Investigation on the Effect of Dynamic Fracture Toughness to Zirconia Ceramic Grinding Performance with Different Grain Sizes

To reveal the material removal mechanism of zirconia ceramics, an improved prediction models of the critical grinding force and maximum subsurface damage depth models are developed based on the dynamic fracture toughness. The effects of three different grain sizes on the material removal mechanism during brittleductile transition process of zirconia ceramics is analyzed through grinding experiments. And the influence of grain size on grinding force, workpiece surface roughness, surface fragmentation rate and subsurface damage depth in grinding are discussed. The results of the experiment results indicated that the value of dynamic fracture toughness tends to decrease with an increase in equivalent grinding thickness, and the ductile removal range of zirconia ceramics expands for the reason that the critical grinding force considering dynamic fracture toughness is higher than the static grinding force considering static fracture toughness, and the maximum subsurface damage depth is closer to actual maximum subsurface damage depth. Besides the smaller the grain size of zirconia ceramics, the higher the surface quality of grinding.

optimize the processing quality.
The material removal mechanism of engineering ceramics is mainly concentrated in two aspects: On the one hand, the critical cutting depth of brittle-ductile transition of single grit is calculated according to the theory of indentation fracture mechanics, and verified by numerical simulation and scratch experiment [5][6][7][8]. On the other hand, it explores the change law between grinding performance and grinding process parameters such as grinding force, grinding specific energy, chip morphology and surface morphology during the grinding process [9][10][11][12][13], so as to find the critical depth of cut for brittleductile transition. However, only based on the morphology of the chips and the surface morphology of the workpiece cannot fully reveal the nature of the brittle-plastic transition of the material. Zhang et al. [14][15][16] argued that the generation of subsurface microcracks cannot be ignored in the processing of hard and brittle materials.
Subsurface damage is an important basis for judging the material removal mode in the processing of hard and brittle materials. In recent years, the subsurface damage has been widely concerned by some scholars. Yang et al. [17] proposed a new theoretical stress field model based on the relationship between the strain rate and material properties which can evaluate the median crack length and determine the dimension of the subsurface damage layer.
Wang et al. [18] analyzed the effects of wheel speed, grinding depth and abrasive tip angle on the subsurface damage of brittle materials in grinding, and the effect of grinding depth on subsurface damage was weaker than that of wheel speed. Meng et al. [19] studied the removal mechanism of silicon carbide in the nanoscale grinding process and proposed that the depth of the residual dislocation line determines the depth of the surface damage layer.
In the process of studying the material removal mechanism, it is found that the fracture toughness of engineering ceramics is an important mechanical property that affects its grinding performance. When the theory of indentation fracture mechanics is used to analyze the brittle plastic transformation of materials, a constant value is often used to calculate the fracture toughness in the formula of critical cutting depth. However, the static fracture toughness under impact load cannot accurately reflect the generation and propagation mechanism of dynamic cracks [20][21][22][23][24], in order to improve the grinding performance of engineering ceramics, studies on dynamic fracture toughness are increasing. Xie et al. [25] proposed that the cutting deformation force of ceramic materials was related to the material removal method, mechanical properties and grinding parameters. When brittle fracture was removed, the higher the fracture toughness and the lower the microhardness were, the greater the cutting deformation force was. Kalthoff et al. [26] [32] analyzed that the increase of strain rate leads to higher fracture toughness, and indicated that brittle materials have the tendency of ductility under impact mechanical load. It is believed that the speed effect of high-speed grinding will change the contact behavior between brittle materials and abrasive particles.
When studying the grinding performance of engineering ceramics, the grain size of grinding wheel cannot be ignored. Yang et al. [33] investigated that the cutting force decreased with the increase of grain size, and believed that the grain boundary hindered the movement of dislocation, thereby improving the strength of the material. Demir et al. [34] investigated the effects of grain size on workpiece surface roughness and grinding force, and concluded that as the particle size of the grinding wheel increases, the surface roughness value increases and the grinding force increases. Kannappan et al. [35] studied the effects of grain size and operating parameters on the mechanics of grinding, and found that the finer the particle size, the larger the wear surface area, and the greater the energy input per unit grinding area, but the smaller the g ratio and the life of the grinding wheel tool. However, the factors affecting the performance of engineering ceramics are often ignored in the grinding process. The difference in grain size makes ceramics have great differences in microstructure, which leads to changes in the mechanical properties of the materials.
It can be seen from the above research that the process parameters in the grinding process of engineering ceramics have a significant impact on the mechanical properties of its materials, and the mechanical properties of the materials affect the quality of the grinding process.

Research methodology 2.1 Experimental setup and grinding parameters
The grinding experiments of ZrO 2 ceramic was carried out on high precision horizontal surface grinder (MGK7120×6/F) equipped with resin bond grinding wheel (brand SDC100N100B, circumferential diameter 200mm).
The grains used in the process were diamond, whose mesh were 100/120#. Since this experiment is mainly to study the influence of grain size and dynamic fracture toughness of ZrO 2 ceramic material on its grinding performance, in order to avoid the influence of grinding fluid on the grinding quality, the dry grinding method is adopted. The grinding experimental setup is shown in Fig

Dynamic critical grinding force model of single grit with cracks (lateral crack, median crack)
Based on indentation fracture mechanics, the crack generates and expands if the grinding force of single grit is greater than the critical load of the crack in the grinding process, and the material removal method is judged as brittle removal. Considering the influence of actual . It can be seen from Eq. (1) and Eq. (2) that the critical load of the material is not only related to the static fracture toughness, but also related to the hardness during the grinding process of ceramic material. Moreover, it shows that the critical load increases with static fracture toughness and decreases with hardness. When the normal grinding force of single grit is less than the critical load, the lateral crack does not appear and the material removal method is ductile removed; On the contrary if the normal grinding force is greater than the critical load, the lateral crack generates and expands, and brittle removed occurs on the ceramic material. Eq.
(2) are calculated based on the static fracture toughness of ceramic materials, but the fracture toughness of ceramic materials varies in actual grinding process, that's why the calculation results are inaccurate. For that reason, it needs to considering the dynamic fracture toughness ID K [2] to describe the critical load, which is described as follows: where & is the strain rate, m and n are material constants and the value of them are determined by actual experiment. Consequently, the new dynamic normal critical grinding force model for a single grit with lateral crack n F and the new critical load model for median / radial cracks of ZrO 2 ceramic grinding can be described as following:

Dynamic maximum grinding subsurface damage depth
In the grinding process of ZrO 2 ceramic, when the actual grinding force of single grit is greater than the critical grinding force for radial cracks, damage will be produced to the surface and subsurface of the workpiece, which will seriously affect the performance and life of the workpiece.
In order to predict the grinding subsurface damage depth, the dynamic maximum grinding subsurface damage depth model of ZrO 2 ceramic was established. Combined with Reference [39] and the dynamic load characteristics of the actual grinding process, the dynamic maximum grinding subsurface damage depth md  of ZrO 2 ceramic is obtained as follows: 4/9 2/3 5/6 2/3 8/9 4 ( ) ( ) Where, x is a constant, g r is the abrasive radius, E is the elastic modulus of the material, and gn f is the grinding force of single grit. It can be seen from Eq. (6) that the maximum grinding subsurface damage depth decreases with the increase of dynamic fracture toughness of ZrO 2 ceramic.

Results and discussion 3.1 The dynamic fracture toughness of ZrO 2 ceramic
In order to calculate the dynamic fracture toughness of ZrO 2 ceramic with three grain sizes, the elastic compression experiment was carried out to measure the static compression strength and elastic modulus, and the hardness indentation experiment was conducted to obtain the hardness and static fracture toughness of ZrO 2 ceramic.
The specific experimental data are shown in Table 2.
According to the mechanical properties in Table 2, the dynamic fracture toughness of ZrO 2 ceramics is obtained by grinding process parameters of sixteen orthogonal experiments, as shown in Fig. 2(a). Comparing the static fracture toughness in Table 2 with the dynamic fracture toughness in Fig. 2(a) in the grinding process, it can be seen that the static fracture toughness is significantly smaller than the dynamic fracture toughness, the strain rate strengthening effect is the main reason for the phenomenon.
It can be seen from Fig. 2(b) that the dynamic fracture toughness is not only related to the equivalent grinding thickness, but also related to the grain size of the material.
Under the same conditions, the dynamic fracture toughness is decreased nonlinearly with the equivalent grinding thickness. This is the reason that the equivalent grinding thickness is determined by processing parameters, and the strain rate is changed by the different processing parameters. In addition, ZrO 2 ceramic is a strain rate strengthening material, which the dynamic fracture toughness is determined by the strain rate.
On the other hand, it can be concluded from Fig. 2

Comparison of static and dynamic critical grinding forces of ZrO 2 ceramic
In order to verify the accuracy of the model, it is necessary to analyze the critical grinding force of brittle ductile transition in the grinding experiment of ZrO 2 ceramic under three grain sizes. And according to the previous analysis, Bifano [40] proposed that the material removal of brittle materials is defined as ductile removal under the condition that the relative area ratio of surface damage less than 10%. Zhang [2] pointed out that attention should be given to subsurface damage in the material removal mechanism analysis for brittle materials. Therefore, the material removal mechanism can be investigated by analyzing the surface cracking rate and subsurface damage depth after grinding. The grinding experiments with grain sizes of 50nm, 500nm and 5000nm were carried out, and the grinding force, the surface cracking rate and subsurface damage were detected in this paper. Table 3 and Table 4 are the static and dynamic critical grinding forces for brittle-ductile transition when lateral cracks and median cracks are generated in the 1 st group of process parameters, respectively. It can be apparently seen that dynamic critical grinding forces is difference from static critical grinding forces for the brittle-ductile transition of ZrO 2 ceramics under three grain sizes.
Comparing Table 3 and Table 4, the material removal was brittle removal according to the static critical grinding force model, while the material removal was ductile removal using the dynamic critical grinding force model.  The surface morphology and the subsurface damage diagram of ZrO 2 ceramic with three grain sizes under the 1 st group of grinding process parameters were shown in Fig.3 and Fig.4 separately. The material removal mechanism in the actual grinding process was analyzed. It can be seen from Fig. 3 that material surface is dominated by plastic scratches, and the surface cracking rate is less than 10 %. Moreover, as shown in Fig. 4, it can be seen that no crack appeared on the subsurface. It indicates that the material removal mechanism should be ductile removal. On the other hand, by analyzing the calculated values and the experimental results in Table 4 and Table 5, it is obtained that the actual grinding force of single grit is smaller than the critical dynamic grinding force generated by lateral / median cracks. Therefore, it is verified that the critical grinding force model based on dynamic fracture toughness is more effective than the static critical grinding force model for brittle-ductile transition.  To further validate the accuracy of the model, the dynamic critical grinding force and the actual grinding force under the grinding process parameters of the 5 th group, the 9 th group and the 13 th group are compared. The comparison results are shown in Table 5. It can be seen from Table 5 that the actual grinding force on single grit is over than the critical grinding force for lateral cracks. It can be concluded that the material removal is brittle removal.
For ZrO 2 ceramics with grain size of 500 nm, the surface morphology under grinding parameters of the 5 th group, the 9 th group and the 13 th group are shown in Fig.5.
It can be concluded that the surface cracking rate is 13.

Influence of grinding process parameters on subsurface damage depth
According to Table 5    It is demonstrated that part of the subsurface damage is not connected to the grinding surface for the reason that the crack propagation is not perpendicular to the grinding surface. If 45° oblique throwing is adopted, the subsurface damage can be more obvious.
For ZrO 2 ceramics with grain size of 500 nm, the subsurface damage diagram under the 1 st group, the 5 th group and the 13 th group are shown in Fig.8. Combined with Table 4 and Fig. 8a, it can be seen that the actual grinding force of single grit under the 1 st group is less than the critical grinding force, and the material removal is ductile removal without subsurface damage. The grinding force of single grit under the 5 th group is greater than the critical grinding force, and the material removal method is brittle removed, and it can be clearly observed from Fig.   8b that median cracks and lateral cracks appeared on the subsurface of the workpiece and the maximum subsurface damage depth is 31μm. Besides, the grinding force of single grit under the 13th group is greater than the critical grinding force, and the material removal is brittle removal. Fig. 8c shows that many cracks arose on the subsurface of the workpiece and lateral cracks occurred, and the maximum subsurface damage depth is 97μm that deeper than under the 5 th group with 31μm. It is indicated that the level of subsurface damage of workpiece can be analyzed according to the grinding force in the grinding process.   Therefore, as the dynamic fracture toughness and critical grinding force increase due to the reduction of ZrO2 grain size, the percentage of ductile removal of ZrO 2 ceramics increases, hence the grinding surface quality is improved.

Effect of grain size on subsurface damage of ZrO 2 ceramic
The subsurface damage of three grain sizes under the 5 th group of grinding process parameters is shown in Fig. 10.
Combined with Fig. 7 and Fig. 10, it is can be seen that the material removal of ZrO 2 ceramic with three grain sizes was ductile removal with no cracks on the workpiece surface and subsurface under the 1 th group, which is consistent with the results shown in Fig. 9(c).
In the 5 th group of grinding process parameters, the subsurface damage depth of ZrO 2 ceramics increased from 27μm to 31μm and 40μm in turn with the increase of grain size. When the grinding process was carried out under the 13th group of grinding process parameters, it was concluded from the above analysis that the material removal was brittle removal and cracks were produced in three different grain sizes of ZrO 2 ceramics, and the subsurface damage depth of ZrO 2 ceramics increased from 52µm, to 97µm, 122µm in order with the increase of grain size. According to Equation (

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