Experimental study on the collisional disruption of porous gypsum spheres

Abstract— In order to study the catastrophic disruption of porous bodies such as asteroids and planetesimals, we conducted several impact experiments using porous gypsum spheres (porosity: 50%). We investigated the fragment mass and velocity of disrupted gypsum spheres over a wide range of specific energies from 3 times 10³ J/kg to 5 times 10⁴ J/kg. We compared the largest fragment mass (m₁/M_t) and the antipodal velocity (V_a) of gypsum with those of non‐porous materials such as basalt and ice. The results showed that the impact strength of gypsum was notably higher than that of the non‐porous bodies; however, the fragment velocity of gypsum was slower than that of the non‐porous bodies. This was because the micro‐pores dispersed in the gypsum spheres caused a rapid attenuation of shock pressure in them. From these results, we expect that the collisional disruption of porous bodies could be significantly different from that of non‐porous bodies.     

Numerical simulations of impacts involving porous bodies: II. Comparison with laboratory experiments

In this paper, we compare the outcome of high-velocity impact experiments on porous targets, composed of pumice, with the results of simulations by a 3D SPH hydrocode in which a porosity model has been implemented. The different populations of small bodies of our Solar System are believed to be composed, at least partially, of objects with a high degree of porosity. To describe the fragmentation of such porous objects, a different model is needed than that used for non-porous bodies. In the case of porous bodies, the impact process is not only driven by the presence of cracks which propagate when a stress threshold is reached, it is also influenced by the crushing of pores and compaction. Such processes can greatly affect the whole body's response to an impact. Therefore, another physical model is necessary to improve our understanding of the collisional process involving porous bodies. Such a model has been developed recently and introduced successfully in a 3D SPH hydrocode [Jutzi, M., Benz, W., Michel, P., 2008. Icarus 198, 242-255]. Basic tests have been performed which already showed that it is implemented in a consistent way and that theoretical solutions are well reproduced. However, its full validation requires that it is also capable of reproducing the results of real laboratory impact experiments. Here we present simulations of laboratory experiments on pumice targets for which several of the main material properties have been measured. We show that using the measured material properties and keeping the remaining free parameters fixed, our numerical model is able to reproduce the outcome of these experiments carried out under different impact conditions. This first complete validation of our model, which will be tested for other porous materials in the future, allows us to start addressing problems at larger scale related to small bodies of our Solar System, such as collisions in the Kuiper Belt or the formation of a family by the disruption of a porous parent body in the main asteroid belt.     

Experimental study on collisional disruption of highly porous icy bodies

Knowing the collisional process among small porous icy bodies in the outer solar system is a key to understanding the formation of EKBOs and the evolution of icy planetesimals. Impact experiments of sintered porous ice spheres with 40%, 50%, 60% and 70% porosity were conducted by using three types of projectiles at the impact velocity from 2.4 to 489 m/s, and we studied the effects of porosity on the collisional processes. Projectile sticking occurred at the impact velocity higher than 44 m/s for 60% porosity targets and higher than 13 m/s for 70% porosity targets. The antipodal velocity of the porous ice target increased with the increase of energy density, Q, and it increased slightly with the increase of porosity, although it was exceptionally high in cases when the projectile penetrated the target. The shattering strength of porous ice targets was found to decrease from 100 to 31 J/kg with the increase of porosity from 40% to 70%. The cumulative fragment mass distribution was found to depend on the energy density and the target porosity, and the slopes of the distribution in the small fragment region were almost flat for more porous targets. We reanalyzed the cumulative fragment mass distribution and first obtained the empirical equation showing the fragment mass distribution of porous ice targets as a function of the energy density and the porosity.     

A strain-based porosity model for use in hydrocode simulations of impacts and implications for transient crater growth in porous targets

Numerical modelling of impact cratering has reached a high degree of sophistication; however, the treatment of porous materials still poses a large problem in hydrocode calculations. We present a novel approach for dealing with porous compaction in numerical modelling of impact crater formation. In contrast to previous attempts (e.g., P-alpha model, snowplow model), our model accounts for the collapse of pore space by assuming that the compaction function depends upon volumetric strain rather than pressure. Our new ?-alpha model requires only four input parameters and each has a physical meaning. The model is simple and intuitive and shows good agreement with a wide variety of experimental data, ranging from static compaction tests to highly dynamic impact experiments. Our major objective in developing the model is to investigate the effect of porosity and internal friction on transient crater formation. We present preliminary numerical model results that suggest that both porosity and internal friction play an important role in limiting crater growth over a large range in gravity-scaled source size.     

Low-velocity collisions between centimeter-sized snowballs: Porosity dependence of coefficient of restitution for ice aggregates analogues in the Solar System

Understanding the collisional behavior of ice dust aggregates at low velocity is a key to determining the formation process of small icy bodies such as icy planetesimals, comets and icy satellites, and this collisional behavior is also closely related to the energy dissipation mechanism in Saturn’s rings. We performed head-on collision experiments in air by means of free-falling centimeter-sized sintered snowballs with porosities from 44% to 80% at impact velocities from 0.44 m s^?1 to 4.12 m s^?1 at ?10 °C. In cases of porosity larger than 70%, impact sticking was the dominant collision outcome, while bouncing was dominant at lower porosity. Coefficients of restitution of snow in this velocity range were found to depend strongly on the porosity rather than the impact velocity and to decrease with the increase of the porosity. We successfully measured the compaction volume of snowballs after the impact, and it enabled us to estimate the dynamic compressive strength of snow with the assumption of the energy conservation between kinetic energy and work for deformation, which was found to be consistent with the upper limit of static compressive strength. The velocity dependence of coefficients of restitution of snow was analyzed using a Johnson’s model, and a diagram for collision outcomes among equal-sized sintered snowballs was successfully drawn as a function of porosity and impact velocity.     

Fragment properties at the catastrophic disruption threshold: The effect of the parent body’s internal structure

Numerical simulations of asteroid breakups, including both the fragmentation of the parent body and the gravitational interactions between the fragments, have allowed us to reproduce successfully the main properties of asteroid families formed in different regimes of impact energy, starting from a non-porous parent body. In this paper, using the same approach, we concentrate on a single regime of impact energy, the so-called catastrophic threshold usually designated by , which results in the escape of half of the target’s mass. Thanks to our recent implementation of a model of fragmentation of porous materials, we can characterize for both porous and non-porous targets with a wide range of diameters. We can then analyze the potential influence of porosity on the value of , and by computing the gravitational phase of the collision in the gravity regime, we can characterize the collisional outcome in terms of the fragment size and ejection speed distributions, which are the main outcome properties used by collisional models to study the evolutions of the different populations of small bodies. We also check the dependency of on the impact speed of the projectile.In the strength regime, which corresponds to target sizes below a few hundreds of meters, we find that porous targets are more difficult to disrupt than non-porous ones. In the gravity regime, the outcome is controlled purely by gravity and porosity in the case of porous targets. In the case of non-porous targets, the outcome also depends on strength. Indeed, decreasing the strength of non-porous targets make them easier to disrupt in this regime, while increasing the strength of porous targets has much less influence on the value of . Therefore, one cannot say that non-porous targets are systematically easier or more difficult to disrupt than porous ones, as the outcome highly depends on the assumed strength values. In the gravity regime, we also confirm that the process of gravitational reaccumulation is at the origin of the largest remnant’s mass in both cases. We then propose some power-law relationships between and both target’s size and impact speed that can be used in collisional evolution models. The resulting fragment size distributions can also be reasonably fitted by a power-law whose exponent ranges between −2.2 and −2.7 for all target diameters in both cases and independently on the impact velocity (at least in the small range investigated between 3 and 5 km/s). Then, although ejection velocities in the gravity regime tend to be higher from porous targets, they remain on the same order as the ones from non-porous targets.     

Experimental determination of the coefficient of restitution for meter-scale granite spheres

We present results of a series of large-scale experiments to measure the coefficient of restitution for 1-m-diameter rocky bodies in impacts with collision speeds up to ∼1.5 m s⁻¹. The experiments were conducted in an outdoor setting, with two 40-ton cranes used to suspend the ∼1300-kg granite spheres pendulum-style in mutual contact at the bottoms of their respective paths of motion. The spheres were displaced up to ∼1 m from their rest positions and allowed to impact each other in normal-incidence collisions at relative speeds up to ∼1.5 m s⁻¹. Video data from 66 normal-incidence impacts suggest a value for the coefficient of restitution of 0.83 ± 0.06 for collisions between ∼1-m-scale spheres at speeds of order 1 m s⁻¹. No clear trend of coefficient of restitution with impact speed is discernable in the data.     

Cratering of icy targets by different impactors: Laboratory experiments and implications for cratering in the Solar System

Studies of impacts (impactor velocity about 5 km s⁻¹) on icy targets were performed. The prime goal was to study the response of solid CO₂ targets to impacts and to find the differences between the results of impacts on CO₂ targets with those on H₂O ice targets. The crater dimensions in CO₂ ice were found to scale with impact energy, with little dependence on projectile density (which ranged from nylon to copper, i.e., 1150-8930 kg m⁻³). At equal temperatures, craters in CO₂ ice were the same diameter as those in water ice, but were shallower and smaller in volume. In addition, the shape of the radial profiles of the craters was found to depend strongly on the type of ice and to change with impact energy. The impact speed of the data is comparable to that for impacts on many types of icy bodies in the outer Solar System (e.g., the satellites of the giant planets, the cometary nuclei and the Kuiper Belt objects), but the size and thus energy of the impactors is lower. Scaling with impact energy is demonstrated for the impacts on CO₂ ice. The issue of impact disruption (rather than cratering) is discussed by analogy with that on water ice. Expressions for the critical energy density for the onset of disruption rather than cratering are established for water ice as a function of porosity and silicate content. Although the critical energy density for disruption of CO₂ ice is not established, it is argued that the critical energy to disrupt a CO₂ ice body will be greater than that for a (non-porous) water ice body of the similar mass.     

On the collisional disruption of porous icy targets simulating Kuiper belt objects

We present results from 27 impact experiments using porous (porosity ranging from 0.39 to 0.54) ice targets and solid ice projectiles at impact speeds ranging from 90 to 155 m/s. These targets were designed to simulate Kuiper Belt Objects (KBOs) in structure. We measured a specific energy for shattering, , of 2.1×¹⁰⁵ erg/g for those snowball targets hit by intact ice projectiles; this is of the same order as that measured for solid ice targets. The fragment mass distribution follows a power law, although the exponent is not simply related to the largest fragment size as assumed by fragmentation models. We provide the first measurement of the three-dimensional mass-velocity distribution for disrupted ice targets and find that fragment speeds range from ∼2 to ∼20 m/s. The fraction of collisional kinetic energy that is partitioned into ejecta speeds is between 1 and 15% (although it should be noted that the lower limit is more reliable than the upper).     

Impact cratering on porous asteroids

The increasing evidence that many or even most asteroids are rubble piles underscores the need to understand how porous structures respond to impact. Experiments are reported in which craters are formed in porous, crushable, silicate materials by impacts at 2 km/s. Target porosity ranged from 34 to 96%. The experiments were performed at elevated acceleration on a centrifuge to provide similarity conditions that reproduce the physics of the formation of asteroid craters as large as several tens of kilometers in diameter.Crater and ejecta blanket formation in these highly porous materials is found to be markedly different from that observed in typical dry soils of low or moderate porosity. In highly porous materials, the compaction of the target material introduces a new cratering mechanism. The ejection velocities are substantially lower than those for impacts in less porous materials. The experiments imply that, while small craters on porous asteroids should produce ejecta blankets in the usual fashion, large craters form without ejecta blankets. In large impacts, most of the ejected material never escapes the crater. However, a significant crater bowl remains because of the volume created by permanent compaction of the target material. Over time, multiple cratering events can significantly increase the global density of an asteroid.     

Propagation of impact‐induced shock waves in porous sandstone using mesoscale modeling

Generation and propagation of shock waves by meteorite impact is significantly affected by material properties such as porosity, water content, and strength. The objective of this work was to quantify processes related to the shock‐induced compaction of pore space by numerical modeling, and compare the results with data obtained in the framework of the Multidisciplinary Experimental and Modeling Impact Research Network (MEMIN) impact experiments. We use mesoscale models resolving the collapse of individual pores to validate macroscopic (homogenized) approaches describing the bulk behavior of porous and water‐saturated materials in large‐scale models of crater formation, and to quantify localized shock amplification as a result of pore space crushing. We carried out a suite of numerical models of planar shock wave propagation through a well‐defined area (the “sample”) of porous and/or water‐saturated material. The porous sample is either represented by a homogeneous unit where porosity is treated as a state variable (macroscale model) and water content by an equation of state for mixed material (ANEOS) or by a defined number of individually resolved pores (mesoscale model). We varied porosity and water content and measured thermodynamic parameters such as shock wave velocity and particle velocity on meso‐ and macroscales in separate simulations. The mesoscale models provide additional data on the heterogeneous distribution of peak shock pressures as a consequence of the complex superposition of reflecting rarefaction waves and shock waves originating from the crushing of pores. We quantify the bulk effect of porosity, the reduction in shock pressure, in terms of Hugoniot data as a function of porosity, water content, and strength of a quartzite matrix. We find a good agreement between meso‐, macroscale models and Hugoniot data from shock experiments. We also propose a combination of a porosity compaction model (ε–α model) that was previously only used for porous materials and the ANEOS for water‐saturated quartzite (all pore space is filled with water) to describe the behavior of partially water‐saturated material during shock compression. Localized amplification of shock pressures results from pore collapse and can reach as much as four times the average shock pressure in the porous sample. This may explain the often observed localized high shock pressure phases next to more or less unshocked grains in impactites and meteorites.     

Evidence for an impact‐induced magnetic fabric in Allende,and exogenous alternatives to the core dynamo theory for Allende magnetization

We conducted a paleomagnetic study of the matrix of Allende CV3 chondritic meteorite, isolating the matrix's primary remanent magnetization, measuring its magnetic fabric and estimating the ancient magnetic field intensity. A strong planar magnetic fabric was identified; the remanent magnetization of the matrix was aligned within this plane, suggesting a mechanism relating the magnetic fabric and remanence. The intensity of the matrix's remanent magnetization was found to be consistent and low (~6 μT). The primary magnetic mineral was found to be pyrrhotite. Given the thermal history of Allende, we conclude that the remanent magnetization was formed during or after an impact event. Recent mesoscale impact modeling, where chondrules and matrix are resolved, has shown that low‐velocity collisions can generate significant matrix temperatures, as pore‐space compaction attenuates shock energy and dramatically increases the amount of heating. Nonporous chondrules are unaffected, and act as heat‐sinks, so matrix temperature excursions are brief. We extend this work to model Allende, and show that a 1 km/s planar impact generates bulk porosity, matrix porosity, and fabric in our target that match the observed values. Bimodal mixtures of a highly porous matrix and nominally zero‐porosity chondrules make chondrites uniquely capable of recording transient or unstable fields. Targets that have uniform porosity, e.g., terrestrial impact craters, will not record transient or unstable fields. Rather than a core dynamo, it is therefore possible that the origin of the magnetic field in Allende was the impact itself, or a nebula field recorded during transient impact heating.     

Restitution coefficients and sticking velocities of a chondrule analogue colliding on a porous silica layer at impact velocities between 0.1 and 80 m s−1

To study the accretional growth of rimmed chondrules and their agglomerates in the solar nebula, we measured the restitution coefficients, ε, and the sticking velocities to a porous silica layer, v_c, by impacting the silica layer with a glass ball at velocities from 0.1 to 80 m s^?1. We used a porous silica layer covering a basalt block with thicknesses ranging from 1/5 of the glass ball radius to equal to the glass ball radius as a rimmed chondrule analogue, and the porosity of the silica layer was set to be 70%, 80%, 85%, and 90%. Collisional experiments were conducted by means of the free fall method or by the use of a spring gun or a gas gun, allowing us to vary the impact velocity. We used a laser displacement meter to estimate the impact and rebound velocities as well as the acceleration during the collision at impact velocities below 1 m s^?1. As a result, the sticking velocity, v_c, of 90%- and 85%- porosity layers with a thickness equal to 1/2 of the glass ball diameter was 0.44 and 2.4 m s^?1, respectively. On the other hand, we found a distinct barrier to sticking for smaller-porosity layers: the silicate layer with a porosity smaller than 80% never exhibited sticking at any impact velocity below 1 m s^?1. Instead, we observed a rebound effect with restitution coefficients larger than 0.2. In the case of a silica layer with a porosity smaller than 80%, we observed the sub-sticking condition defined by ε < 0.1 at velocities extending from 5 m s^?1 to 70 m s^?1.     

Impact Experiments on Porous Icy-Silicate Cylindrical Blocks and the Implication for Disruption and Accumulation of Small Icy Bodies

Impact strength and cratering ejecta were studied for porous targets of pure ice and icy-silicate mixture in order to clarify the accumulation and destruction (shattering) condition of small icy bodies. The icy projectile impacted on the cylindrical targets with the porosity up to 55% at a velocity of 150 to 670 m/s at −10°C. The porosity dependence of the impact strength and that of the maximum ejecta velocity were measured in each type of these targets. As a result, the maximum ejecta velocity normalized by the impact velocity (V_e-max/V_i) is found to depend only on the porosity (φ), irrespective of the target type; a relationship is derived to be V_e-max/V_i=−2.17φ+1.29. The impact strength of pure ice increased with increased target porosity, but that of mixture target had an opposite trend; that is, the strength decreased with increased porosity. These porosity dependencies of the impact strength could be explained by the porosity dependence of the physical parameters such as impact pressure, pressure decay, and static strength. Finally, the accumulation of small icy bodies is discussed to show that the collisional events can be divided into three types by the porosity and the collision velocity according to our experimental results: mass loss, rubble pile formation, and regolith formation (compaction).     

Subsurface deformation in hypervelocity cratering experiments into high‐porosity tuffs

Hypervelocity impact experiments on porous tuff targets were carried out to determine the effect of porosity on deformation mechanisms in the crater's subsurface. Blocks of Weibern Tuff with about 43% porosity were impacted by 2.5 mm and 12.0 mm diameter steel spheres with velocities between 4.8 km s^?1 and 5.6 km s^?1. The postimpact subsurface damage was quantified with computer tomography as well as with meso‐ and microscale analyses of the bisected crater subsurface. The intensity and style of deformation in mineral clasts and the tuff matrix were mapped and their decay with subsurface depth was determined. Subsurface deformation styles include pore space compaction, clast rotation, as well as microfracture formation. Evaluation of the deformation indicates near‐surface energy coupling at a calculated depth of burial of ~2 projectile diameters (d_p), which is in conflict with the crater shape, which displays a deep, central penetration tube. Subsurface damage extends to ~2 d_p beneath the crater floor in the experiments with 2.5 mm projectiles and increases to ~3 d_p for 12 mm projectiles. Based on overprinting relationships and the geometrical orientation of deformation features, a sequence of subsurface deformation events was derived (1) matrix compaction, (2) intragranular crack formation in clasts, (3) deformation band formation in the compacted matrix, (4) tensile fracturing.     

The Asteroid Veritas: An intruder in a family named after it?

The Veritas family is located in the outer main belt and is named after its apparent largest constituent, Asteroid (490) Veritas. The family age has been estimated by two independent studies to be quite young, around 8 Myr. Therefore, current properties of the family may retain signatures of the catastrophic disruption event that formed the family. In this paper, we report on our investigation of the formation of the Veritas family via numerical simulations of catastrophic disruption of a 140-km-diameter parent body, which was considered to be made of either porous or non-porous material, and a projectile impacting at 3 or 5 km/s with an impact angle of 0° or 45°. Not one of these simulations was able to produce satisfactorily the estimated size distribution of real family members. Based on previous studies devoted to either the dynamics or the spectral properties of the Veritas family, which already treated (490) Veritas as a special object that may be disconnected from the family, we simulated the formation of a family consisting of all members except that asteroid. For that case, the parent body was smaller (112 km in diameter), and we found a remarkable match between the simulation outcome, using a porous parent body, and the real family. Both the size distribution and the velocity dispersion of the real reduced family are very well reproduced. On the other hand, the disruption of a non-porous parent body does not reproduce the observed properties very well. This is consistent with the spectral C-type of family members, which suggests that the parent body was porous and shows the importance of modeling the effect of this porosity in the fragmentation process, even if the largest members are produced by gravitational reaccumulation during the subsequent gravitational phase. As a result of our investigations, we conclude that it is very likely that the Asteroid (490) Veritas and probably several other small members do not belong to the family as originally defined, and that the definition of this family should be revised. Further investigations will be performed to better constrain the definitions and properties of other asteroid families of different types, using the appropriate model of fragmentation. The identification of very young families in turn will continue to serve as a tool to check the validity of numerical models.     

Ejecta fragmentation in impacts into gypsum and water ice

Using the light gas gun at the Open University’s Hypervelocity Impact facility, a series of impact experiments exploring impacts into water ice and gypsum have been performed. Fragmentation of solid ejecta was recorded using two different methods, analysed and compared with the total ejecta. Preliminary results show that the size distribution of the ejecta fragments from water ice is very similar to those from gypsum. These results also represent a step towards a better understanding of ejecta fragmentation in geological materials, including icy surfaces in the Solar System.     

Ice-silicate fractionation among icy bodies due to the difference of impact strength between ice and ice-silicate mixture

Laboratory experiments on the impact disruption of ice-silicate mixtures were conducted to clarify the accretion process of small icy bodies. Since the icy bodies are composed of ice and silicates with various porosities, we investigated the effect of porosity on the impact disruption of mixtures. We tested the mixture target with the mass ratio of ice to silicate, 0.5 and with 5 different porosities (0, 12.5, 25, 32, 37%) at the impact velocities of 150 to 670 m/s. The silicate mass ratio was changed from 0 to 0.5 in steps of 0.1 at a porosity of 12.5% and a constant impact velocity of about 300 m/s. The impact strength of the mixture was found to decrease with increasing porosity and the silicate mass ratio between 0.1 and 0.5 could enhance the strength of the icy target. The observed dependence of the impact strength on the porosity is opposite to that observed for pure ice. This difference could play an important role in ice-silicate fractionation during the accretion process. Because, ice rich bodies are easily broken as the porosity decreases in their evolution, the collisional growth could be prohibited. On the other hand, among the silicate rich bodies the collisional growth could be enhanced.     

Some consequences of a phase transition of water ice on the heat balance of comet nuclei

We consider spheres of water ice of about 1 km in radius moving on three different orbits with a common perihelion distance of 8 AU. As evaporation is negligible in these cases, we call them inactive ice bodies. The surface temperature has been numerically calculated for two extreme situations: (1) The spheres are composed of amorphous ice with a heat conduction to the interior presumed to be negligible. (2) The spheres are composed of compact hexagonal ice with a heat conduction coefficient known from laboratory experiments. Whereas in case 1 the temperature is an unambiguous function of heliocentric distance, in case 2 we observe a thermal “hysteresis” and the maximum temperature has a phase lag with respect to perihelion. The perihelion temperature depends on the eccentricity of the orbit. The case of active ice bodies is also discussed. We come to the conclusion that an ice body moving on the orbit of Tempel 2 must contain crystalline ice and the variations of the surface temperature must be smoothed out in an important way. In the case of Halley's orbit, we suppose that the center of the ice body still contains large amounts of amorphous ice.