ISSN 0038-0946, Solar System Research, 2017, Vol. 51, No. 1, pp. 64–85. © Pleiades Publishing, Inc., 2017. Original Russian Text © E.N. Slyuta, 2017, published in Astronomicheskii Vestnik, 2017, Vol. 51, No. 1, pp. 72–95.
Physical and Mechanical Properties of Stony Meteorites E. N. Slyuta V.I. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow, 119334 Russia e-mail:
[email protected] Received May 6, 2013; in final form, June 10, 2016
Abstract⎯The method for experimental research of physical and mechanical properties of stony meteorites is considered. Experimental data on the physical and mechanical properties of samples of three ordinary chondrites are reported. Ordinary chondrites are characterized by a well-defined three-dimensional (spatial) anisotropy of physical and mechanical properties, when a compression strength in one of the directions significantly exceeds that in the other two directions. A measured compression strength of ordinary chondrites is in the range from 105 to 203 MPa, while a tensile strength is in the range from 18 to 31 MPa. As follows from the available published data on the strength of carbonaceous chondrites, they are drastically different in properties from ordinary chondrites. The observed critical aerodynamic loads do not exceed a measured tensile strength value of ordinary chondrites, which is actually the upper limit restricting the maximum aerodynamic load for ordinary chondrites. Keywords: stony meteorites, ordinary chondrites, carbonaceous chondrites, meteoroid, bolide, strength, anisotropy of physical and mechanical properties, scale factor, and defectiveness factor DOI: 10.1134/S0038094617010051
INTRODUCTION Flight and destruction of a large meteoroid in the Earth’s upper atmosphere is accompanied by the formation of a shock wave whose propagation leads to the development of a heated radiating region and the generation of acoustic and seismic waves. The luminescence is generated not by a solid body, but by a surrounding gas envelope. Aerodynamic loading leads to destruction and deceleration of the meteoroid and the occurrence of luminosity maxima (flares) in the light curve. Thermal stresses, resulting from changes in meteoroid temperature in the Earth’s atmosphere, and due to a low thermal conductivity of meteoric stones, affect only the surface layer and lead only to flaking and surface ablation of the meteoroid in flight (Medvedev et al., 1985). For example, the stony meteoroid heating depth at a velocity of 15–60 km s–1 is 0.3–0.5 mm, while the iron meteoroid heating depth is 0.9–1.7 mm (Levin, 1956). Ablation (evaporation, melting, and blowing away of a melt film from the surface) and the formation of a melting crust on the meteorite’s surface affect the stony meteorites surface layer which is only 1–2 mm thick. Inside the meteorite, the temperature within a few seconds of deceleration in the Earth’s upper atmosphere remains constant and almost unchanged. Small meteoroids are abruptly decelerated and completely evaporated in the upper atmosphere. Large and compact meteoroids pass through the atmosphere
almost without slowing down and without substantial changes in their shape (Svetsov et al., 1995), and they can reach the height where the gas pressure in the shock layer (aerodynamic load) is comparable to the strength of the meteorite material. Large meteoroids are commonly destroyed under loads which are lower than the measured strengths of similar meteorite samples (Tsvetkov and Skripnik, 1991; Ceplecha, 1996; Popova et al., 2011). It is noted that in the case of crushing in the denser atmosphere layers, i.e., under high aerodynamic loads, many fragments are formed in a smaller dispersion ellipse, and conversely, the greater the crushing height, the smaller the number of fragments (and they are larger), and thus the larger the dispersion ellipsoid (Krinov, 1955). The meteoroid interaction with the Earthʼs atmosphere is relatively well studied, inter alia, in analytical terms (Levin, 1956; Bronshten 1981; Svetsov et al., 1995), while the crushing process, i.e., the actual meteoroid destruction, which is closely related to physical and mechanical properties of the meteoroid material, is “still known poorly” (Bronshten, 1981). The Chelyabinsk event is once again a reminder to consider this problem. Physical and mechanical properties of stony meteorites, which are studied in this work, are an essential and important component in the investigation of the large stony meteoroid destruction process. 64
PHYSICAL AND MECHANICAL PROPERTIES
SPECIFIC FEATURES IN THE INVESTIGATION OF PHYSICAL AND MECHANICAL PROPERTIES OF STONY METEORITES By elastic properties, meteorites are intermediate between earth and moon rocks (Gorshkov, 1973). The higher the meteoric stone porosity range, the greater the interval (range) of elastic wave velocities. A transversal wave velocity (vs) is characterized by linear dependence on the density of different meteorite classes (Gorshkov, 1973). The Young’s modulus of meteoric stones varies from 5.2 to 8.7 × 1010 Pa, thus corresponding to elasticity (deformation hacracteristics) of terrestrial basic rocks (Table 1). The Young’s modulus of the Tsarev Meteorite is also characterized by elevated values: (10.1–19.1) × 1010 Pa, being close to those of terrestrial peridotite ((13.0–16.0) × 1010 Pa) and olivinite ((11.7–17.5) × 1010 Pa) (Medvedev et al., 1985). The experimental Young’s modulus values of most chondrites, relative to those calculated for an average mineral composition of the polymineral aggregate with perfect intergranular relations ((19– 20) × 1010 Pa), is about 1.5–2 times lower. As in the case with thermal properties, such a considerable difference is indicative of imperfection, i.e., primitive nature of a meteorite structure (Medvedev et al., 1985), which, compared with the terrestrial rocks, is commonly called “loosely compacted”. The higher sensitivity of a compression strength and a destruction strength depending on the loading velocity (elastic strain rate) is also likely explained by the less than perfect and poorly compacted structure as compared with terrestrial rocks (Kimberly and Ramesh, 2011). Measured values of the Poisson’s ratio for chondrites are in the range of 0.15–0.29 corresponding to that of terrestrial crystalline rocks (Medvedev et al., 1985). As shown by the dependence of limiting stresses on the size of gabbro samples (Zotkin et al., 1987), the strength of the samples with a size of less than 15 mm and over 40 mm is reduced. For example, a compression strength of similar gabbro samples decreases from 270 to 145 MPa, i.e., more than 1.5 times, with an increase in their sizes from 30 to 200 mm (Medvedev, 1983). In the case of small samples, for instance, less than 10–15 cm in size, this phenomenon is explained by outcrops and the effect of certain irregularities, pores, and defects at the boundaries of some mineral grains, which are comparable in size with the sample (Nicolas, 1987). The required minimum ratio between the sample size and the mineral grain size should be at least 20–30 (Turchaninov et al., 1967). Deformation characteristics such as the Young’s modulus and Poisson’s ratio also vary depending on the size of the Tsarev Meteorite sample (Zotkin et al., 1987). Such dependence on the size of the Tsarev Meteorite samples is also characteristic of longitudinal and transverse waves vp and vs. SOLAR SYSTEM RESEARCH
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In the case of the samples more than 40 mm in size, a drop in strength is due to an increase in the number and size of large defects and cracks with an increase in the sample volume, i.e., the so-called “scale effect”. From statistical theory, the analytical dependence of a reduced strength on an increased volume for a variety of materials was considered for the first time by (Weibull, 1939, 1951), while the notion of strength was represented as a random variable specified by the distribution function of one or more parameters. If this mathematical definition of the strength is translated into the language of rock mechanics, then it can be stated that the discontinuity begins in the weakest link and does not depend on a strength of other units (Medvedev, 1974a). The scale effect on the object’s ultimate strength is determined by the following equation (Svetsov et al., 1995): α
m (1) σ = σ s ⎛⎜ s ⎞⎟ , ⎝m⎠ where σ is the strength limit for the whole object, m is the weight of this object, σs is the experimental strength limit of a sample of this object, ms is the weight, and α is a scale factor. In the case of the large stone objects (meteoroids), this factor varies within a wide range: from about 0.1 to 0.7 (Popova et al., 2011). It should be noted that an extremely wide variation and dependence on many uncertain factors prevents the use of the factor as a universal value for stone bodies and obtaining any additional information on an unknown object (strength, composition, size, defects, and previous collision history). The scale effect related to the dependence of the sample’s physical and mechanical properties on its size is possible only under uniaxial compression or tension, preferably, in laboratory experiments under uniaxial loading of samples. The geological processes are commonly dominated by a three-dimensional load (Turchaninov et al., 1967; Zharkov and Trubitsin, 1980), including a gravitational deformation of small bodies in the solar system (Slyuta and Voropaev, 1997). Hence, an optimal sample size in fine- and medium-grained rocks and meteoritic stones, at which the mechanical properties are related only to the substance’s mineral composition and structure and are just slightly dependent on other factors, is in the range from 10–15 to 40 mm. Structure defines the degree of connection between the rock mineral grains. The greatest effect is caused by the connection degree and the combination of a major (predominant) mineral and a mineral, whose properties are significantly different from those of the main mineral (Rzhevskii and Novik, 1973). Due to the selective nature of solid body fracturing (a discontinuity begins in the weakest link and does not depend on the strength of other units), the observed variations in strength properties in
SOLAR SYSTEM RESEARCH
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3.90
L6
H5
Kyushu, 2157
Pultusk, 544
2017
5150
3990
5440
6240
6970
7000
6990
4320
4900
vp
2860
2290
3090
3430
3770
4350
4300
2490
3140
vs
0.27
0.26
0.26
0.28
0.29
0.19
0.19
0.24
0.15
Poisson ratio
2.85–2.90** 6200–6300 3300–3500 0.27–0.30
(*) Medvedev, 1974b; (**) Alekseeva, 1958.
Peridotite*
3.54
Kunashak, 1723 L6
3.56
3.24
3.43
3.55
L5
L5
Tsarev, 15384а
3.52
Tsarev, 15391
L5
Tsarev, 15380а
3.50
L5
L5
Elenovka, 1831
3.25
Density, g cm–3
Tsarev, 153846
LL3
Type
Krymka, 1705
Meteorite, sample, rock
Elastic wave velocity, m s–1
8.5–9.1
7.6
5.2
8.7
10.1
19.0
16.1
15.8
5.6
7.8
Youngʼs modulus, 1010 Pa
210–230
213
98
265
157
450
–
222
20
160
σcom
31
11
49
16
54
–
26
2
22
σten
40–50
Strength, MPa
2.1
3.05
2.30
2.89
2.76
3.89
3.71
3.68
–
2.32
0.77
1.03
1.04
1.04
1.17
1.14
1.20
1.13
–
1.05
Thermal Thermal conductivity, diffusivity, W m–1 K–1 10–6 m2 s–1
Table 1. Physical, mechanical, and thermophysical properties of meteoric stones and some terrestrial rocks (Medvedev et al., 1985)
0.95
0.83
0.57
0.78
0.73
0.99
0.87
0.92
0.76*
0.68
Thermal capacity, kJ kg–1 K
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the terrestrial rock samples are considered to be acceptable if the variation coefficient does not exceed 30% (Rocks, 1975). Experience shows that substantial deviations of the variation coefficient from the allowable values are commonly related to noncompliance with experimental procedure and sample preparation requirements or to ignoring additional factors such as considering the sample orientation in the study of anisotropic rocks. Taking into consideration the aforementioned specifics of studies of the physical and mechanical properties of the rocks, it should be noted that obtaining reliable data on physical and mechanical properties requires adequate measurement statistics. And, on the contrary, comparison with single measurements can lead to a serious error, far from being a reliable result. The meteorite strength properties (compression strength σcom and tensile strength σten) given in Table 1 were studied by splitting 10 mm-thick plates with wedges followed by crushing the resulting cubes (Medvedev, 1974b; Medvedev et al., 1985). The strength data differ by almost a factor of three for three samples of the Tsarev Meteorite. The number of measurements and the variation coefficient are given only for sample No. 15384b: 25% (fourteen measurements) and 21% (seventeen measurements) for compression and tensile strengths, respectively. The work of (Zotkin et al., 1987) involves the investigation of the Tsarev Meteorite cubic samples with variable sizes and with a facet length of 10–100 mm (Table 2). A compression strength is in the range of 256–499 MPa, while a tensile strength is 43–62 MPa. Emphasis is placed primarily on a very low variation coefficient, occasionally, up to a few percent, which is commonly not typical of the rocks, and also on high strength values. It is likely related to preliminary and thorough rejection of samples by defects that is methodologically not quite right and can yield a distorted idea of a strength of this meteorite in general. For example, if only the samples with significant defects are selected, then other extreme values are obtained. It is also unknown if samples were taken from one or different fragments of the meteorite. In general, the compression strength distribution depending on the sample size is in fairly good agreement with the above-discussed idea of the optimal sample size for the study by biaxial compression and extension (Table 2). From the data, the optimal sample size is in the range of 10– 50 mm. It should be noted that the investigation of physical and mechanical properties made it possible to identify considerable and inexplicable variations in the strength properties of many fragments of the same meteorite. For example, the strength data differ by almost a factor of three for three samples of the Tsarev Meteorite (Medvedev, 1974b; Medvedev et al., 1985). SOLAR SYSTEM RESEARCH
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Table 2. Physical and mechanical properties of the Tsarev Meteorite based on the data of Zotkin et al., 1987 Sample size, mm
Variation Number Average, coefficient, of measurements MPa %
Compression strength 100 × 100 × 100 2 256 70 × 70 × 70 4 354 50 × 50 × 50 4 383 40 × 40 × 40 5 499 25 × 25 × 25 6 387 20 × 20 × 20 6 388 15 × 15 × 15 6 332 12 × 12 × 12 7 372 10 × 10 × 10 7 419 Tensile strength 50 × 50 × 50 3 43 40 × 40 × 40 3 45 25 × 25 × 25 5 52 20 × 20 × 20 6 48 15 × 15 × 15 6 56 12 × 12 × 12 8 47 10 × 10 × 10 8 62
17 3 21 12 20 17 17 23 13 17 8 7 27 11 22 17
PHYSICAL AND MECHANICAL PROPERTIES OF ORDINARY CHONDRITES The investigation involved the use of ordinary chondrite samples of the Ghubara Meteorite, the Sayh al Uhaymir 001 (SAUH 001) Meteorite, and two different fragments of the Tsarev Meteorite (Slyuta et al., 2008, 2009). Ordinary chondrites being the most common group of chondrites and meteorites in general are subdivided into three chemical subgroups such as H, L and LL, which differ in content of total iron and siderophilic elements (H > L > LL) and the ratio of oxidized iron to metal iron (H < L < LL) (Dodd, 1981). The main minerals include magnesian olivine and low-Ca pyroxene (hypersthene or bronzite), while minor minerals include nickel-iron (kamacite and taenite), acid plagioclase (oligoclase), diopside, and troilite. Accessory minerals occur as apatite, chromite, and ilmenite. A very close correspondence of regulatory mineralogy expressed as a set of anhydrous standard minerals and modal (observed) mineralogy is indicative of the fact that the water effect in the ordinary chondrite evolution was negligible (Dodd, 1981). The occurrence of chondrules in stony meteorites varies within a wide range, from well-defined to barely observed and ingrown into the matrix and vice versa. This correlation of structural and mineral variations in chondrites suggests the thermal metamorphism within parent bodies in the postaccretion period. These
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changes were termed secondary. With an increase in metamorphism, the chondrule contours become less distinct, the matrix becomes more coarse-grained, the composition of the main minerals (olivine and pyroxene) becomes more homogeneous, while the carbon content decreases. Chondrites are subdivided into seven petrological types by the nature and degree of metamorphism: from unaltered or primitive (1), which are commonly referred to as nonequilibrium, to chondrites with the greatest degree of metamorphic changes (7), which are called equilibrium (Krot et al., 2003). Under thermal metamorphism, this range is characterized by an increase in the chemical equilibrium and structural recrystallization degree. Primitive petrological types 1 and 2 are known only for carbonaceous chondrites. Chondrites of type 7 are uncommon, rare and occur as a complex mixture of highly metamorphosed and melted material (Dodd, 1981). No structural deformations characteristic of terrestrial rocks under intense metamorphism at high pressure were observed in ordinary chondrites of petrological types 3–7. No regular orientation of chondrules and other inclusions is observed, while chondrules keep a predominantly spherical undistorted form (Dodd, 1965). This fact is also confirmed by absence of minerals being indicative of high pressure (except for minerals formed in collision events). Based on the replacement of chemical elements being sensitive to pressure, it was found that the maximum static pressures which chondrites were subjected to during their evolution (except for collision loads) did not exceed 100 MPa (Heyse, 1978). By analogy with the terrestrial rock metamorphism, it is suggested that different structural types of meteorites should also be considerably different in physical and mechanical properties. This suggestion does not take into consideration the fact that terrestrial rock metamorphism is characterized by a different range of temperatures and pressures. As follows from the classification of meteorite petrological types, a pressure did not exceed 100 MPa, in other words, it did not exceed even a compression strength of ordinary chondrites. The difference is, perhaps, but hardly significant and strictly progressive, depending on the increase in the meteorite structural type. This issue can be explained only by qualitative experimental data reported in compliance with all necessary requirements and specified standards. But it will be considered below. The collisional history traces of the meteorite parent bodies as deformation and crushing of mineral grains, brecciation, and formation of veinlets are referred to as tertiary changes. Six shock stages—from S1 to S6—are distinguished by the degree of shock impact and shock metamorphism. The shock metamorphism of ordinary chondrites is related to variations in the olivine and plagioclase crystalline structure (Stoffler et al., 1991), while that of carbonaceous chondrites is related to changes in the olivine structure
(Scott et al., 1992). In enstatite chondrites, where olivine is a very rare mineral, the shock impact degree is estimated by defects in orthopyroxene crystals (Rubin et al., 1997). In contrast to the suggested progressive effect of the degree of metamorphism, the shock stages exerts an inverse influence on meteorite strength, at least in its high degrees. For example, the Chelyabinsk Meteorite, with a structural type LL5 and shock stage S4 (Galimov et al., 2013), is characterized by a high defectiveness degree and, respectively, a lower strength. Occurring on the Earth’s surface, the meteorites as well as the terrestrial rocks are subject to geochemical weathering by water, atmosphere, and biosphere (microorganisms). Seven stages of geochemical weathering are distinguished (W0–W6) (Wlotzka, 1993). The sequence of alterations in the stony meteorites due to geochemical weathering is determined in thin sections. The absence of visible oxidation of metals and sulfides corresponds to the W0 stage. No weathering is commonly characteristic of meteorites picked up right after falling. Small veinlets and oxidation films of metal and troilite are referred to the W1 stage. The oxidized metal content of 20–60% is indicative of the W2 weathering stage, while 60–95% is indicative of the W3 stage. Complete oxidation of metal and sulfides in the absence of any changes in silicates corresponds to the W4 stage. The W5 weathering degree is characterized by alterations of dark (mafic) silicates along the fractures. The last (W6) weathering stage is distinguished by comprehensive replacement of silicates by clay minerals and oxides. It should be taken into consideration that as well as in the terrestrial rocks (the higher the weathering stage, the lower the strength), weathering should also have a significant influence on changes in physical and mechanical properties of the studied meteorites. The Ghubara Meteorite is an ordinary chondrite with a petrographic type L5. The meteorite was found in 1954 in the Oman Region in the desert area. It looks very fresh and slightly affected by the terrestrial weathering processes, in other words, it is characterized by an initial stage (Grady, 2000). More accurate data on weathering stages and collision facies are not available. The Sayh al Uhaymir 001 (SAUH 001) meteoric stone rain found on March 16, 2000, is one of the largest Oman meteorite rains (Korochantsev et al., 2003). Over 2670 samples with a total weight of 450.5 kg were collected. Based on the composition, this meteorite is an ordinary chondrite with a petrographic type L4/5 (24.7 mol % fayalite and 21.4 mol % ferrosilite) and a shock stage S2. It is very important for this investigation that it is a quite recent fall slightly affected by terrestrial weathering (W1) (Korochantsev et al., 2003), which did not affect the physical and mechanical properties of the meteorite fragments. The Tsarev Meteorite is also characterized by a fine-grained uniform texture being devoid of wellSOLAR SYSTEM RESEARCH
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(a)
69
(b)
cc
(c)
bc
ac cc
bc ac
ac
cc bc
Fig. 1. Orientation of anisotropy ellipsoid of physical and mechanical properties with semiaxes aс > bс ≥ cс in the meteorite fragment: (a) SAUH 001 Meteorite; (b) Tsarev Meteorite, fragment no. 15390.9; (c) Tsarev Meteorite, fragment no. 15384.1.
defined stratification and separate bodies. The meteorite is distinguished by a bimodal distribution of integrated density of the fragments, which apparently is due to a nonuniform structure (density distribution) of the parent body. About 30% of the meteorite weight is 3.32 g cm-3 in density, and about 70% is 3.48 g cm–3 (Zotkin and Tsvetkova, 1984). No density–weight relation is characteristic of the fragments. The Tsarev stony meteoritic rain was identified in the Volgograd Region in Russia in 1968. In general, sixty-nine samples with a total weight of 1325.203 kg were collected (Slyuta, 2014). The largest fragment was 283.8 kg in weight. Based on the composition, this meteorite is ordinary chondrite L5 with an iron content of up to 20.54% (Barsukova et al., 1982). As well as Ghubara and SAUH 001, the Tsarev Meteorite is characterized by good preservation and slight weathering. Accurate data on the weathering stage and shock stage are not available. The physical and mechanical properties of the meteorites were studied by the comprehensive estimation of strength under repeated splitting and compression in accordance with the established standard (GOST 21153.4-75, Rocks, 1975). The chosen research method makes it possible to obtain sufficient measurement statistics and, therefore, sufficiently reliable data based on a relatively small amount of material, in fact, using one sample with a total size of 10–20 cm. This is very important because of the great value and limited amount of the meteoritic material. This method also appeared to be the most convenient to study the three-dimensional spatial distribution of physical and mechanical properties in a single sample. A compression strength and a tensile strength were estimated using air-dry samples with the help of CD-10 and CD-100 testing devices (VEB Werkstoffpruffmaschnen, Leipzig, Germany), making it possible to provide proportional loading in the range of maximum loads up to 10 and 100 t, respectively. The investigation was carried out in the Institute of Comprehensive SOLAR SYSTEM RESEARCH
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Exploitation of Mineral Resources, Russian Academy of Sciences. Due to the lack of sufficient material, only two plates of 22 × 37 × 62 mm in size and one cube of 20 × 20 × 20 mm were cut out from the Ghubara Meteorite’s fragment (Slyuta et al., 2008). In order to investigate physical and mechanical properties in three areas, the Sayh al Uhaymir 001 Meteorite’s fragment 9 × 10 × 12 cm in size was cut into three perpendicular plates with a thickness of 20 mm each (Fig. 1a) and one cube with sides being parallel to all three plates and a size of 40 × 40 × 40 mm. Two different fragments of the Tsarev Meteorite (nos. 15384.1 and 15390.9) were cut each into three mutually perpendicular plates with a thickness of 20 mm each and a few cubes with sides being parallel to all three plates and with a size of 40 × 40 × 40 mm (Figs. 1b, 1c). The fragment no. 15384 in its primary form represented a cone-shaped polygon with a size of 28 × 28 × 23 cm and with a weight of 24.8 kg (Slyuta, 2014). The primary fragment no. 15390 was characterized by a polyhedral elongated shape, size 50 × 38 × 31 cm, and weight 104.2 kg (Slyuta, 2014). Tensile strength was determined by splitting of sample plates with wedges with a sharpening angle of 90° with measurement of an applied load and a breaking force. A split length was determined with an error of no more than +0.5 mm with a length of at least 20 mm. Depending on size, each plate was split into cubes with a semiregular shape and a size of 20 × (20– 30) × (20–30) mm (Fig. 2). The tensile direction was perpendicular to the splitting line. Each of three plates was split into cubes in two mutually perpendicular directions. Respectively, the tensile strength was also taken into account in two different directions being parallel to common coordinate axes in the sample (for example, x and y, x and z, or y and z). A compression strength was determined by compression crushing of cubic samples with a semiregular form obtained in the course of splitting of plates after determination of the
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(a)
(b)
Fig. 2. Determination of a tensile strength by oriented splitting of plates of the Tsarev Meteorite fragment no. 15384.1 into cubes with a semiregular form: (a) plate marking; (b) plate split into cubes with a semiregular shape.
(a)
(b)
Fig. 3. Determination of a compression strength by compressive crushing of cubic samples with a semiregular shape obtained by plate splitting.
tensile strength (Fig. 3) and by compression crushing of a cube with a size of 40 × 40 × 40 mm during measurement of strain parameters. The compression axis was perpendicular to the plate plane. Stresses exceeding the compressive strength resulted in explosive fragmentation of the studied sample (Fig. 3b). This phenomenon is referred to as a rheological explosion (Gorazdovskii, 1976). The data on the physical and mechanical properties of the Ghubara Meteorite are given in Table 3. The three-dimensional distribution of physical and mechanical properties in the Ghubara Meteorite was not studied due to the lack of sufficient material. The three-dimensional spatial distribution of physical and
mechanical properties of the SAUH 001 and Tsarev samples is shown in Table 4. A compressive strength value in one of three directions is highly (1.6 times) different from the other two, which are almost equal. In all three studied samples, symbols aс, bс and cс were used to mark the coordinate axes directions from the highest to the lowest compression strength values (Fig. 1). Hence, the spatial three-dimensional distribution of a compressive strength in all three samples can be presented as a prolate ellipsoid of anisotropy with semiaxes aс > bс ≥ cс, when the compression strength is higher in one of directions (aс) relative to two other directions (bс ≥ cс). According to the experimental
Table 3. Physical and mechanical properties of the Ghubara Meteorite Name Compression strength Tensile strength
Average value, MPa
Number of measurements
Variation coefficient, %
72 24
5 5
30.7 30.5
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Table 4. Three-dimensional distribution of physical and mechanical properties in ordinary chondrites Anisotropy ellipsoid axes Name
aс
bс
cс
Average for sample
SAUH 001 Meteorite (aс/cс = 1.6) Compression strength, MPa Number of measurements Variation coefficient, % Tensile strength, MPa Number of measurements Variation coefficient, %
143 94 6 7 20 29 18 17 13 13 28 26 Tsarev Meteorite, sample no. 15390.9 (aс/cс = 1.6)
91 10 23 18 14 27
105 23 31 18 40 27
Compression strength, MPa Number of measurements Variation coefficient, % Tensile strength, MPa Number of measurements Variation coefficient, %
262 168 160 25 27 13 19 37 29 28 34 27 23 20 33 32 35 31 Tsarev Meteorite, sample no. 15384.1 (aс/cс = 1.3)
203 65 35 29 76 34
Compression strength, MPa Number of measurements Variation coefficient, % Tensile strength, MPa Number of measurements Variation coefficient, %
223 22 29 31 12 33
182 17 25 34 24 30
data, great unexplainable variations in strength properties, far beyond the allowable variation coefficients, identified in the samples of one meteorite (Medvedev et al., 1985; Zotkin et al., 1987) were caused by considerable spatial anisotropy of these properties. Along the anisotropy ellipsoid axes, the data are in the normal range, i.e., within the acceptable variation coefficients (Table 4). In the SAUH 001 sample, the distribution of tensile strength values, in contrast to the compression strength, is almost isotropic and can be approximated by a pattern similar to a sphere (Table 4). The distribution of tensile strength values in both Tsarev samples differs by 15–20% in one of directions, likely also due to anisotropy (Table 4). The SAUH 001 fragment had a rounded and elongated form and a size of 9 × 10 × 12 cm. The number of measurements corresponded to the number of cubes with a semiregular shape obtained from a plate and subjected to compression and destruction (Table 4). The smallest plate with the lowest number of compression strength measurements was oriented perpendicular to the longest axis of the meteorite sample pattern (Fig. 1a). Hence, in this meteorite fragment, the long axis а of the fragment pattern is consistent with the SOLAR SYSTEM RESEARCH
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174 20 29 29 25 42
194 59 30 31 61 35
direction ас of the anisotropy ellipsoid, i.e., with the long semiaxis of its ellipsoid. The long axis а of the Tsarev fragment no. 15390 (50 × 38 × 31 cm) pattern, reaching 50 cm, is also evidently consistent with the maximum direction ас of the anisotropy ellipsoid (Table 4). The Tsarev fragment No. 15384 was polygonal in form with the axes a = b < c (28 × 28 × 23 cm), and thus it was impossible, in contrast to the previous fragments, to orient accurately the section scheme relative to major axes of the fragment pattern. The sample was cut at an angle to the primary (“sunburn” crust) surface of the fragment being a pyramid base relative to the plane of the previous cutting plane. Considerable difference between the lowest values (bс and cс) of the compression strength in this sample and their higher level relative to bс and cс of the sample no. 15390.9 are likely indicative of the fact that a real orientation of the anisotropy ellipsoid in this sample differs from the obtained anisotropy ellipsoid. This suggestion is also confirmed by the lower anisotropy value (ас/cс = 1.3) relative to the anisotropy value in the sample no. 15390.9 (ас/cс = 1.6). On the other hand, it can be assumed that a more isometric form of the fragment (28 × 28 × 23 cm) is a result of lower anisotropy in this
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sample. It should be noted that SAUH 001 and Tsarev meteorites are characterized by the same anisotropy value, although the compressive strength of these samples is different almost doubled (Table 4). At least, this is true with respect to the Tsarev sample no. 15390.9, where the anisotropy ellipsoid orientation is also evidently consistent with the orientation of major axes of the fragment’s primary form. The observed spatial anisotropy of ordinary chondrites is approximated, on average, by a prolate ellipsoid with the following ratio of the semimajor axes: а : (b = с) = 1.5 : 1. The measured compression strength of ordinary chondrites with account for all extreme average values in certain directions is in the range from 91 to 262 (including the Ghubara Meteorite, 72–262 MPa), and considering only average values for all meteorites, from 105 to 203 MPa. The measured samples are referred to as the most common types of ordinary chondrites. The resulting range being quite wide covers almost all known experimental data and can characterize the whole class of ordinary chondrites. The tensile strength, also in view of the extreme values in certain directions, is in the range of 17–34 MPa, and considering only average meteorite values, from 18 to 31 MPa (Table 4). This procedure for experimental studies of the spatial distribution of strength properties made it possible to obtain up to one hundred forty measurements in one relatively small meteorite sample and, thus, to improve considerably the data reliability. The considerable anisotropy, on the one hand, explains significant variations in strength properties of the meteorite samples and, on the other hand, sets completely new requirements to the procedure for experimental studies of physical and mechanical properties of meteorites and to the data. When evaluating the variation coefficient and providing a sufficient number of measurements, the extreme lower and upper values often differ by more than three times depending on the sample defectiveness degree. Defects are present at different hierarchical levels. They include defects of mineral grains such as cracks, perfect cleavage, gas–liquid inclusions, crystal lattice defects, etc.; defects along mineral grain boundaries; and, finally, defects comparable with the sample’s size. The rock physical and mechanical properties should be measured in compliance with the specified standards with account for possible anisotropy. The use of single measurements for comparison of physical and mechanical properties of the meteorites, for example, of different petrological types, different collision facies, with varying weathering degrees, should be carried out only with an appropriate reservation and only at a qualitative level (more, less), because a single measurement can be drastically different from a reliably established average value obtained accounting for all necessary requirements. Only compliance with this requirement makes it possible to establish the degrees of difference in meteorites of different types.
It should be noted that the reliable comparative analysis of strength properties of different meteorites is currently unavailable due to the small number of known experimental studies of the physical and mechanical properties of extraterrestrial material, as well as due to the continuous improvement of measurement techniques. The comparative analysis of strength properties of ordinary chondrites, which is limited by two petrological types due to no data and based largely on single measurements (Kimberley and Ramesh, 2011), just confirms the above-said statement. Rheological, physical and mechanical properties of the rocks are dependent on specific features of their structure, chemical and mineral composition, and are too complicated for theoretical studies (Slyuta and Voropaev, 1997; Kimberley and Ramesh, 2011). So, direct experimental and observational studies are the only way to obtain reliable data on the strength properties of extraterrestrial matter. COMPARATIVE ANALYSIS OF PHYSICAL AND MECHANICAL PROPERTIES OF CM/CR CARBONACEOUS CHONDRITES Carbonaceous chondrites, which make up C-asteroids, according to the optical (spectral) distance studies, are characterized by the highest oxidation degree of their material among all meteorites and consist largely of hydrated iron–magnesium silicates (serpentine and chlorite). Carbonaceous chondrites are also distinguished by a high content of volatile components, including water (up to 20 wt %), carbon (5 wt %), sulfur and others, and by the presence of organic matter (up to 5 wt % Corg) being abiogenous in origin. Chondrules consist of olivine and (or) pyroxene. Carbonaceous chondrites are subdivided into several subgroups based on their structural and geochemical features. It should be noted that the carbon occurrence is not always indicative of the fact that meteorites are referred to as carbonaceous chondrites. Some fraction of the meteorites from the considered group is enriched in carbon (for examples, CI-, CM- and CRchondrites), while the other part (for example, COand CV-chondrites) contains so low an amount of carbon as some ordinary and enstatite chondrites. The C-chondrite matrix consists mainly of fine-grained material (except for intense metamorphism cases), which is partially or completely composed of hydrous silicates, magnetite, troilite and other minerals resistant to low temperatures. Most carbonaceous chondrites are breccias. In contrast to ordinary and enstatite chondrites, most carbonaceous chondrites were not exposed to the intense thermal metamorphism, in other words, they are more primitive objects in terms of physical and chemical properties (Anders, 1971). Meanwhile, the primary mineral composition of carbonaceous chondrites, especially CI- and CM-types, was subject to considerable hydration, i.e., changes under the influence of water. It is assumed that the SOLAR SYSTEM RESEARCH
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Table 5. Physical and mechanical properties of carbonaceous chondrites (Tsuchiyama et al., 2008, 2009; Jenniskens et al., 2012) Meteorite
Compression strength, MPa
Tensile strength, MPa
Variation coefficient*, %
50
2.0 ± 1.5 8.8 ± 4.8 0.7 ± 0.2 2.8 ± 1.9 0.8 ± 0.3
75 55 29 68 38
Murchison (CM) Murray (CM) Ivuna (CI) Orgueil (CI) Tagish Lake (CI/CM) Sutter’s Mill (CM)
82 ± 6
* The variation coefficient is indicated only for tensile strength values.
Table 6. Average density, specific density, and porosity of the meteorites* (Britt et al., 2002) Meteorite type
Specific density, g/cm3
Density, g/cm3
Н ordinary chondrite L ordinary chondrite LL ordinary chondrite Achondrite CI carbonaceous chondrite CM carbonaceous chondrite CR carbonaceous chondrite CV carbonaceous chondrite CO carbonaceous chondrite
3.84 3.75 3.56 3.20 2.27 2.71 3.11 3.51 3.69
3.40 3.34 3.19 2.97 2.12 2.21 2.92 3.10 3.11
Average porosity, % 11.5 10.8 10.4 7.0 11.0 12.0 6.0 11.0 16.0
* Properties of some samples of different meteorites can be drastically different from average values.
hydration with the formation of numerous phyllosilicates was also characteristic of the parent bodies (asteroids) (Endress et al., 1996). Carbonaceous chondrites are characterized by a stable residual magnetization, apparently, of extraterrestrial origin. The tensile strength of carbonaceous meteorites was not measured instrumentally, it was estimated by the load/displacement curve for a few meteorites upon crushing of meteorite fragments with an irregular shape and about 100 μm in size (Tsuchiyama et al., 2008, 2009). A wide spread in the measured tensile strength values from 0.7 to 8.8 MPa (Table 5), and also in their coefficients of variation are far beyond the generally acceptable values (about 30%); it is because the investigation procedure is not in compliance with the standard requirements for studies of rock physical and mechanical properties (Rocks, 1975), which are described above. The size of chondrules in the Murchison Meteorite sample was about 200 μm (Miura et al., 2008). An average size of the studied carbonaceous chondrite fragments was about 100 μm, while a maximum size did not exceed 200 μm (Tsuchiyama et al., 2008, 2009); hence, it is indicative of a high strength of certain chondrule fragments, matrix, and mineral intergrowths, rather than a meteorite in general. It is also SOLAR SYSTEM RESEARCH
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necessary to consider the relatively high porosity of carbonaceous chondrites, which reaches 20% in the Murchison Meteorite (Miura et al., 2008). Carbonaceous chondrites are characterized by a lower density and a higher porosity than ordinary chondrites (Table 6). A compression strength measured in a sample of the Murchison Meteorite (CM), being a cylinder with a diameter of 5 mm and a height of 10 mm (Miura et al., 2008), mainly refers to a meteorite substance and generally reaches 50 MPa. A compression strength of the Sutter’s Mill Meteorite is 82 MPa (Jenniskens et al., 2012). Unfortunately, the work does not describe the measurement method. The characteristic ratio of a compression strength to a tensile strength of the terrestrial rocks is 8–9 (Protodyakonov et al., 1981; Spravochnik (Kadastr), 1975). The characteristic ratio of a compression strength to a tensile strength of ordinary chondrites is 6–7 (Table 4). A probable tensile strength of carbonaceous chondrites is assumed to reach 9 ± 3 MPa. As can be seen in Table 4, the range of average minimum and maximum values of a compression strength for the studied ordinary chondrite samples, with account for anisotropy, is 105–203 MPa, while that of a tensile strength is 18–31 MPa. Assuming that a relative spatial anisotropy of strength properties of carbo-
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naceous chondrites is approximately the same as that of ordinary chondrites, the likely range of compression strength values can be taken as 35–85 MPa for carbonaceous chondrites, while the range of tensile strength values can be taken as 6–12 MPa. OBSERVED FRAGMENTATION PARAMETERS OF LARGE STONY METEOROIDS IN THE EARTH’S ATMOSPHERE Tables 7 and 8 report the data on thirty-nine meteoroids, which entered the atmosphere and were crushed in the period from 1961 to date, obtained by different instrumental methods such as optical, acoustic, and seismic procedures. Table 7 considers twentyfour meteoroids, for which meteorites were found and whose composition is known reliably. Table 8 provides the data on fifteen meteoroids without found meteoritic falls, but with the expected stone composition. The approximate composition of the meteoroids without meteoritic falls is estimated by the extinction height difference, which within the bolide population with the same or similar parameters (speed, weight, and trajectory inclination) is supposed to be related primarily to different compositions of the meteoroids (Ceplecha and McCrosky, 1976). Three major meteoroid groups were identified. The Group I is allegedly associated with the most durable and dense (>3 g cm–3) ordinary chondrites; the Group II, with the weakest carbonaceous chondrites; and the Group III, with even more fragile and weak cometary matter (Table 8). The last group is subdivided into two subgroups depending on an assumed matter density such as IIIa (about 0.75 g cm–3) and IIIb (0.3 g cm–3) (Ceplecha, 1988, 1994). The ablation coefficient was used as an additional parameter to estimate the approximate bolide composition. Its typical values for the groups I, II, IIIa, and IIIb reach about 0.014, 0.042, 0.1, and 0.21 s2 km–2, respectively (Ceplecha et al., 1998). A more accurate idea of the bolide composition is provided by the radiation spectrum recorded using spectrographs. Currently, Benesov is the only bolide for which the researchers managed to record the high-resolution spectrum and to find meteorites (Borovicka et al., 1998a, 1998b). The estimated approximate initial mass of meteoroids before entering the atmosphere was very different: from ~2.8 kg (Kacov Meteoroid) (Table 8) to ~13000 t (Chelyabinsk Meteoroid) (Table 7). Most meteoritic falls were ordinary chondrites by composition (Table 7). Two meteoroids appeared to be achondrites such as Bunburra Rockhole with an initial mass of about 22 kg (Bland et al., 2009; ReVelle et al., 2004; Spurny et al., 2009) and Almahata Sitta with an initial size of about 4.1 m and an initial mass of about 83 t (Jenniskens et al., 2009). Three meteoroids (Maribo, Sutter’s Mill, and Tagish Lake) were carbonaceous chondrites (Brown et al., 2002; Haack et al., 2012; Jenniskens
et al., 2012). Only one meteorite (Neuschwanstein) from these falls appeared to be enstatite chondrite EL6 (Bischoff and Zipfel, 2003). Most bolides without found meteoritic falls were also associated with dense and more durable chondrites (Table 8). Only one of the observed bolides such as Breclav (and, probably, Chotebor) was associated with the group of carbonaceous chondrites (Table 8). Most cases were characterized by a few welldefined fragmentations (from 3 to 6) with a mass loss from 16 to 60% relative to a mass before fragmentation in each of these points (Popova et al., 2011). A measured meteoroid velocity in the first fragmentation point reached from 12.3 (Almahata Sitta) (Table 7) to 31.8 km s–1 (Munich) (Table 8), and in the last fragmentation point, from 4.1 (Mason Gully) (Table 7) to 29.8 km s–1 (Munich) (Table 8). A ram pressure in the first point was relatively low and, depending on a breakup altitude (atmospheric density) and a meteoroid density, reached from 0.03 (Grimsby) to 3.9 MPa (Villalbeto de la Pena) (Table 7) for ordinary chondrites, or, probably, up to 5.9 MPa (Turji-Remety) (Table 8). At the last fragmentation point, ordinary chondrites were destroyed under aerodynamic loading from 1.0 MPa (Peekskill) to 18 MPa (Chelyabinsk) (Table 7) or, given Table 8, from 0.4 MPa (Kacov). It should be noted that a ram pressure was commonly determined with an accuracy of at least 10–30% (Popova et al., 2011). Slight fragmentations with insignificant mass loss (up to 1–2%) were also observed at the heights from 70 to 55 km at very low aerodynamic loads, within 0.03–0.1 MPa. In contrast to ordinary chondrites characterized by a sufficiently large number of observations, carbonaceous chondrites were still marked by three falls with found meteorites (Table 7) and one bolide associated with a group of carbonaceous chondrites (Breclav) (Table 8). An aerodynamic load was estimated from 0.3 to 0.9 MPa in the first fragmentation point for carbonaceous chondrites and from 2.2 to 3.0 MPa (or, with account for the Chotebor Bolide with an unclear composition, from 0.5 to 2.8 MPa) in the last fragmentation point with a maximum load. Taking into account a currently very small number of observations, the data on carbonaceous chondrites can be used for comparisons only with a certain reservation. In very rare cases (so far, it is the only event which was observed with the help of instrumental methods), large stony meteoroids, undergoing maximum aerodynamic load, likely kept their basic mass and size, reached the Earth’s surface almost without fragmentation in the atmosphere, and formed an impact crater. It is the Carancas Meteorite which fell in Peru on September 15, 2007, and formed a crater with a diameter of 13.5 m (Tancredi et al., 2009; Popova et al., 2011). By composition, this meteorite is referred to as an ordinary chondrite H4-5 (Connolly et al., 2008). According to (Borovicka and Spurny, 2008), the maximum aerodynamic load on the meteoroid, whose priSOLAR SYSTEM RESEARCH
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Benesov
2
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Carancas
Chelyabinsk
Grimsby
Innisfree
Jesenice
Kosice
Krizevci
Lost City
6
7
8
9
10
11
12
Buzzard Coulee
5
4
LL3.5, H5
Ach(U)
Type
2017
H5
H6
H5
L6
L5
Н5
LL5
H4/5
H4
Bunburra Rock- Ach(Euc) hole
Almahata Sitta
1
3
Meteoroid
No.
S4
S3
S3
S3
S2
S2
S4
S3
S2
S1
S3
S0
Shock stage
153
50
3500
170
39
30
13000000
1300–10000
8000
21.5
3000–4000
70000
Mass before fragmentation, kg
14.0
18.21
28.3
13.6
14.5
20.9
19.16
12–17
18.0
13.2
21.0
12.3
I
5.2
4.5
4.5
6.0
7.8
13.0
3.2
–
–
7.6
–
10.9?
II
Velocity, km s–1
41.0
32.0
37.1
46.0
55.6
70.0
54.0
–
–
54.9
56.0
45.0
I
22.0
21.8
30.5
23.0
23.7
30.0
23
–
17.6
31.3
24.0
33.0
II
Breakup altitude, km
0.7
–
~1
0.3a
0.1
0.03
0.2
–
–
0.11
0.2
0.3
I
2.8
3.6
6.0
3.9
3.0
3.6
18
>15
–
0.9
9.0
1.3
Max
Ram pressure, MPa References
McCrosky et al., 1971; Ceplecha, 1996; Ceplecha and ReVelle, 2005
Segon et al., 2011; Borovicka et al., 2015
Borovicka et al., 2013b
Spurny et al., 2010; Bischoff et al., 2011
Halliday et al., 1978; Halliday et al., 1981; Ceplecha and ReVelle, 2005
Brown et al., 2011; Popova et al., 2011
Brown et al., 2013a; Borovicka et al., 2013a; Popova et al., 2013; Galimov et al., 2013; Borovicka et al., 2015
Conolly et al., 2008; Borovicka and Spurny, 2008; Tancredi et al., 2009
Hildebrand et al., 2009; Milley, 2010
Bland et al., 2009; ReVelle et al., 2004; Spurny et al., 2009, 2012a
Borovicka et al., 1998a, 1998b; Spurny et al., 2014
Jenniskens et al., 2009; Borovicka and Charvat, 2009
Table 7. Observed fragmentation parameters of large stony meteoroids in the Earth’s atmosphere, for which meteorites were found*
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Sutter’s Mill
22
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Villalbeto de la Pena
L6
CI/CM
CM
H5
H5
H6
L5
L6
EL6
H5/6
H5
CM2
Type
S4
S1
–
–
S1/S3
S2
S5
S4
S2
S2
S1
S0
Shock stage
530
52000
40000
1200–2000
1200
3000
10000
80
300
1500
40
74
Mass before fragmentation, kg
14.8
15.5
28.6
13.3
20.0
13.7
19.5
13.67
19.0
22.0
14.65
28.5
I
10.5
13
–
12.7
–
5.4
10?
–
12
7.2
4.1
–
II
Velocity, km s–1
30.0
48.0
47.6
36
44.0
41.6
70.0
36.0
34.0
>46
35.8
37.1
I
24.0
32.0
–
25.0
23.3
30.5
22.0
~22
20.8
24.0
23.8
30.5
II
Breakup altitude, km
3.9
0.3
0.9
0.9
0.9
0.7
0.03
–
3.6
<0.9
–
–
I
5.1
2.2
–
–
>0.9
1.0
6.5
–
9.6
5.0
1.5
3.0
Max
Ram pressure, MPa
Llorca et al., 2005; Trigo-Rodríguez et al., 2006; Bischoff et al., 2013
Brown et al., 2000, 2002; Hildebrand et al., 2006
Jenniskens et al., 2012
Brown et al., 1996
Ceplecha, 1961; Spurny et al., 2003; Borovicka and Kalenda, 2003
Brown et al., 1994; Ceplecha et al., 1996
Brown et al., 2004
Jenniskens et al., 2014
Spurny et al., 2002, 2003; ReVelle et al., 2004
Borovicka et al., 2003a, 2003b; Borovicka and Kalenda, 2003
Towner et al., 2011; Spurny et al., 2012b; Borovička, 2014; Borovicka et al., 2015
Haack et al., 2012; Brown et al., 2013b; Borovicka et al., 2015
References
* Altitude and velocity are given only for the first (I) and last (II) breakup (Popova et al., 2011). Ram pressure is given for the first (I) fragmentation, while the maximum value (Max) is commonly consistent with the last (II) fragmentation (except for Lost City, Moravka).
24
Tagish Lake
St. Robert
21
23
Pribram
20
Novato
17
Peekskill
Neuschwanstein
16
19
Moravka
15
Park Forest
Mason Gully
14
18
Maribo
Meteoroid
13
No.
Table 7. (Contd.)
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Table 8. Observed fragmentation parameters of large stony meteoroids in the Earth’s atmosphere, for which meteorites were not found*
No.
Meteoroid
1 2 3
Breclav Chotebor
4
Greenlandb Jesenik Kacov Legnica Martin Munich Oswiecim Senohraby
5 6 7 8 9 10 11 12 13 14 15
El Pasoa
Sumavac Turji-Remety Vimperk Zdiar
Type (group) II I–II I I I I I I I I I – I I I
Mass before fragmentation, kg 500 11 8000
Velocity, km s–1 I 21.8 – 25.0
36000(8000) 5 2.8 65 26 28 72 3.6 5000 4300 105 11
Breakup altitude, km II
20.5 26.6
30.0
Ram pressure, MPa
I
II
I
II
47.7 –
36.2 52.9 ~30
0.6 – –
2.8 0.5 7.5
55.0
26.0 39.2 40.7 37.0 29.3 49.0 32.0 42.0 67.0 21.9 25.9 42.6
0.4–0.6
10.0 1.6 0.4 1.2 2.5 1.2 3.1 0.7 0.14 11.8 3.5 2.0
– 13.1 16.7 16.6 31.8 22.9 17.3
18.0 11.1 14.3 10.9 29.8 15.0 16.0
– 49.0 46.3 67.0 63.1 59.1 46.5 76.0
16.9 13.2 28.1
13.6 9.9 27.1
29.0 34.4 48.6
– 0.2 0.5 0.04 0.25 0.2 0.45 0.025 5.9 1.7 1.0
* Altitude, velocity, and ram pressure are given only for the first (I) and last (II) fragmentation (Popova et al., 2011). a Hildebrand et al., 1999; b Pedersеn et al., 2001; c Borovicka and Spurny, 1996;
mary weight was estimated at 1300–10000 kg, was greater than 15 MPa. According to other estimates (Kenkmann et al., 2009), the maximum aerodynamic load did not exceed 18 MPa. The opposite cases being also rare were characterized by total fragmentation of large meteoroids under very low aerodynamic loads. For example, the Sumava Bolide with an initial mass of about 5000 kg underwent a few fragmentations and explosions in the height range of 76–67 km (Borovicka and Spurny, 1996) under an ram pressure of 0.025–0.14 MPa (Nemtchinov et al., 1999). It is assumed that the object was cometary in origin, although its orbit was not strictly cometary. It should be noted that a typical tensile strength of the comet nucleus material is really very low, reaching about 2 kPa (Slyuta, 2009). The Chelyabinsk Meteoroid entered the Earth’s upper atmosphere at a velocity of about 19.03 km s–1 (Borovicka et al., 2015). In its size (19.8 ± 4.6 m) and initial mass (about 13000 t) the Chelyabinsk Bolide turned out to be the largest of such bodies ever observed and recorded by different instrumental methods (Popova et al., 2013; Borovicka et al., 2015). Meteoroid fragmentation began at an altitude of about 54 km under an ram pressure of about 0.2 MPa (Table 7). A brightness peak caused by the meteoroid destruction was observed at an altitude of 29.7 km. Meanwhile, a SOLAR SYSTEM RESEARCH
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large meteoroid fragment survived a load of 15 MPa without further destruction (Borovicka et al., 2015). The Chelyabinsk Meteorite also refers to the most common type of stony meteorites, i.e., to ordinary chondrites. Based on its iron content and the ratio of its oxidized and reduced forms, the Chelyabinsk Meteorite belongs to the chemical type LL (Galimov et al., 2013). By the thermal metamorphism degree, this meteorite is referred to as the petrological type 5 and is characterized by moderate shock metamorphism S4. The meteorite was discovered right after the falling, and its geochemical weathering degree was, respectively, zero (W0). In terms of a structure, the meteorite is a impact melt monomictic breccia, where numerous cracks are filled by dark fine-grained impact melt veinlets. A chemical composition of the dark impact melt is similar to the bulk composition of the meteorite. Hence, a normal maximum aerodynamic load resulting in the fragmentation of ordinary chondrites was no more than 15–18 MPa, which is about half the tensile strength of ordinary chondrites (Table 4). In rare cases, when a stony meteoroid not subjected to destruction and reached the Earth’s surface, forming an impact crater, the maximum ram pressure could reach 18–20 MPa. As for carbonaceous chondrites, it can only be said that the maximum aerodynamic load at crushing of carbonaceous chondrites is less than 3 MPa, which is about half the tensile strength of carbo-
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naceous chondrites, which is estimated at 6–12 MPa. It is evident that the data on carbonaceous chondrites are preliminary and require further confirmation using both additional observations and experimental studies. It should be expected that more durable objects will be destroyed at higher ram pressures. The Sikhote Alin iron meteorite was destroyed at an altitude of several kilometers (Krinov, 1963). It is assumed that destruction happened at a height of about 10 km, where the meteoroid velocity was at least 10 km s–1, while the aerodynamic load could reach 40 MPa (Bronshten, 1981). According to the modeling data (Nemchinov and Popova, 1997), and considering the size of formed craters and the crater field, the last basic fragmentation proceeded at 14.7–48.9 MPa, depending on the model, in different models with a different number of fragmentation points (from 5 to 1). The model with one basic fragmentation at the height of 14.7–10 km at ram pressure of 37 MPa is the most consistent with the observation data. Even accounting for all reported data, the tensile and destruction strength values of the Sikhote-Alin meteorite polycrystalline sample are also in good agreement with maximum values of aerodynamic loads for large iron meteoroids, reaching 43 MPa (Yavnel, 1963; Slyuta, 2013). GEOMECHANICAL ISSUES OF DESTRUCTION OF LARGE STONY METEOROIDS IN THE EARTH’S ATMOSPHERE The frontal ram pressure is one of few natural loads on small bodies, the nature of which is generally consistent with the uniaxial splitting load at maximum pressure at the front surface and zero pressure at the back surface. The stress field is characterized by maximum shear stresses in the areas of frontal and lateral parts of the body’s surface (Fadeenko, 1967; Grigoryan, 1979). In this case, the meteoroid material strength is dependent on the meteoroid tensile strength, i.e., a tensile stress value resulting in the material destruction. Fracturing occurs along the boundaries of structural elements or along the strength defects (cracks) under static load, which gradually grow with an increase in the atmospheric density during a few seconds of the meteorite flight in the atmosphere with a velocity of 10–30 km s–1. The reason for the observed significant difference between a maximum aerodynamic load and a known strength of meteoric stones can likely be found in the meteoroid strength heterogeneity and structure (Tsvetkov and Skripnik, 1991). Investigation of iron and stony meteorites also showed that fragmentation occurred mainly along the boundaries of the structural elements (Krinov, 1955, 1963). Any defect in a continuous medium (cavity or crack) is a stress concentrator. The closer to the defect,
the greater the stress. The maximum stress concentration is localized in the defect area with a maximum surface curvature, i.e., at the crack tip characterized by local destruction. In general, the stress concentration σ factor can be described by the equation K = max , σn where σmax is the highest local stress caused by a stress concentrator, while σn is a nominal stress which would develop in the absence of a stress concentrator (Hott, 1978; Broek 1980; Parton and Morozov, 1985). The maximum stress concentration at the crack tip can exceed the nominal stress by ten times. The energy supply to the crack tip for growing and destruction is provided by the stored elastic strain energy W under an increase in the static load (ram pressure). The energy ΔG is involved in the fracture enlargement. The fracture growth results in lower deformation in the zone being adjacent to the fracture. This process results in the release of deformation energy –ΔW > 0 (Parton, 1990). If –ΔW > ΔG, the released energy is abundant enough for the material destruction at the fracture tip, and the fracture spreads spontaneously. Upon reaching the critical aerodynamic load and almost instantaneous and simultaneous spontaneous distribution of numerous fractures and their merging, the excessive stored energy of elastic strain, which is equal to the difference –ΔW–ΔG > 0, transforms into kinetic energy. It grows more and more (–ΔW grows in proportion to the fracture area). This process results in an almost explosion-like meteoroid destruction (rheological explosion) (Fig. 3b), which is accompanied by acoustic noise or impact (not to be confused with the ballistic shock wave). The cascading destruction is accompanied by repeated impacts and a few acoustic shocks. If –ΔW < ΔG, then the released energy is insufficient to increase a fracture length, and the fracture remains fixed. Currently, there are no works containing the analysis of instrumental acoustic data on the flight and destruction of large meteoroids. The analysis of the acoustic data on small meteoroids suggests that the source, first, is a shock wave produced by the flight. Because a shock wave generates acoustic disturbances by itself, it is a challenge to distinguish a rheological explosion in this background. The additional energy released by destruction complicates the pressure distribution pattern on the surface, but more accurate identification (pressure change at a given point in the course of time, multiple peaks) requires the analysis of instrumental data on pressure jumps in the forward wave propagation zone (at distances not exceeding 2–2.5 of the source heights). The additional energy released by destruction can increase lateral scattering velocities of the fragments. These velocities are now estimated as a result of the interaction of fragments’ shock waves, and observed values are occasionally higher than (Borovicka and Kalenda, 2003). SOLAR SYSTEM RESEARCH
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The crack initiation period or the so-called incubation period is characterized by gradual emergence and accumulation of microdefects whose dimensions are comparable with characteristic dimensions of a microstructure, i.e., with the mineral grain size. Microdefects or microcracks in the rocks and stony meteorites are often localized in mineral grains and cross them; they are related to an individual body in minerals with an unclear or imperfect cleavage (for example, in olivine) or to cleavage in minerals with a good and eminent cleavage (pyroxene and plagioclase). For example, such microdefects are clearly seen in mineral grains of the ordinary chondrite MacAlpine Hills (Kimberley and Ramesh, 2011). Scattered destruction or microdefect accumulation are commonly characteristic of the boundary of larger structural elements, i.e., in an area where physical and mechanical properties of a structural element, corresponding to the phenomenological model of a homogenous continuous medium, change abruptly or gradually. The incubation period is completed by localization of the scattered destruction process and formation of an initial growing macrocrack. Fractures, along which the meteoroid is destroyed in the upper atmosphere, are fatigue cracks formed in the parent body as a result of cyclic and dynamic impact loads, i.e., the previous collision evolution. Cyclicity consists in the fact that a small initial crack, once formed, with each subsequent collision or impact grows (stable development stage), until it reaches a critical length or area for a given critical stress, which is followed by uncontrolled and spontaneous crack growth (unstable development stage). The crack’s growth velocity at the unstable development stage can be in 107–108 times higher than its growth velocity at the initial stage (Parton and Morozov, 1985). It should be noted that the parent body’s life is dominated not by the incubation period of macrocrack generation, but by the subsequent period of slow quasi-static crack growth from the initial to the critical size. Meanwhile, the crack growth mechanism does not depend on characteristic features of the material microstructure (Paris and Erdogan, 1963). Such fatigue cracks can also develop because of cyclic tidal loads when a parent or a small body (comet nuclei, asteroids, small silicate and icy satellites) passes by the orbit pericenter or near more massive (planetary) bodies. A meteoroid is destroyed in the Earth’s atmosphere along the cracks, whose area is equal to or exceeds the critical value for a given body size, for a given body strength, and for a given critical stress (ram pressure). Each newly formed fragment, depending on its size and strength, is likely characterized by its own critical crack size at a given load. These are cracks whose dimensions in a larger parent body were far from being critical, but could become such for smaller body fragments. In other words, it does not mean that all formed fragments will be more durable than a previous parent body, as is assumed in accorSOLAR SYSTEM RESEARCH
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dance with the scale factor (Weibull, 1939). Such consecutive fragmentation at a lower ram pressure was observed, for example, for fragments of the Moravka Meteoroid, which took place at the height of 32.3–24 km under pressure of 5–2.3 MPa (Borovicka and Kalenda, 2003). Separation of the first fragments from stony meteoroids is observed at an altitude of about 70–40 km under aerodynamic loads of less than 1 MPa. The rapid increase in pressure results in a decrease in the critical crack size and, respectively, a decrease in the total crack size results in a rapid increase in the number of such defects. Such critical fracturing is accompanied by a cascade fragmentation, a bright example of which is Benesov (Borovicka et al., 1998a, 1998b) and Chelyabinsk (Popova et al., 2013) bolides. The fewer critical defects, the larger and heavier the final fragment should be, as, for example, the Carancas bolide (Borovicka and Spurny, 2008; Kenkmann et al., 2009). In fact, if knowing the body’s dimensions, physical and mechanical properties, load value and time before splitting thereof, it is possible to estimate a critical crack size for a given body, leading to its destruction. As noted above, the scale factor α (Eq. (1)), which determines the strength–size relation of objects, is highly variably for stony meteoroids. Accordingly, an extremely wide range of values prevents its use as a universal value for stony bodies and from obtaining any additional unknown information on an object (strength, composition, size, defects, and previous collision history). In these terms, the scale factor is more philosophical (greater size—less strength, scarcely ever) than physical in meaning. In contrast to the scale factor, the defectiveness factor proposed by the author for assessment of meteoroids based on the critical defect theory (critical crack length or area), has a definite physical meaning and reflects the specific, measured and comparable defectiveness degree of a given natural object, depending on its composition, strength, and previous collision history. If the defectiveness factor is designated, for example, as kl, then its dimensionless value can be expressed as a simple relation: kl = lc/Dm, where lc is a critical crack length and Dm is an average meteoroid diameter. Or through a critical crack area: ks = sd/SR, where sd is a critical crack (defect) area for a given stony object, while SR is a cross-section area for a given object recalculated for its average radius. It should be noted that in terms of fracturing mechanics, a critical crack size compared to an object size and a load is an ordinary investigation object in both theory and practice, while in terms of rock physics, the analogous proposed evaluation of defects in a single object is not known to the author. This phenomenon can likely be explained by the fact that in contrast to meteoroids
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and their parent bodies, being closed systems, the rocks, for example, in geotectonics are commonly open systems closely interacting with other rock bodies. Meteoroids Carancas, Moravka, Park Forest, Peekskill, Pribram, and St. Robert consist of ordinary chondrites, in other words, they are characterized by the same chemical and mineral compositions, similar sizes and initial mass. Nevertheless, the main destruction of these bolides proceeded at very different loads: from 0.5 to 18 MPa (Table 7), up to exceeding the maximum loads experienced by the Carancas Meteoroid without destruction. Obviously, the defectiveness factor of these objects, which was primarily related to the previous collision history of parent bodies and meteoroids initially characterized by almost the same chemical and mineral compositions and structures, would be very different and minimal, as, for instance, in case with the Carancas Meteoroid characterized by a zero value. Taking into consideration the fact that the defectiveness factor is a dimensionless value, now, focusing on the breaking load, it is possible to distinguish composition-similar meteoroids with the maximum value of the coefficient, i.e., close to unity. Peekskill and Pribram are meteoroids with found meteorites (Table 7). The defectiveness factor is somewhat lower for Mason Gully. Among bolides belonging to type I (Table 8), the maximum defectiveness factor and, accordingly, the richest collisional history were characteristic of Kacov. And the smallest defectiveness factor in this group was characteristic of Greenland and Turji-Remety. The development of a convenient and relatively simple mathematical model to determine a critical crack length (area) for a given object with a known strength and size, under a given load, to quantify and to compare a defectiveness degree of the above-considered large stony meteoroids in relation to composition and other parameters is one more objective of the current research. It would be interesting to compare the defectiveness factor with other meteorite data, which were critical in the estimation of the meteorite’s previous collision history, for example, with the age of the object exposure after it left the parent body, etc. CONCLUSIONS The considerable observed anisotropy reaching more than 60%, on the one hand, explains significant variations in strength properties in samples of one meteorite and, on the other hand, brings completely new requirements to both the procedure for experimental study of meteorite physical and mechanical properties and the obtained data. The use of single measurements for comparison of physical and mechanical properties of the meteorites, for example, of different petrological types, different shock stages and with varying weathering degrees is possible provided that a corresponding reservation is given, because the single measurement data on the meteorite
sample, which is characterized by anisotropy of physical and mechanical properties, can be drastically different from the results obtained taking into account all necessary requirements. It should be noted that the reliable comparative analysis of strength properties of different meteorites is currently impossible due to the small number of published experimental studies of physical and mechanical properties of the extraterrestrial matter, many of which are considered in this work (physical and mechanical properties of iron meteorites are investigated in the work of (Slyuta, 2013), while the cometary material is studied in (Slyuta, 2009)), and also due to the continuous improvement of measurement techniques. Direct experimental and observation studies are the only way to obtain the reliable data on strength properties of the extraterrestrial matter. It is obvious that only a further quantitative analysis of the accumulation of elastic strain energy and its transformation into kinetic energy will make it possible to assess still neglected additional energy of the “rheological explosion” effect on the acoustic shock and increase in a lateral scattering velocity of fragments and to compare the theoretical results with the observed instrumentation data. It is interesting and promising to develop the analytical model of the proposed meteoroid defectiveness factor which, in contrast to the scale factor, reflects a certain, measured, and comparable defectiveness degree of a given natural object in relation to its composition, strength, and previous collision history (formation age, exposure age, metamorphism degree, shock stages, etc.). The destruction of stony meteoroids, from separation of the first fragments to the main fragmentation and deceleration, is observed in a wide range of aerodynamic loads: from 0.1 to 18 MPa for ordinary chondrites and from 0.1 to 3 MPa for carbonaceous chondrites. Meanwhile, the maximum load value causing the destruction did not exceed the tensile strength of both ordinary chondrites (18–31 MPa) and carbonaceous chondrites (6–12 MPa). Hence, the tensile strength, depending on the meteoroid composition, is likely the upper limit value restricting the maximum destructive aerodynamic load on stony meteoroids. REFERENCES Alekseeva, K.N., The physical properties of stony meteorites and their interpretation in the context of the hypothesis of meteorite origin, Meteoritika, 1958, no. 6, pp. 67–77. Anders, E., How well do we know “Cosmic” abundances? Geochim. Cosmochim. Acta, 1971, vol. 35, pp. 516–522. Barsukova, L.D., Kharitonova, V.Ya., and Bannykh, L.N., Chemical composition of Tsarev meteorite, Meteoritika, 1982, no. 41, pp. 41–43. Bischoff, A., Dyl, K.A., Horstmann, M., Ziegler, K., Wimmer, K., and Young, E.D., Reclassification of VillalSOLAR SYSTEM RESEARCH
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Translated by E. Maslennikova
