Simulation of cBN Grain Wear During Single Grain Engagement Considering Cleavage Planes

Abstract

A large part of the energy introduced during grinding is converted into heat. As not all the heat can be dissipated by the cooling lubricant, thermally induced displacements in machine components occur. These displacements have a negative influence on the component quality. Since the grinding wheel topography changes during the grinding process due to wear, the wear mechanisms of grain splintering, grain breakage as well as abrasion were identified and quantified. In addition, their effect on heat generation was investigated. To predict the wear mechanisms, a Finite Element (FE) simulation model was developed that determines the grain shape change considering the cleavage planes in the grain. Three-dimensional real cBN grain geometries were used for the simulation of a single grain engagement in the workpiece of the 100Cr6 steel. In the presented model, the orientation of the cleavage planes is varied and their influence on the wear mechanisms as well as the resulting forces is investigated. In addition, empirical tests were conducted in order to adjust the model. The simulation showed that a cleavage plane variation resulted in stronger crack propagation when the cleavage plane was oriented away from the workpiece and when the distance of the cleavage plane from the point of application of the load was smaller.

1 Introduction

During grinding process a large part of the introduced energy is converted into heat [1]. Since not all the heat can dissipate into the cooling lubricant, a high thermal load on the surface area of the workpiece can thermally damage the material structure [2] and therefore reduce component functionality. However, the topography of grinding wheels changes over the tool life due to wear. This leads to increasing heat fluxes due to higher friction [3]. Additionally, contact and cooling lubricant conditions in the contact zone between the grinding wheel and the workpiece are changed [4]. In order to analyze the wear behavior of grinding wheel topographies it requires to quantitatively describe grinding wheel wear. As yet, it is unknown whether the wear mechanisms change depending on the cleavage plane in the crystal lattice of the cBN grain. To develop a prediction method for cBN grinding wheel wear it is necessary to first develop a wear prediction method for an isolated cBN grain, in order to ensure clear cause-effect relationships between the thermo-mechanical load and the wear mechanisms. Currently there is no validated FE model taking into account the wear of cBN grains with real grain geometries in the single-grain scratching process depending on the cleavage planes of the cBN crystal. By simulating including cleavage planes, it is possible for the first time to predict the wear behavior of cBN crystals holistically. By adjusting the properties of the cBN crystals accordingly, the production of the cBN abrasive grains can then also be better understood and adapted to the corresponding load situations.

Thus, the aim of this work is to develop and validate a three-dimensional FE model for the wear of cBN grains during single grain engagement as a function of the cleavage planes. To validate the numerical model, empirical data from single-grain scribing studies are used.

2 State of the Art

The first works on the wear behavior of grinding wheels by Malkin and Cook [5] showed that there is a direct relationship between grinding force and grain wear due to the reduction in the grain protrusion in turn due to attrition. The thermo-mechanical load in the grinding process increased because of grinding wheel wear. The change in wear mechanisms over the service life of an electroplated cBN grinding wheel was investigated by Shi and Malkin [3]. For this purpose, the radial wear of the grinding wheel was determined quantitatively. They observed high initial wear that degressively decreased to a stationary wear condition. The initial wear was mainly caused by the breakout of the highest and weakly fixed grains in the bond. The stationary wear was dominated by grain fractures. Malkin and Shi [6] showed that for surface grinding and internal cylindrical grinding of 100Cr6 with electroplated cBN grinding wheels stationary grinding wheel wear was characterized by grain splintering. The attrition wear mechanism had only a minor influence on the tool life of the grinding wheel. Upadhyaya and Malkin [4] also demonstrated experimentally that the wear of electroplated grinding wheels is characterized by the mechanisms of grain splintering, grain breakage and abrasion. Upadhyaya and Malkin [4] showed that the crystal structure has an influence on the wear behavior of electroplated cBN grinding wheels to evaluate the influence of the crystal properties of cBN grains and the bond thickness on the grinding wheel wear. It became apparent that abrasion flattened the grain and increased the active grain density.

Bergs et al. [7] investigated the cBN fracture behavior by means of FEM simulations of individual cBN grains. They identified the wear mechanisms as a function of the mechanical stress on the grain as well as the orientation and shape of the grain. The investigation identified different wear mechanisms for cBN grains depending on the grain geometry. Yiming et al. [8] developed a FE simulation model for the wear of cBN in the single-grain scratching process. In the wear model used for cBN, crack initiation is detected according to the Rankine criterion. The stress-strain behavior during the failure process was modeled using the critical strain energy release rate G_c according to Eq. (1). [8]

$${{G}}_{\text{c}}=\frac{{{K}}_{\text{c}}^{2}}{{E}}$$

(1)

As a result of the simulations carried out with this model, the maximum tensile stresses at the rake faces of the cutting edges leading to grain wear were obtained. In the resulting wear behavior an alternation of blunting phenomena and self-sharpening effects were recorded. Wang et al. [9] developed a two-dimensional FE model to simulate cBN wear during grinding of Inconel 718. A hexagonal geometry was assumed for the grain. Using their wear model both macro- and microsplintering were represented in the simulation. Macrosplintering occurred mainly on the rake face of the grain as a consequence of strong crack propagation. The crack propagation necessary for macrosplintering was caused by high tensile loads. Rao et al. [10] developed a three-dimensional wear model for FEM simulations of pcBN wear. This model is based on the theory of cohesive elements. The simulation results showed that a stress concentration appears around the grain–filler bonding interface region and the grain vertex region when the grinding load is imposed. The stress-strain law based wear model developed by Rao et al. was also used by Huang et al. [11] for the FE simulation of pcBN wear in the grinding process. In this model, a cuboidal grain geometry was used, which was divided into several Voronoi cells to represent the cBN crystals. They investigated the maximum infeed of the grain in order to achieve minimum wear and use the self-sharpening effect. In preliminary work for the paper presented here, Bredthauer et al. [12] developed a three-dimensional FE model to simulate the wear behavior of cBN for single-grain scribing of 100Cr6 steel. Real grain geometries were transferred to the simulation model. As a result of the simulations, grain wear due to abrasion, micro-splintering and macrosplintering were simulated. There were deviations in the expression of these wear phenomena compared to the results of experimental investigations. The deviations were, besides others, justified by the missing implementation of grid planes in the FEM model.

Numerous experimental as well as simulative studies have already been carried out on the wear behavior of grinding wheels. In most of the studies however, idealized grain models were used or the models were simplified. In addition, the simulations did not consider cleavage planes in the crystal structure of cBN and thus anisotropic behavior. Nevertheless, since cleavage planes have a significant influence on the wear behavior of cBN grains, the aim of this work is to develop a three-dimensional FE simulation model that represents the wear of cBN grains as a function of the cleavage planes.

3 Experimental Investigations

The single-grain scratch tests were carried out on the Profimat MT 608 surface grinding machine from Blohm Jung. The experimental setup is shown in Fig. 1. The test setup installed on this machine comprised a scratch wheel on the tool side to which a screw-in sleeve was connected by means of a thread. The screw-in sleeve contained a grain holder onto which a steel base body was glued. The abrasive grain was electroplated onto the steel body. The abrasive grains used were cBN type ABN 900 grains from Element six for which an average grain diameter of d_g = 251 μm was given by the manufacturer. The grain shape selected in this simulation was chosen at random. The grain size and shape is also used in the coating of electroplated cBN grinding wheels and is therefore representative for other grains of the ABN 900 specification. On the workpiece side a cuboid workpiece made of hardened 100Cr6 steel with a hardness of 60 HRC was used. This workpiece was mounted on a piezoelectric dynamometer from Kistler company. A measuring chain with measuring computer was connected to the force measuring platform so that the normal force F_n and the tangential force F_t were continuously recorded during the test (sampling rate 1 MHz). The test kinematics used was a circular path-bound single-grain engagement. For this purpose, a workpiece speed of v_w = 0 mm/min in tangential direction was selected and a sufficiently high axial grinding wheel speed v_s,axial was set to produce a single engagement of the abrasive grain in the workpiece. The grain circle path radius was r_s = 190 mm, a_e = 20 μm was selected for the infeed, and the grinding wheel peripheral speed at the grain was set to v_s = 20 m/s.

Fig. 1.

Experimental setup, materials and process parameters

For the evaluation of the wear condition of the abrasive grains, a negative impression of the abrasive grain used was made before and after each validation test. The Accutrans AB impression material from Coltene was used for this purpose. These negative impressions were optically measured with the aid of the confocal laser scanning microscope VK-X-150 from Keyence and converted into three-dimensional grain topographies. Subsequently, the grain height difference Δh_g and the grain wear volume ΔV_g were determined by comparing the grain height h_g and the grain volume V_g in the initial and worn condition, as shown in Fig. 2.

Fig. 2.

Evaluation methodology of the grain wear

4 Development of a Simulation Model for the Wear Mechanisms of cBN Grains Considering the Cleavage Planes

4.1 Model Setup

Geometry and Discretization

The simulation model was built according to the boundary conditions of the single-grain scribing studies presented previously. The simulation model shown in Fig. 3 represents the contact between cBN grain and workpiece.

Fig. 3.

Structure of the simulation model

Real grain geometries were used for the cBN grain. The grain topographies were converted into three-dimensional CAD files and imported into ABAQUS as deformable solids. The cBN grain was modeled as a Lagrange body with a mesh density of l_Mesh = 2 µm at the grain-workpiece contact. In the non-contact area of the grain a more coarse mesh with l_Mesh = 20 µm was chosen. The advantage of the Lagrange discretization approach was that the wear mechanisms were represented at high resolution by the failure of concrete elements.

For the workpiece a cuboid geometry was used which was created directly in Abaqus. The workpiece had a length of l = 4 mm, a width of w = 0.3 mm and a height of h = 0.05 mm. The workpiece was modeled as an Euler body with a mesh length of l_Mesh = 15 µm. In the Euler approach, the FE mesh is stationary and the material can move within the mesh relative to it.

Kinematic of the Simulation Model

The kinematics of the simulation are shown in Fig. 4. They were identical to the real investigations. It was necessary to ensure compliance with the grinding wheel circumferential speed v_s, the grain circle path radius r_s and the cutting depth a_e from the validation tests. First, an auxiliary coordinate system was placed at a height of r_s = 190 mm above the cBN grain tip in the center of the contact arc, i.e. 189.98 mm above the global coordinate system. Thus, the axis of rotation of the cBN grain was defined. As the initial position of the cBN grain for the simulation of a single grain engagement, the cBN grain was rotated by α_R = 0.9° around the center of rotation. Consequently, (to avoid) an initial contact of the cBN grain with the workpiece in the first time step was avoided. In total, a rotation of α_R = 1.66° which corresponds to the contact arc length of cBN grain with the workpiece was simulated. For the rotational motion of the center of rotation, a velocity boundary condition was created with reference to the reference coordinate system. The angular velocity about the z’ axis was defined to be ω = 105.263 rad/s, which resulted in an orbital velocity at the grain tip of v_s = 20 m/s.

Fig. 4.

Kinematic modelling of the engagement between the cBN grain and the workpiece

Material Model for 100Cr6 Workpiece

The material model of the workpiece was designed for applying a load to the cBN grain during the single-grain scratching process as realistic as possible. Since the validation tests were carried out with a workpiece made of hardened 100Cr6 steel (60 HRC), a material model had to be implemented for this material. The material parameters for 100Cr6 are given in Table 1 and are standard values extracted from Abaqus.

Table 1. Material parameters for 100Cr6

In addition to these physical material parameters, a constitutive material law was implemented to realistically simulate the plastic material behavior. For such processes, the empirical material model according to Johnson and Cook [13] is used in many research works. For this reason, the use of the constitutive material law according to Johnson and Cook was specified for the workpiece after Eq. 2,

$$\sigma = ({{A}}+ {{B}}{ \varepsilon }^{{n}}{) }\cdot { (1 + }{{C}}\cdot \text{ ln(}\frac{\dot{ \varepsilon }}{\dot{{ \varepsilon }_{0}}}{)) \cdot (1 - }{{[}\frac{{{T}} - \, {{T}}_{\text{r}}}{{{T}}_{\text{m}}- {{T}}_{\text{r}}}{]}}^{{m}}{)}$$

(2)

where ε represents the equivalent plastic strain; $\dot{ \varepsilon }$ and ${ \varepsilon }_{0}$ are the equivalent plastic strain rate and reference strain rate respectively; T_melt and T_r are melting temperature and transition temperature respectively. The empirical constants are as follows: A is the yield stress, B is the strain hardening constant, C is the strengthening coefficient of strain rate, n is the work-hardening exponent and m is the thermal-softening exponent. The parameters A, B, C, n and m used in this study are listed in Table 2. The parameters were selected based on those determined by Bilici [14] and Mikhaylkov [15]. These were compared in the simulation and adjusted with the help of the validation by the empirical investigations. The parameters A, B, C and n were varied systematically and the optimum was chosen within the variations. The parameter C was adjusted the most in these investigations compared to Mikhaylov, because the parameter influences the strain rates, which are particularly high during grinding, the most.

Table 2. Johnson and Cook parameter 100Cr6 [BILI07], [MIKH15]

The process forces with the material parameters according to Mikhaylkov were more similar to the process forces from the validation test. The material parameters for the Johnson and Cook model in further verification and comparison with the simulations were set to the parameters selected in Table 2 to represent the actual physical relationships as accurately as possible.

In addition to the material law, the friction between cBN grain and workpiece also has an influence on the process forces. In the simulations discussed previously, a Coulomb friction model was assumed according to Eq. 3

$${\tau}_{{\text{f}} \, }= \left\{\begin{array}{c}{\mu} \, \cdot \, { \sigma }_{\text{n}},{ \tau }_{\text{f}} \, {<} \, { \tau }_{\text{max}}\\ { \, { \tau }}_{\text{max}}, {\tau}_{\text{f}} \geq { \tau }_{\text{max}}\end{array}\right.$$

(3)

with a friction coefficient of µ = 0.4, where τ is frictional stress, σ_n is normal stress and τ_max is maximum frictional stress according to the Von-Mises equivalent stress. Habak et al. [16] investigated the contact between cBN and hardened 100Cr6 steel. For a material hardness of 45 HRC and a cutting speed of v_c = 2.5 m/s, a friction coefficient of µ = 0.2 was determined. Moreover, the effect that increasing the hardness and increasing the cutting speed v_c lead to a decrease in the coefficient of friction µ was found. Therefore, the simulation was repeated with friction coefficients from µ = 0.2 to µ = 0.05. Lowering the coefficient of friction µ resulted in an approximation of the ratio of the normal force F_n to the tangential force F_t from the validation experiments. Since further optimization of the model was necessary by adjusting the material parameters, a decision was made to use µ = 0.1 as the friction coefficient for all further simulations, because for µ = 0.05 the workpiece temperature was too low.

In addition to the constitutive material law, a damage model was implemented in the workpiece material model to allow for material failure. Hence, a more realistic material behavior was simulated. For this purpose, the damage model according to Johnson and Cook was chosen, which is given in Eq. 4 [18].

$${ \varepsilon }^{\text{f}} = \left[{{d}}_{1} + {{d}}_{2}\cdot {\text{exp}}\left({{d}}_{3}\cdot\frac{{ \sigma }_{\text{m}}}{{ \sigma }_{\text{v,M}}}\right)\right]\cdot \left[1 + {{d}}_{4}\cdot{\text{ln}}\left(\frac{\dot{ \varepsilon }}{{\dot{ \varepsilon }}_{0}}\right)\right]\cdot \left[1 + {{d}}_{5} \, \frac{{{T}}- {{T}}_{\text{r}}}{{{T}}_{\text{m}}- {{T}}_{\text{r}}}\right]$$

(4)

where ε^f is the equivalent elongation at break, σ_v,M is the Von-Mises equivalent stress and d₁ − d₅ are material constants. The material constants of the Johnson and Cook damage model for 100Cr6 were taken from the work of Rasim [17].

Material Model for cBN Grain

Similarly to the material model for 100Cr6, in the material modeling of the cBN grain, physical properties, a damage model, as well as cleavage planes were implemented to represent the wear behavior of cBN grains. The physical parameters of the cBN specification used are given in Table 3 after Mei et al. [8]. The selection of the parameters was made on the basis of previous experience at the WZL of RWTH Aachen of the wear simulation of the identical grain specification in the work of Bergs et al. [7]. Therefore, no optimizations of the material parameters were carried out initially.

Table 3. Material parameters cBN grain after Mei et al. [8]

Furthermore, the Concrete Damaged Plasticity (CDP) damage model for quasi-brittle materials was implemented. In this damage model, the material behavior under tensile and compressive loading was considered separately. The basic parameters used in this work for the CDP model are given in Table 4. The dilatancy angle ψ gives the ratio of the plastic volume change rate to the plastic shear deformation rate [18]. Effectively, the dilatancy angle ψ influences the brittleness or ductility of the material behavior and was chosen to be ψ = 10° in order to achieve the brittle material behavior from the empirical investigations [19]. For the other basic parameters, the respective standard values were selected [20].

Table 4. CDP parameters cBN grain

Furthermore, a separate definition of the material behavior under tension and compression had to be made in the CDP model. Therefore, yield stress values and the corresponding inelastic strain after exceeding the linear elastic range had to be specified in each case. The tensile strength R_m = 66 GPa according to Zhang et al. [21] was used as the limit value for exceeding the linear elastic range under tensile load. For the specification of the compressive strength σ_d,max, the investigations of Li et al. [22] were used, in which first-principles calculations were also performed to determine the stress-strain behavior of cBN. According to this, Eq. 5 applies before material failure as the relationship between the tensile stress σ_z and the compressive stress σ_d.

$${\sigma}_{\text{d}} = { \sigma }_{\text{z}}\cdot{\text{tan}}{(68^{\circ})}$$

(5)

According to Eq. 5, a compressive strength of σ_d,max = 163 GPa was calculated for the tensile stress value σ_z = R_m = 66 GPa. Furthermore, the lowest possible elongation at break of ε_ck = 10^–7 was again assumed after exceeding the maximum stress in each case. The reason for this was to ensure rapid material failure after exceeding the linear elastic range. Since the inelastic strain εⁱⁿ had to be specified in Abaqus for the definition of the CDP model instead of the ultimate strain ε_ck, it was calculated using the values presented previously according to the work of Quingfu et al. [23] to be εⁱⁿ = 0.001409 for tensile loading and εⁱⁿ = 0.002817 for compressive loading. The damage parameter D was calculated according to the work of Najafgholipour et al. [24] to be D = 0.0152 for tensile loading and D = 0.0123 for compressive loading.

If the simulation is executed without considering the cleavage planes in the cBN grain, the result shown in Fig. 5 is generated.

Fig. 5.

Comparison of the wear mechanisms between the empirical investigations and the simulation not considering cleavage planes

When comparing the wear state at the end of the simulation with the wear state of cBN grain in the validation test, it was found that the part of the grain worn by abrasion and microsplintering was in both cases the area at the tip of the grain facing the workpiece in the scribing direction (a). In the area at the tip of the grain facing away from the workpiece no wear existed in either case (b). The simulated grain height difference due to wear was higher than the grain height difference in the validation test. The simulated grain wear volume was significantly lower than the grain wear volume in the validation test. The reason for this was the presence of macrosplinters in the validation test, which was not represented in the simulation (c). This can be attributed to the missing cleavage planes in the simulation, which can cause macrosplintering.

Implementation of Cleavage Planes

For the separation of a cBN grain fragment by macrosplintering the crack initiation and crack propagation at the cleavage plane had to be simulated. Abaqus includes in the form of cohesive elements an element type designed for crack propagation at a known crack surface. Furthermore, cohesive elements are suitable for simulating brittle fracture and do not require an initial notch to implement crack initiation [25]. Huang et al. [11] successfully used cohesive elements to simulate the fracture behavior of pcBN grains. With the help of the cohesive elements, different strength at the grain boundaries and within the grains was implemented. Due to these properties of the cohesive elements, the requirements for the modeling of the cBN cleavage planes for the implementation of macrosplinters in the simulation were given.

Since the cleavage plane is a part of the cBN crystal, the physical parameters of cBN were taken from Table 3 for the cohesive elements. The damage model used for the cohesive elements was the stress-crack opening law. The studies of Ichida were used to parameterize this damage model. In his research, fracture tests were performed on cBN grains. Based on the brittle fracture theory according to Griffith, a fracture strength of σ_z = 2,340 MPa was determined for cBN [26]. The brittle fracture theory according to Griffith describes the propagation of cracks in brittle bodies according to Eq. 6 [27].

$${\sigma}_{\text{ck}}= \sqrt{\frac{{{E}}\cdot {{G}}_{\text{c}}}{\pi\cdot {{a}}}}$$

(6)

where σ_ck is the fracture stress, G_c the critical release rate of the strain energy and a the length of the crack. For the use of the fracture strength according to Ichida in the stress-crack opening law, the maximum nominal stress criterion was used as a criterion for damage initialization. With this criterion, the damage in a cohesive element is initialized as soon as one value of the normal stress and the two shear stresses reach the specified maximum. The ultimate strength of σ_z = 2,340 MPa was defined as the maximum value of the normal stress. For the two shear stresses, the tensile strength of R_m = 66 GPa according to Zhang et al. [29] was used as the maximum value of the damage criterion. For the complete parameterization of the stress-crack opening law as a damage model for the cohesive elements of the cleavage plane, the critical release rate of the strain energy G_c also had to be specified. Yiming et al. calculated a critical strain energy release rate of G_c = 0.084 N/mm for cBN [14].

To investigate the influence of cleavage plane position and orientation the variations shown in Fig. 6 were examined. The first variation of the cleavage plane orientation was to incline the cleavage plane by an angle of α₁ = 5° around the vector v₁ parallel to the intersection direction. The second variation consisted of tilting the cleavage plane by α₂ = 5° about a vector v₂ orthogonal to the direction of intersection. Consequently, the first two variations were used to investigate a slight change in the cleavage plane orientation. The third variation consisted of a horizontal positioning of the cleavage plane with a distance of h = 100 µm from the bond bottom. The distance of the cleavage plane from the cBN grain tip in the initial condition of this variation was h_tip = 46 µm. As a fourth variation, the simulation was performed with the initial cleavage plane orientation according to the validation experiment, but with the cutting direction reversed.

Fig. 6.

Variation of cleavage plane orientation

5 Results and Discussion

The simulated wear process with cleavage planes for cBN grain is shown in Fig. 7 for the original orientation. For the initial state of the grain at time t₀ = 0 µs, the two grain parts and the cleavage plane are shown offset to clarify the modeling approach. The first initiation of a crack at the cleavage plane (a) occurred at time t₁ = 33 µs in the region of the grain-workpiece contact. The first difference in grain wear compared to the model without cleavage plane was recorded at time t₂ = 50 µs. At this time, micro splintering occurred due to the crack at the cleavage plane (b). At time t₃ = 83 µs, cracking occurred for the first time at the cleavage plane outside the contact area of the workpiece and cBN grain (c). In addition, at this time, advanced crack propagation occurred in the contact area (d). After exceeding the deepest engagement point, a significant progress in crack propagation outside the grain-workpiece contact occurred in the upward movement of the cBN grain at time t₄ = 156 µs (e). At the wear condition in the end of the simulation (t₅ = 200 µs), macrosplintering had resulted in separated grain fragments due to crack propagation at the cleavage plane (f).

Fig. 7.

Results for cBN wear mechanisms considering cleavage planes

In the simulation of the wear of cBN grain with cleavage plane, additional wear was caused by micro- and macrosplintering compared to the simulation without cleavage plane. A complete failure of the cleavage plane as in the validation test was not mapped. The potential reason for this is that the exact Johnson and Cook parameters of the workpiece material were not known and thus the process forces of the simulation did not match the process forces of the validation test. In addition, an exact positioning of the cleavage plane is not yet possible, so that deviations in results between reality and simulation can occur.

Results for the Variation of the Cleavage Planes

Since limited computational resources were available to perform the simulations with varied cleavage plane orientation, the longest simulated process time achieved for all variations was t_end = 140 µs. Therefore, the evaluation of the simulations was performed for this time. The comparison of the crack propagation at the varied cleavage planes at time t_end = 140 µs is shown in Fig. 8.

Fig. 8.

Results for the crack formation depending on the cleavage plane orientation

This shows that the crack initiation for the variations with slightly inclined cleavage plane occurred at the same locations as in the original simulation. Furthermore, the volume change of the cleavage plane due to crack propagation at time t_end = 140 µs was ∆V₁ = 8.12% for Variation 1. Thus, there was a lower extent of crack propagation in Variation 1 than in the original simulation with ∆V_orig = 19.26%. For Variation 2, the crack propagation had a larger extent with ∆V₂ = 21.64%. For Variation 3 with the cleavage plane positioned horizontally, there was a crack initiation for the side of the grain facing the workpiece. The crack propagation had a very small extent in this simulation with ∆V₃ = 3.02%. The assumed reason for this was that due to the selected height of the cleavage plane, an initial distance of h_tip = 46 µm of the cleavage plane to the point of application of the load to the grain existed. This distance was larger than in all other simulations. For Variation 4 with reversed cutting direction, there existed a crack starting from the grain tip with a significantly wider crack propagation than in the original simulation in the amount of ∆V₄ = 47.13%. Another difference in Variation 4 with reversed cutting direction compared to the original simulation was that no crack initiation occurred outside the contact area of the workpiece and cBN grain. Due to the reversed cutting direction, the cleavage plane in Variation 4 was initially inclined away from the workpiece. In the original situation, the cleavage plane was initially inclined towards the workpiece.

From previously described observations, it was concluded that an orientation of the cleavage plane averted from the workpiece in the cutting direction leading to more severe crack propagation. The reason for this is that the fracture strength of σ_z = 2340 MPa calculated by Ichida was used as the damage criterion for the normal stress [26]. The tensile strength of cBN of R_m = 66 GPa calculated by Zhang et al. was used as the damage criterion for the shear stresses [21]. In this way, the physical agreement of the model with Griffith brittle fracture theory was ensured. It defines the propagation of cracks in brittle bodies based on the fracture stress normal to the fracture plane according to Eq. (6) [27]. As a consequence of this parameterization of the damage model, an orientation of the cleavage plane averted from the workpiece resulted in higher values for the normal stress σ_n compared to an orientation toward the workpiece. This resulted in a stronger crack propagation. As can be seen in the crack propagation in Variation 4 as well as in the strong increase in crack propagation in the original simulation in the upward movement of the cBN grain.

The second conclusion from the wear of the varied cleavage planes was that a greater distance of the cleavage plane to the point of application of the load on the cBN grain results in a lower crack propagation. The horizontal positioning of the cleavage plane in Variation 3 was further away from the grain tip than the original orientation. Although this is conducive to greater crack propagation, very little crack propagation was recorded in Variation 3. In addition to the inclination of the cleavage plane, the difference from the original simulation was the greater distance from the point of application of the load amounting to h_tip = 46 µm. Resulting in lower stresses at the cleavage plane and thus lower crack propagation.

In Variation 1 and Variation 2, minor differences were observed in the extent of crack propagation at slightly inclined cleavage planes compared to the original simulation. These differences were attributed to a combination of the slope of the crack planes and the resulting slight differences in the distance to the point of application of the load.

Figure 9 shows, for the simulations presented previously, the wear mechanisms that occurred in conjunction with crack propagation at the cleavage plane on the entire cBN grain at time t_end = 140 µs.

Fig. 9.

Results for the cBN grain wear depending on the cleavage plane orientation

It was found that in the original simulation and Variations 1–3, micro- and macrosplintering occurred on the cBN grain due to the cracks at the cleavage plane. In Variation 4, no additional wear mechanisms were found on the cBN grain due to the integration of the cleavage plane although the largest crack propagation existed in this simulation with ∆V₄ = 47.13%. Variation 4 also had the lowest grain wear volume with ∆V_g,4 = 24,540 µm³ as well as the lowest grain height difference with ∆h_g,4 = 6.0 µm. From these observations, it was concluded that an orientation of the cleavage plane averted from the workpiece prevents the development of additional wear mechanisms on the cBN grain associated with crack propagation and, in this case, only complete material failure of the cleavage plane leads to macrosplinters. When the orientation of the cleavage plane is toward the workpiece, crack propagation causes micro- and macrosplinters on the grain. The assumed reason is that the elements adjacent to the cleavage plane are subjected to greater tensile loading when the cleavage plane faces the workpiece while the corresponding elements are mainly subjected to compressive loading when the cleavage plane faces away from the workpiece. The significantly higher compressive strength of cBN amounting to σ_d,max = 163 GPa compared to the tensile strength of R_m = 66 GPa thus causes the differences in the wear mechanisms.

The process forces with the varied cleavage plane orientations at time t_end = 140 µs are shown in Fig. 10. The reference point of the results represents the deepest point of engagement of the grain in the workpiece in the simulation and real test. Since the course of the process forces over the engagement was comparable, the maximum scratch force was used as a comparative value. This shows that for Variations 1–3 with a maximum force deviation of ∆F = 10.7% there were minor differences to the process forces in the original simulation. This was because the different cleavage plane orientations had a minor influence on the expression of the wear volume at the cBN grain. In Variation 4, the highest normal force was simulated with F_n = 20.5 N. This was due to the lower wear volume at the cBN grain resulting from macrosplintering not being represented in the simulation. Additionally, the geometric conditions of the cBN grain were different because of the reversed cutting direction. The larger deviation of the tangential force results from the deviating wear volume and height difference of the grain. Due to the lower wear in the simulation, the tangential forces increase accordingly.

Fig. 10.

Process forces depending on the varied cleavage plane orientations

6 Conclusion

In the present work, an FE simulation is set up that can determine the wear of cBN grains depending on the cleavage planes during single grain engagement. Real cBN grain geometries were used in the engagement with a workpiece made of 100Cr6 steel. Experimental single-grain scratch tests were performed to validate the simulation model. The main conclusions are summarized as follows:

• Development of FE simulation model for cBN grain wear during single-grain scratching based on CDP wear model with integration of cleavage planes by stress-crack opening law.

• Identification of cBN wear mechanisms abrasion, microsplintering and macrosplintering in close qualitative accordance to validation tests.

• Identification of cause-effect relationships between cleavage plane orientation and simulated cBN wear.

• Cleavage plane variation resulted in stronger crack propagation when the cleavage plane was oriented away from the workpiece and when the distance of the cleavage plane from the point of application of the load was smaller.

• In the simulation, slightly too low wear volumes were calculated together with too high grain height reduction. This results in deviations in the process forces compared to the test.

The results presented in this paper provide a very well approximated simulation model to represent the wear behavior of cBN grains as a function of cleavage planes. In order to be able to represent the wear behavior exactly, further optimization approaches must be conducted with regard to the material parameters. In addition, further simulation variations with regard to the process parameters used will follow in future investigations in order to investigate the influence of the parameters on the wear behavior. In this way, the real load condition on a grinding wheel (with regard to the engagement condition due to shadowing effects, etc.) can be modelled. This is because the engagement situation presented in this paper does not exist in a real grinding process. However, the engagement situation was necessary to validate the wear behavior in order to be able to reproduce real engagement situations in the next step. Then predictions on grinding wheel wear will also be possible.