006

Thin plates of high-strength steel are frequently being used in ballistic protection systems. In ... more Thin plates of high-strength steel are frequently being used in ballistic protection systems. In this study, the perforation resistance of three different high-strength steel alloys impacted by 7.62 mm AP projectiles has been determined and compared against each other. The considered alloys are Weldox 500 E, Hardox 400 and Domex Protect 500. The yield stress in Domex Protect 500 is almost three times the yield stress in Weldox 500 E, while the opposite trend is found regarding strain to fracture in uniaxial tension. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit velocity of the steels using 6 + 6 = 12 mm thick targets. Moreover, a material test programme including high strain rate tests in a split-Hopkinson tension bar was carried out in order to be able to calibrate a proper constitutive equation and fracture criteria. Here, a simplified identification procedure was used together with a modified Johnson-Cook constitutive relation and the Cockcroft-Latham fracture criterion since it is considered important to limit the number of material tests in design. Finally, results from 2D axisymmetric numerical simulations using the non-linear FEM code LS-DYNA are included, and the different findings are compared.

Research paper thumbnail of On the ballistic and blast load response of a 20 ft ISO container protected with aluminium panels filled with a local mass — Phase I: Design of protective system

Engineering Structures, 2008

In international peacekeeping operations, it is often necessary to send large amounts of equipmen... more In international peacekeeping operations, it is often necessary to send large amounts of equipment and personnel into highly unstable regions of the world. The troops will be particularly vulnerable in the time before and during the establishment of new camps. Therefore, it is important to get sufficient protection within a shortest possible period of time. As in most cases, long-distance transportation of the protective elements is required, and the weight of the system is thus a critical parameter. This paper presents the development of a new, cost-effective and lightweight protection concept for a 20 ft standard ISO container to be used as shelter in international operations. The work was carried out in six major steps. First, the many requirements for such protection systems were established. Then the basic concept idea, which in this study is an extruded aluminium panel filled with a granular material, was formulated. Next, the ballistic perforation resistance of both empty and mass-filled panels was determined experimentally for specified small-arms ammunition threats. In the next step, the panels were assembled to a protection wall and fixed to the container, and the global system was exposed to specified blast loadings using numerical simulations. Then, based on the many requirements and the findings from the experimental ballistic tests and numerical blast simulations, a design of a protection system for a 20 ft ISO container was proposed, before a prototype was constructed and built. Finally, the protection system was full-scale ballistic and blast tested under realistic conditions to validate the concept. In this paper, the steps associated with the design phase will be described, while the validation phase will be presented in an accompanying paper.

Research paper thumbnail of Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Engineering Fracture Mechanics, 2005

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile... more Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500°C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.

Research paper thumbnail of On the influence of fracture criterion in projectile impact of steel plates

Computational Materials Science, 2006

ABSTRACT

Research paper thumbnail of Experimental Tests and Numerical Simulations on the Ballistic Impact Response of a Highly Inhomogeneous Aluminium Foam

Materials

A sandwich structure is a composite material consisting of thin skins encapsulating a cellular co... more A sandwich structure is a composite material consisting of thin skins encapsulating a cellular core. Such structures have proven to be excellent energy absorbents and are frequently found in various types of protection. Even so, few studies exist in the open literature on the response of the core material itself under extreme loadings such as blast and impact. Since a blast load is usually accompanied by numerous fragments, it is important to understand and be able to predict the ballistic impact resistance of the often highly inhomogeneous cellular core materials in design. In this study, the ballistic impact response of an aluminium foam with a complex cell structure has been investigated both experimentally and numerically. First, an extensive material test program involving compression tests on cubic specimens loaded in the thickness direction of the foam was carried out to reveal the mechanical properties of the material. In addition, several of the specimens were scanned befor...

Research paper thumbnail of Ballistic perforation resistance of thin concrete slabs impacted by ogive-nose steel projectiles

International Journal of Impact Engineering, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Research paper thumbnail of Constitutive Relation And Failure Criterion For Three Structural Steels At High Strain Rates

Sustainability, 2002

The effects of strain rate, temperature and stress triaxiality on strength and ductility are stud... more The effects of strain rate, temperature and stress triaxiality on strength and ductility are studied for the three structural steels Weidox 460 E, Weldox 700 E and Weldox 900 E. The material properties are obtained from 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 constitutive relations and fracture criteria for the three steels.

Research paper thumbnail of Ballistic impact on concrete slabs: An experimental and numerical study

EPJ Web of Conferences, 2021

The ballistic perforation resistance of 50 mm thick concrete slabs impacted by 20 mm diameter ogi... more The ballistic perforation resistance of 50 mm thick concrete slabs impacted by 20 mm diameter ogive-nose steel projectiles is investigated experimentally and numerically. Three commercially produced concretes with nominal unconfined compressive strengths of 35, 75 and 110 MPa were used to cast material test specimens and slabs. After curing, ballistic impact tests were carried out to determine the ballistic limit curve and velocity for each slab quality. Material tests instrumented with digital image correlation (DIC) were conducted along the ballistic impact tests. DIC measurements were used to establish engineering stress-strain curves for calibration of a modified version of the Holmquist-Johnson-Cook concrete model. Finite element simulations of the impact tests gave good conservative predictions.

Research paper thumbnail of On the Dynamic Response of Laminated Glass Exposed to Impact Before Blast Loading

Experimental Mechanics, 2019

In this study, the effect of fragment or bullet impact before blast loading on laminated glass is... more In this study, the effect of fragment or bullet impact before blast loading on laminated glass is studied experimentally. First, laminated windows consisting of two 3.8 mm thick annealed float glass plates and a 1.52 mm thick PVB interlayer were blast loaded in a shock tube with various pressures as a reference. In these tests, the blast loading was successively increased until fracture occurred not only in the glass plates but also in the PVB interlayer. Second, a diamond drill was used to make a 5 mm diameter centrally placed hole in some windows before they were blast loaded with the same pressures as those used for the undamaged windows. Third, windows were impacted by 7.62 mm AP bullets, both with and without the brass jacket, before they were blast loaded. Such bullets may have similar mass and velocity to typical primary fragments from an explosive detonation. The results are finally compared with each other and discussed with respect to the blast protection offered. It is found that the capacity is significantly reduced if the laminated glass is perforated by a fragment or a bullet before it is blast loaded and that such impacts should be considered in the design of blast-resistant windows.

Research paper thumbnail of On the ballistic resistance of double-layered steel plates: An experimental and numerical investigation

International Journal of Solids and Structures, 2007

Civil and military ballistic protection systems often consist of thin, high-strength steel plates... more Civil and military ballistic protection systems often consist of thin, high-strength steel plates. Such plates may either be monolithic or layered with or without spacing. The idea of using layered plates instead of a monolithic one in order to increase the ballistic perforation resistance is not new, and the effect of using targets made up of several thinner plates has been investigated in the literature for a long time. However, results by various authors are contradicting and detailed experimental and numerical work is still required. In the present study, the ballistic perforation resistance of double-layered steel plates impacted by blunt and ogival projectiles was investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) targets of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocity, and the ballistic limit velocity of the different target combinations was obtained. In general, good agreement was obtained between the numerical simulations and the experimental results. It was found that in the case of blunt projectiles a large gain in the ballistic limit is offered by double-layered systems. These advantages seem to disappear when ogival projectiles are used. However, the main conclusion from both the experimental and numerical studies is that the overall protection level, i.e. the minimum ballistic limit velocity obtained independently of projectile nose shape, seems to increase significantly by double-layering the target.

Research paper thumbnail of Influence of the constitutive relation in numerical simulations of the perforation of steel plates

WIT Transactions on State of the Art in Science and Engineering, 2014

In the present study, the influence of the constitutive relation in numerical simulations of the ... more In the present study, the influence of the constitutive relation in numerical simulations of the perforation of steel plates has been studied using the nonlinear finite element code LS-DYNA. Two well-known constitutive relations found in the literature are combined with a fracture criterion, and these models have been used in the simulations. The different models have been calibrated and validated for the target material Weldox 460 E using experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Numerical simulations of the perforation process indicate that the physical mechanisms can be qualitatively well predicted independently of the chosen constitutive relation, but quantitatively more severe differences appear.

Research paper thumbnail of On the main mechanisms in ballistic perforation of steel plates at sub-ordnance impact velocities

Predictive Modeling of Dynamic Processes, 2009

This review is a summary of earlier published work carried out by CRISIMLab during the last decad... more This review is a summary of earlier published work carried out by CRISIMLab during the last decade on the ballistic perforation of steel plates at subordnance impact velocities. The reason for carrying out these studies was twofold. First, we wanted to increase our understanding of the many physical phenomena taking place during structural impact by studying some of the main parameters affecting the ballistic perforation resistance of steel plates in the sub-ordnance velocity regime. Second, we wanted to generate high-precision experimental data for the validation of computational tools to be used in the design of protective structures. The main focus in this summary has been on the experimental part. Since several parameters in the experimental studies are similar, such as the velocity regime, the projectile material and mass, and the target material and geometry, the comparison between the various experimental results are both easier and more reliable. The experimental set-up and the various experimental programmes are first presented in brief. Then some main experimental results from five different experimental studies are presented and discussed in some detail. A material model used for numerical simulations of the impact event, together with a short description of the material tests and identification of material constants, are described next. Finally, a selection of results from non-linear finite element simulations of the experimental tests is presented, before some concluding remarks are given.

Research paper thumbnail of Penetration of granular materials by small-arms bullets

International Journal of Impact Engineering, 2015

This paper presents an experimental and numerical study on the penetration of granular materials ... more This paper presents an experimental and numerical study on the penetration of granular materials by small-arms bullets. In the experimental tests, five different types of granular material (0-2 mm wet sand, 0-2 mm dry sand, 2-8 mm gravel, 8-16 mm crushed stone and 16-22 mm crushed rock) were impacted by four different types of smallarms bullets (7.62 mm Ball with a soft lead core, 7.62 mm AP with a hard steel core, 12.7 mm Ball with a soft steel core and 12.7 mm AP with a tungsten carbide core). The tests were carried out using different rifles to fire the projectiles, while the granular materials were randomly packed in a 320 mm diameter specially-designed steel tube. In all tests, the initial projectile velocity and the depth of penetration in the granular material were measured for each bullet type. In the numerical simulations, a discrete particle-based approach was used to model the behaviour of sand during bullet impact. The method works with discrete particles that transfer forces between each other through contact and elastic collisions, allowing for a simple and robust treatment of the interaction between the sand particles and the bullet which is represented by finite elements. An important observation from the study is that the penetration depth in dry sand is strongly influenced by deviation of the bullet from its original trajectory. Good agreement between the available experimental results and the numerical predictions is also in general obtained.

Research paper thumbnail of Ballistic Penetration and Perforation of Layered Steel Plates: An Experimental and Numerical Investigation

In this study, the response to normal impact of hardened ogival steel projectiles on layered stee... more In this study, the response to normal impact of hardened ogival steel projectiles on layered steel plates has been investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) plates of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocities and the ballistic limit of the different target combinations were obtained. Numerical simulations of the perforation processes were carried out using LS-DYNA. Both qualitatively and quantitatively good agreements were found between experimental and numerical results.

Research paper thumbnail of Localised shear banding in Weldox steel plates impacted by projectiles

Mechanics of Materials, 2007

Results from metallurgical investigations of Weldox 460 E, 700 E and 900 E steel plates impacted ... more Results from metallurgical investigations of Weldox 460 E, 700 E and 900 E steel plates impacted by hardened steel projectiles are presented. The strength is considerable higher for Weldox 700 E and 900 E than for Weldox 460 E, while the opposite is true regarding ductility. Penetration tests on the different alloys using blunt projectiles have shown that the ballistic

Research paper thumbnail of Protection performance of double-layered metal shields against projectile impact

Journal of Mechanics of Materials and Structures, 2007

This paper critically evaluates the protection performance of double-layered shields against proj... more This paper critically evaluates the protection performance of double-layered shields against projectile impact at the subordnance velocity using finite element methods. Four types of projectiles of different weight and nose shape are considered, representing various fragments generated from Improvised Explosive Devices (IEDs). It is found that the double-layer configuration is able to improve the ballistic resistance by 8.0%-25.0% for the flat-nose projectile, compared to the monolithic plate of the same weight. The upgrade is due to the transition of the failure mode from less energy dissipating shear plugging to more energy dissipating tensile tearing. Under impact by the conical-nose projectile, the double-layered target is almost as capable as the monolithic plate. The present research helps resolve the long outstanding issue of the protection effectiveness of the double-layer configuration.

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

International Journal of Impact Engineering, 2004

The effect of target strength on the perforation of steel plates is studied. Three structural ste... more 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 ogivalnosed 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.

Research paper thumbnail of Normal and oblique impact of small arms bullets on AA6082-T4 aluminium protective plates

International Journal of Impact Engineering, 2011

Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimental... more Normal and oblique impact on 20 mm thick AA6082-T4 aluminium plates are studied both experimentally and numerically. Two types of small arms bullets were used in the ballistic tests, namely the 7.62 Â 63 mm NATO Ball (with a soft lead core) and the 7.62 Â 63 mm APM2 (with a hard steel core), fired from a long smooth-bore Mauser rifle. The targets were struck at 0 , 15 , 30 , 45 and 60 obliquity, and the impact velocity was about 830 m/s in all tests. During testing, the initial and residual bullet velocities were measured by various laser-based optical devices, and high-speed video cameras were used to photograph the penetration process. Of special interest is the critical oblique angle at which the penetration process changes from perforation to embedment or ricochet. The results show that the critical oblique angle was less than 60 for both bullet types. A material test programme was also conducted for the AA6082-T4 plate to calibrate a modified JohnsoneCook constitutive relation and the Cockcroft eLatham failure criterion, while material data for the bullets mainly were taken from the literature. 3D non-linear FE simulations with detailed models of the bullets were finally run. Good agreement between the FE simulations and the experimental results for the APM2 bullets was in general obtained, while it was more difficult to get reliable FE results for the soft core Ball bullets.

Research paper thumbnail of Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles

International Journal of Impact Engineering, 2009

Thin plates of high-strength steel are frequently being used both in civil and military ballistic... more Thin plates of high-strength steel are frequently being used both in civil and military ballistic protection systems. The choice of alloy is then a function of application, ballistic performance, weight and price. In this study the perforation resistance of five different high-strength steels has been determined and compared against each other. The considered alloys are Weldox 500E, Weldox 700E, Hardox 400, Domex Protect 500 and Armox 560T. The yield stress for Armox 560T is about three times the yield stress for Weldox 500E, while the opposite yields for the ductility. To certify the perforation resistance of the various targets, two different ballistic protection classes according to the European norm EN1063 have been considered. These are BR6 (7.62 mm Ball ammunition) and BR7 (7.62 mm AP ammunition), where the impact velocity of the bullet is about 830 m/s in both. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit of the various steels. In the tests, a target thickness of 6 mm and 6 þ 6 ¼ 12 mm was used for protection class BR6 and BR7, respectively. A material test programme was conducted for all steels to calibrate a modified Johnson-Cook constitutive relation and the Cockcroft-Latham fracture criterion, while material data for the bullets mainly were taken from the literature. Finally, results from 2D non-linear FE simulations with detailed models of the bullets are presented and the different findings are compared against each other. As will be shown, good agreement between the FE simulations and experimental data for the AP bullets is in general obtained, while it was difficult to get reliable FE results using the Lagrangian formulation of LS-DYNA for the soft core Ball bullet.

Research paper thumbnail of On the influence of constitutive relation in projectile impact of steel plates

International Journal of Impact Engineering, 2007

In this paper the influence of constitutive relation has been studied in numerical simulations of... more In this paper the influence of constitutive relation has been studied in numerical simulations of the perforation of 12-mm thick Weldox 460 E steel plates impacted by blunt-nosed projectiles in the sub-ordinance velocity regime. A modified version of the well-known and much used constitutive relation proposed by Johnson-Cook and both the bcc-and hcpversion of the Zerilli-Armstrong constitutive relation were combined with the Johnson-Cook fracture criterion. These models were implemented as user-defined material models in the non-linear finite element code LS-DYNA. Identification procedures have been proposed, and the different models were calibrated and validated for the target material using available experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Perforation tests carried out in a compressed gas gun on 12-mm-thick circular Weldox 460 E steel plates were then used as base in a validation study of plate perforation using LS-DYNA and the proposed constitutive relations. The numerical study indicated that the physical mechanisms during perforation can be qualitatively well predicted by all constitutive relations, but quantitatively more severe differences appear. The reasons for this are discussed in some detail. It was concluded that for practical applications, the Johnson-Cook constitutive relation and fracture criterion seems to be a good choice for this particular problem and excellent agreement with the experimental results of projectile impact on steel plates were obtained under the conditions investigated.

Research paper thumbnail of A preliminary study on the perforation resistance of high-strength steel plates

Journal de Physique IV (Proceedings), 2006

Thin plates of high-strength steel are frequently being used in ballistic protection systems. In ... more Thin plates of high-strength steel are frequently being used in ballistic protection systems. In this study, the perforation resistance of three different high-strength steel alloys impacted by 7.62 mm AP projectiles has been determined and compared against each other. The considered alloys are Weldox 500 E, Hardox 400 and Domex Protect 500. The yield stress in Domex Protect 500 is almost three times the yield stress in Weldox 500 E, while the opposite trend is found regarding strain to fracture in uniaxial tension. Perforation tests have been carried out using adjusted ammunition to determine the ballistic limit velocity of the steels using 6 + 6 = 12 mm thick targets. Moreover, a material test programme including high strain rate tests in a split-Hopkinson tension bar was carried out in order to be able to calibrate a proper constitutive equation and fracture criteria. Here, a simplified identification procedure was used together with a modified Johnson-Cook constitutive relation and the Cockcroft-Latham fracture criterion since it is considered important to limit the number of material tests in design. Finally, results from 2D axisymmetric numerical simulations using the non-linear FEM code LS-DYNA are included, and the different findings are compared.

Research paper thumbnail of On the ballistic and blast load response of a 20 ft ISO container protected with aluminium panels filled with a local mass — Phase I: Design of protective system

Engineering Structures, 2008

In international peacekeeping operations, it is often necessary to send large amounts of equipmen... more In international peacekeeping operations, it is often necessary to send large amounts of equipment and personnel into highly unstable regions of the world. The troops will be particularly vulnerable in the time before and during the establishment of new camps. Therefore, it is important to get sufficient protection within a shortest possible period of time. As in most cases, long-distance transportation of the protective elements is required, and the weight of the system is thus a critical parameter. This paper presents the development of a new, cost-effective and lightweight protection concept for a 20 ft standard ISO container to be used as shelter in international operations. The work was carried out in six major steps. First, the many requirements for such protection systems were established. Then the basic concept idea, which in this study is an extruded aluminium panel filled with a granular material, was formulated. Next, the ballistic perforation resistance of both empty and mass-filled panels was determined experimentally for specified small-arms ammunition threats. In the next step, the panels were assembled to a protection wall and fixed to the container, and the global system was exposed to specified blast loadings using numerical simulations. Then, based on the many requirements and the findings from the experimental ballistic tests and numerical blast simulations, a design of a protection system for a 20 ft ISO container was proposed, before a prototype was constructed and built. Finally, the protection system was full-scale ballistic and blast tested under realistic conditions to validate the concept. In this paper, the steps associated with the design phase will be described, while the validation phase will be presented in an accompanying paper.

Research paper thumbnail of Strength and ductility of Weldox 460 E steel at high strain rates, elevated temperatures and various stress triaxialities

Engineering Fracture Mechanics, 2005

Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile... more Strength and ductility data at high strain rates for Weldox 460 E steel was obtained from tensile tests with axisymmetric specimens. The tests were performed in a Split Hopkinson Tension Bar and the initial temperature was varied between 100 and 500°C. The combined effect of high strain rate, elevated temperature and stress triaxiality on the behaviour was studied by testing both smooth and pre-notched specimens. It was found that the influence of temperature on the stress-strain behaviour differs at high strain rates compared with quasi-static loading conditions. The true fracture strain depends considerably on the stress triaxiality, which is governed by the notch geometry, while the influence of strain rate and temperature is less clear. Numerical simulations with the explicit finite element code LS-DYNA were performed using a model of elasto-viscoplasticity and ductile damage, which is based on the constitutive relation and fracture criterion of Johnson and Cook. The numerical simulations compare reasonably well with the experiments with respect to strength and ductility for both smooth and notched specimens at elevated temperatures.

Research paper thumbnail of On the influence of fracture criterion in projectile impact of steel plates

Computational Materials Science, 2006

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