Numerical simulation on interaction stress analysis of rock with conical picks

Tunnelling and Underground Space Technology 85 (2019) 231–242

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Numerical simulation on interaction stress analysis of rock with conical picks

T

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H.S. Li, S.Y. Liu , P.P. Xu School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China Jiangsu Collaborative Innovation Center of Intelligent Mining Equipment, China University of Mining and Technology, Xuzhou 221008, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Conical pick Rock fragmentation Wear Damage

A conical pick is an essential cutting tool used particularly on mining excavators. The cutting performance and wear of the pick directly affect the efficiency and cost of the rock/mine excavation. In this research, to better understand the mechanism of rock fragmentation using a conical pick and the wear mechanism of the pick itself, a numerical model of rock fragmentation when using a conical pick was established. Linear cutting experiments using conical picks were conducted on rock to validate the simulation results. The results indicate that the elemental damage in the crushed zone shows a plastic behavior, whereas crack failures mainly demonstrate a brittle behavior. Moreover, a “V” type caving area is formed from the caving of rock caused by an extrusion between the pick and rock. Finally, the reaction force in the back face of the pick is the main reason for the pick wear, and the main interaction is the mutual compression and friction with the rock.

1. Introduction A conical pick is widely used in rock cutting and is one of the key parts of a mining machine (Bilgin et al., 2006; Balci and Bilgin, 2007). The conical pick shown in Fig. 1, which is installed on a pick-holder and welded onto a helical vane, plays a vital role in rock fragmentation when mechanical excavators are operated. Thus, researches on rock fragmentation mechanism and the wear of a conical pick are of particular importance. Many scholars have conducted theoretical research in this area, and have adopted various numerical simulation methods to study the rock fragmentation mechanism using a conical pick. The maximum tensile stress theory described by Evans and Rånman (Evans, 1972; Rånman, 1985) has been widely used with coal winning machines, continuous miners, roadheaders, and other types of mining machinery. By analyzing full-sized rock-cut test data, Goktan and Gunes (2005) modified Evans’ cutting theory, and pointed out the strong correlation between the cutting peak force and the average cutting force. Nishimatsu (1972) hypothesized that the shear strength failure is the main reason for the high strength of rock breaking, and established a cutting force formula based on the shear strength failure. Liu et al. (2011) built a relationship model for the impact, inclination, and skew angles. When using the installation angle obtained from this model, the direction of the cutting force is along the pick axis, which can reduce the energy consumption.

⁎

Loui and Karanam (2012) studied rock fragmentation using a two-dimensional nonlinear finite element simulation of advanced rock breaking, and found that when the cutting angle is negative, rock breaking occurs because of the shear failure mode, and when the cutting angle is positive, rock breaking occurs because of the shear and tensile failure mode. Kim et al. (2012) discussed the importance of pick rotation. In order to study the effects of cutting intercept, cutting depth, impact angle, inclination angle, and other relevant parameters, full-size experimental investigations were performed. A new model for estimating the peak indentation force of the edge chipping of rocks when using a conical or a pyramidal point-attack pick was established by Bao et al. (2011), who found that the peak indentation force and the depth of a cut follow a power law, and that the new model can reasonably estimate the experimental measurements. Zhou and Lin (2013) explored the means by which the critical transition depth is obtained, and their results showed that the rock cutting follows the Bažant size effect equation for a quasi-brittle material. Jaime et al. (2015) developed a finite element procedure capable of providing reasonable estimates of the cutting forces, and captured the essential characteristics of the fragmentation process. A three-dimensional numerical modeling of a rock-cutting test was conducted in unrelieved mode, and tool forces acting on the point attack pick were recorded (Su and Akcin, 2011; van Wyk et al., 2014). A coal fragment size model was established by Liu et al. (2015) based on coal and rock cutting theory and the effect of four

Corresponding author. E-mail address: [email protected] (S.Y. Liu).

https://doi.org/10.1016/j.tust.2018.12.014 Received 7 April 2018; Received in revised form 17 December 2018; Accepted 20 December 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.

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study on the detailed characterization of the wear mechanisms of conical picks was recently conducted by Dewangan and Chattopadhyaya (2016), and seven different types of wear mechanisms, namely, cracking and crushing, cavity formation, coal intermixing, chemical degradation along with abrasion, long and deep cracks, the heating effect, and body deformations were observed in the five tool samples. However, although researchers have found that not all loading on a pick results in wear, and there have been a few studies on loading that have demonstrated its occurrence. For this reason, the wear mechanism of picks remains poorly understood. Pick wear is tested under multiple cutting conditions, primarily to study the types of wear on the picks. Under these conditions, pick wear is light, with only some surface scratches, and the tested mass loss from the wear is under 1 mg. Although the fruitful achievements of these previous researches provided a reference point for the present study, room for improvement remains. On the one hand, the mechanism of rock fragmentation using a conical pick is complex and poorly understood. On the other hand, there have been few investigations into the rock fragmentation mechanism on a plastic or brittle failure when applying a conical pick. Moreover, experimental studies on the wear mechanism of a pick and the wear area have been deficient. To better understand the rock fragmentation and pick wear mechanisms, a numerical model of rock fragmentation when using conical pick was established in this study with the aim of revealing and describing the reasons for the crushed zone and crack growth under a cutting load, which include the fracture processes of the rock specimen and the mechanism of crushed zone formation, crack initiation, and propagation.

Fig. 1. Conical pick on different mining excavators.

parameters was analyzed in theory and experiment. New indices based on the punch test to predict the performance of hard rock TBMs were introduced by Jeong et al. (2016) and a series of punch tests was performed on rock specimens representing six rock formations in Korea with different dimensions. The rock fragmentation mechanism and failure process induced by a wedge indenter for TBMs were numerically simulated utilizing the discrete element method (DEM) to reveal the rock indentation process and rock-tool interactions (Li et al., 2016). An experimental method used to investigate the rock cutting process of TBM gage cutters based on the full-scale rotary cutting machine (RCM) was proposed by Qi et al. (2016), who found that the cutting forces and specific energy of the gage cutter are lower than those of a normal cutter. The rock breakage process using a single disc cutter, and the ejection speed of the rock fragments, were simulated using three-dimensional FEM coupled with the SPH method to determine the rock penetration process (Xiao et al., 2017). Researchers have also experimentally studied the loading on picks applied in rock cutting as a way to determine the wear of conical picks during use. Liu et al. (2017a, 2017b) had paid attention to pick failure, and pointed out that its failure styles mainly composed of premature wear, carbide tip dropped off, tipping, fracture and normal wear. Among them, Liu et al. (2017a, 2017b) points out that the failure due to wear, such as normal wear, premature wear and carbide tip dropped off, is about 75%. The wear mechanisms in four conical picks which were used in a continuous miner machine for underground mining of coal was investigated using scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) point analysis, and mainly four types of wear mechanisms, namely, coal/rock intermixing, plastic deformation, rock channel formation and crushing and cracking, have been detected (Dewangan et al., 2015). A

2. Methods 2.1. Geometric model and boundaries A three-dimensional model of rock fragmentation with a conical pick is shown in Fig. 2. The rock and conical pick are simplified as a 40 mm × 40 mm × 20 mm cuboid and a φ8 mm × 5 mm cone, respectively. The rock specimen is fixed by restricting the displacement in the x-, y-, and z-directions, and the six faces of the rock are all set as nonreflection boundaries to avoid the effect of a boundary on the rock fragmentation (Gu and Zhao, 2010; Zhiyong et al., 2014). Automatic Lagrange/Lagrange coupling is adopted to solve the interaction problem between the conical pick and rock (Grujicic and Bell, 2013). In the numerical model, the cutting depth and cutting angle are set as 2 mm and 45°, respectively. The geometric strain is applied to define the erosion where the strain increment of the rock elements will be deleted upon an increase to 1.4. To consider the friction contact between the picks and rock, a static friction contact coefficient 0.5 was added to the interactions (Autodyn). To investigate the mesh size and advancing rate of the pick on the

Rock Pick

Simplify

Cutting area

45°

Fig. 2. Geometric and simplified simulation models. 232

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Fig. 3. Pressure of Gauge#1 with different (a) mesh sizes, and (b) advancing rates.

propagation and attenuation of a stress wave, the pressure for Gauge #1 (14, 0, 2) with different advancing rates (mesh size = 1.0 mm) and mesh sizes (advancing rate = 4 m/s) are discussed (shown in Fig. 3). It can be concluded from Fig. 3 that the advancing rates and mesh sizes have a small influence on the stress propagation. Thus, for the rock model described in this paper, the mesh size is set as 1.0 mm (the rock cells in x-, y-, and z-directions are divided into 40, 40 and 20), and to improve the accuracy of the numerical calculation, the grade zoning is in the y-direction using 20 elements with a fixed size of dx = 0.5 mm. In addition, the number meshes for the pick across radius and cells alone length is 8 and 10, respectively, which means the mesh size alone the length and across the radius are all set as 0.5 mm.

Table 1 Related parameters of conical pick (40CrNiMo). Parameters

Value

Parameters

Value

Equation of State

Linear

1.03

Reference density Bulk Modulus Strength Shear Modulus Yield Stress Ap Hardening Constant Bp Hardening Exponent n Strain Rate Constant Cp

7830 kg/m3 159 GPa Johnson Cook 77 GPa 792 MPa 510 MPa 0.26 0.014

Thermal Softening Exponent m Ref. Strain Rate (/s) Strain Rate Correction Failure Damage Constant, Dp1 Damage Constant, Dp2 Damage Constant, Dp3 Damage Constant, Dp4

1.0 1st Order Johnson Cook 0.05 3.44 −2.12 0.002

2.2. Modeling of conical pick was originally formulated for a description of the brittle response of ceramics, and has also been widely used to simulate the dynamic behavior of brittle or quasi-brittle materials, such as rock, concrete, glass, and ice (Ai and Ahrens, 2006; Zhang et al., 2015; Iqbal et al., 2016).

For the material characteristic of the conical pick, a Johnson-Cook mode is used (Johnson and Cook, 1985). This model uses the following equivalent flow stress:

σ¯p = [Ap + Bp θ¯n][1 + Cp ln θ¯/̇ θ¯0̇ ],

(1)

2.3.1. Equation of state for rock The polynomial equation of state (EOS), which is commonly used with the JH2 model, was used for the rock specimen. The relationship between hydrostatic pressure P and volumetric strain μ for the polynomial EOS in the Johnson–Holmquist model is shown in Fig. 4. Here, μ = ρ/ρ0 − 1 is adopted to describe the compression status, where ρ0 is the reference density, and ρ is the current density. An incremental pressure ΔP is added to the calculated pressure from the polynomial EOS, and the ΔP magnitude is determined based on the damage level the rock has experienced. When the maximum strength of the rock has been reached, the rock damage increases because the elastic distortion energy starts to decrease. The extra pressure ΔP is

where σ¯p is the pick equivalent stress, θ¯ is the pick equivalent plastic strain, θ¯ ̇ is the pick plastic strain rate, θ¯ ̇ is the pick reference strain rate (1.0 s−1), Ap is the pick initial yield stress, Bp is the pick hardening modulus, n is the pick hardening exponent, and Cp is the pick strain rate dependency coefficient. To simulate the wear of a conical pick, a fracture damage model is used based on the cumulative damage law:

Dp =

∑ (Δθ¯/θ¯f ),

(2)

where Δθ¯ is the increment of the equivalent plastic strain. According to the Johnson–Cook model, the cumulative strain Δθ¯ is updated at every analysis increment, and θ¯f is the equivalent strain at failure, and is expressed as follows:

θ¯f = [Dp1 + Dp2 exp (Dp3 ζ / σ¯p)] × [1 + Dp4 ln θ¯/̇ θ¯0̇ ]

(3)

where θ¯f depends on the equivalent plastic strain rate θ¯ ̇ and the ratio of hydrostatic pressure to equivalent stress ζ / σ¯p . It also depends on the damage constants (Dpi, 1 ≤ i ≤ 5), which are determined experimentally. The Johnson–Cook parameter values used to simulate the behavior of a 40CrNiMo pick are specified in Table 1. 2.3. Modeling of the dynamic behavior of the rock material To study the stress field and dynamic fracture of a rock specimen, the Johnson–Holmquist constitutive model (JH2) is used. This model

Fig. 4. Relation between pressure and volumetric strain in JH2 model. 233

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σF* = B (P *) M ·(1 + C lnε *̇ )

caused by the conversion of distortion energy into a potential hydrostatic energy accompanied by an increase in volumetric strain, in which the conversion amount is controlled by the fraction 0 ≤ β ≤ 1 (Ai and Ahrens, 2006; Banadaki and Mohanty, 2012). The polynomial EOS can be expressed as follows:

P = K1 μ + K2 μ2 + K3 μ3 + ΔP

where B and M are the parameters of the fractured material, and P*, C, and ε *̇ are the same as those in Eq. (7). An upper limit σ∗Fmax is used to control the position of the strength-fractured surface. For the damaged material, the normalized strength relating closely to the damage can be given as

(4)

σD* = σI* − D (σI* − σF*)

where K1, K2, and K3 are the material parameters to be obtained from the experiments.

(5)

εpf = Dr1 (P * + T *) Dr2

where J2 is the second invariant of the deviatoric stress tensor; Sij are the components of the deviatoric stress tensor; σ1, σ2, and σ3 are the principal stresses. The equivalent stress is commonly used for a description of the elastic limit of the failure criteria, and is given as

σ=

3J2 =

1 [(σ1 − σ2)2 + (σ2 − σ3)2 + (σ3 − σ1)2] 2

(10)

where Dr1 and Dr2 are two damage constants. The material cannot undertake any plastic strain at P * = −T *. As the material undergoes plastic deformation, damage accumulates in the material, and its value can be calculated as

Dr =

(6)

∑ (Δεp/εpf )

(11)

where Δεp is the effective plastic strain during a cycle of integration. The relation between the equivalent plastic strain εp and normalized pressure P* is shown in Fig. 5(b). In the elastic region, no plastic deformation occurs, and the material remains intact with Dr = 0. The total equivalent plastic strain increases as the material undergoes permanent deformations owing to the large equivalent stresses. This reduces the material strength (0 ≤ Dr ≤ 1). When the equivalent plastic strain becomes equal to the strain to fracture εpf , the material is completely damaged, and its strength decreases to the fractured strength.

For intact material, the normalized strength is given by

σI* = A (P * + T *) N ·(1 + C ln ε *̇ )

(9)

2.3.3. JH2 failure criterion In the JH2 model, the yield and failure surfaces coincide at any point in time. However, the amount of plastic strain required for changing the status of the material from intact to fracture depends on the local pressure. The equivalent plastic strain to fracture for this model is obtained from

2.3.2. JH2 strength model The JH2 model consists of the strength models of intact, damaged, and fractured materials. The strength of the intact materials follows the J2 material theory of plastic mechanics as follows:

J2 = 1 6 [(σ1 − σ2)2 + (σ2 − σ3)2 + (σ3 − σ1)2]

(8)

(7)

where σI = σI/σHEL is the normalized equivalent strength, σI is the actual intact strength, and HEL is the Hugoniot elastic limit of the material, which indicates the elastic limit of the material at the turning point of the linear section of the free surface velocity curve (Feng et al., 2016); in addition, P* = P/PHEL is the normalized pressure, P is the actual pressure, PHEL is the pressure at the Hugoniot elastic limit, T* = T/PHEL is the normalized hydrostatic tensile limit (HTL) that material can withstand, ε *̇ = ε /̇ ε0̇ is the normalized strain rate, ε ̇ is the actual equivalent strain rate, ε0̇ = 1.0 s−1 is the reference strain rate, and A, N, and C are the material parameters. As shown in Fig. 5(a), if the current normalized equivalent stress becomes larger than the intact strength of the materials, it will return to the yield surface, and plastic deformation will take place. With an increase in the unrecoverable plastic deformation, the damage in the material will accumulate, and its strength will gradually decrease from intact strength σI* to a lower state σD*. The new yield surface then depends on the level of damage, 0 ≤ Dr ≤ 1. If the material is completely damaged (Dr = 1), the new yield surface will decrease to a fractured material surface. For the fractured material, the normalized strength is represented as *

2.3.4. Determination of JH2 material constants When the JH2 material model is applied to this numerical model of rock fragmentation using a conical pick, several material constants should be provided. The typical material constants for rock are listed in Table 2. Strength parameters: The value of HEL was derived as 4.5 GPa in this study using Eq. (12) (Feng et al., 2016).

HEL =

1 uH 2

E (1 − υ) ρ0 (1 + υ)(1 − 2υ)

(12)

where E is the elastic modulus, υ is the poison ratio, and uH is the velocity of free surface corresponding to the elastic limit, namely, uH = 720 m/s.

Fig. 5. Normalized equivalent strength and equivalent plastic strain versus normalized pressure: (a) Normalized equivalent strength, (b) Equivalent plastic strain. 234

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Table 2 Constants summary of JH2 model for rock. Parameters

Value

Reference density ρ0 Uniaxial compressive strength σc Uniaxial tensile strength σt Possion's ratio ν Intact rock bulk modulus K Intact rock shear modulus G Strength constants Hugoniot elastic limit (HEL) Intact strength constant A Intact strength exponent N Strain rate coefficient C Fractured strength constant B

2657 kg/m 161.5 MPa 7.3 MPa 0.20 25.7 GPa 21.9 GPa

3

4.5 GPa 0.76 0.62 0.005 0.25

HEL =

3 K3 μHEL

μHEL 4 + G 3 1 + μHEL ⏟ stress Deviatoric

1

σC (−m + 2

m2 + 4 ).

0.62 0.25 25.7 GPa −4500 GPa 3e5 GPa −54 MPa 0.005 0.7 0.5 Hydro

1

(16)

At this time, a series of compatible σ1 can be obtained from Eq. (16). Correspondingly, a series of P and σ values can be calculated from Eq. (6), where P is the hydrostatic pressure, and σ is the effective stress as defined in Eqs. (4) and (6). The hydrostatic tensile limit (HTL) is set at approximately −54 MPa, as obtained through numerical adjustments. The normalized hydrostatic tensile limit is T* = −0.015. Now, sufficient information is available to calculate the parameters of Eq. (8). The parameters A = 0.76 and N = 0.62 can be derived by fitting the series of (P*, σI ∗ ) with Eq. (7). Then, constant B of the fractured rock in Eq. (8) is considered to be one-third of constant A, and constant M is assumed to be the same as constant N. In addition, a normalized strength equal to 25% of HEL is taken as the maximum fractured strength ratio, σ∗Fmax. Damage parameters: Damage under a high confining pressure cannot be measured directly. Therefore, the damage parameters D1 and D2 are assumed to be 0.005 and 0.7, and the same values used in Ai and Ahrens (2006) and Banadaki and Mohanty (2012) are applied.

(13)

(14)

where m and s are the material parameters (for intact rock, s = 1), σC is the uniaxial compressive strength of the intact rock, and σ1 and σ3 are the axial and confining principal stresses, respectively. When σ1 = 0, the tensile strength of the intact rock is expressed as

σt =

Fractured strength exponent M Max fractured strength ratio σ∗Fmax Pressure constants Intact rock bulk modulus K1 Polynomial EOS constant K2 Polynomial EOS constant K3 Failure constants Hydro tensile limit (HTL) Damage constant Dr1 Damage constant Dr2 Bulking factor β Type of tensile failure

2 σ σ1 = σ3 + 161.5 ⎛22.08 3 + 1⎞ 161.5 ⎝ ⎠

where K1, K2, and K3 are the EOS parameters, in which the value of K1 is equal to the bulk modulus (K1 = 25.7 GPa). The parameters K2 and K3 can be obtained by fitting the planar impact experiment data, and K2 and K3 are set as −4500 and 3e5 GPa, respectively (Xia et al., 2017). Here, G is the shear modulus in Eq. (13). By solving Eq. (13), μHEL is determined as 0.02795. Then, substituting μHEL into Eq. (4), the hydrostatic pressure components at HEL-PHEL = 2.99 GPa, and the equivalent stress at σHEL = 1.7 GPa, can be acquired. In the JH2 model, the material constants A and N for granite are derived according to the Hoek–Brown criterion, which was originally developed for an underground excavation design (Eberhardt, 2012). For intact rock, the Hoek–Brown criterion can be expressed as follows:

σ1 = σ3 + σC (mσ3/ σC + s ) 2

Value

derived. In addition, Eq. (14) can be rewritten as

Here, HEL includes both the hydrostatic pressure and the deviatoric stress components, and is given as follows: 2 K1 μHEL + K2 μHEL + ⏟ Pressure(PHEL)

Parameters

3. Verification of the numerical model 3.1. Calibration and verification

(15)

In this section, numerical uniaxial compressive tests conducted to calibrate the mechanical parameters of the rock sample are described.

By substituting the uniaxial compressive strength and tensile strength of the rock specimen in Table 2 into Eq. (15), m = 22.08 can be

Fig. 6. Uniaxial compressive test: (a) Rock parameter testing system, (b) model configuration (with a mathematical mesh size of 0.5 mm and 3156 elements contained), (c) failure mode of the rock sample from laboratory experiment, and (d) failure mode predicted by simulation. 235

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deformation and crack propagation stages under the loading of the pick cutting. A crushed zone can be seen after these rock chips are cleaned out, and the bottom of the groove is a shear-induced fracture. However, during the entire cutting process, no large blocks of rock fall from the rock specimen, and few tensile and radial cracks appear. As shown in Fig. 9(b), only the cutting grooves and some spall cracks can be observed, similar to those during the numerical simulation, and the experimental macro profile of the wear area is similar with that of the simulation results, which validates the simulation results.

To calibrate the mechanical parameters of the numerical models, laboratory uniaxial compressive tests on cylinder specimens conducted using an MTS 815 testing machine (shown in Fig. 6(a)) in accordance with the ISRM standards are first carried out to obtain the properties of the rock samples. On this basis, a numerical uniaxial compressive test is conducted to calibrate the mechanical parameters by approximating the uniaxial compressive curve as well as the failure mode of the rock samples. The cylinder specimens for the uniaxial compression test are φ50 mm × 100 mm. The mechanical properties of the rocks are as shown in Table 3. A configuration size of φ50 mm × 100 mm is adopted in the numerical models (as shown in Fig. 6(b)), which is consistent with that used in the laboratory experiment. Two rigid platens are used in the model, in which the lower platen is fully fixed whereas the upper one moves downward at a constant velocity of 5 mm/s to maintain a quasistatic loading state. The simulated curve agrees well with the corresponding experimental curve. In addition, a similar macroscopic failure mode is simulated (shown in Fig. 6(d)) as compared with that obtained from the laboratory test, in which a major shear fracture along with several extensional cleavages propagate and coalesce, leading to a final rupture of the sample. The axial stress-strain behaviors (given in Fig. 7) obtained by the numerical simulation is basically coincided with that of the laboratory results. It is noteworthy that the fluctuation of the numerical simulation is relatively lager than that of the laboratory, which may be induced by the mesh size in the numerical models. Generally speaking, a good approximation of the mechanical properties, as well as the fracture behaviors, can be obtained using the numerical model. In addition, the rock model used was applied in Xia et al.’s study (2017) to investigate the influence of the side free surface on the rock fragmentation induced by a single TBM disc cutter. As a result, the calibrated rock model is considered to be valid and was used in the following simulations.

4. Results and discussion 4.1. Rock dynamic fragmentation process The rock dynamic fragmentation process induced by a conical pick is shown in Fig. 10. At 40 μs, the pick compresses the rock, producing a compression deformation in the compressive zone, and the rock failure mainly occurs in the vicinity of the contact point against the pick. A crushed zone formed near the contact point occurs owing to the highdensity shear stress field. The maximum Mises stress of the rock underneath the carbide tip is considerably greater than the compressive strength of the rock as the contact area between the pick and the rock increases, thereby causing rock fragmentation and propagation of the crushed zone; however, the crushed zone is not distinct. At 100 μs, the interaction force between the pick and rock increases continuously with the pick cutting, and cracks are developed at the contact point between the pick and rock until the tensile and shearing stresses on the rock exceed the tensile and shear strengths. From 200 μs, the crushed zone in the vicinity of the contact point is enlarged from the extremely high compressive stress, and several cracks are produced around the crushed zone. At 500 μs, the cracks on the upper surface will extend and finally reach the side surface. In this way, a spall crack will be formed and tends to fall from the rock specimen. As the pick continues to cut the rock specimen, the former fracture pattern will be duplicated. To better observe the damage distribution inside the rock, five cross sections in the x-direction are extracted using a clipping plane method shown in Fig. 11. All five cross sections shown in Fig. 11 illustrate that a cutting groove can be observed, and that one or more radial tensile cracks intersect on the upper surface. It is worth noting that a median crack is formed perpendicular to the bottom in the interior of the rock, and radial cracks are generally symmetrical about the cutting direction. These phenomena appear as a result of the rock continuity and isotropy, which have little effect on the rock failure behavior or mechanism. In conclusion, the developed rate-dependent numerical model can reproduce the formation, propagation, and attenuation of stress waves relatively well during the rock fragmentation process, as well as the breakage behaviors of the rock under the action of pick cutting. To investigate the rock fragmentation mechanism for interaction between the rock and pick, the stresses, pressure, and damage versus time, as well as amplified views of the element damage process for an element containing Gauge #4 (14, 0, 2) in the crushed zone, are shown in Fig. 12. Owing to a certain distance between Gauge #4 and the contact point, the stress wave propagates toward Gauge #4 within approximately 30 μs, and before the shock wave reaches the element, the element pressure is equal to zero and the yield stress is approximately 285 MPa. It was found that the yield stress increases with pressure, and reaches its maximum value of 472 MPa at 2.62 ms, where the pressure is equal to 116 MPa. As expected for the JH2 model, this result distinctly shows that the pressure is dependent on the strength. The rock exhibits elasticity during the process of shock wave propagation until the Mises stress reaches the yield stress at Gauge #4, which indicates that the element will not be damaged. As shown in Fig. 12(b), the Mises stress does not reach the yield stress before 2.62 ms, and the element starts to deform plastically. When the element in the crushed zone exhibits plastic deformation, the

3.2. Experimental equipment To validate the simulation results, a series of cutting experiments using a conical pick under different velocities were conducted using a linear cutting experiment system (LCES) when the cutting depth was equal to 5 mm, as shown in Fig. 8. LCES mainly includes a signal acquisition system, hydraulic system, and linear cutting test bench. The hydraulic system is used to realize the feeding motion of a mechanical tool with different velocities and to fix the rock; the signal acquisition system is used to collect the tool displacement and oil pressure of the propulsion hydraulic cylinder. The pick is fixed on the loading device, and a rock specimen with a size of 400 mm × 400 mm × 200 mm is fixed on the supporting platform through the hydraulic cylinder. The propulsion hydraulic cylinder drives the loading device horizontally when cutting the rock specimen. 3.3. Comparison between experimental and numerical results To validate the developed rock-breaking model, comparisons were made between the experimental and numerical results on the cutting force and rock breaking process. Fig. 9(a) shows that the trend in the cutting force used in the experiment at 4 m/min is similar to that of the numerical methods. It is clear that the cutting force of the pick initially increases over time and then fluctuates at a certain value. Fig. 9(b) illustrates the rock fracture patterns and macro profile of the pick wear when applying a different velocity of 2–9 m/min, the cracks profiles of which are marked by the red1 lines and the wear area is marked by the blue lines. The figure indicates that the rock will be subjected to elastic 1 For interpretation of color in Fig. 9, the reader is referred to the web version of this article.

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Table 3 Rock properties.

1 2

Compressive strength σc (MPa)

Elastic modulus E (GPa)

Poisson's ratio μ

Tensile strength T (MPa)

Density ρ (g/cm3)

162.51 166.95

39.09 47.22

0.291 0.315

9.19 10.05

2.60 2.72

The element fails at 2.66 ms, which indicates that the element strength changes from intact to fractured rock. Although the element stresses in the crushed zone are different from each other prior to failure, their failure behaviors are similar. Therefore, it is unnecessary to present the failure behaviors of the other elements in the present paper.

4.2. Propagation and attenuation of stress wave In rock engineering, the damage criteria of the rock under loads are generally governed by the threshold values of wave amplitudes (Gu and Zhao, 2010). Therefore, the wave attenuation across fractured rock is important on assessing the stability and damage of rock under cutting loads. Fig. 13 is the evolution diagram showing the formation, propagation and attenuation of stress wave in rock under cutting load. In the initial stage (t = 30 μs), a dynamic pressure is formed on the rock surface, and the dynamic pressure acts on rock surfaces and propagates inside the rock in the form of a stress wave. From 40 μs, the stress wave propagates on the rock upper surface in a spherical wave-

Fig. 7. Comparison in axial stress-strain behaviors of the rock sample between laboratory test and numerical simulation.

Fig. 8. Linear cutting experiments system.

form centering on the contact point. In fact, the stress propagates as the spherical wave is not sustained, which occurs because, while a stress release zone is formed in the area below the contact point, the compressive stress effect decays rapidly, which is a cyclical process that occurs during cutting; thus, only one rock spalling process was researched. As we can see, the maximum pressure at 280 μs is the highest, and declines sharply in the next step, which means that the fracture zone is formed owing to the release of stress and the elastic potential energy. It is clear that, when the rock is subjected to load shocks, the disturbances are transmitted throughout the rock by stress waves,

damage accumulates from 0 to 0.46, as shown in Fig. 12(b). The complex stress state causes the Mises and yield stresses to be separated from each other briefly. Next, the Mises and yield stresses contact each other within the local region A, where the damage increases from 0.46 to 1 at 2.66 ms. The element pressure consistently presents a positive value when the element is damaged; therefore, the multiple steps that occur during the element damage history indicates that the element damage presents a plastic behavior. Then, the element containing Gauge #4 fails in terms of shear, and the stress declines to 0 at 4.7 ms after the element is deleted when the strain arrives at the erosion level. 237

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Fig. 9. Comparisons between experiment and simulation: (a) cutting force, (b) experimental rock fracture patterns.

Fig. 10. Dynamic rock fragmentation process induced by conical pick.

Fig. 11. Damage distributions of different cross sections in the x-direction at 4 mm interval.

longitudinal wave separates from the transverse wave owing to the difference in speed inside the material, and propagates more deeply into it. As is well known, a longitudinal wave propagates in a compression-tension manner in a solid, which will cause a radial tensile stress when the wave expands rapidly forward. However, the motion in a transverse wave is perpendicular to the propagation direction, which

which include longitudinal, transverse, and Rayleigh surface waves. Both the longitudinal and transverse waves propagate inside the material, whereas the Rayleigh wave propagates on the surface (Lu et al., 2015). The positions of the longitudinal and transverse wave fronts are in accordance with the boundary of the contact area because both of the waves are still attached to the edge of the loading area. However, the 238

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Fig. 12. Pressure and corresponding damage versus time in different positions: (a) Pressure, stress and damage for Gauge#4, (b) Amplified views of region A.

Fig. 13. Evolution diagram of stress wave propagation in the rock.

wave is sufficiently intense, cracks propagate under tensile stress, forming crack surfaces that are distributed rather consistently with the stress wave fronts. Moreover, it can be seen that the pressures are all lower than 0 except for Gauge #4 when the selected points are damaged, which indicates that the points selected fail owing brittle behavior and that Gauge #4 fails owing to plastic behavior. The stress wave is not able to damage the rock when the peak pressure is smaller than the rock tensile strength. At this time, they can only induce radial and spall cracks.

will cause a shear stress and circumferential tensile stress in the solid. The Rayleigh surface wave, with both vertical and horizontal components, will cause tensile and shear stresses accordingly. The form of the stress waves in a solid was monitored using piezoelectric crystals, whereas Swain and Hagan (1980) observed the formation of tensile stress in the radial and axial directions. The tensile and shear stresses caused by the pick may account for the initiation and extension of cracks in a solid. In addition, the interference and reflection of different waves will result in the reinforcement of the stress wave, which is conducive to the generation of cracks. To investigate the propagation and attenuation process of a stress wave, the element pressure (solid line) and corresponding damage (dotted line) at different positions as a function of time were recorded, as shown in Fig. 14. After the rock-bearing cutting load, the pressure of the element containing Gauge #1 achieves the maximum value of 83 MPa at 0.79 ms before being damaged. After approximately 0.4 ms, the maximum pressure value of Gauge #2 decreases to 55 MPa owing to the energy dissipation associated with the stress wave propagation. In addition, the maximum pressure is only 36 MPa when the stress wave propagates to Gauge #3, which indicates that the stress wave intensity weakens sharply during the propagation within the rock medium. This is because the intensity of the stress wave decays rapidly, and local elastic energy is released in the direction opposite the propagation of the stress wave with the deepening of the propagation. When the stress

4.3. Wear process of pick The key to study the pick wearing parts is to analyze the load condition during rock cutting. And the existed research on rock breaking mechanism and theory mainly includes the maximum tensile stress theory, coulomb Mohr theory and fracture mechanics theory. But the existed models don’t consider the friction contact between picks and rock, which resulting in the obtained model can’t simulate the wear of picks as well as the load situation of pick accurately. In order to study the wear condition of the pick, it is necessary to study the load condition of the pick during the cutting process, and the loading area of the picks is shown in Fig. 15. During the cutting process, the pick wedges into the rock at a fixed angle, and the rake face leads to crack generation and a block caving 239

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Fig. 14. Pressure and corresponding damage versus time in different positions: (a) Pressure and corresponding damage, (b) Amplified views of region B.

formation. In addition, a “V” type caving line is formed owing to the caving of rock caused by an extrusion between the pick and rock, and the back face will form interference against the intact rock, which is the main reason for the pick wear. Moreover, the wear process of a pick is far greater than that of the rake face. Area A is where rock caving mainly occurs, and thus the interaction between the pick and rock is an intermittent compression and crashing, which mainly causes a cutting force and a small portion of a normal force, which can be ignored. The interaction between the pick and rock in area B is a continuous compression and friction, which mainly causes the vast majority of the normal force and side force. It should be pointed out that the reaction in area B of the pick is the main reason for the wear. However, it is difficult to measure a side force during the actual process because the side forces will offset each other, which is not conducive to research on pick wear. Thus, a numerical simulation is used to analyze the damage to the pick. As is well known, the pick will not be damaged during the experiment and simulation owing to the short cutting process, and thus changes in the velocity boundary or the related parameters of a conical pick will solve this simulation problem. To investigate the pick wear, the pick is reused and the cutting length is increased during the experimental cutting process. Fig. 16 illustrates the simulated damage area of the pick over time, and it can be seen that the damage area is focused on the center of the fore body during the initial contact process. However, as the pick begins to wedge into the rock, the extrusion force caused by the rock on the pick leads to the damage area gradually spreading to both sides. In

addition, the simulation results demonstrate that the interaction time between the rake face (area A) and rock is clearly less than that of the back face (area B). Moreover, friction occurs between the back face and rock, which can be interpreted as the reason why the damage area in the back face is larger than that of the rake face. In contrast, the interaction between the rake face and rock is a discontinuous mutual extrusion and collision, which is a complicated process for determining the wear mechanism, such as the wear types; in addition, the mechanism is relatively complex, such as micro-cutting wear, deformation fatigue wear, and erosion wear, although the part causing pick wear is relatively small. The reaction force on the back face is the main reason for the pick wear, and the main interaction is the mutual compression and friction with the rock, thereby producing the cutting and side forces, respectively. The simulation result for the damage area is consistent with the theoretical analysis of the load area, which validates the correctness of the simulation results. 5. Conclusions In this study, the three-dimension FEM models of rock fragmentation induced by single conical pick using JH2 model is established to investigate rock fragmentation mechanism and the wear process of pick, which includes the rock fragmentation pattern and pick wear areas. The rock dynamic fracture process, including crushed zone, cracks initiation and propagation, is well simulated. And the damage distribution of the rock is acquired by the clipping plane method. Then,

Fig. 15. Loading area of conical pick. 240

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Damage 6.708e-2 6.037e-2 5.367e-2 4.696e-2 4.025e-2 3.354e-2 2.683e-2 2.012e-2 1.342e-2 6.708e-3 0.000e+0 Damage 4.372e-1 3.935e-1 3.498e-1 3.061e-1 2.623e-1 2.186e-1 1.749e-1 1.312e-1 8.744e-2 4.372e-2 0.000e+0

300ȝs

Damage 1.127e-1 1.014e-1 9.012e-2 7.886e-2 6.759e-2 5.633e-2 4.506e-2 3.380e-2 2.253e-2 1.127e-2 0.000e+0 Damage 1.000e+0 9.002e-1 8.001e-1 7.001e-1 6.001e-1 5.001e-1 4.001e-1 3.001e-1 2.000e-1 1.000e-1 0.000e+0

100ȝs

350ȝs

Damage 1.605e-1 1.444e-1 1.284e-1 1.123e-1 9.628e-2 8.023e-2 6.419e-2 4.814e-2 3.209e-2 1.605e-2 0.000e+0 Damage 1.000e+0 9.002e-1 8.001e-1 7.001e-1 6.001e-1 5.001e-1 4.001e-1 3.001e-1 2.000e-1 1.000e-1 0.000e+0

150ȝs

y

x z

450ȝs

Fig. 16. Simulation results of the pick damage area.

References

the wear mechanism, damage area and macro profile of the pick are investigated based on theoretical analysis, numerical simulation and experiments. Finally, a series of cutting experiments are conducted with LCES to validate the numerical results. According to the above numerical simulation and experiments, the following conclusions are concluded:

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(1) The rock fragmentation process under cutting load, including crushed zone, cracks initiation and propagation is well simulated and verified. It can be concluded that the failure behavior of elements in crushed zone is different from that in the cracks. The element damage in the crushed zone shows plastic behavior, because the corresponding pressure is positive when the element damaged. By contrary, the element in cracks fails mainly in brittle behavior. (2) Stress wave induced by the conical pick propagates on the rock upper surface in a spherical wave form centering on the contacting point. The intensity of stress wave weakens sharply during the propagation in the rock medium because the intensity of stress wave decays rapidly, and local elastic energy is released in the direction opposite to the stress wave propagation with the deepening of propagation. When the stress wave is intense enough, cracks propagate under tensile stress, forming crack surfaces that are distributed rather consistently with the stress wave fronts. (3) The loading area induced by conical pick during cutting process is analyzed and the results indicate that a “V” type caving area is formed due to the caving of rock caused by an extrusion between the pick and rock, and the reaction force in back face is the main factor for the pick wear and the main interaction form is the mutual compression and friction with the rock, and the cutting force and the side force are produced respectively.

Acknowledgements This work is supported by the Fundamental Research Funds for the Central Universities (Grant No. 2018BSCXB16) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX18_1960).

Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.tust.2018.12.014. 241

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