In-depth analysis of asteroid samples will provide a key scientific basis for understanding its evolution history, resource utilization, and life origin. Obtaining rock samples from asteroids is getting more and more attention. However, successful sampling in asteroid is difficult due to extremely complex environmental conditions. In this paper, the dynamic processes of rock failure by sampling device are investigated by a continuum-discontinuum element method (CDEM) to instruct the rock sampling in asteroid. The deformation and failure of rock samples under different conditions (impact speeds, impact positions, rock cut-slot numbers, cut-slot spacings, cut-slot depths and cut-slot widths, etc.) are analyzed, and the relationships between the rock failure and hammer impact method are obtained. The results show that the cut-slot formed by grinding wheel increases the free surface of rock sample, which is beneficial to impact fracture and asteroid sampling. The relative distance between cut-slot free surface and impact position significantly affects the rock fracture under impact loading. The fracture degree of rock with single cut-slot is obviously smaller than that of rock with double cut-slots, the cut-slot scheme of double grinding wheels is more suitable for asteroid sampling. Under the impact loading, the rock fracture is negatively correlated with the cut-slot spacing formed by double grinding wheel cutting, the effective spacing of double cut-slots is 12 mm. The fracture unit number of rock varies nonlinearly with an increase of the depth from impact position, there is an optimal cut-slot depth corresponding to a certain impact velocity, and the rock crushing efficiency of asteroid sampling can be improved as the cut-slot depth matches the crack propagation depth.

Due to extremely low vacuum temperature and low gravity environment, the surface environment of asteroid is complex. The underground sampling of asteroid will provide an important support for understanding its morphology, composition, internal structure, and other characteristics, which is beneficial to obtain the original information at the initial formation stage of the solar system, and reveal the formation and evolution history of the solar system. Therefore, investigating on the scheme, technology and equipment of asteroid sampling, and improving the success rate of asteroid sampling have important significances.

It is difficult to achieve reliable asteroid sampling due to the complex environmental conditions of asteroids. On May 9, 2003, Japan launched the “Falcon Bird” probe to Asteroid 25143 (approximately 500 m in diameter), which is the world’s first probe to asteroid sampling. The probe failed to successfully release the lander, but it still collected a small amount of surface material samples and sent them back to the earth on June 14, 2010. The sample size was mostly smaller than 10 microns of asteroid dust. Japan launched the “Falcon Bird 2” probe in December 2014, arrived near the asteroid 1999 JU3 (about 1000 m in diameter) in June 2018, and landed on the asteroid twice in February and July 2019, as shown in Figure 1(a). As shown in Figure 1(b), the first artificial crater (about 10 m in diameter) on the asteroid was manufactured using metal bullets, ande the surface and underground rock samples of asteroid were collected. In 2005, “Deep Impact” probe of NASA successfully hit the comet’s nucleus and observed the spatter, but no samples were collected. NASA launched the “Osiris-REx” probe in 2016, and the asteroid “Benu” (about 500 m in diameter) was sampled on October 20, 2020. As shown in Figure 1(c) , a beam of nitrogen was emitted and stayed on the asteroid surface for several seconds, and the fine substances on asteroid surface were sprayed and collected. This task will collect at least 60 g samples.

With the advancement of China’s lunar and deep space exploration projects, the task of lunar and deep space exploration has transited from surface patrol survey to sampling return. In April 2019, China officially formulated an asteroid (2016HO3) exploration mission. The surface environment of asteroid is complex. In the past, the successful sampling was mostly surface injection, and the underground sampling was only successful once (using metal projectile impact). Due to poor thermal conductivity of asteroid rock, extremely low vacuum temperature, and low gravity environment, asteroid sampling is very difficult. Therefore, the sampling scheme, technology, and equipment need to be further studied to improve the success rate of asteroid sampling. The understandings of fracture mechanism of asteroid rock under the impact loading and microgravity environment are beneficial to effectively conduct asteroid sampling.

The impact collision can be divided into four categories according to the impact velocity: super-speed impact, high-speed impact, medium-speed impact, and low-speed impact. Under high-speed and super-speed impact conditions, it has obvious penetration effect as the velocity is greater than 500 m/s [1, 2], and it has phase evolution phenomenon as the velocity is greater than 12 Km/s [3]. In the case of medium and low-speed impact (usually less than 50 m/s), the penetration effect is not obvious, mainly presenting the elastic and plastic deformation of the collision [4, 5]. For the low-speed collision, the impact tests of drop hammer are commonly used to investigate the damage effect of explosion or impact on engineering structures. A number of experimental studies have been conducted on the impact resistance of rock-like materials [6-10]. Scholars also have found the dynamic response characteristics of rock-like materials under drop hammer impact are related to the loading rate, with obvious strain rate strengthening effect, and the dynamic and static damage modes of concrete are also significantly different. Concretely, Wang et al. [11] found that concrete dynamic and static responses have obvious differences. Fu et al. [12, 13] found that concrete material has obvious strain rate strengthening effect, the tensile strength are positively correlated with the loading rate, and concrete beams are mainly bending failure at low-velocity impact, and it would transform to the shear failure with increasing the loading rate. Mei and Qin et al. [14, 15] found the failure mode of concrete beams and columns under impact load is similar, which shows shear failure under high strain rate conditions. Gu et al. [16] considered concrete slab appeared flexural-tensile failure under quasi-static load, and appeared local punching shear failure under impact load. Thamburaja and Sarah et al. [17, 18] introduced a three-dimensional finite deformation rate-based constitutive theory to describe the damage and fracture behavior of viscoelastic materials, simulation of crack initiation, and propagation processes achieved by employing a viscoelastic multi-network component theory based on Gibbs potential and a nonlocal fracture criterion, and found that using a nonlocal fracture length scale can yield mesh-independent fracture response.

For the dynamic breaking process under the impact loading of brittle materials such as rock and concrete, the coupling methods of finite elements and discrete elements have been widely used. Gui et al. [19] applied a mixed cohesive fracture model to the mixed continuous-discrete element method, and the dynamic failure process of brittle rocks was investigated. Liu et al. [20] built a discrete-continuous coupling model based on PFC and FLAC, and simulated the change law of acceleration of cement pavement during falling hammer impact. Currently, a continuum-discontinuum element method (CDEM) combines the advantages of finite element method and discrete element method, which has gradually become an effective simulation method to study the failure and breaking mechanisms of rock and concrete materials. Based on CDEM, Zhang et al. [21, 22] investigated the top-coal caving and coal-rock failure characteristics, and the cracking and crushing process of concrete slab and concrete pavement under hammer impact loading were also simulated [23, 24]. However, based on CDEM, the research on the rock breaking of asteroid sampling are fewer in the literature.

In this paper, for different grinding wheel cutting and hammer impact schemes of existing asteroid sampling device, CDEM is used to simulate the dynamic breaking process of rock to improve the success rate of asteroid sampling. Under the microgravity environment, the variation laws of deformation and failure of rock are analyzed, which considers different initial impact speeds, impact positions, rock cut-slot numbers, rock cut-slot spacings, rock cut-slot depths and rock cut-slot widths, etc. The relationships between the rock fracture degree, fracture block distribution, spatial layout and operation parameters of grinding wheel, and impact hammer are discussed.

2.1. CDEM Model

Based on generalized Lagrange equation, CDEM is proposed. CDEM is an explicit numerical solution method for the high integration of grids and particles. The method integrates continuum numerical method with noncontinuum numerical method, which realizes the unification of finite element, discrete element, and meshless algorithm. In recent years, CDEM method has been successfully applied in geotechnical and mining projects [21-24].

The schematic diagram of numerical model is shown in Figure 2(a), which contains eight blocks. As shown in Figure 2(b), one block consists of three triangular elements, one block consists of two triangular elements, and the other six blocks consist of one triangular element. As in Figure 2(c), the red line is real interface and the black line is virtual interface. Based on CDEM, the progressive failure process of geological body and artificial material can be simulated. Not only the elastic, plastic, damage, and fracture process of solid materials under static and dynamic loads can be analyzed, but also the movement, collision, flow, and accumulation process of broken particles can be simulated.

CDEM [22] adopts an incremental explicit algorithm to solve the dynamic problem, which mainly includes two parts: node force calculation and node motion calculation.

The calculation formula of node force is:

F=FE+Fe+Fc+Fd
Fd=dv
(1)

where F is resultant force for nodes, FE is node external force, Fe is nodal forces contributing to element deformation, Fd is the node damping force, d is the damping coefficient, and v denotes the node velocity.

The calculation formula of node motion is:

a=F/mv=t=0TnowaΔtΔu=vΔtu=t=0TnowΔu
(2)

where a is node initial speed, v is node initial speed, Δuis node increment displacement, u is node displacement, m is node quality, and Δt is the time step.

Based on Courant–Friedrichs–Lewy (CFL) stability criterion, the critical time step is:

tmax=L/C
C=E(1v)/ρ(1+v)(12v)

where L is the minimum mesh size, C is the longitudinal wave speed, E is Young’s modulus, v is Poisson’s ratio, and ρ is density.

The alternating calculation based on equation (1) and (2) is an explicit solution process. In the calculation, the fracture model is used to describe the damage and fracture process of rock under impact load.

Linear elastic constitutive model in block element is expressed by incremental method:

Δσij=2GΔεij+(K-23G)Δθδijσij(t1)=Δσij+σij(t0)
(4)

where σij is the stress tensor, Δσij is the incremental stress tensor, Δεij is the incremental strain tensor, Δθ is the incremental volumetric strain, K is the bulk modulus, G is the shear modulus, δij is the Kronecker symbol, t1 is the next time step, and t0 is the current time step.

The interaction between these discrete blocks can be transformed into virtual spring forces. The forces at the contact interface of two blocks in the local coordinate can be expressed as:

Fn=-Kn×Δun
Fs=-Ks×Δus
(5)

where F, K, and Δu are the incremental force, stiffness, and relative displacement of the virtual spring, respectively; and n and s represent the normal and tangential directions, respectively.

When a given failure criterion of the virtual springs is reached, the connected interface between blocks is transformed into a discontinuous fracture surface. In this paper, the maximum tensile stress criterion and Mohr–Coulomb criterion are used to characterize the damage fracture of interface virtual spring.

In calculation, the maximum tensile stress criterion is used to correct the normal stress of interface virtual spring:

IfFn-σ×Ac0
ThenFn=0
(6)

where σ(t) is the tensile strength of interface virtual spring and Ac stands for the effective area of interface virtual spring.

In calculation, Mohr–Coulomb criterion is used to correct the tangential stress of interface virtual spring:

IfFs-Fn×tanϕ-c×Ac0
ThenFs=Fn×tanϕ
(7)

where ϕ denotes the internal friction angle of interface virtual spring and c stands for the cohesion strength.

2.2. Model Validation

In the reference [25] a structure layer model with specific physical meaning in CDEM is verified by comparison with theoretical and numerical results, and a contact detection method based on edge and face in CDEM is applied in the simulation of fracture and slide of joint slope. In this paper, for the tensile failure, shear failure, and dumping failure of material and structure, four numerical tests described in Figure 3 are designed to verify the rationality and correctness of CDEM.

The simulation results are shown in Table 1. The calculated values are basically consistent with the theoretical values, indicating that the simulation method is reasonable and effective.

3.1. Numerical Model

Under the condition of low reaction force in asteroids, hammer impact fracture may be a method to obtain rock samples, the broken rock quality of obtained samples should be not less than 100 g mm or cm. In this study, the asteroid rock breaking is completed by impact breaking device, the device is combined with grinding wheel cutter and impact hammer. The grinding wheel is used to precut rock to form a slot, and an impact hammer is used to knock the slot edge to obtain block samples. The outer diameter of grinding wheel is 80 mm, and there is an opening in the overlap part with impact hammer, which is convenient for reducing the hammer resistance of breaking rock.

According to the existing design drawings, the geometric models of impact hammer and test rock are created by using three-dimensional geometric modeling software, and the general geometric file similar to IGES format is output. As shown in Figure 4, the yellow cone is the impact hammer, and the red part is the rock fragmentation area, which is a square with 2 cm edge length. The general geometric file is imported into the mesh generation software. Tetrahedral is selected for mesh generation, and the mesh size is in millimeters. The boundary conditions of numerical models with single and double grinding-wheel layouts are consistent. The horizontal and normal displacements are constrained at the model bottom, and the normal displacements are constrained around the model. According to the working condition, the impact hammer is given different initial impact speeds.

3.2. Material Properties

This study takes asteroid basalt as the characteristic rock to analyze the impact-induced fracture mechanism of rock in microgravity environment. The physical and mechanical parameters of basalt and impact hammer are shown in Table 2. In simulation, the gravity acceleration is set to zero to simulate the microgravity environment of asteroid sampling.

3.3. Simulation Schemes

In this paper, through the simulation analysis and comparison of the rock specimen failure under different working conditions, the main factors affecting the rock breaking are explored, and the suitable tool configuration and working parameters are optimized. Concretely, the rock samples are cut by grinding wheel to form the slot, the influences of relative distance between slot-free surface and impact position on rock breaking are simulated, the relative distances are respectively 2.8, 5.6, and 8.4 mm. The energy needed for rock breaking comes from the kinetic energy of impact hammer, the rock-breaking performance under different impact speeds of impact hammer (8, 12, and 16 m/s) are simulated. The influences of impact speed, slot number, slot spacing, slot depth, and slot width on rock-breaking performance are discussed by analyzing the relationships between the rock failure (volume proportion, block size and fracture distribution, fracture degree) and the hammer impact method (spatial arrangement, operation parameters).

4.1. Influences of Relative Distance Between Cut Slot and Impact Position

As the relative distances (L) between cut-slot and impact position are 2.8, 5.6, and 8.4 mm, and the impact speed of hammer is 8 m/s, the rock-breaking results are shown in Figure 5. The vertical displacement of rock under impact loading is shown in Figure 5(a1), (a2) and (a3), as the relative distance (L) increases, the response range of vertical displacement gradually reduces, and the vertical displacement value also gradually becomes small. The crack spatial distributions of rock under impact loading are shown in Figure 5(b1), (b2) and (b3). As the relative distance (L) increases, the rock crack number gradually decreases, and the crack expansion range also decreases. Concretely, when the relative distances (L) are 8.4 and 5.6 mm, the rock cracks do not expand to the slot-free surface of rock formed by the grinding wheel cutting. However, as the relative distance (L) is 2.8 mm, the number of rock cracks near the slot-free surface increases significantly. Therefore, the relative distance (L) between cut-slot and impact position significantly affects the crack number of rock under impact loading.

As the free surface of cut-slot is on the right side of impact position, keeping the initial velocity of impact hammer unchanged at 8m/s. As the relative distance (L) between slot-free surface and impact position varies, taking the 5.6 mm position from hammer impact to cut-slot as the origin, the spatial distribution of fracture element number of rock under the impact loading is analyzed, as shown in Figure 6. Generally, as the relative distance (L) of hammer impact increases, the fracture elements (Nb) of rock decrease. Concretely, from Figure 6(a), the fracture elements (Nb) of rock in the horizontal direction (x) are largest near the impact position of hammer, the maximum fracture element numbers (Nb) are 286, 282, and 188 as the relative distances (L) are 2.8, 5.6, and 8.4 mm. With an increase of horizontal distance from impact position, the fracture element number (Nb) of rock rapidly decreases near cut-slot side. However, on the side far away from cut-slot, the fracture element number (Nb) of rock slowly decreases as the horizontal distance increases, and the fracture element numbers (Nb) are close to 0 as the horizontal distance is larger than 5 mm. The fracture element number variation of rock in the vertical direction (z) is shown in Figure 6(b). The fracture element numbers (Nb) near the impact position are also largest, the largest fracture element numbers are close as the relative distances (L) are 2.8 and 5.6 mm, which are obviously larger than that of the relative distance (8.4 mm). With an increase of vertical depth from impact position, the fracture element number (Nb) of rock decreases rapidly. The fracture element number (Nb) of rock is close to 0 as the vertical depth is larger than 6 mm. Compared with Figure 6(a) and (b), as the initial velocity remains unchanged, the variation of the relative distance (L) between cut-slot and impact position has smaller effect on the crushing depth of rock than the horizontal propagation of rock cracks.

To quantitatively analyze the variation law of rock fracture with impact time, the fracture degree (φ) of rock is defined as the ratio of fracture element number and total element number. As the relative distance (L) between slot-free surface and impact position varies, the statistical results of rock fracture under the impact loading are shown in Figure 7.

Generally, as the relative distance (L) is larger, the fracture degree is smaller. From Figure 7 (a), the rock fracture degree increases with an increase of impact time, which experiences five stages (slow increase-I, rapid increase-II, platform-III, rapid increase-IV, and platform-V). As the relative distance (L) is 2.8 mm, the fracture degree of the rock sample reaches to 0.15% in the slow increase stage-I, the fracture degree reaches to 0.9% in the rapid increase stage-II, the fracture degree remains about 0.9% in the platform stage-III, the fracture degree reaches to 1.42% in the rapid increase stage-IV, and the fracture degree finally remains about 1.42% in the platform stage- V. As the relative distance (L) is 5.6 mm, the fracture degree of the rock sample reaches to 0.09% in the slow increase stage-I, the fracture degree reaches to 0.52% in the rapid increase stage-II, the fracture degree remains about 0.52% in the platform stage-III, the fracture degree reaches to 1.1% in the rapid increase stage-IV, and the fracture degree finally remains about 1.1% in the platform stage- V. As the relative distance (L) is 8.4 mm, the fracture degree of the rock sample reaches to 0.15% in the slow increase stage-I, the fracture degree reaches to 0.5% in the rapid increase stage-II, the fracture degree remains about 0.5% in the platform stage-III, the fracture degree reaches to 0.98% in the rapid increase stage-IV, and the fracture degree finally remains about 0.98% in the platform stage- V. Furthermore, for the effect of the relative distance on the impact time, the fracture degrees of rock reach a stable value after 0.065 ms of impact time. As the relative distance (L) is larger, the time for fracture degree to reach a stable value is shorter, namely, the earlier the rock stops failure. Moreover, as the distance (L) increases to a certain value, the fracture degree change with time is not sensitive. From Figure 7(b), the fracture degree curves of fracture rock are counted and fitted. As the relative distance (L) is 1, 2, 3, 4, 5, and 6 mm, the final fracture degree of rock is 2.24%, 1.64%, 1.39%, 1.25%, 1.15%, and 1.08%, respectively. This indicates that the initial velocity is constant, and that the fracture degree presents a nonlinear rapid decline with an increase of relative distance between slot surface and impact position.

After rock is crushed, the characteristic block (D) of fracture rock is selected as 1–5 mm, and the variation of characteristic block number (Ns) is analyzed, as shown in Figure 8.

From Figure 8 (a), as the relative distance (L) is 2.8, 5.6, and 8.4 mm, the block size between 1 mm and 2 mm of fracture rock accounts for 82.5%, 76.2%, and 71.8%, respectively. With an increase of impact relative distance (L), the characteristic block (D) of fracture rock does not change significantly, but the characteristic block number decreases rapidly. From Figure 8(b), the characteristic block number (Ns) of fracture rock is counted and fitted. As the relative distance (L) is 1, 2, 3, 4, 5, and 6 mm, the characteristic block number (Ns) is 127, 98, 76, 58, 45, and 41, respectively. This indicates that the characteristic block number (Ns) decreases nonlinearly and rapidly with an increase of relative distance (L). In the fitting curve, there is an inflection point near L = 5 mm, which indicates as the relative distance between slot-free surface and impact position is greater than a certain value, rock fracture under impact loading cannot reach the free surface of rock cut-slot, and the fracture element number (Nb) of rock will decrease slowly. This could lead to the design failure of setting free surface by grinding-wheel cut to increase rock fragmentation.

4.2. Influences of Cut-Slot Number and Impact Velocity

In this Section, the influences of cut-slot number on the rock breaking are investigated. For the one cut-slot formed by single grinding wheel, the relative distance (L) between slot-free surface and impact position is 5.6 mm. For the two cut-slots formed by double grinding wheels, the impact position is at the center of two cut-slots in rock sample. Because the energy needed for rock breaking comes from the kinetic energy of impact hammer, the influences of initial impact speeds on rock-breaking performance are also considered.

For rock samples with one cut-slot and two cut-slots, under different impact speeds (8, 9, and 10 m/s), the simulation results of impact fracturing of rock samples are shown in Figure 9.

From Figure 9(a), for rock with one cut-slot, when the impact speeds increase, the number of rock cracks gradually increases, and the impact cracks gradually expands in the horizontal and vertical directions of rock sample. Concretely, the impact cracks not extend to the free surface of rock cut-slot as the impact speed is 8 m/s. However, as the impact speed is 12 m/s, the impact cracks expand near the cut-slot free surface, and the number and density of impact cracks obviously increase. As the impact velocity increases to 16 m/s, rock cracks far away from slot-free surface also continue to expand. However, the impact cracks near cut-slot surface do not obviously expand. From Figure 9(b), for rock with double cut-slots, due to the free-face symmetry of double cut-slots, the crack distribution in horizontal direction of rock is similar, showing a symmetrical shape. Moreover, as the impact velocity is larger, the crack propagation distance is farther. In the vertical direction of rock sample, rock cracks gradually develop to the deep with an increase of impact velocity. Generally, the crack density and fracture range of rock with double cut-slots are obviously larger than those of rock with single cut-slot, which indicates the cut-slot number of rock significantly affect the rock fracturing, and the free-face setting by the grinding wheel cut is conducive to the local fracture of rock under the impact loading.

Taking the impact position of rock as the origin, the number distributions of rock fracture unit in the horizontal direction (x) are analyzed under different cut-slot numbers and initial impact speeds, as shown in Figure 10. From Figure 10(a), for single cut-slot rock sample, the fracture element number (Nb) of rock increases with an increase of impact speeds, and the fracture element number (Nb) of rock is largest near the impact position. Far away from the impact position, the fracture element number of rock gradually decreases. Affected by the rock cut-slot, rock fracture far away cut-slot decreases linearly as the impact distance increases; however, rock fracture near cut-slot nonlinearly decreases. From Figure 10(b), for double cut-slot rock sample, the fracture element number of rock on both sides of impact position is slightly larger than that of impact position. Affected by the symmetrical free face of double cut-slots, the fracture element number on both sides of impact position is close to symmetrical distribution.

Taking the impact position of rock as the origin, the unit number distributions of rock fracture in the vertical direction (z) are analyzed under different cut-slot numbers and initial impact speeds, as shown in Figure 11.

From Figure 11(a), in the depth direction (z) of rock with single cut-slot, the fracture element number (Nb) obviously increases with an increase of impact speed. Near the impact position, the fracture element number of rock are relatively close under different impact speeds. At the 5 mm depth far away impact position, the number of differences of fracture elements are largest under different impact speeds. As the depth is larger than 5 mm, the number differences of fracture element decrease gradually. From Figure 11(b), in the depth direction of rock with double cut-slots, the fracture element number (Nb) of rock generally increases as the impact speed increases. As the depth is smaller than 2 mm, the element numbers of rock fracture are relatively close under different impact speeds. At the 5 mm depth far away impact position, the number differences of fracture element are also largest under different impact speeds. As the depth is near 8 mm, the fracture element numbers under different impact speeds are close to 0. Generally, Figure 11 indicates the cut-slot number of rock has different influences on the rock fracture in the depth direction, and the influences of single cut-slot on the rock fracture depth are larger than that of double cut-slots under different impact speeds.

Near the impact position of rock sample, the variation law of fracture element number is fitted as the cut-slot numbers and the impact speeds vary, as shown in Figure 12.

From Figure 12, as the initial impact speed is 8, 10, 12, 14, and 16 m/s, the maximum unit number of rock fractures near the impact position shows an exponential increase. Concretely, from Figure 12(a), for single cut-slot rock sample, when the initial velocity increases from 8 to 16 m/s, the initial velocity is doubled, that is the initial kinetic energy increases four times. However, the maximum number of rock fractures increases by only 8.5%. From Figure 12(b), for double cut-slot rock sample, as the initial kinetic energy increases four times, the maximum unit number of rock rupture increases only 5.56%. Therefore, it can be speculated that as the impact speed is greater than a certain value, its influence on rock fracture near impact position is relatively limited.

To further analyze the variation law of rock fracture with impact time, the rock fracture curves under different cut-slot numbers and impact speeds are shown in Figure 13. Generally, the fracture degrees of rock samples with single-sot are smaller than those of rock samples with double cut-slots. With an increase of impact time, the rock fracture degree curves all experiences five stages (slow increase—rapid increase—platform—rapid increase—platform). The fracture degrees reach stable values after 0.07 ms of impact time. Concretely, from Figure 13(a), for single cut-slot rock sample, the values of fracture degree curves obviously increase as the initial speed increases. As shown in Figure 13(b), for double cut-slot rock sample, the final fracture degrees under the impact loading of 8 and 12 m/s are close, which are obviously larger than that of 16 m/s impact.

To further analyze the variation of rock fracture, the statistical results of final fracture degree of rock under different cut-slot numbers and impact speeds are shown in Figure 14. For single cut-slot rock sample, as the impact speed is 8s, 10, 12, 14, and 16 m/s, the final fracture degree of rock is 1.11%, 1.6%, 2.14%, 2.72%, and 3.35%, respectively. Compared with the final fracture degree of 8 m/s impact, the final fracture degree respectively increases by 44.14%, 92.79%, 145.05% and 201.8% as the impact speed is 10, 12, 14, and 16 m/s, respectively. This indicates that the final fracture degree of rock with single cut-slot shows a linear increase as the impact speed increases. For double cut-slot rock sample, as the impact speed is 8, 10, 12, 14, and 16 m/s, the final fracture degree of rock is 3.27%, 3.31%, 3.42%, 3.8%, and 4.5%, respectively. Compared with 8 m/s impact, as the impact speed is 10, 12, 14, and 16 m/s, the final fracture degree increases by 1.22%, 4.59%, 16.21%, and 37.6%, respectively. This indicates that the final fracture degree of rock with double cut-slots increases exponentially with a linear increase of initial impact velocity. Furthermore, analyzing Figure 14, the fracture degree difference is 1.16% under single cut-slot and double cut-slots; however, the fracture degree difference is 2.24% under different impact speeds. From Figure 7, the fracture degree difference is 1.6% under different relative impact distances. Therefore, the influence of impact speed is greater than that of the relative impact distances, and the influence of the relative distances between slot-free surface and impact position is greater than that of the cut-slot number.

Generally, for the single and double cut-slots of rock samples formed by single and double grinding wheel cut schemes, the fracture degree of rock with single cut-slot is obviously smaller than that of rock with double cut-slots. The fracture degree of rock is positively correlated with impact velocity, and the fracture degree of rock with single cut-slot increases linearly with an increase of impact velocity, while the fracture degree of rock with double cut-slots increases exponentially. Moreover, the fracture degree of rock with double cut-slots is not sensitive to the change of lower impact speed.

Under different cut-slot numbers and impact speeds, the characteristic block (D) of fracture rock is selected as 1–5 mm, and the changes of characteristic block number (Ns) are also analyzed, as shown in Figure 15. As shown in Figure 15(a), for single cut-slot rock sample, as the impact velocities are 8, 12, and 16 m/s, the block size between 1 and 2 mm account for 76.2%, 73.9%, and 75%, respectively. From Figure 15(b), for double cut-slot rock sample, as the impact velocities are 8, 12, and 16 m/s, the block size between 1 and 2 mm accounts for 89.2%, 85.6%, and 85.0%, respectively. Generally, the proportion of smaller characteristic block of fracture rock with single cut-slot is obviously smaller than that of rock with double cut-slots. Moreover, the characteristic block distribution of fracture rock with single and double cut-slots does not change significantly with a variation in impact speed.

Under different cut-slot numbers and impact speeds, the total numbers of characteristic block of fracture rock are counted and fitted, as shown in Figure 16. For single cut-slot rock sample, the total number of characteristic rock block increases almost linearly with an increase of initial impact speed. At different initial impact speeds of 8, 10, 12, 14, and 16 m/s, the total numbers of characteristic blocks of fracture rock are 42, 67, 92, 118, and 144, respectively. For the double cut-slot rock sample, the characteristic rock block number increases exponentially with an increase of initial impact speed. As the initial impact speeds are 8, 10, 12, 14, and 16 m/s, the characteristic rock block numbers are 263, 282, 306, 337, and 374, respectively.

Generally, as the impact speed varies, the characteristic block distribution of fracture rock samples does not change significantly, but the characteristic block number (Ns) obviously increases with an increase of impact speed. The total characteristic block number of fracture rock with double cut-slots is obviously larger than that of rock with single cut-slot, which indicates the characteristic block size of fracture rock with double cut-slots is smaller than that of rock with single cut-slot.

4.3. Influences of Cut-Slot Spacing, Depth, and Width

In the cut-slot scheme adopted with double grinding wheel, the impact position is located in the center of double cut-slots, so the impact crack development of rock is close to the center symmetry. The influences of double cut-slot spacing are similar to the influences of relative distance between cut-slot and impact position. As the initial impact speed is kept constant, the characteristic block number (Ns) is negatively correlated with grinding wheel spacing. Based on the curve inflection point value(6 mm) in Figure 8 of Section 4.1, the effective spacing of double cut-slots formed by grinding wheel is about 12 mm. As the cut-slot spacing is greater than 12 mm, the characteristic block number (Ns) rapidly decreases with an increase of cut-slot spacing. The rock fracture degree rapidly decreases as the relative distance between cut-slot and impact position increases from 1 to 6 mm. The impact position in the double cut-slot middle can achieve better crushing efficiency and fracture results of rock sample.

From Figure 11, as the cut-slot depth of rock is 5 mm and the initial impact speed increases from 8 to 16 m/s, the fracture unit number of rock near the impact position changes little; however, the impact cracks gradually develop to the deep of rock sample. It can be speculated that the increase of cut-slot depth is beneficial to rock fragmentation. For single cut-slot rock sample, from Figure 11(a), with an increase of vertical distance far away impact position, the fracture unit number of rock firstly decreases rapidly and then slowly decreases to 0. It can be speculated that the cut-slot depth matching the curve zero point of Figure 11(a) will be beneficial to rock fragmentation. Therefore, as the initial impact speed is 8m/s, the depth at the zero fracture unit point is 6 mm, the cut-slot depth should be greater than 6 mm. As the initial impact speeds are 12 and 16 m/s, the depths at the zero point of curves are 11mm and 16mm, and the predicted cut-slot depth should be greater than 11 and 16 mm, respectively. For rock with double cut-slots, the fracture element number also varies nonlinearly as shown in Figure 11(b), it can be speculated that the 8 mm cut-slot depth will be beneficial to the rock fragmentation under the impact loading of different initial speeds.

In addition, based on the displacement distribution of fracture rock under different impact speeds and impact positions, the horizontal displacement produced by rock fragmentation is in the order of 10-4 m, which has not reached the minimum value (1 mm) of cut-slot width. Therefore, as the cut-slot widths of rock formed by grinding wheel are 1.0, 1.5, 2.0, and 2.5 mm, there is little effect on the rock fracture.

The surface environment of asteroids is very complex, such as extreme temperature, vacuum, microgravity, etc. Obtaining rock samples from asteroids is getting more and more attention, albeit with great difficulty. To improve the success rate of asteroid sampling, the dynamic fracturing process of rock by impact breaking rock device is investigated based on CDEM. Under different grinding-wheel cutting and hammer impact schemes, the influence factors of rock breaking are analyzed to optimize suitable working parameters of asteroid sampling device. The following conclusions can be obtained:

  1. The relative distance between slot-free surface and impact position significantly affects the rock fracture under impact loading. As the relative distance increases, the rock crack number, crack expansion range, rock fracture degree and fracture rock block number decrease nonlinearly. As the relative distance of hammer impact is greater than 6 mm, the design of setting free surface by single grinding-wheel cut to increase the rock fragmentation of asteroid sampling could be failure.

  2. The grinding wheel cut-slot increases the free surface of rock sample, which is beneficial to the impact fracture and asteroid sampling. For rock with single cut-slot, the fracture degree and fracture block number increase linearly with an increase of impact speed, while the fracture degree of rock with double cut-slots is not sensitive to the change of lower impact speed. Moreover, the fracture degree of rock with single cut-slot is obviously smaller than that of rock with double cut-slots. Therefore, the double grinding wheel scheme is more suitable for the asteroid sampling.

  3. The rock fracture under the impact loading is negatively correlated with the cut-slot spacing formed by grinding-wheel cutting. The effective double cut-slot spacing is 12 mm. As the cut-slot spacing is greater than 12 mm, the characteristic block number of fracture rock rapidly decreases with an increase of cut-slot spacing. As the double cut-slot spacing is smaller than 12 mm, the characteristic block number slowly decreases with a variation of the relative distance between cut-slot and impact position.

  4. The fracture unit number of rock varies nonlinearly with an increase of the vertical depth from impact position. For asteroid sampling, there is an optimal cut-slot depth corresponding to a certain impact velocity. As the depth of rock cut-slot matches the crack propagation depth, the rock crushing efficiency can be improved. Moreover, the optimal depth of single cut-slot is significantly positively correlated with the impact initial velocity. However, the impact initial velocity has a weak influence on that of double cut-slots. In addition, the cut-slot widths of rock formed by grinding wheel have little effect on the rock fracture of sampling.

The date that support the findings of this study are available from the corresponding author upon reasonable request.

The authors declare that they do not have any commercial or associative interest that represents a confict of interest in connection with the work submitted.

Data curation, writing—original draft, formal analysis and writing—review and editing, Q.Z., C.F., P.C., and S.W. Software and Methodology, C.F., J.F., M.J. Writing—review and funding acquisition, J.F., C.F., and P.C. All authors have read and agreed to the published version of the manuscript.

This research was supported by the National Key Research and Development Project of China (No. 2023YFC3007203); GHfund A of HIECO of China (No. 202302017772); Key Research and Development Project of Henan Province (No. 242102240029 and 232102321130); and Key Research Project of institutions of Higher Education in Henan Province (No. 24A580001).

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