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Behind-Armour Debris Behind-Armour Debris - Modelling and simulation A literature review Mats Hartmann FOI-R--1678--SE Weapons and Protection June 2005 ISSN 1650-1942 Base data report FOI is an assignment-based authority under the Ministry of Defence. The core activities are research, method and technology development, as well as studies for the use of defence and security. The organization employs around 1350 people of whom around 950 are researchers. This makes FOI the largest research institute in Sweden. FOI provides its customers with leading expertise in a large number of fields such as security-policy studies and analyses in defence and security, assessment of different types of threats, systems for control and management of crises, protection against and management of hazardous substances, IT-security an the potential of new sensors. FOI Defence Research Agency Tel: +46-8-5550 3000 www.foi.se Weapons and Protection Fax: +46-8-5550 4143 SE-147 25 Tumba Behind-Armour Debris - Modelling and simulation A literature review FOI-R--1678--SE Weapons and Protection June 2005 ISSN 1650-1942 Base data report Issuing organization Report number, ISRN Report type FOI – Swedish Defence Research Agency FOI-R--1678--SE Base data report Weapons and Protection Research area code SE-147 25 Tumba 5. Strike and protection Month year Project no. June 2005 E2007 Sub area code 51 Weapons and Protection Sub area code 2 Author/s (editor/s) Project manager Mats Hartmann Gunnar Wijk Approved by Sponsoring agency Swedish armed forces Scientifically and technically responsible Report title Behind-Armour Debris - Modelling and simulation A literature review Abstract (not more than 200 words) The ability to model behind armour debris (BAD) is important in assessment of vulnerability and lethality. It is very hard to find a suitable model, despite the well recognized importance of the phenomena. A literature review of models and simulations of BAD is presented together with a short description of some hydrocodes and important concepts in numerical simulations. Many physical, empirical and statistical models handle only part of the problem; either target failure or BAD cloud characteristics. Numerical simulations have problems with fracturing of the target material. Numerical erosion is sometimes used to assess which computational cells that form BAD. The numerical simulations are often combined with a post processor to include the stochastic behaviour of the debris cloud. It is concluded that this is a research field that still needs a lot of work, both experimentally and numerically, before the models are reliable and usable in or as pre-processors to vulnerability assessment. Keywords BAD, behind armour debris, fragment, spall, modelling, simulation, hydrocode, analytical, statistical, empirical, vulnerability, lethality, assessment, penetration, perforation Further bibliographic information Language English ISSN 1650-1942 Pages 52 p. Price acc. to pricelist 2 Utgivare Rapportnummer, ISRN Klassificering FOI - Totalförsvarets Forskningsinstitut - FOI-R--1678--SE Underlagsrapport Vapen och skydd Forskningsområde 147 25 Tumba 5. Bekämpning och skydd Månad, år Projektnummer Juni 2005 E2007 Delområde 51 VVS med styrda vapen Delområde 2 Författare/redaktör Projektledare Mats Hartmann Gunnar Wijk Godkänd av Uppdragsgivare/kundbeteckning Försvarsmakten Tekniskt och/eller vetenskapligt ansvarig Rapportens titel (i översättning) Splitter bakom skydd - Modellering och simulering En litteraturstudie Sammanfattning (högst 200 ord) Möjligheten att modellera sekundärsplitter bakom skyddspaneler är viktigt i verkans- och sårbarhetsvärderingar. Trots det välkända behovet är det mycket svårt att hitta lämpliga modeller. En litteraturstudie över modeller och simuleringar av sekundärsplitter presenteras tillsammans med en kort beskrivning av några numeriska beräkningsprogram och några, till beräkningsprogrammen, viktiga begrepp. Många av de fysikaliska, empiriska och statistiska modellerna hanterar endast en delmängd av problemet, antingen brottmekanismen i målet eller splittermolnets egenskaper. De numeriska simuleringarna har problem med brott i målmaterialen. Numerisk erosion används ibland för att bestämma vilka beräkningsceller som bildar sekundärsplitter. Ofta kombineras de numeriska simuleringarna med en postprocessor för att kunna inkludera det stokastiska uppträdandet hos splittermolnet. Det konstateras att detta är ett forskningsområde som fortfarande kräver mycket arbete, både experimentellt och numeriskt, innan modellerna är trovärdiga och användbara i eller som underlagslämnare till värderingsarbeten. Nyckelord Sekundärsplitter, fragment, modell, simulering, analytisk, statistisk, empirisk, sårbarhet, verkan, värdering penetration, perforation, krossning Övriga bibliografiska uppgifter Språk Engelska ISSN 1650-1942 Antal sidor: 52 s. Distribution enligt missiv Pris: Enligt prislista 3 Contents 1 Introduction..................................................................................................................................5 2 Physical, statistical and empirical models....................................................................................7 2.1 Target failure and fragment generation................................................................................7 2.2 Debris cloud characteristics ...............................................................................................13 2.3 Combined models..............................................................................................................16 2.4 Models for evaluation of witness plates.............................................................................19 3 Numerical methods ....................................................................................................................21 3.1 Important concepts in numerical simulations ....................................................................21 3.1.1 The finite element method .........................................................................................21 3.1.2 The finite difference method......................................................................................21 3.1.3............................................................................................................................................22 3.1.4 The finite volume method..........................................................................................22 3.1.5 Problem formulation techniques ................................................................................22 3.1.6 Equation of State (EOS).............................................................................................25 3.2 Hydrocodes ........................................................................................................................26 4 Hydrocode simulations ..............................................................................................................28 4.1 Target failure and fragment generation..............................................................................28 4.1.1 Failure and fragment generation in hypervelocity simulations..................................31 4.2 Debris cloud characteristics ...............................................................................................32 4.2.1 Debris cloud characteristics in hypervelocity simulations.........................................33 4.3 Combined simulations.......................................................................................................35 4.3.1 Combined simulations in hypervelocity simulations.................................................38 4.4 Simulations for witness pack evaluation............................................................................39 4.5 Other simulations with some relation to BAD...................................................................39 5 Discussion ..................................................................................................................................44 6 Conclusions................................................................................................................................47 7 References..................................................................................................................................48 Appendix 1: Summary of reviewed models.......................................................................................51 Appendix 2: Abbreviations ................................................................................................................52 4 1 Introduction When a projectile or a shaped charge jet perforates a target plate there will often be a cloud of debris around the residual projectile behind the plate. These particles may hit and injure personnel or components inside an armoured vehicle. To be able to predict the consequences of an attack one has to estimate the number of particles, their masses, velocities and directions in the cloud, as well as the residual velocity, mass and direction of the projectile. This need is recognized by numerous authors [1, 2, 3, 4] working with terminal ballistics applications. The task is illustrated in and Figure 1, where the black lines represent the impacting projectile and the behind-armour debris (BAD) trajectories inside an armoured fighting vehicle, and in Figure 2, where the numerous holes around the center hole are created by BAD. It is, despite the widely recognised need for the ability to model BAD, hard or impossible
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