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We conducted four sets of impact experiments using sedimentary rock targets and three different kinds of projectiles at a variety of impact angles in order to examine how the density of a projectile affects the dimensions of a cra...
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We conducted four sets of impact experiments using sedimentary rock targets and three different kinds of projectiles at a variety of impact angles in order to examine how the density of a projectile affects the dimensions of a crater as the angle of impact decreases, the threshold angle for the formation of elliptical craters, and the threshold angle for the formation of pits. The crater profiles, crater volume, equivalent diameter, length, width, depth, and ellipticity of each set were carefully measured to be used in comparison with small craters that formed on the weak rocky surfaces of planetary bodies. The results indicate that the crater volume, equivalent diameter, width, and depth decrease with the impact angle, while the length of the crater within a set does not decrease monotonically with impact angle. This trend in crater length is consistent with the results of previous studies. Although craters formed at higher impact angles have a central pit, the pit becomes unclear and eventually disappears as the impact angle decreases. A larger threshold angle is required for the formation of pits at slower impact velocity than at higher impact velocity. Our results suggest that the presence of a central pit is indicative of impacts at higher angles and/or higher velocity. The ratio of the volume of craters resulting from oblique impacts to that of craters formed by normal impacts was proportional to the power of the sine of the impact angle. The power index was found to range between 1.46 and 2.20, with an average of 1.57. Comparison of the averaged power index to the power index of the p-group crater scaling rules, it is experimentally suggested that the hypothesis indicating that the vertical velocity component controls crater formation is plausible on a brittle target. The threshold angles for the formation of elliptical craters for three different kind of projectiles were almost consistent with those obtained in previous studies. Our results strongly suggested that the threshold angle for the formation of elliptical craters for high-density impactor, such as iron meteorites, are higher than for rocky impactors. We then obtained a relationship between the threshold angle for the formation of pits and the cratering efficiency. It is revealed that the threshold angle for the formation of pits is greater than the threshold angle for the formation of elliptical craters, when the cratering efficiency is in the range 7-30. A well-developed pit-spall structure in the crater may be used to indicate both, the impact angle and the vertical component of the impact velocity.
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A method for establishing the shock conditions in two solids resulting from an oblique impact of one solid onto the other is presented. The theoretical development is limited to impacts that produce attached shocks in the two soli...
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A method for establishing the shock conditions in two solids resulting from an oblique impact of one solid onto the other is presented. The theoretical development is limited to impacts that produce attached shocks in the two solids. Five non-linear equations are deduced which must be solved simultaneously with a numeric solver function such as MATLAB's 'fsolve' function. Multiple impact scenarios between two solids over a range of obliquities are analyzed and compared to CTE hydrocode predictions and normal impact Rankine-Hugoniot theory to verify the approach.
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The effect of impactor obliquity and shape on crater evolution for a typical celestial impact event is examined in this numerical study. An important overall finding is that for a given obliquity angle, crater volume is not indepe...
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The effect of impactor obliquity and shape on crater evolution for a typical celestial impact event is examined in this numerical study. An important overall finding is that for a given obliquity angle, crater volume is not independent of impactor shape. The most varied behavior occurs at large obliquity angles, where the crater crest becomes highly elliptical and the ejecta pattern exhibits characteristic butterfly wings. Impacts at large obliquity angles can also produce craters with roughly equivalent dimensions from a wide range of impactor shapes and volumes. Conventional energy scaling can be applied to these results at moderate obliquities if the energy based on the vertical component of the velocity is used. For example, for a given impactor shape the crater volume scales with this energy and the depth with the cube root of this energy. However, at large obliquities, these relationships are invalid. Applying these results to the meteor crater at Odessa [Littlefield DL, Bauman PT, Molineux A. Analysis of formation of the Odessa Crater. Int J Impact Eng, accepted for publication.], some interesting conjectures can be made. First, the small depth-to-diameter ratio of that particular crater suggests that the impact occurred at a large obliquity angle, with a trajectory extending from the southwest to the northeast. Second, the circular entrance hole and the absence of additional impact craters along this trajectory suggest that the meteor may have been either disk-like or highly elliptical in shape.
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The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into accou...
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The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggested model is capable of describing oblique impacts of spherical bodies, which can be important in many applications, including dynamical simulation of granular materials. We find that the behaviour of the bouncing fly-wheel is sensitive to the initial conditions, and the escape time plots are used to illustrate this observation.
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It is difficult to examine the interior of a solid ball to determine what happens when it bounces. A soft rubber disk was used as a substitute, impacting on edge, to film the two-dimensional deformation of the disk versus time. Th...
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It is difficult to examine the interior of a solid ball to determine what happens when it bounces. A soft rubber disk was used as a substitute, impacting on edge, to film the two-dimensional deformation of the disk versus time. The disk bounced in a similar manner to a rubber ball. Results are presented for oblique as well as vertical impacts. The results provide an explanation of the puzzling feature that an obliquely incident ball can 'overspin' without losing its grip on the bounce surface. That is, the rebound angular velocity, omega, can be larger than v(x)/R despite the fact that omega must be equal to v(x)/R in order for a ball or a disk to maintain its grip. The explanation is that the upper and lower parts of a ball or disk rotate at different angular velocities during an oblique impact.
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This paper describes a computationally aided design process of a thin wall structure subject to dynamic compression in both axial and oblique directions. Several different cross sectional shapes of thin walled structures subjected...
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This paper describes a computationally aided design process of a thin wall structure subject to dynamic compression in both axial and oblique directions. Several different cross sectional shapes of thin walled structures subjected to direct and oblique loads were compared initially to obtain the cross section that fulfills the performance criteria. The selection was based on multi-criteria decision making (MCDM) process. The performance parameters used are the absorbed crash energy, crush force efficiency, ease of manufacture and cost. Once the cross section was selected, the design was further enhanced for better crash performances by investigating the effect of foam filling, increasing the wall thickness and by introducing a trigger mechanism. The outcome of the design process was very encouraging as the new design was able to improve the crash performance by an average of 10%.
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Target hole sizes and geometries were measured for a series of highly oblique hy- pervelocity impact of steel spheres against thin laminated targets. The impact velocity was nominally 4.6 km/s for most of the experiments with a fe...
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Target hole sizes and geometries were measured for a series of highly oblique hy- pervelocity impact of steel spheres against thin laminated targets. The impact velocity was nominally 4.6 km/s for most of the experiments with a few tests conducted at 7.3 km/s. Impact obliquity ranged form 60 deg. To 80 deg from the normal to the target plane. Projectiles were stainless steel spheres with masses of 222 g, 25 g, and 1 g. Targets were laminated MX-2600 silica phenolic bonded to a 2024-T3 substrate. Target thickness, t, was varied to give thickness to projectile diameter, d, ratios of t/d=0.6 and 0.3 for each projectile. CTH Eulerian wavecode calculations of selected tests were performed to improve our understanding of the experimental results.
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A general impact friction model with application to solid particle erosion is presented. The modeltreats the friction coefficient as a function of the impact process and the initial impact angle. Theproposed friction model for mea...
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A general impact friction model with application to solid particle erosion is presented. The modeltreats the friction coefficient as a function of the impact process and the initial impact angle. Theproposed friction model for mean particle erosion has a significant influence on the tangential workdone by the abrasive, and has less influence on the normal work. The characteristic impact angle atwhich the erosion reaches maximum can be determined by numerical calculation. The computationalmean particle erosion model is effective in simulating the erosion rate obtained by experiments.
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Oblique impacts produce asymmetric damage patterns due to asymmetric, directed shock waves; these patterns are seen for both laboratory and planetary scale craters [1,2]. Previous laboratory and computational studies of impact-ind...
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Oblique impacts produce asymmetric damage patterns due to asymmetric, directed shock waves; these patterns are seen for both laboratory and planetary scale craters [1,2]. Previous laboratory and computational studies of impact-induced damaged have focused mainly on tensile failure following hyperve-locity impacts. Though extension plays a significant role in impact-induced damage, it is widely accepted that shear failure also occurs during hypervelocity impacts. Shear failure occurs over a variety of scales both during and after impacts [3—5]. Here we examine this process in more detail for oblique impacts. Experiments not only provide a general view of small-scale processes (including damage patterns in their final form), but also can be difficult to relate to larger impacts with confidence, even though similarities can be documented [e.g. 1]. Detailed computer models provide complementary information. Although they detail underlying processes during crater formation, they do not always contain adequate constitutive models, thereby requiring simplifying assumptions. A comprehensive model taking into account deformation following failure of rocks is still unavailable, which limits conclusions based solely on numerical simulations. Consequently, a combination of models and experiments must be used. Impact experiments into planar porymethylmethacrylate (PMMA) targets at small scale are examined in an attempt to constrain the sequence, location and style of failure. Two- and three-dimensional CTH models (with identical conditions to the experiments) were computed using a variety of failure criteria in order to determine the parameter set that best matches the experimental results. High-speed imaging recorded the sequence and location of failure within various PMMA targets, which was then compared with results from theoretical models. The CTH models provide critical details about specific failure style and indicate only minimal failure due to extension following the impact except for tensile failure at the base of the block. Instead, shear failure dominates below the crater. While the CTH hydrocode models generally match the extent of the damaged region, some differences remain. Projectile properties (density, composition, size) for impacts with the same kinetic energy affect the extent, style, and growth of damage in a given target. This includes differences in degree of uprange damage, subarcuate fractures, and sub-parallel failure planes. Comparisons between experiment and hydrocode results reveal that projectile failure (even at hypervelocity) contributes to the observed differences.
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Given that the Earth's surface is covered in around two-thirds water, the majority of impact events should have Occurred in marine environments. However, with the presence of a water layer, crater formation may be prohibited. Inde...
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Given that the Earth's surface is covered in around two-thirds water, the majority of impact events should have Occurred in marine environments. However, with the presence of a water layer, crater formation may be prohibited. Indeed, formation is greatly controlled by the water depth to projectile diameter ratio, as discussed in this paper. Previous work has shown that the underlying target material also influences crater formation (e.g., Gault and Sonett 1982; Baldwin et al. 2007). In addition to the above parameters we also show the influence of impact angle, impact velocity and projectile density for a variety of water depths on crater formation and projectile survivability. The limiting ratio of water depth to projectile diameter oil cratering represents the point at which the projectile is significantly slowed by transit through the water layer to reduce the impact energy to that which prohibits cratering. We therefore study the velocity decay produced by a water layer using laboratory, analytical and numerical modelling techniques, and determine the peak pressures endured by the projectile. For an impact into a water depth five times the projectile diameter, the velocity of the projectile is found to be reduced to 26-32% its original value. For deep water impacts we find that up to 60% of the original mass of the projectile Survives in an oblique impact, where survivability is defined as the solid or melted mass fraction of the projectile that could be collected after impact.
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