Impact fragmentation of high-velocity compact projectiles on thin plates: a physical and statistical characterization of fragment debris

The high-velocity impact of a projectile onto a structure results in the creation and energetic expulsion of fragments of the interacting materials. The nature of this fragment debris is of concern in certain applications. Although more broadly applicable, the present study is motivated by a need to characterize the size and velocity distribution of fragments generated by orbital debris impacting external components of spacecraft structure, such as shielding and radiators. In this effort, statistical relations are developed to predict size, momentum and trajectory distributions of the debris. The underlying physics applied are those used in the fields of impact mechanics, thermodynamics of shocks, and statistical fragmentation. Equations from impact mechanics lead to predictions for mass, global momentum, and excess energy of the fragment debris. Relations from shock thermodynamics are developed to partition the initial kinetic energy into thermal and mechanical energies, and therefore to predict mass fractions of solid, liquid and vapor components and the subsequent dispersing motion of this fragment debris. Statistical methods of the energy-based Maxwell-Boltzmann type are pursued to characterize the inherently stochastic fragmentation event, emphasizing the extremes of fragment size and velocity. Computational simulations of impact events and data from impact fragmentation experiments are exploited in validating the underlying theoretical assumptions and the resulting impact fragmentation model.     

Experimental observations and computer simulations for metallic projectile fragmentation and impact crater development in thick metal targets

Stainless steel (3.18 mm diameter) spherical projectiles impacting 2.5 cm thick targets of nickel, copper, 304 stainless steel, and 70/30 brass at velocities ranging from 0.52 to 5.12 km/s were observed by SEM to form decreasing average fragment sizes with increasing impact velocity, beyond a fragmentation onset velocity of 0.7 km/s. Crater observations by optical microscopy and SEM were qualitatively simulated using an AUTODYN numerical analysis code, which also illustrated a decrease in fragmentation density within the target craters with increasing impact velocity. However, extrapolated simulations corresponding to impact velocities as high as 10 km/s showed residual fragmentation within these craters in contrast to extrapolations of the experimental fragment size versus impact velocity data indicative of zero fragment size at 6 km/s.     

A model for deformation and fragmentation in crushable brittle solids

A unified framework of continuum elasticity, inelasticity, damage mechanics, and fragmentation in crushable solid materials is presented. A free energy function accounts for thermodynamics of elastic deformation and damage, and thermodynamically admissible kinetic relations are given for inelastic rates (i.e., irreversible strain and damage evolution). The model is further specialized to study concrete subjected to ballistic loading. Numerical implementation proceeds within a finite element context in which standard continuum elements represent the intact solid and particle methods capture eroded material. The impact of a metallic, spherical projectile upon a planar concrete target and the subsequent motion of the resulting cloud of concrete debris are simulated. Favorable quantitative comparisons are made between the results of simulations and experiments regarding residual velocity of the penetrator, mass of destroyed material, and crater and hole sizes in the target. The model qualitatively predicts aspects of the fragment cloud observed in high-speed photographs of the impact experiment, including features of the size and velocity distributions of the fragments. Additionally, two distinct methods are evaluated for quantitatively characterizing the mass and velocity distributions of the debris field, with one method based upon a local energy balance and the second based upon global entropy maximization. Finally, the model is used to predict distributions of fragment masses produced during impact crushing of a concrete sphere, with modest quantitative agreement observed between results of simulation and experiment.     

Fragmentation of a sphere initiated by hypervelocity impact with a thin sheet

Selected results of tests in which 9.53-mm-diameter, 2017-T4 aluminum spheres impacted 0.25-mm- to 4.80-mm-thick, 6061-T6 aluminum sheets are presented. Impact velocities for these tests ranged from 1.98 km/s to 7.38 km/s. Flash x-rays were used to view the debris clouds produced by the impacts. As impact velocity was increased, failure of the aluminum sphere progressed through the following stages of fracture and fragmentation: (1) formation of a spall failure at its rear surface, (2) development of a detached shell of spall fragments, and (3) complete disintegration of the sphere. The threshold impact velocity for development of the spall failure in the sphere was observed to be a function of the bumper-thickness-to-projectile-diameter ratio (t/D), and to increase as the t/D ratio decreased. When the debris cloud was fully developed, the disintegrated projectile formed its dominant feature--an internal structure, composed of a front, center, and rear element, located at the front of the debris cloud. The front element was small and consisted of finely-divided projectile and bumper material. The bulk of the fragmented projectile was contained in the center element, a disc-like structure made up of a large central fragment surrounded by numerous smaller fragments. A shell of fragments, spalled from the rear of the sphere, formed the rear element. Radiographs of the debris clouds were analyzed to determine the size and size distribution of certain fragments within the cloud. The size of the large fragment was shown to be dependent on impact velocity and t/D ratio. The smaller fragments in the center element were several times larger than the fragments in the shell of spall fragments forming the rear element. Detailed analyses of fragments in the shell of spall fragments were made. The analyses indicated their median Martin's statistical diameter exhibited an orderly dependence on impact velocity and t/D ratio.     

Comparison of hypervelocity fragmentation and spall experiments with Tuler–Butcher spall and fragment size criteria

The present investigation compares predictive theories of dynamic spall and fragmentation with previously reported experimental data. In the experimental tests, aluminum spheres normally impacted thin aluminum plates at over approximately 4.5–7.5 km/s. Scaling features of the impact breakup phenomenon were explored through selected variation in sphere size and plate thickness. The principal diagnostic was high-resolution flash radiography. Fragment-size features of resulting fragment clouds were determined through detailed analysis of the recorded radiographs. Other investigators have measured the spall strengths for aluminum at comparable ultra-high strain rates. Spall strength amplitude and the corresponding strain rate dependence are principal results of the study. Existing dynamic fracture criteria are specialized here to the sphere impact spall and fragmentation event, and compared with empirical data. Velocity and strain rate scaling relations are developed for fragmentation size in the sphere impact event.     

Response of simulated propellant and explosives to projectile impact—II. Fragmentation

This paper is the second of a series concerned with the penetration and perforation phenomena in two types of propellant and explosive simulant, named Propergol, due to the impact at normal incidence of both blunt and conically-tipped steel strikers. The collision results in fragmentation, plug formation and generation of a cloud of debris that includes particles of measurable dimensions traveling with significant velocities. Both the fragment size and area as well as the ejecta mass are determined experimentally as a function of Propergol specimen thickness and impact velocity or energy. The cumulative number of fragments as a function of size for the Propergol is uniformly found to be a bi-linear semi-logarithmic relationship with the bifurcation occurring at the mean crystal radius. Individual crystals and the crater generated are examined by means of a scanning electron microscope.

A phenomenological model of the fragmentation process is constructed, based on an assumed spherical shape of the fragments and the bi-linear fragment distribution, using energy methods. This is combined with a perforation analysis that considers the process to be sequentially composed of initial indentation, fragmentation, and sliding and deflection of the Propergol disks. An evaluation of this model providing fragment volumes as a function of impact velocity is compared with experimental results and found to be in good agreement.     

Effects of scale on debris cloud properties

Results of tests using various thicknesses of 6061-T6 aluminum sheet and 6.35-, 9.53-, 12.70-, and 15.88-mm-diameter, 2017-T4 aluminum spheres are described. Impact velocities for these tests ranged from 3.77 to 7.38 km/s. Multiple-exposure, orthogonal-pair, flash radiographs of the debris clouds produced by the impacts were analyzed to provide quantitative data which described the size and velocity of a number of characteristic morphologic features in the debris clouds and the sizes and size distributions of fragments in the structural elements of the debris cloud.The axial and diametral velocities of these morphologic features were shown to be the same, regardless of sphere diameter, when debris clouds produced by impacts with similar bumper-thickness-to-projectile-diameter ratios and impact velocities were compared. As a result, the dimensions of these debris clouds differed only by the differences in the diameters of the spheres that produced them.An analyses of fragment sizes showed that the equivalent diameter of the large projectile fragment along the center line of the debris cloud scaled with projectile diameter; the dimensions of fragments forming the shell of spall fragments at the rear of the debris cloud did not scale with projectile diameter. The large central fragment appeared to originate from near the center of the sphere and was a part of the sphere which remained intact after all processes that worked to reduce the size of the sphere were complete. Formation of spall-shell fragments was a shock-related process which was sensitive to rate effects and other material properties that did not scale.     

Fracture and impulse based finite-discrete element modeling of fragmentation

A numerical method for fragmentation is presented that combines the finite element method with the impulse-based discrete element method (impulse-based FDEM). In contrast to existing methods, fragments are not represented as a conglomeration of spheres; instead, their shapes are represented using solid modeling techniques, and are the result of multiple fracture growth. Fracture growth within each three-dimensional fragment is controlled by stress intensity factors computed using the finite element method and the reduced virtual integration technique. Non-convex fragment interaction and movement is modeled using impulse dynamics, rather than a penalty-based method. Collisions leading to fracture are handled individually by propagating pre-existing internal flaws and cracks. The method utilizes decoupled geometry and mesh representation, and local failure and propagation criteria. Fractures that reach volume boundaries lead to further fragmentation. The approach is demonstrated by the fragmentation of a sphere, which exhibits a velocity-dependent fragment size distribution. The distribution is characterized by a two-parameter Weibull distribution, an emergent property of the simulation. Results are in good agreement with experimental data.     

Statistical characteristics of a debris cloud behind a shield

To determine a function of size distribution of debris behind a perforated shield, we have studied diameter distribution of craters produced on the target, which was placed behind a thin shield. The distribution parameters are established to be connected with the characteristics of impact conditions. Based on statistical representations of the material strength, we have developed the model for fragmentation of a projectile, which allows us to explain why the size distribution of debris obeys the Rosin - Rammler (or Weibull) law.     

Length scales and size distributions in dynamic fragmentation

The shatter of a cherished wine glass on impact with the kitchen tile, the spallation in the high-energy collision of atomic nuclei, the fragmentation of the Shoemaker-Levi comet on passage of the Roche limit of the Jovian gravitational field, collectively span vast length scales, yet are each examples of dynamic fragmentation with a number of commonalities. In the above examples, as well as many other dynamic fragmentation events, the consequence is the breakage of the body into some number of fragments that are distributed over size. At the heart of a satisfactory theory is the prediction of the number of fragments and the statistical distribution of these fragments over size. A theory based on energy principles is found to provide length scales that govern both the characteristic fragment size and the distribution spread. Fundamental failure and fracture properties of the material are central in determining the nature of the fragment size distribution. Fragment size distributions can range from relatively tight exponential functions to power-law relations spanning a number of decades in fragment size. The fragment distribution and the dynamic fracture processes leading to power-law distributions bear striking similarities to hydrodynamic turbulence. Onset of fracture asymptotes to a range of length scales in which destruction is self-similar and fractal, requiring that consequences, including the fragment size distributions, exhibit a power-law dependence on the length scale. The theory is described and supporting experimental evidence is provided.     

Crater distribution on the rear wall of AL-Whipple shield by hypervelocity impacts of AL-spheres

All spacecraft in low orbit are subject to hypervelocity impact by meteoroids and space debris, which can in turn lead to significant damage and catastrophic failure. In order to simulate and study the hypervelocity impact of space debris on spacecraft through hypervelocity impact on AL-Whipple shield, a two-stage light gas gun was used to launch 2017-T4 aluminum alloy sphere projectiles. The projectile diameters ranged from 2.51 mm to 5.97 mm and impact velocities ranged from 0.69 km/s to 6.98 km/s. The modes of crater distribution on the rear wall of AL-Whipple shield by hypervelocity impact of AL-spheres in different impact velocity ranges were obtained. The characteristics of the crater distribution on the rear wall were analyzed. The forecast equations for crater distribution on the rear wall of AL-Whipple shield by normal hypervelocity impact were derived. The results show that the crater distribution on the rear wall is a circular area. As projectile diameter, impact velocity and shielding spacing increased, the area of crater distribution increased. The critical fragmentation velocity of impact projectile is an important factor affecting the characteristics of the crater distributions on the rear wall.     

Behind-armor debris from the impact of hypervelocity tungsten penetrators

Behind-armor debris is the main mechanism by which targets are destroyed by projectile impact. The behind-armor debris generated from the impact of tungsten heavy alloy (THA) penetrators with a length-to-diameter ratio (L/D) of 20 against 6061-T6 aluminum targets was characterized. Behind-armor debris characteristics described were the number of debris particles, their positions, and their size distribution. Experiments were performed against two nominal target thicknesses, 100 and 150 mm, and covered a velocity range from 1.7 to 2.6 km/s. Two methods of obtaining data were used—radiographs were taken of the behind-armor debris, and perforation patterns were generated on steel witness packs placed behind the aluminum target. Debris particles recovered from the witness packs were also studied. Results are discussed for the effect of changes in target thickness and impact velocity on behind-armor debris particle characteristics.     

Experimental and numerical simulation of high velocity impact on steel targets

The perforaton process of steel plates at normal impact by cylindrical steel fragments together with the debris cloud expansion have been studied in the velocity range 2 - 3 km/s. The fragments have a length-to-diameter ratio of 1.035 and a mass of 51g. Fragment and target materiass are 9SMn28 and C45, respectively. Two plate thicknesses of 20 and 30 mm have been tested. These thicknesses are in the order of the penetration depth in the semi-infinite target. In addition the cratering in the semi-infinite target has been investigated. The crater dimensions on the target front side are comparable for both, the plate targets and the semi-infinite targets. The degree of fragmentation in the debris cloud increases with velocity and is smaller in case of the 30 mm target. The ratio of longitudinal to lateral dimensions of the debris clouds is independent of the target thickness, but dependent on the distance from the plate rear side. This ratio increases with distance and converges at larger distances versus nearly hemispherical expansion. A further goal of this paper is the application of a Lagrangian code to the numerical simulation of the impact process in the semi-infinite target. For this purpose the LS-DYNA2D code with a new erosion option has been used. Material input data are the static material properties as well as shock wave data determined from planar impact tests for the steels used here. LS-DYNA2D with its new erosion option can predict in a good agreement the particle velocity history of the planar impact tests and the crater shapes in the semi-infinite target.     

椭球弹丸超高速撞击防护屏碎片云数值模拟

低地球轨道的各类航天器易受到微流星体及空间碎片的超高速撞击.本文采用AUTODYN软件进行了椭球弹丸超高速正撞击及斜撞击防护屏碎片云的数值模拟.给出了三维模拟的结果.研究了在相同质量的条件下,不同长径比椭球弹丸以不同速度和入射角撞击防护屏所产生碎片云的特性,并与球形弹丸撞击所应产生的碎片云特性进行了比较.结果表明:在相同的速度下,不同长径比椭球弹丸撞击的碎片云形状、质量分布和破碎程度是不同的,随撞击入射角的增加弹丸的破碎程度增大,滑弹碎片云的数量增加;随撞击速度的增加,弹丸的破碎程度也增加.     

Debris cloud expansion studies

Properties of fragment clouds produced by hypervelocity perforation of metal plates have been experimentally investigated. Replica model techniques have been applied. Targets consisted of steel dual-plate systems. Projectiles were hard metal spheres of tungsten carbide (3 mm, 7 mm and 10 mm diameter, HRc 79) and steel spheres (6 mm and 12 mm diameter, HRc 63) at velocities ranging between 2.3 km/s and 4.5 km/s. Cloud expansion velocities have been measured by means of in-flight flash X-ray photograph series. Maximum and minimum fragment velocities at front and rear side of clouds have been determined. From impact crater patterns on witness plates, and X-ray photographs of debris clouds, projectile and shield fragments have been identified. It has been found that plate perforation holes and debris cloud parameters scale geometrically for 6 mm and 12 mm diameter steel and 7 mm and 10 mm diameter hard metal spheres. For the 3 mm diameter hard metal spheres only the maximum debris cloud velocity v_rmax scales; all other parameters show deviations, indicating non-uniformity of the plate perforation process at different plate thicknesses. The shape of the inner part of debris clouds of steel spheres is different from that of hard metal spheres, caused by the density difference. For steel spheres the debris cloud shape is a convex lense, the shape of the hard metal fragments becomes in the rear nearly hemispherical. Increasing of the impact velocity causes an increasing of the expansion velocity and a flattening of the debris clouds.     

Spin velocimeters for impact debris fragments

An experimental technique for determining the velocity of individual debris fragments from hypervelocity impacts and correlating these velocity data to fragment size is presented. Design trades and experimental results for fragment spin velocimeters based on this technique are also presented. Validation tests were conducted to verify and optimize the performance of these instruments, and they were subsequently used to collect data for four hypervelocity impact tests. Such data are critical to the development of accurate debris environment models and to support safety hazard analyses of flight tests involving impacts. Comparisons with model predictions are presented.     

Debris clouds behind double-layer targets

It is demonstrated that the impedance mismatch and the order of the layers in two-layer sandwiches strongly influences the crater hole size formed in the target, the down-range debris cloud peak velocity, the fragment number and size, and the angles of downrange and uprange debris. Full and half scale test series with aluminum spheres of 10 mm and 5 mm diameter are performed with two-stage light gas guns against glued sandwiches of two layers at about equal areal density and different as well as equal shock impedances in the velocity range of 3–8 km/s. In the case of the titanium/tungsten plate sequence the transmitted shock wave is much stronger than for the tungsten/titanium target. This leads to a higher degree of fragmentation of the participated materials. For titanium/tungsten the hole diameter formed in the titanium layer is distinctly larger than in the tungsten layer for tungsten/titanium. For the titanium/tungsten target the larger crater diameter on the impact side is in agreement with the lower maximum debris cloud velocity.     

Study on the fragmentation of shells

Fragmentation can be observed in nature and in everyday life on a wide range of length scales and for all kinds of technical applications. Most studies on dynamic failure focus on the behaviour of bulk systems in one, two and three dimensions under impact and explosive loading, showing universal power law behaviour of fragment size distribution. However, hardly any studies have been devoted to fragmentation of shells. We present a detailed experimental and theoretical study on the fragmentation of closed thin shells of various materials, due to an excess load inside the system and impact with a hard wall. Characteristic fragmentation mechanisms are identified by means of a high speed camera and fragment shapes and mass distributions are evaluated. Theoretical rationalisation is given by means of stochastic break-up models and large-scale discrete element simulations with spherical shell systems under different extreme loading situations. By this we explain fragment shapes and distributions and prove a power law for the fragment mass distribution. Satisfactory agreement between experimental findings and numerical predictions of the exponents of the power laws for the fragment shapes is obtained     

Fragmentation in oblique impaction for nanoparticle-agglomerates with different structures

Impact fragmentation can be used to disperse nanoparticle-agglomerates. While the fragmentation of openly structured (fractal dimension D_f?<?2) agglomerates during perpendicular impaction was the subject of several investigations, the fragmentation during oblique impaction is not experimentally investigated so far. During oblique impaction a tangential velocity component acts on the agglomerates leading to an increased fragmentation for the investigated agglomerate structures (with D_f?=?1.6, 1.8, 2.3, 2.6 and 3.0). For the agglomerates with D_f?=?1.6. 1.8, 2.3 and 2.6 the degree of fragmentation can be described with the Weibull-statistics using the tangential impact velocity. This shows that the fragmentation during oblique impaction is determined by the tangential velocity component. The reason for the differing behavior of spherical agglomerates could not be elucidated but it is hypothesized, that a transition from sliding to rolling during the impact occurs affecting the fragmentation behavior.The breakage pattern is obtained by analyzing the fragment size distribution as a function of the impact energy. For agglomerates with fractal dimensions of D_f?=?1.6, 1.8, 2.3 and 2.6 a broad size distribution is observed containing small clusters/primary particles, bigger fragments and intact agglomerates at low impact energies. Increasing the impact energy shifts the whole fragment size distribution to smaller sizes. A nearly total disintegration at high impact energies is reached. The spherical agglomerates fracture into nearly equal sized fragments resulting in a narrower size distribution, which is shifted to smaller sizes at higher impact energies.