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Abstract

Simulation of brittle regime machining of materials (such as ceramics) is often difficult because of the complex material removal mechanisms involved. In this study, the discrete element method is used to simulate the dynamic process for machining of slip-cast fused silica ceramics. Flat-joint contact model is exploited to model contacts between particles in synthetic discrete element method models. This contact model is suitable for modeling of brittle materials with high ratios (higher than 10) of unconfined compressive strength to tensile strength. The discrete element method has the ability to simulate initiation, propagation, and coalescence of cracks leading to chip formation in the brittle regime of cutting. Applying the discrete element method, the influences of operating conditions on the creation of surface/subsurface damages, chip formation, and cutting forces are studied. It is shown that the parameters of the material model determined from conventional calibration tests do not provide quantitatively accurate prediction of cutting forces. As such, model updating is carried out using the forces obtained in the cutting experiments, and the numerical results are verified against experimental cutting forces. The differences between experimental and numerical machining forces are in the range of 10%–30%. Finally, the results of discrete element method simulations reveal that the nature of micro-crack propagation is brittle in the machining process of ceramics.

Keywords

Ceramic machining slip-cast fused silica ceramic discrete element method crack propagation

Introduction

The use of ceramic parts in various applications is increasing due to their superior physical and mechanical properties such as high melting temperature, low thermal conductivity, low electrical conductivity, chemical stability, high corrosion resistance, and high wear resistance. However, machining of ceramic parts is often a challenging task because of its inherent hardness and brittle nature. There is a vast body of literature on ceramic machining which focus on overcoming their machining difficulties.^1–4 Problems such as surface and subsurface damages are common in machining of ceramic materials.^5–7 Therefore, it is worthwhile to model the machining process of ceramics to gain better understanding of the effects of various parameters on the quality of the machined ceramic part.

Few studies have been conducted to model brittle regime machining of ceramic materials. In contrast, ductile regime machining is usually modeled using the finite element method (FEM). For instance, Kumbera et al.⁸ simulated the machining of silicon nitride ceramics at the micrometer scale in ductile regime utilizing FEM. Brittle regime machining of ceramics causes a large number of cracks and damages which are difficult to model using FEM.

The discrete element method (DEM) is a better alternative to the FEM analysis in modeling of the behavior of brittle materials. The DEM was first introduced by Cundall⁹ to analyze rock mechanics problems. It simulates a brittle material as a collection of compacted particles with interactions between them. The particle flow code (PFC) is an explicit dynamic implementation of DEM. In the PFC, particles are assumed to be rigid, and the shape of each particle is usually a disk (in two-dimensional (2D)) or a sphere (in three-dimensional (3D)). Potyondy and Cundall¹⁰ presented a bonded-particle model (BPM) based on DEM theories for rock. In the BPM, particles can move (rotate and translate) independent of each other, while bonds can exist at contact points between them (particles interact only at contact points). Bonds have limited strengths and can break under load. In the BPM, a crack forms when a bond breaks. When broken bonds increase, cracks propagate, and may coalesce to separate sections from the compacted particles and form fragments. Hence, the crack formation mechanism in the DEM is much easier than that in the FEM. In synthetic samples composed of bonded particles, there are completely different crack patterns for tensile and compressive (confined and unconfined) tests. Moreover, micro-cracks and localized macro-fractures occur spontaneously. Reproducing these phenomena by continuum-based models (e.g. FEM) is often inefficient.¹⁰

Although the DEM method can be used to model ceramics in various applications, here, only the literature on the application of DEM in machining of ceramics is briefly reviewed. Tan et al.¹¹ utilized DEM to simulate crack initiation and propagation in polycrystalline Al₂O₃ during the machining process. Their simulation results demonstrated that cracks are initiated right under or in front of the cutting tool. In addition, the machined surface had many micro-cracks; some of them propagated downward to form macro-cracks or forward to remove material from the workpiece. Also, Tan et al.¹² used DEM to model fracture and damage in the machining process of polycrystalline SiC. Their study demonstrated the capability of DEM in simulating the micro-cutting process of ceramics. Their simulations showed that lower cutting depth with higher cutting speed in the machining process could reduce the damage to the machined surface and provide optimal machining results. Jiang et al.¹³ utilized the DEM method to simulate the grinding process of SiC ceramics. They indicated that the number of cracks and the average grinding forces increased smoothly with increasing grinding time. Also, the number of cracks rapidly rose when grinding forces change intensely. Their results revealed that the workpiece speed and the depth of grinding had the greatest effects on the grinding forces, respectively. Qiu et al.^14,15 studied the machining mechanism of glass by the DEM method. Their 3D simulation results showed that tool rake angle had the greatest impact on chip deformation and cutting force. They suggested that a positive rake angle is more effective for reducing the fluctuations of cutting force and for chip detachment in the plastic removal mode of glass. Their milling simulations demonstrated that for the axial depth of cut higher than the subsurface depth of fracture, a high surface quality was achieved by removing the fracture-induced damage by the subsequent flute. Ye and Kang¹⁶ studied the numerical simulation for pre-stressed machining of granite by DEM. Their simulation results depicted that increasing the pre-stress could prevent the radial crack from propagation, shorten the propagation length of transverse crack, and reduce the damage in the machining process. Jiang et al.^17,18 worked on DEM simulations and experimental tests for pre-stressed machining of SiC. Their numerical and experimental results showed that the number of radial cracks decreased with an increase in the value of pre-stress. They concluded that the tool edge radius had a great influence on the number of surface cracks, while the value of pre-stress had a great influence on the maximum crack depth. Peng et al.¹⁹ established a DEM model to describe the friction and abrasion behavior between the Sialon ceramic tool and chip interfaces in machining of superalloys. Their numerical results demonstrated that higher cutting speed within a certain range reduced the tool wear, while increasing the depth of cut greatly raised the tool wear. Yang et al.²⁰ applied DEM modeling to investigate the material removal process for conventional and laser-assisted machining of silicon nitride ceramics. Their studies depicted that the material removal mechanism for conventional machining was brittle fracture (by lateral cracks or crushing), while the material removal mechanism for laser-assisted machining was mostly the propagation of lateral cracks. Shen et al.^21,22 utilized the DEM method for laser-assisted milling of silicon nitride ceramics. Their experimental observations and numerical results showed that the fundamental mechanism of material removal in laser-assisted milling was brittle fracture. Furthermore, the formation and propagation of cracks were the most important factors that affected machining forces. Also, with an increase in the depth of cut, the machining forces and edge chipping increased. Shen and Lei^23,24 used the DEM method for laser-assisted milling of silicon nitride ceramics. They illustrated that the machining forces were highly dynamic with large peaks. Moreover, numerical results depicted that a long median crack propagated downward when the thrust force reached its peak. They showed that a long lateral crack propagated forward when the main cutting force reached its peak. Li et al.²⁵ modeled grinding wheels using the DEM method. They demonstrated that the DEM had the ability to simulate the topography, microscopic structure, fracture behavior, and grinding performance. Blaineau et al.²⁶ studied the subsurface mechanical damage for fused silica glass during diamond abrasive grinding using DEM. They illustrated that for rough bound abrasive grinding, by minimizing feed rate and depth of cut and maximizing spindle speed, the maximal depth of subsurface damage was minimized. More recently, Ruitao et al.²⁷ utilized the DEM method to simulate ceramic tool wear in pre-stressed machining of superalloy GH4169. They simulated the effect of pre-stress, cutting depth, and cutting speed on tool wear. Yang et al.²⁸ investigated on the DEM simulation of orthogonal machining of soda-lime glass. They compared the machining of regular and grooved workpieces and showed that cutting forces were reduced and subsurface cracks were eliminated for grooved workpieces in comparison with regular workpieces.

Slip-cast fused silica (SCFS) is a porous, optically opaque, and white body ceramic. This amorphous ceramic possesses outstanding properties such as high resistance to thermal shock as well as proper electromagnetic characteristics.²⁹ Machining of SCFS ceramics is often performed by diamond grinding with low wheel speeds and feed rates. High feed rates can cause tensile failure in the SCFS workpiece due to the low tensile strength of SCFS ceramics.

In this article, a DEM model is developed for simulation of brittle regime turning of the SCFS ceramic. In order to create a synthetic model of SCFS ceramic with the same mechanical macro-properties as the real material, micro-parameters of the flat-joint contact model (FJCM) contact model are adjusted using conventional numerical calibration tests. The suitability of these tests for simulation of cutting process is investigated, and DEM model updating is used to estimate machining forces.

Discrete element modeling and calibration

The DEM model used in this study is created within the PFC^2D software environment. Figure 1(a) shows an assembly of compacted particles. Figure 1(b) displays the network of black lines connecting the centers of each pair of contacting particles in the assembly. A synthetic sample (in 2D) of a brittle material can be generated (based on BPM) in PFC^2D by performing the following steps: (1) a rectangular assembly of compacted circular particles is generated. Porosity, width, height, range of particle size (radius of particles varies uniformly), and density for this sample should be determined. Each particle is placed in an arbitrary location in the rectangular vessel (Figure 1(a)). In 2D problems, each particle has two translational and one rotational degrees of freedom. (2) Contact model and proper bonds are installed between all adjacent particles (Figure 1(b)). Two BPMs which can be used to model brittle material behavior are parallel bond model and FJCM. These bonding models are described subsequently. (3) The contact and bond parameters should be adjusted using numerical calibration tests (e.g. biaxial compression test). The micro-parameters of the synthetic sample must be adjusted such that the macro-properties (such as modulus of elasticity, Poisson’s ratio, and compressive strength) of the sample correspond to the real properties of SCFS ceramics.

Figure 1.

A synthetic sample of compacted particles generated by PFC^2D: (a) assembly of particles which have a certain porosity, and each particle is placed in an arbitrary location and (b) contact network between particles.

In the DEM method, the standard governing equations of rigid body dynamics for pth particle (in 2D) are as follows

m_{p} {\overset{\cdot\cdot}{u}}_{p} = F_{p}

(1)

I_{p} {\overset{\cdot}{ω}}_{p} = T_{p}

(2)

where m, $u$ , $F$ , I, $ω$ , and T are the mass of particle, the centroid displacement vector of particle, the vector of resultant force, the moment of inertia of particle, the angular velocity of particle, and the resultant moment, respectively. The resultant force and moment of each particle are due to contact forces between adjacent particles.

Parallel bond model

The parallel bond acts as a cement between two contacting particles. An assembly that uses the parallel bond (as a contact model) displays two types of behavior in contact zones: grain behavior and cement behavior. Figure 2 demonstrates a schematic view of the parallel bond model. The grain behavior occurs due to particles overlapping and may lead to normal and shear forces that are transmitted between contacting particles (Figure 2(a)) as follows

F^{n} = K^{n} U^{n}, U^{n} > 0

(3)

Δ F^{s} = - k^{s} Δ U^{s}, F^{s} \leq μ F^{n}

(4)

in which

K^{n} = \frac{k_{n}^{A} k_{n}^{B}}{k_{n}^{A} + k_{n}^{B}} = 2 E_{c}

(5)

k^{s} = \frac{k_{s}^{A} k_{s}^{B}}{k_{s}^{A} + k_{s}^{B}}

(6)

where $F^{n}$ , $F^{s}$ , $U^{n}$ , $U^{s}$ , $K^{n}$ , $k^{s}$ , $k_{n}$ , $k_{s}$ , $E_{c}$ , and $μ$ are normal contacting force, shear contacting force, the overlap of particles, the relative shear displacement, the contact normal stiffness, the contact shear stiffness, the normal stiffness of particles, the shear stiffness of particles, Young’s modulus of particles, and the minimum friction coefficient of particles, respectively. Figure 2(b) exhibits a mechanical contact force model for the grain behavior. This model shows that when a gap exists between two contacting particles, the grain behavior cannot occur. Clearly, unbonded particles can only show grain behavior. On the contrary, parallel bonds can transmit moments as well as normal and shear forces due to their cement behavior (Figure 2(c)) as follows¹⁰

Δ {\bar{F}}^{n} = 2 \bar{R} {\bar{k}}^{n} Δ U^{n}

(7)

Δ {\bar{F}}^{s} = - 2 \bar{R} {\bar{k}}^{s} Δ U^{s}

(8)

Δ {\bar{M}}^{s} = - \frac{2}{3} {\bar{R}}^{3} {\bar{k}}^{n} Δ θ^{s}

(9)

in which

\bar{R} = λ \min (R^{A}, R^{B})

(10)

{\bar{k}}^{n} = \frac{{\bar{E}}_{c}}{R^{A} + R^{B}}

(11)

where ${\bar{F}}^{n}$ , ${\bar{F}}^{s}$ , and ${\bar{M}}^{s}$ are normal force, shear force, and bending moment carried by the parallel bond, respectively. In addition, ${\bar{k}}^{n}$ , ${\bar{k}}^{s}$ , $θ^{s}$ , R, $\bar{R}$ , ${\bar{E}}_{c}$ , and $λ$ are normal stiffness of parallel bond, shear stiffness of parallel bond, the relative rotation, the particle radius, the parallel bond radius, Young’s modulus of contacts, and the radius multiplier, respectively. Furthermore, the cement behavior enables bonded particles to withstand tensile normal forces. If tension or shear forces exceed from strength limit of parallel bonds, the bonds are broken. The maximum tensile and shear stresses of the parallel bond are as follows¹⁰

{\bar{σ}}_{\max} = \frac{3 | {\bar{M}}^{s} |}{2 {\bar{R}}^{2}} - \frac{{\bar{F}}^{n}}{2 \bar{R}}

(12)

{\bar{τ}}_{\max} = \frac{| {\bar{F}}^{s} |}{2 \bar{R}}

(13)

Figure 2.

Parallel bond model: (a) schematic of grain behavior, (b) contact force model for grain behavior, and (c) schematic of cement behavior.

The parallel bond model is widely used to simulate brittle materials (e.g. ceramics), because of its ability to model brittle failure behavior and crack propagation. However, the ratio of unconfined compressive strength to tensile strength ( $UCS / T$ ) of compacted assemblies is low in the parallel bond model. Potyondy³⁰ introduced FJCM as an alternative. The parallel bond model applied in BPM gives $UCS / T$ ratios of 3–7,³¹ while most of the brittle materials and ceramics have $UCS / T$ ratios higher than 10. For instance, SCFS ceramics have $UCS / T$ ratios of approximately 13.7.³²

FJCM

Grains in BPM are round particles, while they are angular in real materials. Thus, if all bonds of a particle are broken, the rotation of this particle cannot be suppressed. The main difference between FJCM and parallel bond model is that after bond breaking, the parallel bond model has no resistance to rotation, while the FJCM can resist rotation.³⁰ Due to these reasons, the FJCM is a new contact model which provides $UCS / T$ ratios higher than 10, compared to the lower $UCS / T$ ratios of the parallel bond model.³¹ The formulas governing the FJCM are very similar to those of parallel bonds that are presented in detail by Potyondy.³⁰

Figure 3 depicts a schematic view of the FJCM. In FJCM, each of the contacts between two contacting particles is modeled by two notional surfaces (lines in 2D) which are rigidly connected to the corresponding particles³³ (Figure 3(a)). A material with flat-joint contacts is shown in Figure 3(b). As shown in this figure, notional surfaces (while each surface has $N_{r}$ segments) build polygonal grain structures that resist against rotational motion of particles by interlocking of grains. After bond breaking, interfaces still exist, and hence the FJCM contacts can prevent rotations, while parallel bond model cannot do so due to vanishing of the interfaces. Furthermore, the failure envelope of a bonded flat-joint contact is shown in Figure 4. Obviously, bonds with their stress states within the envelope experience no failure. The micro-parameters of the FJCM and properties of compacted material with brief descriptions of them are listed in the nomenclature. The FJCM model has more cracks in comparison with the parallel bond model in the same loading conditions, but because of the flat-joint contact resistance to rotation, the compressional strength (UCS) of FJCM is higher than that of the parallel bond model.

Figure 3.

(a) Flat-joint contact and (b) material with FJCM contacts.³³

Figure 4.

Failure envelope of a bonded flat-joint contact.

Calibration procedure for macro-properties

Adjustment of micro-parameters of the FJCM is done by performing a number of numerical calibration tests. Micro-parameters of the FJCM include $E_{c}$ , ${\bar{E}}_{c}$ , $k_{n} / k_{s}$ , ${\bar{k}}_{n} / {\bar{k}}_{s}$ , $λ$ , $μ$ , $N_{r}$ , $g_{0}$ (installation gap), $ϕ$ (friction angle), c (bond cohesion), and $σ_{c}$ (bond tensile strength). Before adjusting micro-parameters, guidelines for the calibration procedure and some simplifying assumptions are introduced. In this regard, the number of free parameters can be reduced by setting Young’s modulus and normal to shear stiffness ratio of FJCM equal to their values for particles (i.e. $E_{c} = {\bar{E}}_{c}$ and $k_{n} / k_{s} = {\bar{k}}_{n} / {\bar{k}}_{s}$ ).¹⁰ Furthermore, radius multiplier is usually set to 1 (i.e. $λ = 1$ ).¹⁰ Also, minimum particle radius and particle size ratio are calculated from grain size of SCFS ceramic which is in the range of 10–20 µm.³⁴ On the contrary, $N_{r}$ , $g_{0}$ , and $μ$ are determined independently and their effects on the macro-properties of bonded material are not considered. In addition, friction angle is set to zero for simplicity. Consequently, four micro-parameters of FJCM are adjusted using numerical tests which include ${\bar{E}}_{c}$ , ${\bar{k}}_{n} / {\bar{k}}_{s}$ , c, and $σ_{c}$ .

Four numerical tests employed to calibrate the model are biaxial compression test, unconfined compression test, direct tension test, and four-point bending test. These numerical tests are selected to calibrate Young’s modulus of elasticity, Poisson’s ratio, compressive strength, tensile strength, and modulus of rupture of the synthetic model. Calibration procedure should be continued until the values of these mechanical properties have insignificant deviations from the corresponding values for SCFS ceramics. In this regard, Yang³⁵ investigated the effects of micro-parameters on the macro-properties of the parallel bond model. He showed that Young’s modulus is mainly affected by ${\bar{E}}_{c}$ and ${\bar{k}}_{n} / {\bar{k}}_{s}$ , and Poisson’s ratio is a logarithmic function of ${\bar{k}}_{n} / {\bar{k}}_{s}$ . These results are also true for the FJCM model. For constant values of ${\bar{E}}_{c}$ and ${\bar{k}}_{n} / {\bar{k}}_{s}$ (in FJCM), compressive strength is only dependent on c, while modulus of rupture and tensile strength are only related to $σ_{c}$ . Consequently, the calibration procedure is performed by applying the following three steps: (1) biaxial compression test for adjusting ${\bar{E}}_{c}$ and ${\bar{k}}_{n} / {\bar{k}}_{s}$ , (2) unconfined compression test for adjusting c, and (3) four-point bending test and direct tension test for adjusting $σ_{c}$ .

Biaxial compression test

Figure 5 presents schematic setup for the biaxial compression test. The test sample has a width of 1 mm and a height of 2 mm. The assembly contains 9623 particles, in which the minimum radius of particles, the maximum radius of particles, and the porosity of sample are 5 µm, 10 µm, and 13%,²⁹ respectively. In the biaxial test, the top platen moves toward the bottom platen with velocity $V_{P}$ , while the bottom platen is fixed (Figure 5(a)). In addition, the lateral walls exert confining stress of 1 MPa (as a controlling servo-mechanism) on the synthetic sample. Figure 5(b) displays the synthetic sample after loading. It should be noted that Figure 5(b) shows the sample just a little after starting to insert the compressive load and thus is far from the failure situation. In this figure, small red and black lines demonstrate micro-cracks which are created and propagated in the specimen. Shear and tensile cracks are illustrated by black and red lines, respectively. In this study, biaxial test is utilized to calibrate Young’s modulus and Poisson’s ratio. Thus, ${\bar{E}}_{c}$ and ${\bar{k}}_{n} / {\bar{k}}_{s}$ are determined.

Figure 5.

(a) Schematic setup for biaxial compression test and (b) sample under compressive load.

Unconfined compression test

Figure 6 shows the schematic setup for the unconfined compression test. The only difference between biaxial test and unconfined compression test (Figure 6(a)) is that the lateral walls are removed in the unconfined compression test (i.e. there are no confining stress and controlling servo-mechanism). Figure 6(b) depicts flat-joint material after unconfined compression loading. As observed in this figure, the dominant cause of failure of the synthetic sample (calibrated sample) is tensile cracks. Because of low tensile strength of brittle materials in comparison with shear strength of them, the number of shear cracks in the sample is much less than the number of tensile cracks. Unconfined compression test is used to calibrate compressive strength, and hence c is determined.

Figure 6.

(a) Schematic setup for unconfined compression test and (b) failed sample under compressive load.

Four-point bending test

Figure 7 depicts the schematic setup for the four-point bending test and failed sample after loading. The test sample has a length of 3 mm, a height of $d = 0.2 mm$ , and a width of $b = 0.2 mm$ . The assembly contains 2929 particles. Distances between two bottom circular walls and two top circular walls are L = 2.6 and 1.3 mm, respectively (Figure 7(a)). The radii of all circular walls are 0.15 mm. In the bending test, bottom circular walls are fixed as supports, while top circular walls move downward, which provides a quasi-static loading. The modulus of rupture of the sample in the four-point bending test can be expressed as

σ_{f} = \frac{3 F (L - L_{i})}{2 b d^{2}}

(14)

where F is the maximum force that the sample can experience before failure. Furthermore, Figure 7(b) shows that the sample is failed only by tensile cracks. The four-point bending test is applied to calibrate modulus of rupture and thus $σ_{c}$ can be determined.

Figure 7.

(a) Schematic setup for four-point bending test and (b) failed sample under bending load.

Direct tension test

Figure 8 shows the schematic setup for the direct tension test. The difference between unconfined compression test and direct tension test (Figure 8(a)) is that the top platens are deleted in the direct tension test. Moreover, the upper row of particles (these particles are fixed together) of the sample moves upward with velocity $V_{R}$ , while the lower row of particles moves downward at the same velocity. Figure 8(b) depicts flat-joint material after direct tension loading. It is observed that the cause of failure of the synthetic sample is tensile cracks. Direct tension test is used to calibrate tensile strength and thus $σ_{c}$ can be determined. It should be noted that $σ_{c}$ is determined using both direct tension test and four-point bending test. Hence, the value of $σ_{c}$ must be specified in such a way that modulus of rupture and tensile strength of the calibrated sample have minimum differences in comparison with those from the real SCFS ceramics.

Figure 8.

(a) Schematic setup for direct tension test and (b) failed sample under tensile load.

The values of adjusted micro-parameters of FJCM and properties of particles can be expressed as follows: (1) material properties—ρ = 2200 kg/m³,³⁶R_min = 5 µm,³⁴R_max/R_min = 2,³⁴µ = 0.2, E_c = 28.0 GPa, and k_n/k_s = 3.0; (2) micro-parameters of FJCM— ${\bar{E}}_{c} = 28.0 GPa$ , ${\bar{k}}_{n} / {\bar{k}}_{s} = 3.0$ , λ = 1,¹⁰c = 233.0 MPa, ϕ = 0°, σ_c = 42.0 MPa, µ = 0.2, N_r = 4, and g₀ = 0.05 µm. In addition, comparison between mechanical properties of real SCFS ceramics and the FJCM material is listed in Table 1. It can be seen from Table 1 that the synthetic model has good agreement with SCFS ceramics. Furthermore, Table 1 shows that Young’s modulus of elasticity, Poisson’s ratio, and compressive strength for both real material and synthetic sample have negligible differences, since these three macro-properties are calibrated by determining three independent micro-parameters (i.e. ${\bar{E}}_{c}$ , ${\bar{k}}_{n} / {\bar{k}}_{s}$ , and c.). On the contrary, modulus of rupture and tensile strength for both real material and synthetic sample have significant differences due to the fact that these two macro-properties are calibrated by determining just one micro-parameter (i.e. $σ_{c}$ ). Thus, modulus of rupture and tensile strength of the synthetic sample involve some errors.

Table 1.

Comparison between mechanical properties of real SCFS ceramics and the FJCM material.

Mechanical properties	Real SCFS³²	FJCM
Young’s modulus of elasticity (GPa)	25.9	25.9
Poisson’s ratio	0.13	0.13
Compressive strength (MPa)	362	362
Modulus of rupture (MPa)	28.8	33.0
Tensile strength (MPa)	26.5	21.4

SCFS: slip-cast fused silica; FJCM: flat-joint contact model.

Experimental setup

The experimental setup for the turning process of SCFS ceramics is depicted in Figure 9. The machining operations were performed on a 1.5 hp Hardinge lathe. Cylindrical SCFS specimens with a diameter of 30.5 mm and a length of 100 mm were used. To create orthogonal cutting geometry, initial shallow grooves at an axial distance of 2.5 mm between them were machined by parting off inserts (Figure 9(b)). Material between the grooves was turned by parting off inserts which were fed in the radial direction. Thus, the machining force in the axial direction was practically zero. The alignment of the workpiece in the three-jaw chuck was performed utilizing a dial gauge. The cutting force components were measured in global directions by attaching the tool to a Kistler dynamometer of type 9257B, together with a charge amplifier of type 5070.

Figure 9.

Experimental facility for the turning process of SCFS ceramics: a) cutting of the ceramic in orthogonal mode and b) Detailed view of the ceramic part.

Turning was carried out applying a SANDVIK parting off tool holder model RF151.22-2020-40 along with N151.2-400-4E 1125 inserts. Tool insert geometric parameters were as follows: rake angle of $α_{r} = - 7^{°}$ , clearance angle of $β = 7^{°}$ , inclination angle of $i = 0^{°}$ , and the cutting width of 4 mm. The tool holder was fixed on the dynamometer by a fixture, and the dynamometer was also clamped on the cross-slide table by another fixture.

Numerical modeling of the orthogonal cutting process

In this section, a DEM simulation of the turning process for machining of SCFS in orthogonal mode is presented. In orthogonal cutting, the cutting process is analyzed in a 2D plane strain model, where the cutting edge is perpendicular to the direction of tool–specimen relative motion. Therefore, there are no axial machining forces. When plunge mode cutting is used similar to the experimental setup described earlier, the uncut chip thickness ( $a_{c}$ ) equals the feed per each revolution in the radial direction, and the width of cut ( $w_{c}$ ) is equal to the axial distance between the grooves in the experiments.

A representation of equivalent orthogonal cutting and DEM model of material is shown in Figure 10. The cutter is assumed to be sharp (without cutting edge radius or a chamfer). Moreover, the tool is assumed to be ideally rigid, which is modeled by a set of three lines (i.e. walls in PFC^2D). Consequently, phenomena such as tool wear and edge chipping are not considered. To make the numerical results comparable to experimental ones, the length of machining in the experiments was very small to decrease the influence of tool wear and avoid possible edge chipping. Tool–specimen friction coefficient is assumed to be 0.2 (the friction coefficient of most ceramics is in the range of 0.1–0.3).³⁷ The machining sample in the simulation has a width of 2 mm and a height of 1 mm, and the assembly contains 9623 particles.

Figure 10.

A representation of equivalent orthogonal cutting.

Results and discussion

Experimental operating conditions for the turning process of SCFS ceramics are tabulated in Table 2. In all test cases, only the feed is changed and the other machining parameters are fixed. The measured machining forces (the main cutting force ( $F_{c}$ ) and the thrust force ( $F_{t}$ )) of the orthogonal turning experiments for test 1 are plotted in Figure 11. A low pass filter with a cutoff frequency of 300 Hz is applied on input signals to eliminate the noise. The figure shows the dynamic nature of measured cutting forces of brittle materials. In addition, a comparison of the averaged measured machining forces for the three experimental tests is represented in Figure 12. The figure shows that the machining forces increase with increasing values of feed, as expected.

Table 2.

Experimental operating conditions for the turning process of SCFS ceramics.

Test	Rotationalspeed (rpm)	Width ofcut (mm)	Feed(µm/rev)
1	1000	2.5	12.5
2	1000	2.5	17.5
3	1000	2.5	22.5

Figure 11.

Time histories of the cutting forces from experimental measurements for test 1.

Figure 12.

Comparison of the averaged experimental cutting forces for different feeds.

The simulation procedure is performed for the case studies of Table 2. The relative tool–specimen velocity in simulations is assumed to be equal to the experimental cutting speed, and the total simulation time is set to 1.0 ms. Figure 13 presents the simulated chip formation in the orthogonal cutting process for test 1. It is observed that when the cutting tool engages with the material and exerts force on it, micro-cracks are initiated because normal or shear stresses in FJCM contacts exceed the strength of bonds (Figure 13(b)). As the cutting tool moves forward, micro-cracks are propagated to form lateral and median macro-cracks in the specimen (Figure 13(c)). Then, the growth and coalescence of macro-cracks lead to chip formation. Furthermore, this figure shows that the cutting process of SCFS ceramics results in discontinuous chip formation as expected, and separated chips from the specimen have various sizes (Figure 13(d)). Hence, the machining of SCFS ceramics is carried out in the brittle regime. Moreover, the cutting process creates many surface/subsurface cracks and damages, and the machined surface is significantly non-smooth with peaks and valleys. In addition, more than 96% of micro-cracks are tensile cracks and only less than 4% of other micro-cracks are shear cracks.

Figure 13.

Simulated orthogonal cutting process and chip formation for test 1: (a) t = 0, (b) t = 0.1 ms, (c) t = 0.3 ms, (d) t = 0.7 ms, and (e) t = 1 ms.

Figure 14 displays time histories of the simulated main cutting force, thrust force, and number of micro-cracks for test 1. As observed in this figure, the nature of cutting forces is dynamic. It can be found from the figure that the number of micro-cracks is increased rapidly when cutting forces rise significantly to cut large amounts of the material. Moreover, the ratio of mean values of cutting forces (i.e. $F_{t} / F_{c}$ ) is approximately equal to 0.5, that is nearly matched to experimental results (Figure 12). It is observed that the values of averaged numerical cutting forces are much less than the values of averaged experimental machining forces. Although the trend of the numerical and experimental results agrees, the results differ by a large amount. These differences in the results is an indication that the parameters identified from common calibration tests may not be adequate for modeling of the machining process of brittle materials. It is common to use calibration tests such as compression, direct tension, three- or four-point bending, fracture toughness, and Brazilian tests for determining the properties of a compacted assembly of particles for use in the DEM simulations. However, these simple numerical tests are not necessarily indicative of the complex situation that is present in applications such as machining of brittle materials. Machining of ceramics with extensive surface and subsurface cracks and damages may need more rigorous numerical calibration tests. In this article, we propose to use the experimental machining forces to calibrate the parameters. Therefore, the results of conventional calibration tests are used as initial values for updating the DEM model. Then, the DEM model is updated utilizing some of the experimental machining forces, and the updated model is validated for other experiments.

Figure 14.

Time histories of simulated main cutting force, thrust force, and number of micro-cracks for test 1.

Updating the DEM model

As shown earlier, the lack of accuracy in estimation of machining forces may be attributed to the inadequacy of the conventional tests for determining the necessary parameters to be used in machining simulation. Among micro-parameters of FJCM contacts ( ${\bar{E}}_{c}$ , ${\bar{k}}_{n} / {\bar{k}}_{s}$ , c, and $σ_{c}$ ), the two micro-parameters c and $σ_{c}$ have the greatest impact on the values of machining forces, while the other micro-parameters have a much lower impact. Thus, c and $σ_{c}$ are selected for model updating, while the two other micro-parameters are assumed to be constant. The micro-parameters c and $σ_{c}$ are updated using trial and error method. The objective is to minimize differences between averaged experimental and numerical thrust and main cutting forces for test 1 as follows

min (| \frac{F_{te 1} - F_{tn 1}}{F_{te 1}} | + | \frac{F_{ce 1} - F_{cn 1}}{F_{ce 1}} |)

(15)

where $F_{te 1}$ , $F_{tn 1}$ , $F_{ce 1}$ , and $F_{cn 1}$ are averaged values for experimental thrust force, numerical thrust force, experimental main cutting force, and numerical main cutting force (for test 1), respectively. The values of updated micro-parameters are c = 4340 MPa and $σ_{c}$ = 1410 MPa. The percentage differences between averaged thrust and main cutting forces from experimental and numerical simulation of updated DEM model results are less than 10%. The time histories for simulated machining forces and number of micro-cracks of updated model for test 1 are shown in Figure 15. In addition, a comparison of the averaged experimental and numerical cutting forces of the updated model for two other feeds is presented in Figure 16. This figure shows that the use of updated parameters in the simulations provides a much better estimate of cutting forces. The difference between the simulated and experimental cutting forces is in the range of 14%–30%, which seems to be reasonable considering the complicated nature of the machining process of brittle materials. For comparison of the results, it is useful to note that in the works of Shen et al.^21,22 and Yang et al.,²⁸ the differences between the experimental and numerical results were in the range of 20%–25%, 10%–17%, and 7%–26%, respectively. Therefore, the error range reported in this work is consistent with similar results in previous studies.

Figure 15.

Time histories of simulated main cutting force, thrust force, and number of micro-cracks of updated model for test 1.

Figure 16.

Comparison of the averaged experimental and numerical (for updated DEM model) cutting forces for different feeds.

Conclusion

In this study, mechanical modeling of machining of SCFS ceramic was carried out utilizing the DEM method and the FJCM contact model. The initiation, propagation, and coalescence of micro-cracks in the samples leading to chip formation for machining processes were modeled. In the first step, the micro-parameters of FJCM contacts were carefully adjusted using numerical calibration procedures to create a DEM model of SCFS ceramics with the same mechanical properties as the real material. However, the parameters obtained from conventional calibration tests did not produce cutting forces close to experimental results. Due to the complexity of the cutting process, the FJCM model parameters were directly updated using the cutting experiments. The comparison of results shows that predicted forces obtained based on the updated parameters are within 14%–30% of the experimentally measured forces, which is a reasonable prediction. Therefore, it is shown that the DEM model with updated parameters is a reliable model for the prediction of behavior of SCFS ceramic material in the cutting process.

Footnotes

Appendix 1 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Sharif University of Technology.

ORCID iD

Mohammad Reza Movahhedy

References

Guo

Zhao

Jackson

. Ultrasonic vibration-assisted grinding of micro-structured surfaces on silicon carbide ceramic materials. Proc IMechE, Part B: J Engineering Manufacture 2012; 226: 553–559.

Liu

Camfield

. Machinability experimental study of sintered alumina (Al₂O₃) ceramics material by chemical vapor deposition diamond coating milling tools. Proc IMechE, Part B: J Engineering Manufacture 2015; 229: 1535–1546.

Wang

Shimada

, et al. Smoothed particle hydrodynamics simulation and experimental study of ultrasonic machining. Proc IMechE, Part B: J Engineering Manufacture 2017; 232: 1875–1884.

Prakash

Kumar

Singh

, et al. Micro-electrical discharge machining of difficult-to-machine materials: a review. Proc IMechE, Part B: J Engineering Manufacture 2019; 233: 339–370.

Liu

Zhang

, et al. Machining performance and surface integrity of SiC ceramic machined using electrical discharge milling and the mechanical grinding compound process. Proc IMechE, Part B: J Engineering Manufacture 2010; 224: 1511–1518.

Singh

Singhal

. An experimental study on rotary ultrasonic machining of Macro ceramic. Proc IMechE, Part B: J Engineering Manufacture 2018; 232: 1221–1234.

Zhang

. Study on grinding surface deformation and subsurface damage mechanism of reaction-bonded SiC ceramics. Proc IMechE, Part B: J Engineering Manufacture 2018; 232: 1986–1995.

Kumbera

Cherukuri

Patten

, et al. Numerical simulations of ductile machining of silicon nitride with a cutting tool of defined geometry. Mach Sci Technol 2001; 5: 341–352.

Cundall

. A computer model for simulating progressive, large-scale movement in blocky rock system. In: Proceedings of the international symposium on rock mechanics, Nancy, 4–6 October, 1971. International Society for Rock Mechanics (ISRM).

10.

Potyondy

Cundall

. A bonded-particle model for rock. Int J Rock Mech Min Sci 2004; 41: 1329–1364.

11.

Tan

Yang

Sheng

. Study of polycrystalline Al₂O₃ machining cracks using discrete element method. Int J Mach Tool Manu 2008; 48: 975–982.

12.

Tan

Yang

Sheng

. Discrete element method (DEM) modeling of fracture and damage in the machining process of polycrystalline SiC. J Eur Ceram Soc 2009; 29: 1029–1037.

13.

Jiang

Tan

. A DEM methodology for simulating the grinding process of SiC ceramics. Procedia Engineer 2015; 102: 1803–1810.

14.

Qiu

Zhang

, et al. Study on machining mechanism of glass using discrete element method. Appl Mech Mater 2014; 577: 108–111.

15.

Qiu

Wei

. Machining mechanism research of glass by discrete element method. J Mech Sci Technol 2015; 29: 1283–1288.

16.

Kang

. Numerical simulation of granite on pre-stressed machining by discrete element method (DEM). Appl Mech Mater 2013; 372: 646–649.

17.

Jiang

Tan

Zhang

, et al. DEM simulation and experimental investigation of silicon carbide on pre-stressed machining. Adv Mater Res 2010; 126: 241–245.

18.

Jiang

Tan

Zhang

, et al. DEM simulation of machining damage in SiC pre-stressing cutting process. Adv Mater Res 2011; 177: 165–169.

19.

Peng

Tang

, et al. DEM simulation of ceramic tool abrasion in machining superalloy. Mater Sci Forum 2014; 800: 385–389.

20.

Yang

Shen

Lei

. Distinct element modelling of the material removal process in conventional and Laser Assisted Machining of silicon nitride ceramics. Int J Manuf Res 2009; 4: 74–94.

21.

Shen

Yang

Lei

. Distinct element modeling of laser assisted milling of silicon nitride ceramics. J Manuf Process 2010; 12: 30–37.

22.

Shen

Yang

Lei

. Microstructural modeling and dynamic process simulation of laser-assisted machining of silicon nitride ceramics with distinct element method. J Manuf Sci Eng 2012; 134: 021011.

23.

Shen

Lei

. Distinct element simulation of laser assisted machining of silicon nitride ceramics: surface/subsurface cracks and damage. In: ASME 2005 international mechanical engineering congress and exposition, Houston, TX, 13–19 November 2005, pp.1267–1274. New York: American Society of Mechanical Engineers.

24.

Shen

Lei

. Cutting simulation of laser assisted milling of silicon nitride ceramics using PFC2D. In: ASME 2009 international manufacturing science and engineering conference, West Lafayette, IN, 4–7 October 2009, pp.293–299. New York: American Society of Mechanical Engineers.

25.

Zhu

, et al. Modeling and simulation of grinding wheel by discrete element method and experimental validation. Int J Adv Manuf Technol 2015; 81: 1921–1938.

26.

Blaineau

André

Laheurte

, et al. Subsurface mechanical damage during bound abrasive grinding of fused silica glass. Appl Surf Sci 2015; 353: 764–773.

27.

Ruitao

Heng

Xinzi

, et al. FEM-DEM coupling simulations of the tool wear characteristics in prestressed machining superalloy. MATEC Web Conf 2016; 80: 04001.

28.

Yang

Alkotami

Lei

. Discrete element simulation of orthogonal machining of soda-lime glass. J Manuf Mater Process 2018; 2: 10.

29.

Smith

Chowdary

. The fracture toughness of slip-cast fused silica. Mater Sci Eng 1975; 20: 83–88.

30.

Potyondy

. A flat-jointed bonded-particle material for hard rock. In: Proceedings of the 46th US rock mechanics/geomechanics symposium, Chicago, IL, 24–27 June 2012. Alexandria, VA: American Rock Mechanics Association.

31.

Ding

Zhang

. Simulation of rock fracturing using particle flow modeling: phase i-model development and calibration. In: Proceedings of the 45th US Rock Mechanics/geomechanics symposium, San Francisco, CA, 26–29 June 2011. Alexandria, VA: American Rock Mechanics Association.

32.

Harris

Welsh

. Fused silica design manual. Defense Technical Information Center 1973.

33.

Potyondy

. The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions. Geosyst Eng 2015; 18: 1–28.

34.

Bažant

Kazemi

. Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length. J Am Ceram Soc 1990; 73: 1841–1853.

35.

Yang

. Experimental and numerical investigation of laser assisted milling of silicon nitride ceramics. PhD Dissertation, Kansas State University, Manhattan, KS, 2009.

36.

Fleming

. Fused silica manual. Report, Georgia Institute of Technology, Atlanta, GA, 1 September 1964.

37.

Hussey

Wilson

. Advanced technical ceramics directory and databook. Cham: Springer Science & Business Media, 2012.

Dynamic modeling of the turning process of slip-cast fused silica ceramics using the discrete element method

Abstract

Keywords

Introduction

Discrete element modeling and calibration

Parallel bond model

FJCM

Calibration procedure for macro-properties

Biaxial compression test

Unconfined compression test

Four-point bending test

Direct tension test

Experimental setup

Numerical modeling of the orthogonal cutting process

Results and discussion

Updating the DEM model

Conclusion

Footnotes

Appendix 1

Declaration of conflicting interests

Funding

ORCID iD

References