Modeling of fragmentation of rapidly expanding cylinders

U radu se razmatra proces fragmentacije košuljica projektila parčadnog dejstva, tj. generisanja parčadi rasprskavanjem metalnog cilindra koji je izložen visokim vrednostima unutrašnjeg pritiska usled detonacije eksploziva. Detaljno je razmotren klasični Mott-ov model fragmentacije metalnog prstena na osnovu koga je realizovan odgovarajući program za računar. Analiziran je zakon raspodele dužine (mase) fragmenata, kao i srednja dužina parčadi u funkciji osobina materijala prstena i karakteristika ekspanzije prstena. Razmotren je uticaj relevantnih parametara fragmentacionog procesa na karakter raspodele parčadi. Teorijska raspodela dužine fragmenata upoređena je sa dostupnim eksperimentalnim podacima pri čemu je dobijeno dobro podudaranje rezultata.The paper considers fragmentation process of high-explosive projectile casings, i.e. rapidly expanding cylinders loaded by extreme internal pressure generated by detonation of explosives. The classical, physically based, Mott model of the ring fragmentation is examined and the adequate computer program is realized. The fragment size (or mass) distribution is analyzed and the average fragment size is related to the characteristics of expansion and the casing material properties. The influence of the fragmentation process parameters on the nature of fragment length distribution is analyzed. The theoretical distributions are compared with experimental data and good correspondence is obtained

Fragment size distribution in dynamic fragmentation: Geometric probability approach

Dinamička fragmentacija je kompleksna pojava koja karakteriše brojne prirodne i tehničke sisteme. Određivanje zakona raspodele veličine (odnosno mase) generisanih fragmenata predstavlja jedan od najznačajnijih zadataka pri modeliranju dinamičke fragmentacije. U radu se razmatra uopšten pristup ovom problemu zasnovan na jednostavnoj pretpostavci o slučajnoj geometrijskoj segmentaciji tela. Polazeći od binomne raspodele mesta loma (tačaka, pravih ili ravni), izvedene su funkcije raspodele veličine fragmenata za 1D, 2D i 3D geometriju. Analizirani su modeli geometrijske fragmentacije zasnovani na pristupima Mott-a i Grady-Kipp-a. Takođe su razmatrani zakoni raspodele zasnovani na primeni Voronoi dijagrama. Rezultati razmatranih modela upoređeni su sa numeričkim simulacijama i eksperimentalnim rezultatima, pri čemu je pokazano da postoje značajna podudaranja, kao i izvesna ograničenja modela. Zaključeno je da preferirani teorijski model zavisi od dimenzionalnosti fragmentacionog procesa. .Dynamic fragmentation is a complex phenomenon inherent in numerous natural and engineering systems. Determination of the fragment size (or mass) distribution law is one of the most important objectives in dynamic fragmentation modeling. In the present paper, a general approach based on the simple assumption of random geometric partition of a body has been considered. Starting from the binomial distribution of fracture sites (points, lines or planes), size distribution laws are derived for 1D, 2D and 3D geometries. Geometric fragmentation models based on Mott's and Grady-Kipp's approaches are analyzed. The models originating from the Voronoi diagrams are also considered. The results of presented models are compared with numerical simulations and experimental data, showing significant compatibility as well as certain limitations. It has been concluded that preferred theoretical model depends on dimensionality of fragmentation process.

Modeling of fragmentation of rapidly expanding cylinders

U radu se razmatra proces fragmentacije košuljica projektila parčadnog dejstva, tj. generisanja parčadi rasprskavanjem metalnog cilindra koji je izložen visokim vrednostima unutrašnjeg pritiska usled detonacije eksploziva. Detaljno je razmotren klasični Mott-ov model fragmentacije metalnog prstena na osnovu koga je realizovan odgovarajući program za računar. Analiziran je zakon raspodele dužine (mase) fragmenata, kao i srednja dužina parčadi u funkciji osobina materijala prstena i karakteristika ekspanzije prstena. Razmotren je uticaj relevantnih parametara fragmentacionog procesa na karakter raspodele parčadi. Teorijska raspodela dužine fragmenata upoređena je sa dostupnim eksperimentalnim podacima pri čemu je dobijeno dobro podudaranje rezultata.The paper considers fragmentation process of high-explosive projectile casings, i.e. rapidly expanding cylinders loaded by extreme internal pressure generated by detonation of explosives. The classical, physically based, Mott model of the ring fragmentation is examined and the adequate computer program is realized. The fragment size (or mass) distribution is analyzed and the average fragment size is related to the characteristics of expansion and the casing material properties. The influence of the fragmentation process parameters on the nature of fragment length distribution is analyzed. The theoretical distributions are compared with experimental data and good correspondence is obtained

Fragment size distribution in dynamic fragmentation: Geometric probability approach

Dinamička fragmentacija je kompleksna pojava koja karakteriše brojne prirodne i tehničke sisteme. Određivanje zakona raspodele veličine (odnosno mase) generisanih fragmenata predstavlja jedan od najznačajnijih zadataka pri modeliranju dinamičke fragmentacije. U radu se razmatra uopšten pristup ovom problemu zasnovan na jednostavnoj pretpostavci o slučajnoj geometrijskoj segmentaciji tela. Polazeći od binomne raspodele mesta loma (tačaka, pravih ili ravni), izvedene su funkcije raspodele veličine fragmenata za 1D, 2D i 3D geometriju. Analizirani su modeli geometrijske fragmentacije zasnovani na pristupima Mott-a i Grady-Kipp-a. Takođe su razmatrani zakoni raspodele zasnovani na primeni Voronoi dijagrama. Rezultati razmatranih modela upoređeni su sa numeričkim simulacijama i eksperimentalnim rezultatima, pri čemu je pokazano da postoje značajna podudaranja, kao i izvesna ograničenja modela. Zaključeno je da preferirani teorijski model zavisi od dimenzionalnosti fragmentacionog procesa. .Dynamic fragmentation is a complex phenomenon inherent in numerous natural and engineering systems. Determination of the fragment size (or mass) distribution law is one of the most important objectives in dynamic fragmentation modeling. In the present paper, a general approach based on the simple assumption of random geometric partition of a body has been considered. Starting from the binomial distribution of fracture sites (points, lines or planes), size distribution laws are derived for 1D, 2D and 3D geometries. Geometric fragmentation models based on Mott's and Grady-Kipp's approaches are analyzed. The models originating from the Voronoi diagrams are also considered. The results of presented models are compared with numerical simulations and experimental data, showing significant compatibility as well as certain limitations. It has been concluded that preferred theoretical model depends on dimensionality of fragmentation process.

Fragment mass distribution of naturally fragmenting warheads

U radu se razmatraju statistički aspekti fragmentacije razornih bojnih glava. Modeliranje raspodele mase fragmenata je od velikog značaja pri određivanju efikasnosti razornih projektila. Dat je pregled sedam relevantnih teorijskih modela raspodele mase parčadi: Motov (Mott) model, generalizovani Motov model, Grejdijev (Grady) model, generalizovani Grejdijev model,lognormalna raspodela, Vajbulova (Weibull) i Heldova (Held) raspodela. Poređenje ovih modela sa reprezentativnom bazom podataka za 30 razornih projektila pokazalo je veoma dobro podudaranje teorijskih i eksperimentalnih rezultata. Analiza koeficijenata determinacije ukazala je da generalizovana Motova, generalizovana Grejdijeva i Vajbulova raspodela najbolje opisuju rezultate eksperimenata. Dalje poređenje ovih modela zasnovano na analizi medijane favorizuje generalizovanu Grejdijevu raspodelu čija se bimodalnost može fizički opravdati. Predloženi zakon raspodele mase fragmenata može se primeniti u složenom simulacionom modelu efikasnosti razornih projektila.The paper considers statistical aspects of high explosive warhead fragmentation. The modeling of fragment mass distribution is of great importance for determination of fragmenting warhead efficiency. Seven relevant theoretical fragment mass distribution models are reviewed: the Mott, the generalized Mott, the Grady, the generalized Grady, the lognormal, the Weibull and the Held distribution. Comparison of these models with representative experimental database of 30 fragmenting projectiles has shown, generally, a very good correspondence between theoretical models and experimental data. The goodness of fit analysis has indicated that the generalized Mott, the generalized Grady and the Weibull distribution enable the best description of experimental fragment mass distribution data. Further comparison of these models based on the median analysis prefers the generalized Grady distribution, and its bimodal characteristic can be physically justified. The suggested theoretical fragment mass distribution law can be applied in a complex fragmenting projectile efficiency simulation model

A Model for Shaped Charge Warhead Design

A model for shaped charge warhead design was developed. The model is incorporated in the computer code - CUMUL. The code includes detonation wave profile estimation, liner collapse, arrival of collapsed liner to the centerline of shaped charge, jet creation and jet breakup. The penetration phenomena are discussed and governing equations are presented. Two cases dealing with the target type are included: homogenous and non-homogeneous targets. For the purpose of verifying CUMUL, a set of 20 specimens of shaped charges was tested. The tests were directed to investigate the effect of cone apex angle and stand-off distance on the performance of shaped charge. From the comparison between experiments and CUMUL results, it was concluded that CUMUL program shows a good agreement with the experiments. That enables it to be a powerful tool for shaped charge warhead design

Kriterijum efikasnosti i optimizacija mase fragmenata projektila parčadnog dejstva

У раду се разматра проблем оптимизације масе парчади која настају фрагментацијом пројектила парчадног дејства. Показано је да оптимална маса парчета првенствено зависи од његових кинетичких карактеристика на циљу, као и од усвојеног критеријума ефикасности. Прорачуни показују да су постојећи критеријуми, минимална захтевана кинетичка енергија фрагмента, односно минимална кинетичка енергија по јединици нападне површине, несагласни – односно да дају битно различите вредности оптималне масе. Закључено је да критеријум специфичне енергије парчета подразумева мању масу оптималног парчета и указује на значај парчади веома мале масе са становишта ефикасности. Јасно је да овако одређена оптимална маса ефикасног парчета представља веома важан параметар пројектила парчaдног дејства, при чему је неопходна eкспериментална верификација добијених теоријских резултата. In the paper it has been considered the problem of optimization of HE projectile fragments’ mass. It is shown that optimum fragment’s mass is a function of its kinetic characteristics at the target and adopted efficiency criterion. Computations show that the most prominent criteria, minimum required kinetic energy and minimum kinetic energy per unit of cross-sectional area, are incompatible – i.e. they provide significantly different values of optimal mass. It is concluded that criterion of specific kinetic energy corresponds to lower optimum fragment mass, which indicates the importance of fragments of low masses from the aspect of efficiency. Theoretically determined optimum fragment mass represents very significant parameter for design optimization of fragmentating projectile, but experimental verification of obtained results is essentially important

Dynamic fragmentation: Geometric approach

Dynamic fragmentation is a complex and common phenomenon in nature and technological systems. The main task in fragmentation modeling is determination of the fragment size (or mass) distribution law. There are several approaches to the fragmentation problem – empirical, probabilistic, energetic, approach based on fracture mechanics, etc. In the present paper we consider a general approach based on the simple assumption of random geometric partition of a body, following early Lineau [1], Mott [2] and well-known Grady-Kipp work [3]. Starting from the Poisson distribution of fracture sites (points, lines or planes), size distribution laws are derived for 1D, 2D and 3D geometries. Geometric fragmentation models based on the Mott and Grady-Kipp approaches are discussed, as well as the model originated from the Voronoi diagrams. The results of presented models are compared with numerical simulations and experimental data, showing significant compatibility with certain limitations

Simulation of changes in temperature and pressure fields during high speed projectiles forming by explosion

The research in this paper considered the temperatures fields as the consequently influenced effects appeared by plastic deformation, in the explosively forming process aimed to design explosively formed projectiles. As the special payloads of the missiles, used projectiles are packaged as the metal liners, joined with explosive charges, to design explosive propulsion effect. Their final form and velocity during shaping depend on distributed temperatures in explosively driven plastic deformation process. Developed simulation model consider forming process without metal cover of explosive charge, in aim to discover liner's dynamical correlations of effective plastic strains and temperatures in the unconstrained detonation environment made by payload construction. The temperature fields of the liner copper material are considered in time, as the consequence of strain/stress displacements driven by explosion environmental thermodynamically fields of pressures and temperatures. Achieved final velocities and mass loses as the expected explosively formed projectiles performances are estimated regarding their dynamical shaping and thermal gradients behavior vs. effective plastic strains. Performances and parameters are presented vs. process time, numerically simulated by the Autodyne software package

Modeling of fragmentation of rapidly expanding cylinders

The paper considers fragmentation process of high-explosive projectile casings, i.e. rapidly expanding cylinders loaded by extreme internal pressures generated by detonation of explosives. The classical Mott's model as well as the alternative approaches to the problem are examined. The distribution laws of fragment size and mass are analyzed and the average fragment size (mass) is related to the characteristics of expansion and the casing material properties. The theoretical distributions are compared with experimental data and good correspondence is obtained. Finally, the possibilities for improvement of characteristics of projectile fragmentation are investigated