Friction and wear characteristics of silicon nitride ceramics under dry friction condition

In order to reveal the friction properties and improve the wear resistance of silicon nitride ceramic materials, a calculation model of static friction coefficient of silicon nitride ceramic is established. The influence law of contact surface roughness on friction coefficient under different contact load and friction speed is analyzed. The test and the results verification are carried out by using Friction Wear Testing Machine. Then the dry friction process of silicon nitride ceramic is simulated based on UDEC, and the wear failure form is analyzed. In the dry friction process of silicon nitride ceramics, the coefficient of friction is directly proportional to the contact surface roughness, inversely proportional to the contact load, and directly proportional to the friction speed. There is a critical value for the roughness of friction sub-contact surface. Silicon nitride ceramics can self-lubricate by friction when the contact surface roughness is less than this critical value. In the dry friction process, the oxidation of SiO2 has little effect on the friction. The wear surface of silicon nitride ceramics consists of shear failure units and tensile failure units, and their formation is related to the surface roughness. The results play an important role in revealing the frictional properties of engineering ceramics such as silicon nitride, as well as helpful to improve the wear resistance and service life of ceramic materials.


Introduction
The engineering ceramics represented by silicon nitride ceramics has the advantages of high elastic modulus, low density, high temperature resistance, corrosion resistance and high hardness [1,2]. It has gradually become an indispensable key material for cutting-edge technology. Countries all over the world regard it as a new high-tech material that has a significant impact on the development of human society [3][4][5]. Due to the particularity of materials, silicon nitride ceramics are more and more widely used in high-end fields, such as bearings and seals [6,7]. Therefore, the study on the friction performance of silicon nitride ceramics has become one of the hot spots and frontiers. Manzoor Shahid, Qin Wenbo and Yeo Reuben et al have done a lot of researches on the frictional wear and machine rationality of hard brittle materials [8][9][10][11]. The following conclusions are mainly formed: (1) under the dry friction, the ceramics mainly break, crack and break, and then cause the wear of the grinding grain. Under the lubrication condition, it mainly appears in the frictional chemical wear. (2) In the case of low contact load and sliding speed, the wear mechanism is sticky and peeling. When the contact load and sliding speed are high, the ceramic wear surface would melt. The melted part falls off during friction and solidifies into flake debris after cooling. (3) Non-oxide ceramics may experience frictional oxidation and wear of the oxide layer [12][13][14][15][16][17][18][19][20]. Sun Jian analyzed the factors that affect the surface quality of silicon nitride ceramics. It has found that between friction depth and speed, the latter factor has a greater impact on friction force and the quality of surface [21,22]. The frictional wear performance of ceramics is influenced by the nature of materials, the environmental conditions, the pairing friction materials and more. However, there is no universal mechanism to explain the frictional wear of all ceramics. In addition, there are few studies on the factors affecting the surface quality of silicon nitride ceramics, especially the influence of surface roughness on the frictional properties of silicon nitride. In fact, the frictional behavior of silicon nitride ceramic is very sensitive to surface roughness, which has a great effect on the friction factor and wear performance of ceramics.
In this paper, the methods of theoretical calculation and experimental verification are used. By analyzing the frictional sub-contact on the processing surface of silicon nitride ceramics, the relationship between static friction coefficient and surface roughness is obtained from the Florida model. Under the dry friction at room temperature, comprehensive friction tests were carried out on silicon nitride ceramics with different surface roughness. The wear surface morphology and wear debris of the specimen were analyzed by scanning electron microscope to understand the friction process of ceramic materials. The frictional wear mechanism of silicon nitride ceramics and its influence on surface quality are revealed. It provides a favorable basis for accumulating and perfecting the tribology properties of silicon nitride ceramic materials.

The calculated model of static friction coefficient of silicon nitride ceramics
When the two surfaces of silicon nitride ceramics contact each other, only a few rough peaks contact on the surface due to the influence of surface roughness, and the contact points are also discrete. Therefore, the actual contact area is only a small part of the nominal contact area, and the applied load is mainly borne by these small rough peaks. The rough peaks of contact would change accordingly when the roughness of one of the contact surfaces changes. Therefore, the coefficient of static friction also changes with the surface roughness. In order to study the relationship between the static coefficient of friction and surface roughness, the contact model of rough surface should be established first.
The Florida model is shown in figure 1, which shows that the friction sub-interactions appear in the process of relative motion. It includes the ploughing effect and adhesion of rough peak as well as the effect of tear debris sliver on the surface after friction sub-wear in the process of friction.
It can be seen from figure 1 that the coefficient of static friction between the friction subs is as follows [23]: Where, μ a is the adhesion part of rough peak in the static friction coefficient; μ ap is the action part of rough peak ploughing in the static friction coefficient, μ d is the action part of the grinding debris ploughing in the static friction coefficient; β is the percentage of rough peak effect in the static friction coefficient of rough peak ploughing, and the value of silicon nitride ceramic materials is 1. When only the ploughing and adhesion of rough peak are considered, the static coefficient of friction is: According to the existing relationship between friction and stress-strain, it can be obtained: Where, τ a1 and τ a2 are the adhesion shear stresses of contact materials; σ τ2 and σ τ2 are the shear strength of the material; A a is the actual contact area formed by rough peaks, and P is the total load in the vertical direction. Where, H 1 and H 2 are the hardness of the material. (3) and (4) into (2), it can be obtained that:

Substituting equations
Where, r is the average radius of the spherical rough peak; σ is the conversion value of the standard deviation for the height of rough peak; D α is the number of spherical rough peaks on the unit area; A 0 is the nominal contact area; d is the separation distance of the rough peak reference plane of friction surface; p c is the contour contact pressure, and p r is the actual contact pressure. Substituting equations (7) into (6), the correlation between the surface roughness of silicon nitride ceramics and the coefficient of friction can be obtained.

The test device and method
The instrument used in the test is Rtec Friction Wear Testing Machine made in the United States. Its load range is 1 μN −2000 N, and reciprocating motion range of the carrier is 30 mm. The high-speed linear reciprocating motion frequency is 70 Hz, and the range of ambient cavity temperature is −120 ℃-1000 ℃. The test device and its principle are shown in figure 2.
Taking silicon nitride ceramic friction as the research object, hot isostatic pressing method is used to prepare silicon nitride ceramic materials. The sintering temperature is 2000°C; the holding time is 60 min; the sintering pressure is 200 MPa, and the sintering aid is Al 2 O 3 . The physical properties of the sample are shown in table 1. The specimen 2 in figure 2(b) is machined as j25 mm×5 mm. The pre-test wear surface of specimen 2 is polished to the mirror with a diamond grinding wheel on the precision plane grinder named BLOHM Orbit 36. This pair is a silicon nitride ceramic ball of the same material, which is the ground on a ball rubbing machine named 3ML4780D. The diameter of the ball is j9.525 mm and the spherical error is less than 0.0025 mm. Specimen 1 is placed on the surface of specimen 2 under the action of legal load, and specimen 2 will make highspeed linear reciprocating motion within 20 mm shown as figure 2(b).
Before and after the test, all specimens are cleaned with acetone ultrasonic for 15 min, and the dryer is placed in the dish for drying.
The test is carried out at no lubricated room temperature. The friction and wear test system automatically records each test, and the temperature test system records the temperature change in real time. The surface wear  morphology of silicon nitride ceramics is observed by Hitachi s-4800 scanning electron microscope, including grain shedding, micro-cracks and plastic deformation. Using single factor test method, four groups of tests are carried out on the contact load, the friction speed and the friction contact surface roughness. Silicon nitride ceramic friction pair is ceramic ball and ceramic plate shown as figure 2(b). The roughness of the surface of the ceramic ball is divided into G3, G5, G10, G16 and so on according to the standard grade shown as [25] from high to low. Therefore, the contact surface roughness of friction pair in the experiment is selected according to the standard. The test time for each group is 10 min. The test parameters and levels are shown in table 2.

Influence of different conditions on friction coefficient of silicon nitride ceramics
The variation of friction coefficient of silicon nitride ceramics with contact load, friction speed and contact surface roughness under dry friction at room temperature is shown in figure 3. Compared with the four pictures in figure 3, it can be concluded that the smaller the contact surface roughness, the larger the contact load, the smaller the friction speed, and the smaller the friction coefficient of silicon nitride ceramics. Among the above factors, surface roughness has the greatest influence on the friction coefficient, while the friction speed has the least effect. In the range of test data, when the value of R a is 0.01 μm, F is 160 N and v is 20 m min −1 , the minimum value of silicon nitride friction coefficient μ is 0.025 μm. When R a is 0.04 μm, F is 20 N and v is 80 m min −1 , the minimum value of μ is 0.889 μm. Furthermore, when the contact surface roughness is less than 0.014 μm, regardless of the contact load and friction speed, the friction coefficient of silicon nitride is always in the small range of 0.025-0.048 μm, and the change is basically the same. This shows that when the contact surface roughness is less than a certain value, the friction coefficient of silicon nitride ceramics is not affected by external factors, which can achieve self-lubrication of friction.

Analysis of the wear surface morphology of silicon nitride ceramics
The dry friction surface wear morphology of silicon nitride ceramics under different conditions is shown in figure 4. In order to reveal the friction characteristics and wear of silicon nitride ceramics, a large number of experiments were done. Then, typical test results were selected under 4 operating conditions. The friction coefficient in figure 4(a) is measured, and the value of μ is 0.037 μm. It can be seen that its surface is very smooth without visible scratches. Thus when the surface roughness of silicon nitride is less than 0.014 μm, dry friction has no effect on its surface, and the friction characteristics of ceramics are ideal. The friction coefficient measured in figure 4(b) is 0.426 μm. There are friction scratches on the surface, which destroys the processed surface morphology of silicon nitride. The value of friction coefficient is 0.031 μm measured in figure 4(c) and the cracks are visible on its surface. This is because the surface of figure 4(c) has a roughness of R a =0.014 μm and the surface quality is good. However, due to the high contact load and friction speed, a small amount of thermal crack will appear on the surface of silicon nitride ceramics under dry frictional conditions, which has no effect on the surface friction coefficient. The value of friction coefficient is 0.891 μm measured in figure 4(d). Because of the large roughness, the surface is poor. At the same time, under the action of large contact load, the wear phenomenon of friction surface is more obvious and fatigue wear appears.

Chemical composition of the friction surface of silicon nitride
The surface chemical composition of silicon nitride ceramics after friction test is analyzed as shown in figure 5. The chemical composition of the silicon nitride surface is detected before test as shown in figure 5(a). It can be seen from the test results that the pre-test part is composed of silicon nitride and contains a small amount of Al2O3 sinter agent. After the friction test, the chemical composition analysis of the grinding debris on the wear surface of silicon nitride is shown in figures 5(b) and (c). From the results, it can be seen that the components of grinding debris are mainly SiO 2 and Al 2 O 3 . Among them, SiO 2 is a newly produced substance. In addition,     shows that silicon nitride ceramic dry friction does not necessarily produce SiO 2 . Under certain friction conditions, dry friction of silicon nitride ceramics may also not change the material content. Comparing the four images before and after the experiment in figure 5, it can be seen that the new substance SiO 2 is oxidized under the dry friction of silicon nitride. However, SiO 2 is a silicon oxide that has no lubrication properties and cannot be used as a friction lubricant. Therefore, when the contact surface roughness of silicon nitride ceramic is less than 0.014 μm, the self-lubricating will appear. This process is not due to the new lubrication material being generated during friction, but entirely dependent on the physical properties of silicon nitride and the finish on its surface.

The simulation models
In this paper, UDEC two-dimensional discrete unit method is used to simulate the wear of silicon nitride ceramic surface during dry friction [26]. When the method is used for numerical simulation, it mainly includes block generation, material generation, boundary condition simulation, and load and speed application. Among them, the physical model is mainly established through the formation of blocks and materials as well as the simulation of boundary conditions. The simulation of the motion process is mainly completed by the application of load and speed. The ceramic friction pair is defined as a deformable body, the initial separation state between deformation bodies is realized by the CELL command, and the material parameters are assigned to the deformable body according to table 1. In order to effectively compare with the results, the simulation boundary conditions are completely consistent with the experimental factors, and the target dimensions of the simulation process are set according to the actual size of test parts. The physical model of silicon nitride ceramic friction pair has been established as shown in figure 6.
A certain initial condition is applied to the friction pair of silicon nitride ceramics, including the vertical load and moving speed. The simulation material is given a certain value to normal stiffness and shear stiffness, and the mechanical effect between the friction pair of ceramic block is realized. The Mohr-Coulomb guidelines, as corrected in UDEC, are used in the model shown as figure 7 [27,28]. The yield criterion of Mohr-Coulomb is indicated by f s in figure 7.
Where, σ 1 is the first primary stress; σ 3 is the third primary stress; b is the sticky force and f is the friction angle.
The tensile yield criterion is indicated by f t .
Where, σ t is the tensile strength.
The numerical simulation results of UDEC provide an intuitive representation of surface wear of silicon nitride ceramics under dry friction. It is also possible to observe and calculate the ceramic wear failure pattern, the unit area ratio of ceramic plastic destruction, the crack expansion and more.

Analysis of the simulation results
As non-oil self-lubricating, the wear simulation results of silicon nitride ceramics under different friction conditions are shown in figure 8. It can be seen that the surface of silicon nitride ceramics is wore after friction. The wear failure unit consists of shear failure unit and tensile failure unit. Comparing the simulation results in figure 8, it can be seen that when the surface roughness of silicon nitride ceramics is less than 0.014 μm, the amount of friction surface failure unit is less, and the surface wear is basically the same. The wear condition is not affected by the external friction conditions. When the value of surface roughness is greater than 0.014 μm, the surface wear becomes more serious with the increase of the contact load and friction speed. When the value of contact surface roughness of silicon nitride is less than 0.02 μm, the wear surface is mainly shear failure unit. Conversely, the wear surface is dominated by tensile failure units. When the surface roughness is about 0.02 μm, the number of shear and tensile failure units is basically the same. As shown in figures 8(g)-(l), when the value of contact surface roughness increases gradually from 0.025 μm, the failure unit begins to expand from the contact surface to the interior of the ceramics, and the expansion process of the failure unit is the formation process of frictional thermal crack. Meanwhile, it can be seen that in the process of the failure unit of ceramic material from friction surface to internal expansion, the tensile failure unit gradually changes to shear failure unit. It can also be seen from figures 8(g)-(l), when the value of surface roughness is constant, the contact load and friction speed increases, and the surface wear would be more serious. However, the wear failure unit does not extend to the interior of the ceramics in the form of cracks. When the value of contact load and friction speed is constant, the surface roughness increases, the surface wear would also be more serious, and the wear failure unit would extend to the interior of the ceramics.

Discussion
When the contact surface roughness of silicon nitride ceramic friction pair is less than 0.014 μm, the contact load and friction speed will not affect the friction and wear process of the ceramics, and self-lubrication can be realized. When the surface roughness is greater than 0.014 μm, the wear of the ceramic surface is greatly affected by the contact load and friction speed. The surface wear is more serious with the increase of the contact load and friction speed under dry friction. This shows that there is a critical value in the contact surface roughness of silicon nitride ceramics in the process of dry friction, and its value is 0.014 μm. This is consistent with the experimental and theoretical research results.
From the experimental and simulation results, they are concluded that the friction coefficient is inversely proportional to the contact load when other conditions remain unchanged in the process of dry friction. From simulation results, it is concluded that the surface wear after friction is proportional to the contact load. Under the large contact load, the wear of contact surface is obvious, and the surface fatigue wear appears. This shows that the friction coefficient of silicon nitride ceramics will decrease if the contact load continues to increase during fatigue wear. The above phenomena can be derived from both experimental and simulation studies. This shows that the theory is consistent with the results of the experiment.
When the surface roughness of silicon nitride ceramics is low, the main phenomenon in the friction process is shear failure. In the friction process with higher roughness, the main phenomenon is tensile wear. This shows that when the surface roughness is small, the extrusion effect would appear between smooth friction surfaces under large load and high-speed friction. It causes shear failure of the material. When the roughness of the contact surface is large, the scratching and tearing effect in the friction is more obvious, and the surface wear is serious. The failure unit is mainly tensile, and a large number of cracks formed on the surface begin to expand into the interior of the ceramics. In the process of expansion in the form of cracks, the failure unit will change under the thermal stress of frictional high temperature. At the same time, under the brittle extrusion of silicon nitride ceramics, the tensile failure gradually transforms into the shear failure unit.