Characterization of projectile's interaction on thin metallic plates

Characterization of Projectile’s

Interaction on Thin Metallic Plates

Supervisor: Professor Marco V. Boniardi

Co- Supervisor: Ingegner Andrea Casaroli

Riccardo Maria Fossati

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All’inizio di questo lavoro di tesi, mi permetto di esprimere i ringraziamenti utilizzando la lingua italiana; credo sia doveroso nei confronti delle persone a cui questo lavoro viene dedicato. Credo altresì che, in questa maniera, io possa essere anche più esaustivo e “colorito” in questo capitolo che è tutto fuorché tecnico.

Alla fine di questo percorso di studi universitario, innumerevoli sono le persone che debbo ringraziare perché, in una maniera o in un’altra, hanno contribuito nell’accompagnamento verso questo grande “inizio”; le prove sono terminate, ora c’è da correre la gara della vita, per utilizzare una metafora tratta dal mondo delle corse.

Il primo pensiero va alla mia famiglia, senza la quale non sarei qui a scrivere in questo momento. A mio padre Giancarlo che mi ha trasmesso la passione per la meccanica e per le corse, a mia madre Marina che, come si conviene ad una madre, ha sopportato le mie “paturnie” universitarie lungo questo percorso vissuto tra alti e bassi. Un pensiero va a mio fratello Alessandro e mia sorella Aurora; il nostro legame ha fatto sopportare loro i miei differenti stati d’animo in questi anni, ma sempre con l’allegria e il bene che solo tra fratelli ci si vuole.

Quando il legame invece non è di sangue, ma lo si sceglie ogni giorno dentro un rapporto, si impara ancor meglio cosa significhi amare; ringrazio con tutto il cuore Alice, il mio faro nella notte. In questi lunghi anni siamo cresciuti insieme, mano nella mano, e in questo momento che apre le porte al futuro, auguro a noi con tutto il cuore di continuare a crescere accompagnandoci ed amandoci in tutto ciò che la vita ha da offrirci quotidianamente.

Ringrazio anche Franco, Loredana e Marta; con la vostra allegria e la vostra accoglienza mi avete sempre fatto sentire a casa, in ogni occasione di condivisione e di gioia che ci è stata offerta.

Ringrazio Martina, Matteo, Francesca, Andrea e Loris; siete stati dei compagni di viaggio unici, ognuno con le sue peculiarità che ci hanno reso un gruppo eterogeneo e compatto. Senza di voi avrei arrancato sulle salite che spesso ci si sono parate davanti, le quali con la vostra presenza si sono “spianate”. Avrei mille parole e mille aneddoti da spendere su ciascuno di voi, ma non mancherò di riportarvele personalmente dal vivo per non trasformare questo capitolo in un best seller a sé stante che finirebbe col rendere la mia tesi un’appendice di poco interesse.

È doveroso ringraziare Marco, Sonia, Giacomo, Tecla, Valentina, Alessandro, Giovanni e, dulcis in fundo, Giuseppe; ciascuno impegnato nella sua vita quotidiana, ma sempre con una buona parola o solo un pensiero nei miei confronti. Questa è l’amicizia come la intendo io: non importa quanto frequentemente ci si incontra, ma quanto ogni volta sembri la prima. Grazie di cuore a tutti voi.

condiviso in questi anni migliaia di ore di sala prove e altrettanti momenti della mia vita. Grazie per aver sopportato il mio “essere ingegnere” anche in questo campo dove il lasciarsi andare è prerogativa per una buona performance.

Ringrazio davvero di cuore il “Prof”, Marco V. Boniardi e l’Ingegner Andrea Casaroli. Grazie davvero per tutto ciò che mi avete insegnato, e non solo tecnicamente parlando: l’approccio al lavoro dell’ingegnere, lo sguardo che deve avere sul modo esterno, la curiosità e l’entusiasmo che questo “mestiere” richiede sono insegnamenti che mi porterò dentro in futuro. Grazie per la gratuità e la generosità con cui mi avete donato il vostro tempo e le vostre perle; la simbiosi creatasi nella vostra decennale collaborazione mi ha insegnato quanto la diversità e la voglia di far bene possano portare a risultati eccezionali.

Ringrazio la sezione di Balistica del RIS di Roma, nelle figure del Maggiore Sergio Abate, il Tenente Colonello Paolo Frattini e il Tenente Ester Sita; con grande accoglienza e professionalità mi avete donato il vostro tempo durante i test Romani. Spero, con questa tesi, di essere stato all’altezza dell’opportunità offertami di collaborare con una sezione così importante e rinomata dell’arma dei Carabinieri.

Ringrazio Riccardo Andreotti che, altrettanto gratuitamente, si è occupato della sezione di simulazione agli elementi finiti. Mettendo a disposizione la sua grande esperienza e professionalità ha indubbiamente contribuito a migliorare questo lavoro di tesi.

Ringrazio anche Maurizio Pardi del Dipartimento di Meccanica del Politecnico di Milano; la sua abilità ed esperienza come tecnico di laboratorio mi hanno permesso di ottenere risultati importanti per lo sviluppo di questa tesi; la sua passione per il tiro sportivo di conoscere di più riguardo a questo mondo così articolato e ricco di spunti curiosi ed interessanti.

1. Aim of the Work ………. 2. Theoretical Background on Terminal Ballistic ……… 2.1. BALLISITIC’S BRANCHES ……….. 2.1.1. Internal Ballistics ……….. 2.1.2. External Ballistics……….. 2.1.3. Terminal Ballistics ………..………. 2.2. TARGET – MATERIAL INTERACTION ……… 2.2.1. Impact Velocity ……….. 2.2.2. Material’s Deformation Modality ………. 2.2.3. Loading Geometry………. 2.3. PENETRATION AND INTERACTION MODALITIES ……….. 2.3.1. Hole Enlargement ……….……… 2.3.2. Dishing ……… 2.3.3. Petaling ……….. 2.3.4. Plugging ………. 2.3.5. Spall Failure ………. 2.3.6. Splashing ……… 2.4. ENERGETIC MODEL FOR Vbl …..………. 3. Tests ... 3.1. EXPERIMENTAL PLAN ……… 3.2. MATERIAL SELECTION ……….. 3.2.1. Creusabro …….………. 3.2.2. Durostat ………….……… 3.2.3. Alform ……….……… 3.2.4. AISI 304 L ………. 3.2.5. Aluminium Alloy 6111 ….……… 3.2.6. Material Comparison …….……….……… 3.3. WEAPON AND AMMUNITION SELECTION ……… 3.3.1. Weapon and Ammunition Operating Principle ….……… 3.3.2. Beretta Storm D Px4 Techincal Info ………

7 8 9 9 9 10 10 10 11 14 16 16 16 17 18 18 19 20 25 25 25 27 28 29 30 31 32 33 33 40

3.5. R.I.S. BALIPEDIUM ………. 3.5.1. Shooting Area Parameters ……….……….. 3.6. INSTRUMENTS ……….……… 3.6.1. Shooting Machine ……….……… 3.6.2. Speed Measurement ………... 3.6.3. Plate Holder ……….………… 4. Results ……….……….. 4.1. BALIPEDIUM REPORT ………. 4.1.1. Ricochet of The Projectile ………. 4.2. VISUAL ANALYSIS ……….. 4.2.1. Hard Steels Case ……….……….…. 4.2.2. Inox Case ……….…….. 4.2.3. Aluminium Alloy Case ……… 4.2.4. Energetic Model Considerations ……….. 4.3. LABORATORY TESTS ……… 4.3.1. Back Plate Deformation ………. 4.3.2. Micrographic Analysis ……… 4.3.3. Micro Hardness Test ……… 4.3.4. SEM Microscopy ……… 4.4. FEM Analysis ………..…………. 4.4.1. Problem Modelling ……….. 4.4.2. Improvement Steps ……….. 4.4.3. Results Validation ………. 5. Conclusions ………... References ………..……… ANNEX A - Photographic Characterization of the Impacted Plates ………... 43 44 45 45 45 46 47 47 49 50 50 52 53 57 57 58 60 65 72 81 81 82 87 90 93

In this thesis work the interaction between a projectile shot from a firearm and a target metallic material will be studied. More in detail, the deformation phenomena in the target, due to the kinetic energy transfer from the shot projectile, will be characterized depending on several parameters. Different impact angle of the shot, different microstructures of the chosen material and the deriving hardness values will be considered to evaluate and describe the target’s behaviour under different stress conditions given by the high-speed impact of the projectile itself.

Making use of visual analysis and measurement, microscopy and micro-mechanical tests on the deformed material near the impact point, several data will be collected in a forensic ballistic prospective; the characterization of the impact point and the search for linked objective parameter will be carried out with the aim to recreate the fact in an investigation field, where only the evidences are available, making use of the metallurgical knowledge of the involved phenomena.

Background on Terminal Ballistic

Before describing in details the experimentation about target-material interaction, it’s mandatory to have a look at the macro field of the ballistic and, in particular, to the terminal ballistic branch. This first look to such a complicated research field could help the reader to not lose the path studded of empirical, theoretical and simulated equations; several essay and report has been published along the years, several of this used and reported as reference of this thesis work. Interested readers could find all the info in the dedicated section.

2.1 - BALLISTICS’ BRANCHES

First, we need to define what ballistic is. Briefly, ballistic is the physics’ branch dealing with all the phenomena involved in the motion and the dynamic of a projectile all along the path inside and outside a weapon. It’s possible to distinguish three principal and macroscopic sectors in which ballistic is divided, corresponding to distinct phases of the bullet’s motion during the shooting action.

2.1.1 - Internal Ballistics

Starting from the first phase of the motion inside the weapon, the Internal

Ballistic studies the causes and the modalities of the bullet’s acceleration. The

calibration of the detonation energy, achieved with the choice of the desired powder quantity and quality, is of primary importance to achieve the correct muzzle velocity of the bullet. The chemical reaction of the powder inside the cartridge is the primary source of kinetic energy of the projectile. The detonation, which generates the pressure profile along time, must be carefully chosen depending on the kind of internal structure the weapon has (i.e. maximum pressure the material can withstands, internal geometry of the gun barrel). The firearm and cartridge internal structure will be analysed in paragraph 3.3.1.

2.1.2 - External Ballistics

After the projectile has been accelerated from the beginning of the barrel to the muzzle, free from the cartridge, all the interaction among the fluid in which is immerged and the projectile itself is matter of study for the External Ballistic. Therefore, is clear the strong link between External Ballistic and the fluids dynamic and, in particular, the aerodynamic field. The nose and the body shape of the bullet become of crucial importance since high relative velocity are involved. If on one hand the aerodynamic efficiency is important not to lose too much kinetic energy during the flight time, especially in the long shots, on the other hand a good precision should be kept. For this reason, bullets, in most cases, are gyroscopically stabilized introducing rotation to their motion by means of striations engraved on the inner side of the barrel. This smart feature allows

the projectile to dynamically stabilize itself after the gasses, which are ejected from the muzzle, have induced non-symmetric forces on the bottom of it.

2.1.3 - Terminal Ballistics

In the last stage of the flight, the projectile probably interacts with the target;

Terminal Ballistic is the ballistic branch which deals with the interaction among

these two entities. Since the characterization of this interaction is the final aim of the thesis work, it’s needed to go more deeply inside this matter.

Terminal Ballistic is the most complex sector of the ballistic field since involves lots of parameters which are very difficult to control and evaluate all in one. Different approach has been tried along the years and, after the experimentation era, the computers computational power began to prevail; FEM simulation became the most studied way to evaluate different impact cases in a faster and more economical way. Only simple cases have been characterized in a mathematical way, which have become somehow didactical demonstrations introducing basic concepts linked to this matter

2.2 - TARGET – MATERIAL INTERACTION

The focus in this introduction needs to be kept on the possible interaction among the bullet and a target metallic plate; here the main parameters that determine penetration modality will be listed and analysed.

2.2.1 - Impact Velocity

The first analysed parameter is the Impact Velocity. This is one of the parameters which mostly affects the penetration modality since, for different range of speed, the nature of the impact and penetration mechanics dramatically changes. In literature, it’s possible to find four different speed range, which should be taken as indicative value to better understand and foresee the interaction modality. Under 300 m/s, the projectile is shot in the sub-ordnance range. Starting from 300 up to 2000 m/s it’s possible to define the so-called ordnance velocity range; from 2000 to 5000 m/s the projectile it’s shot in the hypervelocity range and from 5000 to 8000 m/s the last speed range is defined.

In the ordinance speed range, the penetration mechanics follows the well-known laws of the solid bodies, based on parameters like the strength of the material, its hardness and all the mechanical proprieties. In this thesis work the ordnance range is the only evaluated projectile speed range; fracture mechanics, brittle and ductile materials and solid bodies impact are already meaningful terms that will be evaluated in the experimentation chapter.

When a projectile it’s shot at the hypervelocity range, it usually has the shape of a long rod also called penetrator; in this case, the penetrator literally erodes the target meanwhile the target does the same with the projectile itself. In this way, the longer the rod, the deeper the potential penetration in the target; the radical change in the projectile shape is justified by this penetration phenomenon. When the velocity of the shot object exceeds the upper limit of the Hypervelocity range, the laws determining the penetration in the target are the ones from the fluids dynamics. The most important parameter is the correlation among the target and the projectile densities and the traditional mechanics laws must be set aside.

Now on, the argumentation will only be developed referring to the ordinance velocity range in which, as said previously, the penetration phenomena could be described by the classical mechanic’s laws.

Few words on the ballistics velocity limit is needed in this bullet’s speed chapter before going on with the treatise. With the term Ballistic Velocity Limit the minimum projectile’s speed useful to completely penetrate the target is indicated. To be noticed, the value is only to be referred to a specific target-bullet couple and to specific shooting condition. Now, one can argue about what terms like “complete penetration” or “perforation” mean; in the ballistic protection field, different point of view on the debate are reported, depending on the institution which report the analysis. For example, for the U.S. Army the complete perforation occurs when the nose of the projectile exits the back surface of the

target, while for the U.S. Navy light must be seen through the hole opened by the shot. It’s important to underline that a deterministic value of the Ballistic Velocity Limit could not be found experimentally; statistical methods have to be used even with a fixed projectile-target couple. As a matter of fact, the Ballistic Velocity Limit is also known as V50, since is defined as the speed that has 50% of probability to perforate the target. The same reasoning could be done for the angle at which a determined shot achieves the complete perforation; with a similar procedure of the V50, θ50 could be determined. This value has a key role in the ballistic protection field since could be used to design, for example, tank’s armours which have different performances depending on the inclination of the protection panels. This need of a statistical approach underlines the complexity of the penetration phenomenon and its dependence from a vast number of factors barely controllable all in one.

2.2.2 - Material’s Deformation Modality

The second factor influencing the penetration modalities is the material’s

deformation modality. It seems to be trivial, but every material has the inclination

to react to the load of the projectile’s impact as its microstructure, its chemical components, its manufacturing history imposes. As a matter of fact, load geometry and time characteristic of the impact must be kept in consideration too, and, under certain condition, could lead to a significantly different material’s behaviour with respect to the one deriving from the nominal tensile tests. This consideration will be further analysed in the followings.

Brittle Materials

A brittle material is a material that has a very little percentage of plastic deformation before fracture, even if it can reach high UTS values. Microscopically, this macroscopic behaviour could be translated in a short dislocation’s mean path. In other words, the imperfection of the lattice, which allow the material to absorb the deformation energy through their movement, are blocked by some features (i.e. small grain size, presence in the lattice of chemical element of different size with respect to the fundamental ones, development of precipitates) giving to the material a great resistance to plastic deformation, to the detriment of the capability of absorbing energy without collapsing. The most evident macroscopic behaviour of a brittle material is the fragmentation failure modality with very low plastic deformation; the failed piece could be ideally recomposed by the fragments which do not lose their original shape. It’s possible to recognise this failure modality also looking at the fracture surface: no plastic deformation could be notice; flat and shiny surfaces could be seen both in trans and intergranular failure modality. Glass, ceramics and casted iron are some example of material following this failure criterion.

Ductile materials

A ductile material is a material that could undergoes very high plastic deformation values before reaching the failure conditions. After a linear stress-strain field, necking phenomenon takes place and the material, even if the stress value is kept constant, is still deforming, increasing the percentage deformation value. Having a closer look to the microscopic behaviour, it’s possible to notice that the dislocation could move on longer path with respect to the brittle case, giving the macroscopic characteristic of good formability before fracture. The fracture surface highlights the presence of very characteristic features known as microvoids, which are points where the dislocations come together generating little eggs-shaped hollows. The coalescence of several micro-voids generates the macroscopic fracture. It’s possible to recognise a ductile failed piece looking at its noticeable deformation and the absence of fragments (i.e. some aluminium alloys or Inox steels). To be notice, the necking phenomenon leads ductile materials to the strain hardening effect: after imposing a plastic deformation, the stress-strain curve of a specimen change since residual deformation has moved dislocation to the point that they stop each other. Therefore, a significant increase in strength of the material is achieved.

Adiabatic Shear Failure

In terminal ballistics, the adiabatic shear failure mode has been deeply investigated since is a potential source of unexpected failure that, from an armour design point of view, becomes dramatically important for safety and protection, especially in brittle materials applications. This failure mode takes place only under dynamic loading conditions; as a matter of fact, people who worked in

ballistics research field discover this phenomenon comparing the strain to failure of some titanium and aluminium alloys, resulting from dynamic impact tests, with their static test counterpart. For example, as reported in Rosenberg and Dekel (2010), the Ti6Al4V alloy fail in a static condition after a percent strain of 30%, while in a ballistic dynamic and impulsive test the same value is set around 20% with a strain rates of 103 _{Hz. The explanation for this phenomenon is a} thermo-mechanical coupling effect in the zone of maximum shear loading (also called Adiabatic Shear Bands, or ASB) that globally reduce the strain to failure of the material. The sites of maximum shear in the specimen undergoes a softening process due the local and fast rise of the temperature which do not allow the material to dissipate heat resulting in faster nucleation of voids and, in some cases, in a change of phase and microstructure in the ASB.

Strain Rate Effect

As introduced in the previews, the time profile of the load application on a metallic material could deeply influence its behaviour. Since the ballistic usually deals with speeds that are far from the one used in the technological process a metal undergoes, strain rate dependency of the mechanical characteristics could not be neglected.

Strain rate effect is a hardening effect that depends on the speed of the load application. Microscopically, the information of the impact travels in the material as a pressure waves at the speed of sound in that specific material; that pressure waves make the dislocation moves and compacts in the metallic grains, generating a defect concentration that leads the material to fail when the damage part becomes of a certain size. When the load increases the velocity, the information about the impact phenomenon travels in the material at a speed that could exceed the dislocations motion’s maximum speed; the dislocations’ motion, being not able to follow such a high-speed deformation, results in improved material’s overall mechanical characteristics as an increasing of the Yield Stress and UTS values.

Figure 2.3 –On the left, a cross section of a Ti6Al4V plate impacted by a blunt projectile deformed by

means of ASB modality [Rosenberg and Dekel (2010)]. On the right, microvoid coalescence from a ductile failed surface.

As the figure 2.4 shows, the stress-strain curves clearly represent the aforementioned dependence on the strain rate; the material tends to extend its linear zone to the detriment of the plastic one, resulting in high performance but more brittle overall behaviour.

It’s clear that the a more plastic material has a higher improvement margin with respect to a more brittle one that is already near to its maximum performance’s limit; this fact deserves to be investigated in the ballistic field, since the differential improvement margin of the two initially different material needs to be clarify before one could state what is the best performing one under dynamic conditions.

2.2.3 - Loading Geometry

The last factor analysed is comprehensive of all the geometric parameters which generate the specific loading condition; i.e. Plate thickness, projectile diameter, nose shape and impact angle are the quantities which determine a specific failure mechanism in the target.

Target Thickness

The failure mechanism induced by a projectile strongly depend on target’s thickness, since the pressure waves coming from the impact travel inside the material and could be reflected from the back surface if the thickness is small enough; this reflection phenomenon generates an interaction among those waves which could generate particular failure modality, especially in brittle materials. In literature, the tests with material proprieties characterization aim has been done shooting on semi-infinite target to exclude the back-reflection

phenomenon and to evaluate the penetration modality in a clearer way. Furthermore, the stretching and banding capability of a thin plate (with respect to a semi-infinite target), allow the material to absorb a higher energy quantity so that a lower fraction of it is used to perforate the material.

Projectile Nose Shape and Diameter

Since the failure modality depend on both the target and projectile’s geometry, the bullets must be carefully evaluated to predict correctly the kind of induced failure in the target.

Firstly, the nose shape. This important parameter of the projectile is clearly a factor that determines the loading geometry in the impact area. The term nose shape means all the design parameters of the frontal part of the bullet: blunt, round or sharp nose shape could be roughly recognised as the main categories of nose shapes. As the theory suggests, fixing the bullet speed and mass, sharper nose shape induces a more intense stress concentration factor in the material, resulting in a different failure modality with respect to a blunter one that induces a flatter and more uniform distribution. This is true only if the deformation of the projectile during the impact could be neglected (i.e. a steel-cored projectile on a very soft or thin metallic target); in the presented experimentation and in the vast majority of the real application cases, the nose shape as a really small and negligible influence on the penetration capability of a bullet. Actually, the deformation of the projectile in the interaction phases makes the projectile change completely it’s shape, losing the deigned nose parameters and all the deriving benefits.

Starting from this consideration, is better to evaluate the penetration capability depending mainly from the inertial characteristics of the bullet: the density and so, through the diameter and the length, the mass.

As a matter of fact, the geometrical parameter which has demonstrate to have the biggest importance is the diameter. Not only the speed of the impact plays an important role in the phenomenon; its interaction with the diameter and its mass result in a value called “Sectional Energetic Density” (defined as the ratio of the kinetic energy over the contact surface among the projectile and the target) which, under terminal ballistics point of view, is the most representative factor to be controlled. With a high sectional density, the projectile will penetrate easily the material since is more capable to reach higher stress values on the contact surface. All these matters will be more deeply analysed in the next section on penetration modalities (2.3) and in the projectile basics and operating principle’s chapter (3.3.1).

Impact Angle

A viable way to variate the SED maintaining the same projectile geometrical characteristics could be changing the impact angle on the target. Same aforementioned reasoning applies in this case: a perpendicular-shot projectile will increase is SED resulting in a higher penetration capability; an angulated shot,

instead, will lower the SED value that will generate a less concentrated stress distribution, losing in penetration capability. The energetic point of view would keep in evidence discussing this parameter’s variation, since could manage all the matters regarding the ricochet and the deformation of the projectile itself. Therefore, a more inclined shot will produce a less accentuated deformation of the impacting projectile, while a normal impact will induce the maximum achievable deformation that, consequently, variates the SED parameters also during the interaction phenomenon. On the other hand, an inclined shot left the projectile a higher amount of residual energy (the residual velocity after the ricochet is the most evident proof of this evidence) to the detriment of the one transferred to the target.

The experimentation presented in the followings focus its efforts in the evaluation of this energy’s dynamics changing linked to the impact angle variation.

2.3 - PENETRATION AND INTERACTION MODALITIES

After a brief introduction about the main parameters playing a role in the terminal ballistic field, here is presented a characterization of the main failure modalities of a plate hit by a projectile. The choice not to deal with semi-infinite target penetration is determined by the vastness of the topic and by the aim of this experimentation; the interested reader could find in the references section several books dealing with this topic. Here the characterization is kept as clear as possible presenting the possible cases one by one in separate chapters; this situation could be found only in very simple cases with certain determined conditions. In the clear majority of the cases, the impact area on the deformed and perforated plate could be linked to different superimposed cases all in one.

2.3.1 - Hole Enlargement

The first analysed penetration modality is the “Hole Enlargement Process”; this is considered as the simplest one since does not involve a real failure mechanism in the plate. The projectile, usually a sharped nose one, thanks to its nose geometry, simply push away the material generating a hole. This capability of material flowing is characteristic of ductile materials, which have a low flow stress value easily achievable with the energy level involved. The plate undergoing this first process is not bent or stretched in a significant way thanks to the high penetration capability of the projectile; the impact area is easily recognisable since a front and a back “lips” occurs (where with “front” is indicated the entrance surface and with “back” the exit one).

2.3.2 - Dishing

A very similar penetration mode is represented by the “Dishing” phenomenon; here the target’s material is “pushed away” too, generating a hole which has lips only in the exit face of the plate, differently from the previous case. Some

simulating and experimental works from Rosenberg and Dekel (2010) have shown that, evaluating the H/D ratio, known as “Normalized Thickness” (where H is the thickness of the plate and D is the projectile’s diameter), a threshold value of 0.3 has been founded for the Hole Enlargement to Dishing transition. With lower H/D values the phenomenon tends to pure dishing (or, in other worlds, with a thinner plate keeping the projectile calibre constant); otherwise, with H/D values higher than the threshold one, penetration modality tends to pure hole enlargement. One of the causes of the abovementioned transition is the improved capability of a thin plate to bend and stretch itself under the bullet load (with respect to the previous case), so that part of the impact energy is spent from the projectile to deform and bend the target plate.

2.3.3 - Petaling

The third penetration modality which can occur dealing with a ductile material is called “Petaling”. If the first phases this phenomenon is really like the ones analysed previously. The bullet nose (especially if it’s sharp) starts to make the material flowing, generating the back-surface lip pushing and bending the material. If the hoop stress value overcomes the material stress limit, some crack will separate the bent material from both the front and the back surface, generating the so called “Petals”; their bending can overcome 90° angle around the plastic Hinge. A variable thinning of the petals is always present, increased going from the root to the top of the petals: this is the evidence of a remarkable

plastic deformation that forerun the initialisation of the crack that propagates from the top of the backside dome of the plate to the peripheral zones.

2.3.4 - Plugging

Looking at the penetration modality of a projectile in a brittle material (naturally or induced by the load conditions), plugging phenomenon should be analysed. Due to the nature of the material, the parameter to be carefully evaluated now is the maximum shear stress the plate can withstand; the zone in which the maximum shear value is reached will be probably the ones that fail first. For example, if a blunt projectile hit a brittle material plate, it will probably separate a little cylinder (or a little disc) without deforming too much the impact zone. In the plugging model, the projectile hitting the plate generates a pressure wave which propagates in the plate thickness at the speed of sound in that specific material. This pressure distribution induces a stress differential distribution that pushes the material around the penetration area to its shear limit, generating cracks in a longitudinal direction with respect to the bullet path. The speed at which the phenomenon occurs does not allows the material to absorb the impact energy, resulting in a very narrow shear deformed zone; this characteristic increase the maximum shear value since the deformed area width is relatively small. Once the pressure wave reaches the back side of the plate, the plug is free to be pushed away from the projectile. The plugging phenomenon does not take place immediately since is foreruns by an initial hole enlargement phase; it starts only after the maximum shear load is reached, giving birth to a fracture surface with different characteristic coming from the combined penetration modality. To be noticed, in materials which have shown high propensity for adiabatic shearing (i.e. titanium alloys, carbon steels) the plug is formed in the very early stage of the perforation process, even at low impact velocity. In those materials, the Hardness value could play a detrimental role in the material’s penetration resistance; if a plane stress condition occurs (i.e. with very low H/D ratios), the hardness actually decreases the material’s resistance to the penetration since the onset of adiabatic shear band induced plugging, as reported in Dikshit et al. (1993).

2.3.5 - Spall Failure

With “Spall Failure”, all the phenomena which give birth to a crater on the back surface of a plate without the complete perforation of it are indicated. Since the bullet does not physically enter in contact with this part of the plate, the reason of the failure must be found in the pressure waves generated by the impact and propagating in the material. In case of materials which have different traction and compression maximum load, the reflection of the waves by the back-surface separates fragments of the target, since it induces a traction-compression load distribution. Since fragmentation occurs, it easy to predict that this kind of failure mechanism would occur dealing with brittle material. Short impact time result in high intensity pressure waves. Even if in the compression phase the material has a higher maximum acceptable load, microcracks could take place, so that, when

the waves are reflected and generates a traction load case, the resulting crater appears bigger than the one predictable by the theory of back reflection.

2.3.6 - Splashing

Even if is not a perforation process, splash phenomenon could be briefly analysed since is a possible projectile-target interaction modality. This phenomenon take place when a relatively “soft” projectile is shot on a high strength material; in this interaction modality, the bullet behaves as liquid body just splashing on the surface of the target, completely losing its original shape and projecting some fragment in the shot’s opposite direction. If the pressure distribution generated by the impact overcomes the maximum stress value, a crater could be generated in the front or in the back surface of the plate (like in the spall failure case); this phenomenon has not to be confounded with the crater generation after a hypervelocity impact, which will be not matter of this thesis work.

2.4 - ENERGETIC MODEL FOR V

At the end of this chapter, where the factors which affects the interaction modalities of a projectile on a target thin plate has been exposed and analysed one by one, a simple but useful predictive model on the Vbl accounting of those dependences is presented. The model includes considerations from several researchers who worked on that in the middle of the XX century and has been confirmed by recent numerically-based analysis. The model, given some basic mechanical and geometrical parameters from the material and the projectile, it’s capable to determinate the minimum impact speed at which the material will be penetrated, leaving a null speed to the exiting bullet.

As reported in Rosemberg and Dekel (2016), the model of Recht and Ipson (1963) could be used to estimate in significant way the Vbl value for ductile material’s thin plates penetrated by sharp nose rigid projectile and, with a small correction, also for the plates hit by round nose ones. The model is described by the relation: 1 2𝑀𝑝𝑉0 2 ₌ 1 2𝑀𝑝𝑉𝑟 2_{+ 𝑊} 𝑝

In this first attempt model the only differential values among the entrance and the exiting projectile’s kinetic energy is Wp, that is work spent for the perforation by means of a dishing process.

Simplifying the model introducing the definition of Vbl, that is, as mentioned above, the speed at which the projectile perforates the material and results in a null exiting speed, one can write:

1 2𝑀𝑝𝑉𝑏𝑙

2 _{= 𝑊} 𝑝

Before going on, the Penetration Energy Wp value must be analysed and determined. Bethe (1941) and Taylor (1948) propose a model that is:

𝑊_𝑝 = 𝜋𝑟2𝐻 ∙ 𝑐𝑌_𝑡

where r2 _{is the radius of the projectile (and so, of the hole), H the thickness of} the plate and Yt is the plastic flow stress of the material. The term cYt represent the value of the effective resisting stress σr, which is the principal source of discussion among the researcher. In order to maintain a simple writing for this model, c values as to account all the phenomenon like the back-plate influence and the work hardening effect that ductile materials could undergoes. Rosenberg and Dekel (2010) presented a numerical-based approach to derive the effective stress value using several simulations and fitting the outcoming data. Different H/D ratios was analysed and a general trend could be described, accordingly to the results of Bethe and Taylor. For different ductile materials, it’s possible to

distinguish three different σr/Yt behaviour, depending from different H/D thresholds: 𝑓𝑜𝑟 𝐻 𝐷 ≤ 1 3→ 𝜎_𝑟 𝑌𝑡 = 2 3+ 4 𝐻 𝐷 𝑓𝑜𝑟 1 3≤ 𝐻 𝐷 ≤ 1 → 𝜎_𝑟 𝑌_𝑡 = 2 𝑓𝑜𝑟 𝐻 𝐷 ≥ 1 → 𝜎_𝑟 𝑌_𝑡 = 2 + 0.8 𝑙𝑛 𝐻 𝐷

The behaviour of the curve (figure 2.6) shows that for H/D values lower than 1/3, a linear trend could be noticed. Then, a plateau around σr/Yt = 2 is present; in this case, the resulting planar state of stress could explain the constant value up to H/D = 1 and agreement with the Bethe’s model could be found. Finally, for H/D > 1 the curve asymptotically approaches σr/Yt = (4-5), which is the cavity expansion stress value coming from the most demanding 3d state of stress. Note that the σr/Yt ratios are constant values once the H/D ratio is determined; this means that the σr values is constant and is not changing along the perforation phenomenon. This could be considered a too heavy assumption thinking at the complexity of the time-varying phenomena occurring during the perforation process. As a matter of fact, this value comes from the idea to replace the actual time-varying stress by a constant and effective one, which results in the same energy loss for the projectile. In this way, integrating the equation, the same amount of energy will be spent in the penetration process.

Once the σr/Yt ratio has been defined, one can finally write:

𝑉𝑏𝑙 = √

2𝜋𝑟2_𝐻𝜎 𝑟 𝑀𝑝

This simple equation has a good accuracy that Rosember and Dekel (2010) sets around ±2,5% from several analysed experimental data sets; keeping a clean writing, a reasonable agreement between model and data could be achieved.

A critical analysis of the of the hypothesis on the application of this simple model is needed, in order to evaluate its applicability on real cases which implies some of the neglected effects.

First, the deviation from the perfect elasto-plastic behaviour. Rosember and Dekel (2010) performed a simulation campaign taking as a target material an AISI 304 stainless steel. This material is characterized by a plastic behaviour affected by a strong work hardening effect, which continuously vary its plastic flow stress along the deformation phenomena. Surprisingly, the campaign results in a σr = σr (H/D) trend which reports the same features of the Aluminium Alloy previously analysed. Since Yt is not as well defined as in the perfect elasto-plastic behaviour, σr is not normalized in the graphs. It’ worth to notice that the threshold values of the H/D ratio are slightly changed because of the hardening effect itself. So, a tuning of the coefficients of the first model it’s enough to achieve satisfactory results also in materials which behave in that way.

A second hypothesis that has to be justified is the neglecting of all the form of plate deformation’s energy involved. For very low thickness plate, the deformation of the area around the hole play an important role in the total energy expense. Gupta et al. (2001) propose a modify relation based on the RI model which accounts also the energy needed to bend and stretch the material around the impact area, resulting in an accurate numerically-based model which fits very well the experimental data. To be noticed that this energetic discrepancy is dampened with the increasing H/D ratio and for increasing speed value. Gupta designs the experimental plan in the sub-ordinance range (up to 100 m/s) and dealing with Aluminium sheets of 0.5, 0.74, 1.0, 1.5 and 2.0 mm thicknesses; in this experimental area, the significance of the extra energetic components plays an important role. With the increasing of the thickness and with the increasing of

Figure 2.7 – On the left σr/Yt curve for perfect elastic-plastic materials, on the right σr/Yt curve for

the impact velocity, the influence of this neglected energetic parts results of minor importance and the RI model become again significant.

RI model considers the projectile as a completely rigid body which do not undergoes deformation during the impact; this hypothesis could be seen as a too restrictive one to give significant results. As a matter of fact, the deformation of the projectile during the perforation of ductile aluminium plates results negligible for certain H/D range near the one studied in this experimental work, while is not anymore negligible in the penetration of materials as the inox steel; in that case an indicative value, even if satisfying, could only be achieved with the chosen projectile-target coupling.

Last concern about the off-hypothesis usage of the RI model deals with the nose shape. The experimental campaign which confirms the RI results was carried out by means of conical nosed projectile. As evaluated in the previews, the nose shape, under certain conditions like the rigid body hypothesis just mentioned, has an influence on the penetration modalities, and so possible changings has to be discussed. Borovik et al. (2002) carried out an experimental campaign to analyse this phenomenon; the results show that for not too thin plate, the experimental campaign confirms the RI model trend for what concern the residual speed of the projectile. The remarkable difference consists in the asymptotic behaviour of the Vr; the spherical nosed projectile approaches the Vr = V0 values always with a difference that increases for increasing thickness of the target plate. The motivation of this constant gap among the results of the RI models comes from the generation of a small plug that, with an increasing thickness, increases its mass and so, the energetic absorption to the kinetic residual energy. A correction of the Ri model accounting the plug formation has been proposed, and the energetic balance firstly proposed becomes:

1 2𝑀𝑝𝑉0 2 ₌ 1 2𝑀𝑝𝑉𝑟 2₊1 2𝑚𝑝𝑙𝑉𝑟 2_{+ 𝑊} 𝑝

Where mpl is the mass of the ejected plug of material generated by the round nose shape of the projectile. Dealing with Vbl, the influence of the plug presence does not affect the RI model validity (except for the possible changings due to the less energetic-demanding brittle fracture with respect to the supposed ductile one), while in the Vr / Vbl evaluations, a multiplicative factor has to be added at the basic model, that becomes:

𝑉_𝑟 𝑉_𝑏𝑙 = √ 1 1 +𝑚_𝑀 ∙ √( 𝑉₀ 𝑉_𝑏𝑙) 2 − 1

As it clear from the model, the influence of the plug decreases with the decreasing of the m/M ratio; the ratio among the densities of the projectile and target material and the H/D ratio has to be carefully evaluated to determine the effective influence of the plug inertia on the overall energetic balance.

Evaluating the physical phenomenon, we can classify the round nosed projectile has an intermediate step between the sharp nosed and the flat nosed one. If the first, due to a higher capability to penetrate in the target material caused by the stress distribution that could generates, interacts with a prevalent hole enlargement process, the blunt one tends to generate some crack in the stress concentration areas which, propagating until the back surface, separates a plug of material which is ejected during the penetration phenomenon. All the intermediate-shaped projectiles mix the two abovementioned behaviours, resulting in a combined penetration modalities that, with some coefficients tuning, it’s possible to describe with the presented model.

In literature, several researchers developed the RI model performing analytical evaluation (followed by numerical and experimental validation) of the energetic problem, both for perpendicular impact as in Yarin et al. (1994) and oblique impact as reported in Warren and Poormon (2000) and Roisman et al. (1996). Attempts in accounting different deformation modality than the dishing has been made along the years; petalling failure process was accounted as reported in Qiaoguo and Heming (2014). Those are only some example of the efforts that the researcher made for the validation of a new and improved model for the penetration mechanics of projectile in target materials accounting for all the impacts’ parameters changings that the real problem requires.

In this thesis work, the simplicity of the RI model will be compensated with the right choose of the parameters form bullet and material. A more accurate evaluation could be taken in account for further studies.

In the followings, the RI model will be adopted to evaluate the Vbl for some of the experimented materials which match the hypothesis’s requests. The penetration event will be foresight starting from geometrical and mechanical data that will be collect in the next chapter; by means of the experimental work the results will be verified.

In this chapter, the experimental plan, the used materials, firearm and measurement instruments are presented. When the firearm choice will be treated, a brief background on the technical details of the weapon and bullet working principles will be presented. As usual, the treatise will be focused on the final characterization aim of the thesis work; the weapon and bullets theory will be analysed for what concern the ones used in this experimental campaign. In the references chapter treatise about firearms technique and history are reported; the interested reader could find there all the details.

3.1 - EXPERIMENTAL PLAN

As said in the chapter 1, the aim of this thesis work is to characterize the behaviour of different material hit by the same projectile shot from different angles. Five materials have been chosen to cover a wide range of different structures and mechanical characteristics. In a decreasing hardness order, they have been labelled basing on their commercial name as follow: CRE, DUR, ALF, INOX and ALU; their complete characterization will be matter of the next paragraph where they will be deeply investigated. Four shooting angles have been selected: 90°,85°,60°,45°, indicated as the angle among the direction of the projectile trajectory and the plane laying on the target’ front surface. Two replicates have been performed for each angle-material combination.

Resuming the experimental plan: • 5 materials

• 4 angles • 2 replicates

results in a 40 shots experimental campaign.

3.2 – MATERIAL SELECTION

In this chapter, the five chosen materials will be presented; their mechanical features will be pointed out through mechanical and chemical tests and the microstructures will be analysed using microscopy. This characterization work of the original and undeformed material will be of crucial importance when compared with the corresponding features of the same materials after the impact in the deformed zone; it will be an indicator of the impact energy and of the projectile effect on the target. Materials are presented here in a decreasing hardness order using their commercial names. This mechanical parameter will be one of the most important when dealing with impact in the ordnance speed range; on purpose, in this way, this importance is put in evidence.

For what concern the mechanical tests, a tensile test has been performed for all the five materials involved in this experimental work; following the UNI EN ISO

6892-1-2009 at ambient temperature, the samples have been designed with a proportional logic, taking into account the thickness of the plate from which they have been cut (4 mm for all the materials with the only exception of the Aluminium Alloy, whose thickness was 3 mm). Two replicates for each material have been cut using waterjet technology and prepared for the test. All the data coming from tensile test have been evaluated according to the abovementioned standard and reported under each material section.

Chemical analysis has been performed to point out the composition of the base material of the plates by means of a quantometric analysis; if one hand those data could help to define more precisely the nature of the materials, it could also be useful to detect if some residual of non-base material is deposited near the impact zone during the final SEM analysis.

Figure 3.1 – CAD designed sample for 4mm thickness plates according to UNI EN ISO 6892-1-2009

[quotes in mm]

3.2.1 – Creusabro

The first analysed material, commercially known as “Creusabro”, is the hardest material tested. With a declared Vickers Hardness of about 480, it has been specifically thought for anti-wear applications.

For what concern the mechanical proprieties, Creusabro has shown very high mechanical proprieties, reaching an ultimate tensile strength of 1720 MPa. The low value for the elongation at breakage of (A = 11%) shows the inclination of the material to behave in a brittle way under loading conditions.

The chemical analysis does not underline any remarkable alloying element. The presence of small quantity of Cr and Mo, through the formation of carbides, gives the material the declared extra hardness; this could be classified as structural steel for general usage.

The high strength characteristics are due mainly to the heat treatment history this steel has undergone; the material has been quenched and subsequently tempered in order to achieve a mixed martensitic-bainitic structure, as the micrographic analysis has underlined. Very fine and regular grain gives Creusabro a very good ability to avoid plastic flow.

C Si Mn P S Cr Ni Mo Cu Fe

0,205 0,743 1,18 0,0093 0,0022 0,697 0,490 0,26 0,21 96,073

Table 3.2 – Creusabro’s mechanical proprieties

Table 3.1 – Creusabro’s Chemical Elements’ content

Figure 3.3 – Creusabro’s stress – strain curve

Materiale CRE E [Mpa] 206000 Rp0,2 [MPa] 1191 Rm [Mpa] 1720 A [%] 11 Z [%] 38

3.2.2 – Durostat

The Durostat Steel has chemical and microstructural characteristics really similar to the abovementioned Creusabro, since it has a slightly lower hardness value and reduced carbon content. It could be classified in the structural Steel for generic use category.

The micrographic analysis reveals that its structure is a mixed bainitc-martensitic structure that explains the high hardness value of around 450 Vickers. The main application field, as for the Creusabro, it’s the anti-abrasion field, but with an improved weldability given by the lower carbon and alloying elements content.

Looking at the stress strain curve resulting from the tensile test, it’s possible to recognise the typical behaviour of a high strength steel; a noticeable elastic part up to an elevated strength value of 1287 Mpa and a low A% are the main feature of this steel. The martensitic tetragonal cell (also present in the Creusabro) gives to the two materials a similar behaviour with high strength and low elongation capabilities.

C Si Mn P S Cr Ni Mo Cu Fe

0,101 0,160 2,22 0,0077 0,0022 0,264 0,015 0,0006 0,066 97,049

Table 3.4– Durostat’s mechanical

proprieties

Table 3.3 – Durostat’s chemical elements’ content

Figure 3.4 – Durostat’s stress – strain curve

Materiale DUR E [Mpa] 205000 Rp0,2 [MPa] 1107 Rm [Mpa] 1278 A [%] 11 Z [%] 51

3.2.3 – Alform

Alform steel could be categorized in the High Strength Low Alloyed (HSLA) family, since it has low carbon content value (0,062%) and very low quantity of alloying elements; the only remarkable presence of an alloying element is the titanium content.

Even if it could appear a general steel, the right choice of the technological route confers very good mechanical proprieties and good weldability.

A ferritic-perlitic prevalent structure is underlined by the micrographic analysis, where the presence of the small precipitates is also evident. Grain size are kept small to improve the mechanical behaviour.

The stress-strain graph analysis put in evidence a noticeable striction part and a high overall elongation for a carbon steel (A = 23%);

C Si Mn P S Cr Ni Mo Ti Fe

0,062 0,041 1,87 0,0069 0,0019 0,027 0,018 0,0035 0,13 97,669

Figure 3.5 – Alform’s stress – strain curve Table 3.6 – Alform’s mechanical

proprieties

Table 3.5 – Alform’s chemical elements’ content

Materiale ALF E [Mpa] 200000 Rp0,2 [MPa] 773 Rm [Mpa] 802 A [%] 23 Z [%] 51

3.2.4 - AISI 304 L

The inox steel here presented is a well-know X2 CrNi 18-9, also commercially called AISI 304L. L stands for “low carbon”; this feature, underlined by the chemical analysis which shows the lower presence of Carbon (<0.035%) with respect to the traditional AISI 304, gives the material an improved weldability and better plastic performances.

The high strength and fragile behaviour of the above-presented carbon steels now give way to good formability and high toughness values. With a very high overall elongation (63%), this austenitic steel shows the strongest strain-rate dependency. A very high plastic flow stress is achieved with strain rate comparable to the one coming from the ballistic test, making its performance comparable with the strongest abovementioned carbon steels.

Looking at the microscopy, austenitic grains are clearly recognisable; deformation bands given by the lamination process are quite evident. In this kind of steel, the influence of the elastic part is smaller at quasi-static tests conditions; the plastic flow is activated at lower stress values and cover the biggest part of the deformation process.

C Si Mn P S Cr Ni Mo Cu Fe

0,023 0,351 1,46 0,0291 0,0017 18,11 8,11 0,25 0,46 70,809

Table 3.8– AISI 304 L’s mechanical

proprieties

Table 3.7– AISI 304 L’s chemical elements’ content

Figure 3.6 – AISI 304L’s stress – strain curve

Materiale INOX E [Mpa] 205000 Rp0,2 [MPa] 297 Rm[Mpa] 673 A [%] 63 Z [%] 61

3.2.5 - Aluminium Alloy 6111

The last analysed material comes from the aluminium 6000 family, based on Al-Mg-Si alloy. The mechanical characteristics of this aluminium are evidently lower than the carbon and inox steel just analysed, having instead a low weight, good formability and favorable characteristics including corrosion resistance and precipitation hardening after heat treatment. Therefore, Aluminum 6111 alloy is chiefly used in the automotive sector for components such as exposed body panels to reduce the overall weight of the vehicle.

The reduced thickness and mechanical characteristics of the plate made of this aluminum alloy make this material the candidate to be perforated by the chosen weapon-projectile couple.

Al Si Fe Cu Mn Mg

97,4 0,627 0,167 0,792 0,165 0,720

Table 3.10 – Aluminium 6111’s

mechanical proprieties

Table 3.9 – Aluminium 6111’s chemical elements’ content

Figure 3.7 – Aluminium 6111’s stress – strain curve

Materiale ALU E [Mpa] 70000 Rp0,2 [MPa] 154 Rm[Mpa] 285 A [%] 32 Z [%] 41

3.2.6 – Material Comparison

Superimposing the stress-strain curves, it’s possible to notice the wide range of mechanical proprieties that will be test in the following experimental campaign, varying from the high strength and low elongation Creusabro steel to the tough and deformable AISI 304L. Even if the appearance underlines the strong behavioural difference between these steels thanks to the direct comparison, it’s worth remembering that the test, from which those graphs are extracted, are performed at low strain rate in accordance with the dedicated normative. As a matter of fact, the strain rate at which the ballistic tests are performed differs from the regulation value of several order of magnitude; this fact will be deeply analysed in the results part (chapter 4) when a specific FEM modelling will be implemented accounting the changings in the material behaviour depending on the strain rate.

Just qualitatively speaking, it’s possible that since the capability of absorbing energy depend on the area of the stress strain curve, the anti-penetration performances of the Inox steels differs less than the expected from the extremely hard Creusabro, that has not the margin to increase its mechanical characteristic as much as the AISI 304L steel.

3.3 – WEAPON AND AMMUNITION SELECTION

3.3.1 – Weapon and Ammunition Operating Principles

The selected firearm used for the experimental shooting campaign is a Beretta PX4 Storm loaded with 9x21 FMJ cartridge; before entering in the technical detail, a brief explanation of the basic principle of the ammunition and semiautomatic handgun’s functioning is needed.

Ammunition

The ammunition is the element which is fed into a firearm to accomplish the final aim of shooting the bullet to the target. It’s composed by four principal parts: the projectile, the casing, the powder and the primer. The basic functioning principle of a cartridge is to transform the chemical energy stored in the firing powder into kinetic energy of the projectile; to do that, the expansion of the gases generated from the exothermic reaction of the powder is used.

In the European Nomenclature, the ammunition name contains info about the diameter of the projectile, the length of the cartridge and some additional information about the nose shape (i.e. RN for Round Nosed projectiles, FN for Flat Nosed), the jacket (i.e. SJ stands for Semi Jacket, HP for Hollow Point) or the manufacturer (i.e. Luger, Remington). For example, the ammunition used in this experimental campaign is a 9x21 mm FMJ, where the 9 mm is a medium diameter of the cave of the barrel of the shotgun (and so, of the projectile), 21 mm is the length of the cartridge (where all the priming and the firing apparatus

is located) and finally the nomenclature FMJ is the additional information about the Jacket of the projectile, which in this specific case is a “Full Metal Jacket”. A British and American nomenclature also exist, which is made by a single number referred to the calibre of the firearm or to the diameter of the projectile, written in hundredth of inches after a point; then, additional information is reported (i.e. the well-known .38 Special). In some cases, the first number is followed by a – and a second number: this nomenclature is used for the most “ancient” type of ammunition and report the calibre and the load of black powder’s grain used to fulfil the cartridge.

To better understand how an ammunition works, is useful to report some information about each single part composing it.

Projectile

The projectile is the only flying part of an ammunition, and, in terminal ballistics point of view, the most important since is the one impacting the target. Even if it could appear as a simple object, its final shape comes from many iterations along the years. The nose shape, the body length, the tail shape and the core-jacket material are all constructive parameters which strongly influence both the flying efficiency and precision and the final effectiveness on the target.

For what concern the nose shape, chiefly external ballistics’ issue determines the final design; low drag resistance it’s required to achieve long shots maintaining a good portion the velocity gained from the detonation of the powder, which is stock as chemical energy in the cartridge.

As briefly said in the previews, the diameter and its relationship with the mass are the key issues concerning the design of a bullet from the terminal ballistics point of view. For a better understanding of this matter, the Sectional Energy Density concept, already introduced in chapter 2, should be enforced. As reported in 2.2.3, with Sectional Energy Density, the ratio among the projectile kinetic energy and the area of the impacting bullet’s section is indicated. With high SED, a projectile has a higher perforation capability since is faster, heavier and with low interaction area with respect to a projectile with a lower SED. This kind of projectiles are used, for example, with Armor’s perforation intent: their lower diameter and higher kinetic energy allows to achieve higher stress values in the target-projectile’s interaction zone. In this way, the bullet maintains higher entering (due to good aerodynamics proprieties) and exiting speed (due to improved penetration capability), investing a lower amount of energy in the penetration process. In those cases, a hard steel metal core could be used to enforce the projectile, in place of the traditional lead one; this technical expedient improves its mass and deformation resistance.

On the other hand, low SED value must be achieved by projectile with soft target damaging intent: a higher impact area gives the possibility to better transfer the energy to the target. For this scope, semi hollow projectiles or semi jacket ones exist: the nose lead uncovered part is the one which expands during impact,

decreasing dramatically the SED only when it’s required. In this way, the aerodynamic proprieties are not influenced, since the nose shape could be kept sharp until the impact takes place.

An interesting fact to be noticed is that not only the constructive parameters of the bullet determine the SED: the shot parameter also have a considerable influence on the evaluation of this index. For example, if the shot line is not perpendicular on the target surface, a higher impact area will result: different penetration modalities will take place since the SED could be reduced by this fact. Also referring to a perpendicular shot it’s possible to varying the SED without varying the constructive bullet’s parameter: it’s sufficient that the projectile it’s not well-stabilized to achieve a non-perpendicular impact, resulting in a SED variation.

For what concern terminal ballistic, the body and the tail shape of the projectile assume a smaller importance; the fields which deeply investigate those parameters are the internal and external ballistics. For what concern internal ballistic, those shapes will influence how the projectile interact with the barrel rifling and with the expanding gases that push the projectile to the muzzle; external ballistics branch is interested in reducing the drag component of the aerodynamic forces acting on the bullet during its flight. For example, a boat tail can reduce the turbulences arising from the rapid expansion of the gasses exiting the muzzle immediately after the projectile; the combined effect of a lower interaction area and gyroscopic stabilization reduces the undesired motion of the bullet in the proximity of the ideal trajectory.

To be notice that since now, only projectiles which transfer its motion energy have been investigated: they are called Kinetic Energy or KE, since no other energy forms are included in the energy transfer phenomenon. A different bullets’

class is, for example, the Chemical one. Those projectiles use a small charge of explosive contained in a cave in the body; when impact takes place, the charge is triggered and the chemical reaction gives an extra damaging action to the shot. In this thesis only KE projectiles are evaluated and investigated, since is the most utilized when dealing with short guns.

Few words could be spent on the jacket of the bullets. This structural part has been introduced when too high shear forces induced on the plumb-made projectiles was noticed; those forces cause damages to the external part of the projectile and reduce bullets functionality. So, the soft plumb core has been covered by a deep-drawn brass or steel jacket, which improved the abovementioned ballistics matters, resulting also in collateral reduced expanding capability during the impact on the target. Recently, also galvanic covering or Teflon and polymeric wrapping has been introduced, substituting the conventional one.

Case or Cartridge

The second Ammunition’s analysed part is the cartridge; this case has multiple duties to fulfil. Surely, the main one is to contain the powder needed to propel the projectile; this feature will be analysed in the next paragraph. Since is made of ductile material, it also works as a sealing to contain the expanding gasses; the detonation of the powder generates a loading condition which expand the cartridge to seal the firing chamber to prevent the exit of the gasses from the back part of the firearm. When the gasses are released, the elastic return allows the cartridge to be ejected. Furthermore, the case keeps the projectile aligned with the barrel and with the firing pin, which is the device that trigger the firing of the ammunition. Last, the cartridge ejects a huge heat quantity from the firearms, delaying the overheating process.

The inner geometry of the specific firearms in which an ammunition is used determines how the cartridge is hold by the firing chamber; this design parameter determines also how the empty case will be ejected during the shooting procedure. This procedure, for what concerns to a semiautomatic handgun, will be analysed in the next paragraph.