Int J Adv Manuf Technol (2015) 81:483–492 DOI 10.1007/s00170-015-7195-y

ORIGINAL ARTICLE

Investigation on surface micro-crack evaluation of engineering ceramics by rotary ultrasonic grinding machining Wei Shiliang 1 & Zhao Hong 1 & Jing Juntao 2 & Liu Yunfeng 3

Received: 30 November 2014 / Accepted: 19 April 2015 / Published online: 9 May 2015 # Springer-Verlag London 2015

Abstract Rotary ultrasonic grinding machining (RUGM) is regarded as the most powerful machining method for engineering ceramic. However, there are micro-cracks on the machined surface inevitably for lower fracture roughness of material. As part of surface integrity, effective parameter and unified criterion are not proposed for micro-crack evaluation. In the paper, surface micro-crack evaluation of engineering ceramics by RUGM was investigated. Micro-crack generation area ratio calculation model and information dimension calculation model were established. On the basis of those, a new evaluation parameter, called micro-crack fractal density, was proposed to reveal the characteristics of micro-crack. The parameter was proved to evaluate micro-crack evolution rule effectively with the advantages of statistics and multi-scale. Meanwhile, the factors affecting micro-crack fractal density evaluation were investigated. It is found that the micro-crack fractal density increases with cutting force rising, while it decreases as fracture toughness rises. The results provide the support for surface integrity evaluation of engineering ceramics.

Keywords Rotary ultrasonic grinding machining . Micro-crack evaluation . Engineering ceramics . Fractal density

* Zhao Hong [email protected] 1

Harbin Engineering University, Harbin, China

2

Tsinghua University, Beijing, China

3

China Aerospace Science & Industry Corp Harbin Fenghua CO.LTD, Harbin, China

1 Introduction Engineering ceramic materials are applied in aerospace, precision machinery, inertial guidance fields, and so on, with small density, high strength, high wear resistance, and other excellent features. Pei et al. draw conclusions that rotary ultrasonic grinding machining (RUGM) was the most powerful machining method for engineering ceramic with the smaller cutting force, the higher machining efficiency, and the better surface integrity [1–5]. However, engineering ceramic materials possess high hardness, low fracture toughness, and other characteristics; the material removal mechanism of RUGM is fracture in brittle zones, so there are surface micro-cracks inevitably in the process [6–10]. Index parameters and evaluation criteria of engineering ceramics by RUGM are those adopted those of metal material. But it is difficult to generate surface micro-crack in metal material processing, and there is no surface micro-crack evaluation parameter in the surface integrity evaluation system [11]. Meanwhile, the material properties and material removal mechanism of engineering ceramic are different from those of metal materials, so it is not accurate and comprehensive to evaluate engineering ceramic surface integrity characteristics with surface integrity evaluation parameters of metal material processing. The evaluation parameters and calculation method are not presented for surface micro-crack evaluation of engineering ceramics by RUGM. The parameters, used in material fracture surface of mechanical engineering subject or in rock surface of geology subject, are referred to evaluate the surface microcrack, such as the average size of crack length, crack density (crack number per unit area), and so on [12–15]. Lin et al. measured the thickness of micro-crack damage layer with oblique polishing method, and proposed the effective depth of micro-crack damage layer as evaluation index [16]. The evaluation parameters are single, not full to reflect the characteristics and change rule of the surface micro-crack. Akhavan et al. put forward the parameter of crack tortuosity with fractal dimension

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to estimate crack [17]. However, the application range is only the single and regulate crack profile, as toughness profile. For engineering ceramics surface cracks of rotary ultrasonic grinding, they are tiny, independent, and irregular, so the method is unsuitable. Sun and Zhou studied the fractal characteristics of the surface cracks and the damage evolution process of rubber concrete beams under concentrated load [18]. Chen et al. thought that the surface cracks possess fractal characteristics and could be evaluated with fractal dimension when they research the process of gas-containing coal extrusion [19]. Yang et al. furtherly proposed a segmentation method of combining gray-level threshold and fractal feature for crack images [20]. The above conclusions provide the research idea for the surface micro-crack evaluation of engineering ceramics by RUGM. Surface micro-crack is related to fatigue strength and performance of the component directly, and how to evaluate surface micro-crack of engineering ceramics by RUGM accurately is the first problem to solve for engineering ceramics parts application. In this paper, we will establish the fractional Brownian random field (FBRF) model of engineering ceramics surface gray image by RUGM, and area ratio of micro-crack generation is deduced. Then the information dimension model is analyzed. The feature evaluation parameter of surface micro-crack is proposed based on the above analysis. It provides the corresponding evaluation index for engineering ceramics surface integrity comprehensive evaluation.

2 Theoretical description 2.1 Micro-crack generation area ratio calculation model It is known that there are medium cracks and lateral cracks in the surface of engineering ceramics by RUGM, as shown in Fig. 1 [21]. The expansion direction of lateral cracks is parallel to machined surface, while the expansion direction of medium cracks is vertical to machined surface. The material removal mechanism is a series of medium cracks and lateral cracks generation, then coupling and combining of the adjacent lateral cracks to cause the material fall off. The lateral cracks are the boundary for material loss, so

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residual micro-cracks on the surface of engineering by RUGM are mainly medium cracks. The length of medium cracks and lateral cracks is longer as the cutting force is greater. Longer lateral cracks lead to material removal volume increasing, resulting in a flat surface morphology. Meanwhile, it is easy to see on the machined surface for longer medium cracks. It is also verified that surface micro-cracks of engineering ceramics by RUGM seen in the morphology area were smooth mostly, based on a lot of experimental results and study. For the morphology area that changes dramatically, it is hard to observe the micro-cracks. The surface micro-cracks of engineering ceramics by RUGM are not seen easily and clearly in all kinds of places. The residual micro-crack on the surface are mainly medium cracks, and the appearing section morphology is gentle, based on the results above. So the micro-crack generation area ratio can be calculated by image analysis. The surface morphology of engineering ceramic surface by RUGM possesses fractal characteristics with self-similar and self-affine. The FBRF theory was applied to investigate the surface gray image of engineering ceramics by RUGM. Every pixel of gray image is only a color, and shows any color from all black to all white usually. There are many color steps between all black and all white. The surface morphology amplitude is different at each position due to feature differences of surface microstructure. The differences arouse the brightness change on gray image, and the color step of each pixel is not the same yet, as shown in Fig. 2. Set the surface morphology distribution of engineering ceramics by RUGM is zH(x,y) mapped to gray image distribution. The distribution satisfies two-dimensional fractional Brownian movement under certain scale. First of all, gray values of two different points subtract and change the result into absolute value, then the mean of them can be expressed as Eq. (1). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiH E ½jzH ðx2 ; y2 Þ−zH ðx1 ; y1 Þj∝ ðx2 −x1 Þ2 þ ðy2 −y1 Þ2 ð1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N o t e d t h a t z H ( r ) = z H ( x , y ) , Δr ¼ Δx2 þ Δy2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðx2 −x1 Þ2 þ ðy2 −y1 Þ2 , and the following relation

Fig. 1 The generation of microcracks

Lateral crack Medium crack

ZH(x,y)

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300 200 100 0

30 25

30

20 20

15 10

10 Y direction

5 0

0

X direction

fractal dimension is, and the machined surface is rough. The surface gray image of engineering ceramics by RUGM is disposed with the above analysis, and the Hurst index distribution is obtained. The appearing sections of surface microcracks are mainly gentle, and the Hurst index is lower. While in the area where the morphology amplitude change is dramatic, the Hurst index is greater, and the micro-cracks are not found. Therefore, the Hurst index is regarded as the criteria. The engineering ceramic-machined surface can be divided into the area of micro-crack generation and the area of no micro-crack with the Hurst index. Micro-crack generation area ratio is calculated as Eq. (7).

Fig. 2 The gray value of different position

λ¼ equation is given in Eq. (2). ! zH ðr þ ΔrÞ−zH ðrÞ P ≤ I ¼ F ðI Þ kΔrkH

ð2Þ

where H is the Hurst index and 0
ð3Þ

where C is constant. Take the log on both sides of Eq. (3), respectively. It is transformed to the following equation. log½E ðI Δr Þ ¼ HlogðΔrÞ þ logC

ð4Þ

For the geometry graphics with self-affine and self-similar, it can be described by fractal dimension. Hurst index is also a parameter describing graphics complex, and the mathematical relationship between fractal dimension and Hurst index can be expressed as Eq. (5). D ¼ d þ 1−H

ð5Þ

where d is topological dimension. For profile, d=1, for twodimensional surface, d=2. So for surface gray values distribution of engineering ceramics by RUGM, the following relationship is given in Eq. (6). D ¼ 3−H

ð6Þ

It is found that the change of surface morphology amplitude is related to the Hurst index directly from Eq. (4). The Hurst index reflects the roughness of fractional Brownian surface. The greater the Hurst index is, the smaller the surface fractal dimension is, and the machined surface is flat. In contrast, the smaller the Hurst index is, the greater the surface

S crack N H ≤ H s ¼ S total N

ð7Þ

where Scrack is the area of micro-crack generation for measured surface. Stotal is the area of total measured surface. N H ≤ H s is the number of H≤Hs for the measured surface Hurst index distribution, and Hs is the criteria value. N is the total number for the measured surface Hurst index distribution. 2.2 Information dimension calculation model of micro-crack The characteristics of surface micro-crack are random and irregular. The structure does not change notably under different magnification with self-similarity, and it is fractal. So it is reasonable to study micro-crack characteristics change with fractal theory after image processing. The fractal dimension is also calculated. In all definition and calculated method of fractal dimension, information dimension is valuable. The number of covering mesh is not only involved, the probability of fractal elements in covering mesh is also showed. It is objective to reflect the fractal features of discrete micro-cracks. Dimension information reveals the relationship and rule of complex micro-cracks in different scales and also shows the scale change of complex structure. Less information dimension shows that the scale change of micro-crack structure is weak, and the structure of micro-crack is simple. In contrast, large dimension information suggests that the structure of microcracks is complex. So information dimension can be applied to evaluate micro-crack structure complexity. And information dimension calculation model of micro-crack can be expressed as follows. Firstly, surface micro-cracks of engineering ceramics by RUGM are dissociated, then define that the length of the side of squares is ε. Micro-cracks image is covered by the squares, as shown in Fig. 3. Assumed that the number of the squares is N(ε), and the number of micro-cracks in the square noted i is n(i), the probability of micro-cracks that fall into the square

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In order to evaluate the surface micro-crack of engineering ceramics by RUGM comprehensively and accurately, a new evaluation parameter, called micro-crack fractal density, is proposed in the paper, based on the above analysis and the advantages of the information dimension. The definition of micro-crack fractal density is the total length of micro-cracks in unit area times the information dimension. The calculation formula is given in Eq. (11). ρ ¼ Ds ˙L˙

e e Fig. 3 Mesh division for information dimension calculation of microcracks

noted i can be expressed as Eq. (8). P i ðε Þ ¼

nð i Þ

ð8Þ

N ðεÞ

X

nð i Þ

i¼1

Information equation is defined as follows: I ¼−

N ðεÞ X

Pi ðεÞlnPi ðεÞ

ð9Þ

i¼1

The size of ε is changed, and the corresponding values of I are calculated. Then fit point coordinates of (lnε−I) with the straight-line. The absolute value of the straight-line slope is equal to information dimension, and its mathematical expression is given as Eq. (10). N ðεÞ . . X Pi ðεÞlnPi ðεÞ lnε DI ¼ − lim I lnε ¼ lim ε→0

ε→0

λ S

ð11Þ

where Ds is the information dimension of surface microcracks. L is the total length of micro-cracks in machined surface image, micrometer. S is the actual area of machined surface image, micrometer square. λ is the micro-crack generation area ratio, and it is introduced in Section 2.1. The statistical characteristics of surface micro-crack can be analyzed for traditional evaluation parameters. They reflect the numerical value change of micro-crack, but cannot reveal the structure complexity and the structure evolution. Information dimension shows the micro-crack complexity in the function and the multi-scale analysis. Micro-crack fractal density combines traditional evaluation parameters with information dimension to evaluate surface micro-crack characteristics objectively in the perspective of function, statistics, and multiscale. It keeps the numerical quantitative of micro-crack, and also reflects the numerical changes of micro-crack. Accurately, it is found that micro-crack fractal density is greater with more complex micro-crack structure and larger micro-crack length in a unit from Eq. (11). The greater micro-crack fractal density is, the more significant engineering ceramic surface micro-crack is, and the surface integrity is worse, effecting the application of machined parts.

ð10Þ

i¼1

The information dimension of micro-crack can be calculated with the above equation, which reflects surface micro-crack structure complexity by different processing. 2.3 Definition of micro-crack fractal density Information dimension can be used to analyze machined surface micro-crack in the perspective of multi-scale to some extent, and it is scale-free. However, the value is relative when it is applied in evaluating surface micro-crack. It reveals the structure complexity of micro-crack, does not shows numerical value of micro-crack in quantitative. Meanwhile, the results may be the same to evaluate different surface microcrack with information dimension only, and the evaluation conclusions are not reasonable, because the parameter is relatively simple.

3 Experimental setup In order to calculate the area ratio of micro-crack generation, exact the micro-crack, and verify the valuation parameter validation, surface topography of engineering ceramics by RUGM should be obtained firstly. So experiments were designed. Al2O3 ceramics, ZTA ceramics, Nano-Si3N4 ceramics, and Self-Si3N4 ceramics, which have been widely applied in aerospace, were selected in the experiments. The size of samples is Φ 50×10 mm. The engineering ceramics are produced by sintering process and are typically hard and brittle homogeneous material. Parameters of the main material properties are shown in Table 1. The experiments were conducted by DMG Ultrasonic 50, which can achieve conventional grinding and rotary ultrasonic grinding machining. The ultrasonic vibration frequency is

Int J Adv Manuf Technol (2015) 81:483–492 Table 1 The main parameters of materials

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Flexural strength (MPa)

Fracture toughness (MPa·m1/2)

Hardness (GPa)

Parameters Material

Modulus of elasticity (GPa)

Al2O3 ZTA Nano-Si3N4 Self-Si3N4

126.69±15.6

410±8.5

2.081

11.82

120.73±15.847 155.7±14.5 262.1±1.6

445.6±8.5 304.5±3.0 525.9±20.8

2.463044 3.64±0.35 3.64±0.11

12.98857 10.62804 8.442999

between 19.7 and 48 KHz and the amplitude is about 6 μm in rotary ultrasonic grinding process. The cutting tools used in the experiments were bronze-bonded diamond tools made by DMG Sauer company. The outer diameter of diamond tool is 10 mm and the inner diameter is 7 mm. The diamond size is D126 and the concentration is 100 %. The 3-factor-and-2level orthogonal experimental program and machining parameter are listed in Table 2, reference to the experience of the experiments before. The ceramic samples were bonded to the tablet, respectively, and fixed to the dynamometer bench. They were machined by RUGM, shown as Fig. 4, with machining width 5 mm, according to the experimental sequence and parameters. In the process of experiments, the cutting forces were measured by KISTLER 9257A dynamometer and KISTLER 5070 charge amplifier. The machined surface of each sample was observed by FEI HELIOS NanoLab 600I FIB/SEM double beam system.

dramatical and the machined surface is rough. In addition, it is hard to find micro-cracks. So we can draw the conclusion that the flat section of observed surface is also the micro-crack generation area. The Hurst index of Fig. 6 was calculated based on the theoretical analysis and calculation method in Section 2.1. The distribution statistics of the Hurst index are shown as Fig. 7. It is found that the Hurst index is less than 0.2 for more than 95 % in the micro-crack generation area, and the Hurst index is greater than 0.2 for more than 95 % in the no microcrack generation area, so Hs =0.2 is taken as the criteria value. In other words, that is the watershed of the micro-crack generation area and the no micro-crack generation area. It is drawn that the micro-crack generation area ratio of Al2O3 ceramics and ZTA ceramics by RUGM are 27.95 % and 42.21 %, respectively, with the statistics results and Eq. (7).

4 Results and discussion

Machined surface micro-cracks are random and irregular. Micro-cracks should be separated from the surface image with image processing, in order to evaluate the surface micro-crack and analyze the statistical feature easily. It can be seen that the gray values of micro-cracks are small, approximately zero, and the gray values of its surrounding are 100 to 200 from Fig. 6. Therefore, the gray values mutation and brightness change have happened around the micro-cracks obviously. These characteristics are identical with edge features, so canny operator edge detection algorithm can be used to dissociate micro-cracks from the surface image. Meanwhile, particular area processing is implemented to fill and filter the structure of no micro-crack after the edge detection. Figure 8a, b show the micro-cracks extracted from Fig. 6. The same method is applied in surface images of nanotoughening Si3N4 and self-toughening Si3N4 by RUGM under

4.1 Micro-crack generation area ratio Figure 5 shows the surface morphology of Al2O3 ceramics and ZTA ceramics by RUGM, respectively, under the conditions that the speed is 6500 r/min, the cutting height is 55 μm, the feed rate is 100 mm/min, with DMG bronze-bonded diamond tool. It is hard to see the micro-cracks due to small magnification. But it is easy to find that the surface morphology of the two images is composed with two sections of difference. One section of scanning electron microscope image, the gray value change is equal and the machined surface is flat. However, there are micro-cracks in the section for further observation, as shown in Fig. 6. The other section of scanning electron microscope image, the gray value change is

4.2 Evaluation validity analysis of micro-crack fractal density

Table 2 Experimental program Experimental no.

Speed (r/min)

Cutting depth (μm)

Feed rate (mm/min)

Tools type (Ф 10 mm)

1 2 3 4

6500 6500 7000 7000

55 35 55 35

100 90 90 100

DMG bronze-bonded DMG bronze-bonded DMG bronze-bonded DMG bronze-bonded

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Ultrasonic vibration system Diamond tool Self-toughening Si3N4

ZTA ceramics

a Al2O3 ceramics Nano-toughening Si3N4

Cutting force measuring system

Fig. 4 Rotary ultrasonic grinding machining experiment

b Area of micro-crack generation

a

Area of micro-crack generation

b Fig. 5 Surface of Al2O 3 ceramics and ZTA ceramics by RUGM (×13,000). a Al2O3 ceramics. b ZTA ceramics

Fig. 6 Micro-cracks of Al2O3 ceramics and ZTA ceramics surface by RUGM (×50,000). a Al2O3 ceramics. b ZTA ceramics

the machining parameters the same as above, and the microcrack figures are shown in Fig. 8c, d. The surface micro-cracks of Al2O3 ceramics by RUGM are also separated to verify the effectiveness of micro-crack fractal density for evaluation under the machining parameter nos. 2, 3, and 4 in Table 2. They are shown in Fig. 9. Surface micro-crack statistic characteristic of engineering ceramics by RUGM, under the typical machining parameter, as shown in Figs. 8 and 9, are obtained in Table 3. The fractal density evaluation results, the traditional evaluation parameters, and information dimension evaluation results were analyzed and compared. It is drawn that the surface micro-crack evaluation of Al2O3 ceramics under the machining parameter nos. 1 and 2 are the same with the average crack length per unit area applied from the table above. However, the micro-crack intensity of Al2O3 ceramics under the machining parameter no. 2 is far less than that of no. 1 from Figs. 8a and 9a. The micro-crack length per unit area is 0.391 μm/μm2, also less than that is 2.522 μm/ μm2, under the machining parameter no. 1. Similar problems have occurred for the results under the machining parameter

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a

b Fig. 7 Hurst index distribution of Al2O3 ceramics and ZTA ceramics surface by RUGM (×13,000). a Al2O3 ceramics. b ZTA ceramics

489

nos. 3 and 4 with the average crack length per unit area evaluation. It suggests that the average crack length per unit area is not suitable for micro-crack evaluation. When micro-crack density is applied to evaluate, it is seen that the result of Al2O3 ceramics under the machining parameter no. 3 is the same with that of self-toughening Si3N4 ceramics under the machining parameter no. 1. For further analysis of the figures, the number of surface micro-cracks is equal in the two kinds of conditions, but the total micro-crack length of Al2O3 ceramics under the machining parameter no. 3 is greater than that of self-toughening Si3N4 ceramics, and the surface quality is worse. So it is also not inappropriate to evaluate surface micro-crack of engineering ceramics. The result of Al2O3 ceramics under the machining parameter no. 1 is the greatest from the table above, when micro-crack fractal density is applied to evaluate. Figure 8a shows that the number of its surface micro-cracks is the most, the total length per unit is the maximum, and the structure of surface microcrack is complex too. So the surface quality is the worst. While the result of Al2O3 ceramics under the machining parameter no. 2 is the smallest, following that the number of its surface microcracks is the least, the total length per unit is the minimum, and the structure of surface micro-crack is simple. Therefore, the surface quality is the best. More analysis were made. It is found that the order result of surface micro-crack with the microcrack fractal density evaluation in the above table is consistent with the machined surface quality in the experiments. Micro-

Fig. 8 Micro-crack profiles of different ceramics surfaces by RUGM (×50,000). a Al2O3 ceramics. b ZTA ceramics. c Nano-toughening Si3N4. d Selftoughening Si3N4

a

b

c

d

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Fig. 9 Micro-crack profile of different machining parameters (×50,000). a The second test. b The third test. c The fourth test

a

b

c crack fractal density, as an evaluation parameter of micro-crack characteristics, is effective and reasonable. 4.3 Affecting factors analysis of micro-crack fractal density evaluation It is known that cutting force and material performance parameters are the main factors influencing the micro-crack generation and propagation based on material removal mechanism. So they are also the main factors affecting surface micro-crack evaluation result. Micro-crack fractal density, as an effective evaluation parameter of surface micro-crack, has proved in the conclusion above. The investigation on cutting force and material performance parameters affecting surface micro-crack evolution, with micro-crack fractal density, was developed to offer guide of process parameter optimization. Table 3

(1) Cutting force influence on the fractal density Figure 10 shows the relationship between the cutting force and the micro-crack fractal density of typical engineering ceramics by RUGM. It is found that the cutting force increase corresponds to the enlarged surface microcrack fractal density values whatever the engineering ceramics is. The length of micro-crack can be expressed as follows according to reference [1, 3].  c¼

χr ˙ F K IC

2=3 ð12Þ

where χr is the stress intensity factor of the micro-crack tip. F is the cutting force. KIC is fracture roughness. The number of micro-crack generation and the length of micro-crack propagation increase with the cutting force

Parametric statistics of surface micro-cracks

Materials

Experimental no.

Total micro-crack length per unit (μm/μm2)

Average crack length per unit (μm/μm2)

Micro-crack density (/μm2)

Information dimension

Micro-crack fractal density (μm/μm2)

Al2O3

1

2.522

0.065

1.374

1.222

3.082

ZTA Nano-toughening Si3N4 Self-toughening Si3N4

2 3 4 1 1 1

0.391 1.447 1.229 1.760 0.581 0.830

0.065 0.056 0.056 0.352 0.053 0.032

0.211 0.916 0.785 0.176 0.388 0.916

0.2196 0.6027 0.8540 1.283 0.6685 0.1837

0.086 0.853 1.042 2.258 0.388 0.152

Micro-cracks fractal density ( µm/µm2 )

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3

491

MPa·m1/2. It can be explained that the materials plastic index is more obvious with fracture toughness increases. Then, it is not benefited for micro-crack generation and propagation. The number, the length, and the complexity of micro-crack reduce. They lead to the descent of information dimension and the total length per unit inevitably, resulting in the micro-crack fractal density dropping.

Al2 O3 ZTA

2.5

Nano-Toughening Si3 N4

2

Self-Toughening Si3 N4

1.5 1 0.5 0

5 Conclusion 40

60

80 100 Cutting force (N)

120

140

Fig. 10 The relationship between cutting force and micro-crack fractal density

Micro-crack fractal density ( µm/µm2 )

ascending. It leads to a bigger length per unit area of microcrack, and micro-crack structure is complex. The change causes the micro-crack fractal density rising, but the surface quality becomes poor. However, it is important to note that for Al2O3 ceramic and ZTA ceramics, the micro-crack fractal density variation is significantly, while the results of nanotoughening Si3N4 and self-toughening Si3N4 are indistinctive. (2) Fracture roughness influence on the fractal density Al2O3 ceramic, ZTA ceramics, nano-toughening Si3N4, and self-toughening Si3N4 were selected in the experiments and their fracture roughness are different. So we can analyze fracture roughness influence on the fractal density with the experimental results. Their micro-crack fractal density were calculated, and the relationship lines between fracture roughness and microcrack fractal density under the same machining parameters are given in Fig. 11. It is found that surface micro-crack fractal density decreases as fracture toughness rises when the material fracture toughness changes between 2.08 and 3.64 S=6500r/min f=100mm/min h=55µm

3

Surface micro-crack evaluation of engineering ceramics by RUGM was investigated in this paper. The analyses and experimental results allow the following conclusions to be drawn: Surface micro-cracks of engineering ceramics by RUGM seen in the morphology area were smooth mostly, and microcrack generation area ratio calculation model was established based on FBRF. The area of micro-crack generation and that of no micro-crack are divided by the Hurst index. The microcrack generation area ratio is calculated base on Hs =0.2 in the experimental results. Micro-crack information dimension calculation model was established. And a new evaluation parameter, called microcrack fractal density, was proposed to evaluate the characteristics of micro-crack. It is verified that the parameter is effective and reasonable. The parameter covers the insufficiency of traditional evaluation parameters that cannot reveal the structure characteristics and the evolution. It reflects the characteristic evolution and the numerical changes of micro-crack in the perspective of function, statistics. and multi-scale. The micro-crack fractal density increases with cutting force rising. The micro-crack fractal density variation is significantly for Al2O3 ceramic and ZTA ceramics, while the result is not notable for nano-toughening Si3N4 and self-toughening Si3N4. Surface micro-crack fractal density decreases as fracture toughness rises when the material fracture toughness changes between 2.08 and 3.64 MPa·m1/2.

S=7000r/min f=90mm/min h=55µm

2.5

S=7000r/min f=100mm/min h=35µm

2 1.5

Acknowledgments The authors would like to thank the Space Support Technology Pre-research Project and Heilongjiang Provincial Natural Science Foundation of the Republic of China under No 61801060103 and ZD201313.

1

References 0.5 0

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2.5 3 3.5 1/2 . Fracture roughness (MPa m )

Fig. 11 The relationship between fracture toughness and micro-crack fractal density

2.

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