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Debris cloud distributions at oblique impacts
Abstract
The purpose of this study is to obtain mass, spray angle and velocity distributions of fragments in debris cloud generated by oblique impacts on an aluminum alloy plate. Hypervelocity impact tests were performed with a two-stage light gas gun at Kyushu Institute of Technology. The impact angles were changed to 0°, 15°, 30°, 45° and 60°. The projectile impacted on the targets at 2km/s. After the impact, the debris cloud was taken with flash X-rays and an ultra high-speed video camera. The fragments were then captured in a stack of polystyrene sheets. As a result, the projectile was broken up into smaller fragments by oblique impacts with the larger impact angles. Lower velocity fragments dispersed in wider spray angles according to the increase of the impact angles.
... Shi-chang et al. 10) obtained the fragment characteristic and the fragment distribution of debris clouds from the SPH simulation. Higashide et al. 11) obtained mass distributions of the debris clouds by capturing the particles in the debris clouds at hypervelocity impact experiments. However, the damage of debris clouds on pressure walls cannot be measured by this experimental method. ...
... There have been some studies to investigate the characteristics of the debris clouds either by the impact experiments, [5][6][7][8][11][12][13] or by the numerical simulations. 9,10,14) Although previous experimental studies, 12,13) have investigated the damage of debris clouds on pressure walls in the impact experiments, they focused on the derivation of empirical equations based on numerous experimental results. ...
In order to analyze the shielding performance of Whipple bumpers, it is essential to clarify the characteristics of a debris cloud that is created owing to a hypervelocity impact. However, lesser attention has been paid on studies on the debris clouds produced by oblique impacts compared to those produced by normal impacts. We thus evaluate the damage of the pressure walls after oblique impacts. Two energy indices are proposed that can determine the destructive capability to the pressure wall. The proposed energy indices are related to the kinematic energy of the debris clouds. These energy indices are demonstrated to show the destructive capability and to uniformly evaluate the damage of the pressure wall. The spatial distributions of the kinetic energy are calculated by the smoothed particle hydrodynamics simulation. In addition to the simulation, impact experiments are conducted with two pieces of apparatus: a two-stage light gas sun and a single-stage powder gun. We discussed the correlation between the characteristics of the debris clouds at the oblique impacts and the damage of the pressure walls. Nomenclature b t : thickness of bumper w t : thickness of pressure wall θ : impact angle between bumper and projectile p V : impact velocity of projectile E : total kinetic energy of debris cloud passing unit area of surfaces of pressure walls max E
... There have been some studies to investigate the characteristics of the debris clouds either by the impact experiments, [5][6][7][8][11][12][13] or by the numerical simulations. 9,10,14) Although previous experimental studies, 12,13) have investigated the damage of debris clouds on pressure walls in the impact experiments, they focused on the derivation of empirical equations based on numerous experimental results. ...
... 1,2,15) There have been some studies about oblique impacts. [10][11][12][13][14][16][17][18] Ryan et al. 16) derived a ballistic limit equation for the metallic opencell foam configuration in oblique impacts. They also characterized failure limits of Whipple shield made of an aluminum alloy in oblique impacts. ...
To analyze the shielding performance of Whipple bumpers, it is essential to clarify the characteristics of a debris cloud that is created owing to a hypervelocity impact. However, lesser attention has been paid on studies on the debris clouds produced by oblique impacts compared to those produced by normal impacts. We thus evaluate the damage of the pressure walls after oblique impacts. Two energy indices are proposed that can determine the destructive capability to the pressure wall. The proposed energy indices are related to the kinematic energy of the debris clouds. These energy indices are demonstrated to show the destructive capability and to uniformly evaluate the damage of the pressure wall. The spatial distributions of the kinetic energy are calculated by the smoothed particle hydrodynamics simulation. In addition to the simulation, impact experiments are conducted with two pieces of apparatus: a two-stage light gas sun and a single-stage powder gun. We discussed the correlation between the characteristics of the debris clouds at the oblique impacts and the damage of the pressure walls.
... Based on dimensionless analysis, numerous studies have developed empirical formulas for a perforation size applicable to different target materials at different attack angles [16][17][18][19][20][21][22] . Moreover, the morphology and distribution characteristics of debris clouds have been analysed [22][23][24] . Further engineering models ...
Space debris impacts on whipped shields are dominantly non-vertical. Shock initiation and interaction govern the fragmentation of projectiles and plates, directly determining the features of the produced debris cloud. During the initial impact stage of a projectile on a target, wave propagation and evolution occur in their interior with co-dominant material fragmentation. In this study, the effects of the impact conditions (impact velocity and attack angle) on the critical conditions for jet generation were examined based on the asymmetric jetting theory. In the Geometric Propagation Model (GPM), the effect of the attack angle was considered, and a wave front deflection angle parameter was introduced. The modified GPM could describe the geometric features and position of a wave front during an oblique impact. Combined with smoothed particle hydrodynamics numerical simulations, the interior of projectiles, fragmentation features, and pressure attenuation were studied. It was found that in large attack angle cases, the projectile material is more likely to reach the critical conditions for jet generation, and the jet mass proportion of the projectile material increases with increasing attack angle. The modified GPM is an oblique elliptic Eq. that is a function of the equivalent speed, impact velocity, attack angle, time, and deflection angle. It may be applicable to hypervelocity events involving any monolithic material as long as the equivalent speed and deflection angle can be provided from numerical simulations. The impact conditions exhibit a quantitative relationship with the pressure attenuation in a projectile, among which the impact velocity has a more significant effect. This study established a quantitative analysis method for initial impact stage of the oblique hypervelocity impact of a spherical projectile on a flat plate.
... Other examples of radiograph diagnostics include calculations of fragment areal mass densities within the cloud (Tamura et al., 2003(Tamura et al., , 2011, and combined diagnostics with high-speed cameras to measure velocities and ejection angles (Higashide et al., 2008). Finally, multiple high-speed radiographs have been combined together to create an in-situ computed tomography of impact events (Moser et al., 2014(Moser et al., , 2019. ...
This dissertation develops an experimental technique for measuring fragmentation initiated by hypervelocity impacts performed in the laboratory. Hypervelocity impact fragmentation is relevant for many applications such as monitoring orbital space debris or researching planetary impacts. Researchers typically use two-stage light-gas guns to recreate hypervelocity impact experiments in the laboratory. My goal in this dissertation is to develop a non-intrusive, time resolved, measurement technique to track and measure the positions, trajectories, and velocities of individual fragments in 3D. I accomplish this by using measurement setups and tracking methods from photogrammetry, specifically adapting approaches developed for fluid flow measurement, such as Particle Tracking Velocimetry. The basic fragment-tracking setup consists of multiple high-speed cameras with converging views to record impact fragments. The analysis algorithm can be separated into four steps: fragment detection, tracking, matching between views, and triangulation. I develop algorithms catering to the specific characteristics of hypervelocity impact fragments to efficiently and accurately accomplish each step. I examine both individual algorithms and the entire workflow in detail using synthetic data to determine optimal approaches specific to the hypervelocity setting. I quantify measurement uncertainties and analyze the characteristics of the tracked fragments. Finally, I present some example tracking results which demonstrate my method's capability to measure 3D fragment positions, trajectories, and velocities, as well as 2D sizes, in a wide range of impact materials and conditions.
... The process of space debris impact the front panel of honeycomb sandwich plate and formed debris cloud, and the process of debris cloud impacts honeycomb core and rear panel is unelasticity. The existing research is mainly focused on the damage of honeycomb core and panel [7,8], and analyzing the form of projectile debris cloud from the side of the projectile motion path by using the flash X-ray radiography system [9] or numerical simulation [10,11]. ...
... The first debris cloud on the timeline exits the sandwich panel in the normal direction. These particles stem from the impact-induced shock inside the front face sheet, are channeled through the honeycomb structure and finally leave the panel in normal direction through the rear face sheet [11]. ...
The micrometeoroid and orbital debris (MM/OD) environment poses a threat to satellites and manned spacecraft. This threat lies in the risk of individual components being affected by an impact of a particle from the MM/OD population. Among spacecraft components, harnesses are especially exposed to that risk due to their ubiquity inside a spacecraft and their importance for fundamental spacecraft functions such as supplying power and relaying digital and analog communications. The degradation or breakdown of such a mission-critical component can shorten the lifetime of a satellite or, in the worst case, lead to loss of a mission.
Past impact tests have shown that mechanical damage to cables like cratering and removal of insulation can result in permanent functional degradation after impact. However, during the impact event, transient processes develop which until now have not yet been characterized. These processes include voltage spikes that propagate along a cable potentially damaging connected equipment such as on-board computers, sensors and other electronics.
A hypervelocity impact test campaign was performed on space-grade unshielded single conductor, screened twisted pair and radio-frequency coaxial lines in a representative experimental setup. This comprised both representative operational parameters and a representative mechanical setup behind an aluminum sandwich panel similar to an actual spacecraft structure wall. Impactors were aluminum spheres with diameters ranging from 2 mm to 5 mm with impact velocities between 3 km/s and 7 km/s. Impact-induced transient responses were recorded. Observed voltage spikes go up to twice the nominal voltage level. The work presented in the paper at hand was performed as part of a European Space Agency contract.
... One leaves the sandwich panel in normal direction (known as channeling) and a second one in flight direction (Figure 4). The debris cloud in normal direction stems from the impact-induced shock inside the front face sheet, is channeled through the honeycomb structure and finally leaves the panel in normal direction through the rear face sheet [7]. The projectile on the contrary penetrates the sandwich panel mostly undeflected [8] and exits it slightly divergent around the shot axis. ...
A standard method to assess the risk posed upon space assets from the micrometeoroid and space debris (MM/SD) environment is to evaluate the probability of no penetration (PNP) of the spacecraft outer hull. It implies catastrophic spacecraft failure upon a single particle penetration through the spacecraft structure wall. The method is justified by its conservative approach, however may result in overly protected structure walls. A more accurate approach is possible with the Schäfer-Ryan-Lambert (SRL) ballistic limit equation (BLE). It takes into consideration the components' individual capability to defeat particles without functional effect. The initial equation [1] is calibrated with some 90 hypervelocity impact tests on fuel and heat pipes, pressure vessels, electronic boxes, harness and batteries. The paper at hand publishes results obtained from another 40 impact tests on three vulnerable components, namely the harness, electronics boxes and fuel pipes, with focus on oblique impacts at 45° and 60°. The obtained data complements the initial data base and a recalibration and validation of the SRL equation for oblique impacts is achieved. Applications for the SRL equation in the domain of spacecraft MM/SD risk assessment as well as in the domain of survivability enhancement are discussed.
... As regards debris cloud description, a quite significant amount of experimental as well as numerical results is available in the technical literature with reference to simple plate targets, for which fragments properties are reported for different impact conditions [24,10,9,17,4,23,1,14,2,7,25,6,8]. However, the vast majority of these references considers only aluminum-alloy plates, and debris cloud information is given in a rather heterogeneous way which makes difficult to extrapolate a single synthesis model. ...
All spacecraft in Earth orbit are exposed to the risk of impact with micrometeoroids and orbital debris. When such particles have enough energy to penetrate the hull of the vehicle, clouds of fragments are ejected into spacecraft and they can eventually compromise the functionality of various components encountered in their flight path. Knowledge of the clouds' properties (e.g. fragments mass and velocity) is therefore a key factor to obtain accurate predictions of the response of interior equipment to space debris threat. However, generation and evolution of debris clouds from hypervelocity impact is a complex phenomenon governed by a large number of parameters, and existing models mostly refer to fragments originated by impact on simple aluminium plates only, while the few models available for sandwich panels do not provide information on the fragments mass. In such context, this paper presents an engineering model describing debris clouds created by space debris impacts on honeycomb sandwich panels representative of satellites structural bodies. The model consists of a set of empirical equations providing three pieces of information, i.e. the geometric description of the cloud, the velocity distribution and the mass distribution of the fragments. The proposed equations are derived from analogous formulas for debris clouds originated by impacts on simple aluminium plates, by applying proper corrections to account for different materials effects and different behaviour of sandwich panels compared to plates of same material. The model is finally evaluated by comparing its predictions with few experimental data on triple wall structures (sandwich panel plus internal equipment cover plate), where debris clouds exiting the panels' rear skin are used to assess the failure of the third wall. In this latter case, the proposed model is also compared with the SRL equations. Copyright © 2014 by the International Astronautical Federation. All rights reserved.
The space debris in Earth’s orbit has increased drastically due to the failure of spacecraft, rocket bodies, and mission-related objects. These objects in orbit increase the space waste and challenge other flying objects such as spacecraft. A hypervelocity impact of space debris on spacecraft structures can have a range of effects (mechanical damage and functional failure), raising significant concerns about spacecraft safety. This paper reviews the different studies on the performance and development of the Whipple shield against the hypervelocity impact of space debris. The study focuses on the impact mechanism, dynamic Fragmentation of materials, strength models, Equation of state, characteristics, and model of the debris cloud. The strength models (Steinberg–Guinan and Johnson–Cook) and Mie–Gruneisen equation of state, primarily used for hypervelocity impact applications, are thoroughly covered in this study. The study also reported the various experimental and numerical techniques for high and hypervelocity impact. The study concluded that mesh-based, mesh-free, and hybrid finite element methods are reliable for analyzing Whipple shield targets to resist hypervelocity impact. The study also observed that the two-stage light gas gun technique investigates most experimental analyses of hypervelocity impact on the Whipple shield. Alongside reviewing the abovementioned aspects, this paper also underlines the future scope of study in this paradigm. The authors strongly believe that this study provides more insights into the fundamentals and perceptions of the Whipple shield to protect the spacecraft against the hypervelocity impact of space debris.
All spacecraft are subject to the possibility of high-speed particle impacts during their mission life. Such impacts create debris clouds that travel toward and eventually impact downstream spacecraft components. In addition to the impulsive load that such debris clouds deliver, the largest fragment in these debris clouds also poses a significant threat to spacecraft elements. To assess the severity of the threat posed by such a fragment, we must be able to predict the size of this largest fragment and its associated velocity. In this paper, we present empirical equations to predict these quantities in terms of the material properties of the surface that sustains the initial impact, the characteristics that define the impact event, and the material properties of the impacting projectile. We compare the predictions of these equations against experimental values for largest fragment size and its associated velocity and the predictions of these quantities obtained using numerical simulations of high-speed impact events. These comparisons indicate that the empirical equations for the largest debris cloud fragment size and velocity fare very well, as a whole, across the entire impact velocity regime of ∼2–55 km/s.
Hypervelocity impacts involving big objects in space are expected to occur more frequently in the next years, generating a significant number of new debris. In this context, understanding the physical mechanisms involved in orbital collisions and modelling space debris production after fragmentation are fundamental prerequisites to predict the long-term evolution of the space debris environment. In this work we present impact experiments on aluminium thin plates with the purpose to evaluate the effect of impact velocity and target thickness on the fragments generation. Results are presented as cumulative characteristic length distributions and shapes distributions. It is shown that characteristic length distributions can be modelled by a power law similar to the NASA SBM and that shape distributions are independent from target thickness and impact velocity.
This work revisits the classical hypervelocity impact problem of a cylindrical projectile impinging upon a thin plate at an attack angle. A methodology is described to identify the potentially dangerous fragments that can perforate the rear plate in a Whipple shield configuration. The attack angle is re-calculated based on the reported orthogonal view angles, followed by numerical modeling of the hypervelocity impact event using the SPH method in AUTODYN-3D, and the qualitative and quantitative post-processing of the debris cloud generated from the hypervelocity impact. The model predictions are compared to results from the experimental data from the literature for two different attack angles – they will be shown to be in good agreement. The concentrated area of dangerous fragments in the debris cloud is quantified in detail, and its damage mechanism to the rear plate is revealed. The majority of the projectile fragments are located inside the inner cone and the cross-wing of the debris cloud, where the latter bridge connecting the inner cone and the outer bubble, and they are defined according to their geometry shapes being as the components of the debris cloud. The accumulative effect of the two structures are shown to attribute to the potential damage in the rear plate. This work aims to help Whipple shield designers seeking a theoretical method to estimate the threat of yaw hypervelocity impact.
To expand the field of view and obtain a full-scale image of a debris cloud, a large-field pulsed digital in-line holography (DIH) system is developed to study the three-dimensional (3D) positions and shapes of debris clouds generated by hypervelocity impact. A general model for the large-field pulsed DIH system is introduced. Derived from strict theoretical analysis, it suggests that the hologram recorded by a large-field pulsed DIH system can be described by an equivalent lensless system. At the Hypervelocity Impact Research Centre of the China Aerodynamics Research and Development Centre, based on hypervelocity impact equipment with a 7.6 mm bore, experiments on a 3 mm aluminium sphere impacting a 1 mm thick aluminium target plate with a velocity of 3.58 km/s were carried out. Ensuring the successful capture of the transient state of debris clouds, the large-field pulsed DIH system is synchronised with the impact event and the combination of the neutral density filter and the bandpass filter is proposed, to eliminate the plasma radiation and enhance the signal-to-noise ratio of the hologram. The experimental results show that the holographic fringes are clearly recorded and the detailed shapes and structures of both large and small aluminium fragments are observed after reconstruction. The structure of debris clouds can be divided into three parts: front, core and shell, agreeing well with results measured by laser shadowgraph. The study demonstrates the feasibility of a large-field pulsed DIH system for accurate measurements of ultrafast debris clouds and shows great potential in the diagnostics of hypervelocity impacts.
Whipple shield, a dual-wall system, as well as its improved structures, is widely applied to defend the hypervelocity impact of space debris (projectile). This paper reviews the studies about the mechanism and process of protection against hypervelocity impacts using Whipple shield. Ground-based experiment and numerical simulation for hypervelocity impact and protection are introduced briefly. Three steps of the Whipple shield protection are discussed in order, including the interaction between the projectile and bumper, the movement and diffusion of the debris cloud, and the interaction between the debris cloud and rear plate. Potential improvements of the protection performance focusing on these three steps are presented. Representative works in the last decade are mentioned specifically. Some prospects and suggestions for future studies are put forward.
The amount of space debris will increase in the future because of collisions with other debris, even if no future space launches are carried out. Therefore, debris removal is essential for sustainable space development. The electrodynamic tether system is a promising method to remove debris because it does not require any propellants; however, it can be severed by a collision with a small piece of debris. As a tape tether is wider and thinner than a conventional solid cylindrical tether, it may overcome this drawback. The tape tether, however, can be twisted and transformed to a non-ideal shape. This paper considers a scenario in which the tape tether is twisted to create a loop shape. Every impact generates a debris cloud, which may subsequently impact another part of the tether that happens to be located in the direction the debris cloud is emitted to. This could cause a cascade effect where a single impact results in multiple collisions that lead to significant damage of the tether. Through hypervelocity impact experiments, collisions on the loop part are evaluated to gain new insights into the loop phenomenon of the tape tether system. Based on the experimental results, the rate of severance of the tape tether was compared with that of the conventional solid cylindrical tether. When only a small part of the tape tether is in loops, the rate of severance of the tape tethers is much lower than that of the conventional solid cylindrical tethers. Hence, tape tethers have a considerable advantage over conventional tethers when the looped range is narrow.
The effects of projectile diameter and impact velocity on fragment size distribution were investigated by striking aluminum alloy 6061-T6 targets with aluminum alloy 2017-T4 spheres of 1.6 to 7.0 mm in diameter at impact velocities ranging from 2 to 7 km/s. Two-stage light-gas guns from the Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency and Nagoya Institute of Technology were used for the experiments. After the impact experiments, fragments were collected from the test chamber, and the fragment lengths were measured. Scaling laws for size distribution of fragments were discussed. The fragment length was directly proportional to projectile diameter. When the horizontal axis of the fragment length distribution was divided by the projectile diameter, the normalized fragment length distribution was proportional to the impact velocity raised to the power 1.5. The empirical formula with respect to the fragment length distribution could be expressed using the projectile diameter and impact velocity. The proposed scaling law with respect to fragment length could be applied to projected areas of fragments and fragment masses and the validity of the scaling law was confirmed. The fragment length was directly proportional to crater size such as crater diameter and crater depth. The horizontal axis of the fragment length distribution could be normalized by each crater depth or crater diameter.
In order to simulate and study the oblique hypervelocity impacts of space debris on bumper of spacecrafts, a series of oblique hypervelocity impact experiments of aluminum Whipple shields are carried out by a two-stage light gas gun. The aluminum alloy projectile diameter is 3.97 mm, the impact velocities range from 1.14 to 5.35 km/s, and the impact angles range from 0° to 70°. The crater distributions on the rear wall of aluminum Whipple shield obliquely impacted by aluminum spheres are obtained and analyzed. In addition, the forecast equations for crater distribution on the rear wall of aluminum Whipple shield by oblique hypervelocity impact are derived. The results indicate that there are two crater distribution areas on the rear wall under hypervelocity oblique impact. The critical fragmentation velocity of projectile will bring effect on the relationship between the impact damage law of rear wall and impact angle. For aluminum alloy Whipple shield, there exists a critical initial collision angle at which the impact damage on the rear wall is the most severe.
In order to assess the damage characteristics of the debris cloud to the electronic apparatus and equipment inside the satellite, a concept about the distribution in impacted sheet is proposed, and the relevant definition is presented in this paper. Taking Swift's model of the debris cloud as an application example, this paper gives the position of the debris cloud particle, the distribution function, the density function and its extremums. A comparison of the density functions between Swift's model and large numbers of experiments shows that the Swift's debris cloud model is not in accord with the experiments, and thus cannot reveal impact characteristics of the debris cloud correctly.
The protection capability of dual steel flying plates against obliquely impacting tungsten heavy alloy long-rod penetrators was simulated using NET3D code. The major variables considered in this work include thickness ratios of front to rear plate (5/0, 3.3/1.7, 2.5/2.5, 1.7/3.3, and 0/5) and plate velocity (0.2 and 0.5km/s) at obliquity of 60°. Based on the residual kinetic energy of the penetrator after perforating the plates system, the protection capability of the system increased with an increase in the ratio of rear plate thickness. Such a trend was confirmed at a normal ordnance velocity (1.5km/s) as well as a hypervelocity regime (2.5km/s) and was shown to be best exploited when the relative velocity between the penetrator and rear plate was appropriate. A design guideline for an effective flying plate protection structure was proposed.
A numerical study for the analysis of oblique ceramic/metal composite armour systems against L/D = 20 projectiles has been performed. The ballistic performance of the add-on lightweight armours was examined by determining the effect of areal density of the system on ballistic limit or depth of penetration (DOP). To do this, a series of three-dimensional numerical simulations has been conduced. The impact velocities considered are 2.2 and 2.6 km/s. The oblique angle of the plate is 60 degrees. Simulation results for ballistic limits appear to match fairly well with the test values. Although the previous data for the penetration of 7.62 AP projectile into relatively thin alumina/aluminium composite targets revealed an optimum value of the front plate to back plate thickness ratio in the region of 1.5, the current data for the impact of long rod into relatively thick composite targets are scattering. This is because the distinguishing features of thin composite armour systems against 7.62 AP and 40.7g steel projectiles are crack propagation, ceramic conoid formation and failure of backing plate, while these effects are less significant in thick targets, especially at high impact velocities.
During their missions in space, spacecraft are subjected to high velocity impacts by orbital debris particles. Such impacts are expected to occur at non-normal incidence angles and can cause severe damage to the spacecraft as well as to its external flight-critical components. In order to ensure crew safety as well as the proper function of internal and external spacecraft systems, the characteristics of debris clouds generated by such impacts must be known. In this paper, a first-principles-based analytical model is developed for the characterization of the penetration and ricochet debris clouds created by the hypervelocity impact of a spherical projectile on a thin aluminum plate. This model employs normal and oblique shock wave theory to characterize the penetration and ricochet processes. The predictions of the model are compared against numerical and experimental results.
Perforation experiments were conducted with 26.3 mm thick, 6061-T651 aluminum plates and 12.9 mm diameter, 88.9 mm long, 4340 Rc = 44 ogive-nose steel rods. For normal and oblique impacts with striking velocities between 280 and 860 m/s, we measured residual velocities and displayed the perforation process with X-ray photographs. These photographs clearly showed the time-resolved projectile kinematics and permanent deformations. In addition, we developed perforation equations that accurately predict the ballistic limit and residual velocities.
In this paper, we document the results of a combined experimental, analytical, and computational research program that investigates the penetration of steel projectiles into limestone targets at oblique angles. We first conducted a series of depth-of-penetration experiments using 20.0 g, 7.11-mm-diameter, 71.12-mm-long, vacuum-arc-remelted (VAR) 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.4 and 1.3 km/s using a 20-mm powder gun into 0.5 m square limestone target faces with angles of obliquity of 15° and 30°. Next, we employed the initial conditions obtained from the experiments with a technique that we have developed to calculate permanent projectile deformation without erosion. With this technique we use an explicit, transient dynamic, finite element code to model the projectile and an analytical forcing function based on the dynamic expansion of a spherical cavity to represent the target. Due to angle of obliquity we developed a new free surface effect model based on the solution of a dynamically expanding spherical cavity in a finite sphere of incompressible Mohr–Coulomb target material to account for the difference in target resistance acting on the top and bottom sides of the projectile. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test castings of the projectile trajectories.
Direct linear transformation from comparator coordinates into object space in close-range photogrammetry
- Adbel-Aziz Yi
- Karara
- Hm
Adbel-Aziz YI, Karara HM. Direct linear transformation from comparator coordinates into object space in close-range photogrammetry. In: Proceedings of the symposium close-range photogrammetry; 1971. p. 1–18.
Velocity distributions obtained from images taken with the ultra high-speed video camera (a) q ¼ 0 and 15 (b) q ¼ 30 , 45 and 60
- M Fig
- Higashide
Fig. 13. Velocity distributions obtained from images taken with the ultra high-speed video camera (a) q ¼ 0 and 15 (b) q ¼ 30, 45 and 60. M. Higashide et al. / International Journal of Impact Engineering 35 (2008) 1573–1577