Mechanism of irregular crack-propagation in thermal controlled fracture of ceramics induced by microwave

. Microwave cutting glass and ceramics based on thermal controlled fracture method has gained much attention recently for its advantages in lower energy-consumption and higher ef ﬁ ciency than conventional processing method. However, the irregular crack-propagation is problematic in this procedure, which hinders the industrial application of this advanced technology. In this study, the irregular crack-propagation is summarized as the unstable propagation in the initial stage, the deviated propagation in the middle stage, and the non-penetrating propagation in the end segment based on experimental work. Method for predicting the unstable propagation in the initial stage has been developed by combining analytical models with thermal-fracture simulation. Experimental results show good agreement with the prediction results, and the relative deviation between them can be < 5% in cutting of some ceramics. The mechanism of deviated propagation and the non-penetrating propagation have been revealed by simulation and theoretical analysis. Since this study provides effective methods to predict unstable crack-propagation in the initial stage and understand the irregular propagation mechanism in the whole crack-propagation stage in microwave cutting ceramics, it is of great signi ﬁ cance to the industrial application of thermal controlled fracture method for cutting ceramic materials using microwave.


Introduction
The application of advanced ceramic has become more and more widely and it is an indispensable material in high-tech intensive fields such as aerospace. Most of the occasions that ceramics are competent mainly relay on its unique properties such as high hardness, high melting point and low thermal expansion. However, these excellent properties make the cutting procedure difficult. In conventional cutting technic, material-removal process is almost ineluctable in both mechanical mode and thermal mode [1][2][3]. Generally, material-removal process would cause high energy-consumption, redundant material-waste and environmental pollution, and induce poor surface integrity and low processing precision [1][2][3][4][5]. Moreover, materialremoval process by mechanical force would encounter serious tool wear as well as high processing cost.
Unlike these conventional cutting technic, thermal controlled fracture method (TCFM) is a green and pollution-free cutting mode, which uses tensile stress to separate the brittle material into two parts. The tensile stress is usually thermal stress induced by a heat source. Because this process only needs to overcome the surface energy between the new sections, it causes no materialremoval. The TCFM was invented by Lumley et al in 1969, and was mainly used to treat glass sheets [6]. At the early stage, CO 2 laser with wavelength of 10.6 mm was used as heat source to induce thermal stress, which can only be absorbed on the surface of the glass and would not cutoff glass thoroughly. This always needs some subsequent breaking process. Then, some scholars found that laser with wavelength of 1064 nm could penetrate a certain thickness of glass to form a full-body cutting mode, and the priority of this cutting mode has been demonstrated [7][8][9].
During the development of half a century, scholars in this community have carried out many experimental and theoretical research on monocrystalline silicon, polycrystalline silicon, glass/silicon two-layer bonding materials and some ceramics [10][11][12][13][14][15]. The main difference between these materials and glass is that they can't form a full-body cutting mode with the commonly used laser wavelength. During laser cutting silicon sheets (usually <0.5 mm) process, it is generally considered that laser produces a surface heat source with a negligible laser-absorption depth [12][13][14][15]. In other words, laser is absorbed at the surface of the silicon wafer, and the heat in the whole thickness is mainly generated by heat transfer.
In the past, TCFM is mainly used to treat these thin plates [16,17]. Although it has also been used to cut thick ceramics, the TCFM induced by laser is reported not competent for high-quality cutting process. This is because that laser is not easy to induce full-body cutting mode for ceramics [18,19]. Wang et al. first proposed to use microwave to treat ceramics based on TCFM [20]. They have successfully cut SiC ceramic with a thickness of 3 mm with full-body cutting mode. However, some ceramics are difficult to absorb microwave, even though they could be completely penetrated. Then, Wang et al. used graphite to coat the surface of these ceramics to realize TCFM based on micro-discharge mechanism. Although under the similar mode of surface absorption, the micro-discharge makes its cutting quality better than that of laser cutting [18,19,21].
Wang et al. have found that crack-propagation path always deviates from the expected propagation path during TCFM [20][21][22]. This irregular crack-propagation hinders the industrial application of this advanced process. To deal with this problem, it is important to understand the mechanism of irregular crack-propagation. However, there are few reports on this issue.
In this paper, analytical models have been developed to reveal the irregular crack-propagation mechanism in microwave cutting ceramics using TCFM. Simulation of thermal fracture was conducted by general finite element simulation software to simulate the temperature and stress distribution. Combining the analytical models with the simulation work, the prediction of the maximum deviation range and the initial unstable crack-propagation length have achieved. Microwave cutting experiments with regards to glass, SiC, Al 2 O 3 and ZrO 2 ceramics were conducted to verify this prediction method. Simulation work was also used to reveal the mechanism of the irregular crack-propagation in the middle stage and end segment.
2 Materials and Method 2.1 Principle of microwave cutting ceramics based on thermal controlled fracture method The main physical process in the microwave cutting ceramics based on TCFM is shown in Figure 1. It can be divided into three procedures. Firstly, microwave heating ceramics as shown in Figure 1a: this process mainly consists of the dielectric loss of ceramic materials to microwave, the generation and conduction of heat. The incident microwave could penetrate the ceramics and be absorbed by the materials. According to absorptive capacity to microwave, it can be divided into bulk-heating mode (ceramics can absorb microwave well by themselves) and surface heating mode (coating graphite on ceramics to add absorption of microwave); secondly, the generation of thermal stress as shown in Figure 1b: this process is mainly based on the theory of thermal stress. Tensile stress occurs where temperature is lower than the average value, while compressive stress occurs where temperature is above the average value. The absolute value of thermal stress is mainly determined by the temperature gradient. Finally, the crack propagation process as shown in Figure 1c: this process is mainly based on the theory of fracture mechanics of solid materials. When the initial crack on the ceramic encounters a tensile stress greater than the fracture strength of the ceramic, it will propagate. If the tensile stress can guide the crack to propagate continuously at a certain speed, the cutting process achieves. Figure 2 shows the experimental apparatus of microwave cutting system. It is produced by Nanjing Huiyan Microwave System Engineering Co., Ltd of china and its maximum output power is 1.5 kW. The type used in this study is MY1500S. The system is composed of a microwave source and a cutting machine (2.45 GHz) shown in Figure 2a, microwave controller shown in Figure 2b, a x-y moving plate, and a circular focusing waveguide shown in Figure 2c. The circular focusing waveguide is used to generate circular heat source. Previous studies have shown that the circular heat source is more feasible for curve cutting of glass [22].  To improve the security of the experiment, the inner wall of the machine tool shield is made of absorbing material, and four utensils containing water are placed into the cabin to absorb the leaky microwave during experiment. The material is placed on the workbench which could adjust the distance between the waveguide and workpiece.

Experimental equipment, materials, and methods
The experimental materials include NaCa glass, SiC ceramic, Al 2 O 3 ceramic and ZrO 2 ceramic. The dimensions of these materials are 100 Â 100 Â 1 mm.
Curve cutting experiments are carried out. The start point of scanning position on the workpiece was marked in advance for recording the relative position of the crackpropagation path conveniently. Optical microscope was used to observe the crack-propagation path after the cutting experiments. The controllable processing parameters are microwave power and scanning speed. The values of these parameters for each material are given in Table 1. Each group of experimental parameters were tested six times repeatedly.

Simulation model for cutting ceramics based on thermal controlled fracture method
The main physical process during microwave cutting are microwave absorption, heat transfer, thermal induced stress and crack propagation. The modeling process are as following: The thermal power density P v in the workpiece when loading with microwave can be given by [23]: where P v is thermal power density (W/m 3 ); f is microwave frequency (Hz); e 0 is vacuum dielectric constant (F/m); e is relative dielectric constant of material; tand is dielectric loss tangent of material. |E out | is RMS of electric field intensity for output microwave (V/m). When heated to a steady temperature, the temperature at any point in a linear elastic half space at the initial crack can be given by: where a is thermal conductivity (W/m ·°C), r is density (kg/m3), c is specific heat capacity (J/(kg ·°C), z 0 is workpiece thickness (m). According to thermal stress theory, this would produce a thermal stress field in the material. The normal stress s x along X-direction and s y along Y-direction at any point at the initial crack caused by temperature field are given by: and where G is modulus of elasticity in shear, e x and e y are normal strain, b is thermal stress coefficient. According to thermal stress theory of fracture mechanics of brittle solid materials, the critical fracture stress s F at the crack front can be given by [24]: Where c 0 is the size of the pre-crack, g is the free surface energy per unit area, E' is the equivalent modulus, which is equal to the elastic modulus E under the condition of thin specimen. When the thermal stress loaded at crack front is greater than or equal to s F , the crack system begins to expand.
The goal of analyzing the main physical process during microwave cutting is to simulate the dynamic process of crack-propagation. The crack-propagation process is discontinuous, so the conventional finite element method (FEM) can't be used to calculate the crack-propagation process directly. To resolve this problem, the extended finite element method (EFEM) is used. This method needn't to refine grid dynamically in simulation process, and it has good convergence characteristics when the mesh around the crack is subdivided to a certain extent. These simulations are implemented in commercial finite element software ABAQUS 6.14-1.
In the simulation model, the element type is C3D8R, and the material damage type is evolution damage. As shown in Figure 3, the grid density nearby the microwave scanning position is increased. In this way, the calculation results of the concerned areas become more accurate, and the calculation efficiency can be improved.
The physical parameters of the ceramics are shown in Table 2. The parameters are effective in room temperature, however, since the processing temperature of the TCFM is low (can be lower than 200°C), these can also be used in the prediction model. Physical parameters given in the table include electromagnetic parameters, mechanical parameters and thermal parameters. The dielectric constants of these materials are provided by AET Corporation of Japan. The mechanical and thermal parameters of these materials are provided by Harbin Xinhui Special Ceramics Co., Ltd of china. According to the Equation (1), e and tand are two material property which determines the microwave absorption and heat production capacity of materials. 3 Results

Crack-propagation in initial stage
To observe the crack-propagation state, cutting experiments on glass were conducted. Figure 4 shows the crackpropagation in the initial stage during cutting glass with microwave. When the initial crack propagates, it makes a sharp blasting noise. As shown in Figure 4, the initial crack-propagation deflects form the scanning path. The distance between the starting point of crack-propagation and the heat source center is defined as the starting point deviation (Y 1 0 ). The length of the initial unstable propagation segment in scanning direction is defined as the unstable propagation length (X 1 0 ). It is found that Y 1 0 is approximately 3 mm and X 1 0 is approximately 7 mm. It is notable that micro-cracks on the left of the heat source center are about 250 mm, and micro-cracks on the right side are about 327 mm. As shown in Figure 4, the crack propagates from the micro-crack with 327 mm.
According to the Equation (5), the larger the crack size c 0 , the smaller the critical stress s F is required for crack initiation. The critical stress corresponding to 327 mm is about 87.4% to it of 250 mm. The tensile stress at the crack front is determined by its distance from the heat source center. Therefore, for micro-cracks with same distance, these of 327 mm have greater opportunities to propagate than these of 250 mm.

Crack-propagation in middle and end stage
The crack-propagation morphology of curve cutting of glass is shown in Figure 5. The red reference line represents the scanning path. The crack-propagation path consists of   an initial straight-line segment, a middle curve segment and a final straight-line segment. It is noteworthy that in the curve cutting segment the crack path deviates from the scanning path and inclines to the inside of the curve. There is a lag between the crack front and the heat source center in the curve cutting segment. The crack undergoes a nonpenetrating propagation (the crack do not propagate close to the outlet of scanning) in the end segment.

Prediction of the unstable crack-propagation in initial stage
The irregular crack-propagation phenomena shown in Figure 5 indicate that the realistic crack-propagation path is not along with the expected scanning path accurately. These non-ideal propagation phenomena can be simplified as a diagram shown in Figure 6. It shows that the actual crack initiation point S deflects from the ideal point P in the initial propagation stage. Because of this deflection, the initial realistic crack-propagation deflects from the ideal path (the microwave scanning path) evidently. In the intermediate segment, the crack path deviates from the heat source path obviously in curve cutting site. In the end segment, the crack does not penetrate the specimen in the outlet. In order to understand the mechanism of irregular crack-propagation, models for predicting the maximum crack initiation range and the length of the initial unstable crack-propagation have been established respectively. In the fracture mode I, the critical conditions for crack initiation can be written as [24]: where K I is the stress intensity factors in fracture type I,K Ic is the fracture toughness of an infinite plate with unilateral crack. According to theory of fracture mechanics, under the condition of edge crack, K I can be written as: where s r is tensile stress at the crack front without considering of stress concentration; l r is the crack length.
The K Ic can be the expressed by: where s c is the critical stress for crack initiation (when the tensile stress at crack front is beyond s c , the crack would propagate). It can also be written as: where l c is the critical crack-length for crack initiation. According to Equations (8) and (9), s c and l c can be written by: and l c ¼ ðK Ic Þ 2 1:12 2 pðs r Þ 2 Equation (10) is the critical stress for crack-propagation and Equation (11) is the critical crack-length for crackpropagation. The crack initiation condition is: s r ≥ s c or l r ≥ l c .
Generally, there are many micro-cracks on the edges of ceramic and glass workpieces as shown in Figure 4. Experimental results show that the crack system tends to trigger from the micro-cracks with longer length. These micro-cracks commonly distribute randomly with different length at the edge of workpiece. Reference to Figure 6, the ideal propagation location is P and the actually propagation location is S. According to Equation (10) and the crack initiation condition, the stress conditions for crack propagating from P not S are:   According to Equation (11) and the crack initiation condition, the crack-length conditions for crack propagating from P not S are: l rp ≥ l cp ¼ ðK Ic Þ 2 1:12 2 pðs rp Þ 2 l rs < l cs ¼ ðK Ic Þ 2 1:12 2 pðs rs Þ 2 The meaning of these parameters consults the parameter description in Equations (9) and (10), just adding P or S as subscripts to represent the corresponding value in these two places shown in Figure 6.
Because of the random distribution of the micro-crack at the edge of specimen, the location of crack initiation is random and can't be accurately determined. However, the region of it could be predicted theoretically by analyzing the crack initiation condition above. Figure 7 shows the principle to predict the crack-propagation region under typical stress distribution conditions. The curve L r in Figure 7 represents the length variation of micro-crack along the edge of specimen. The crack length at the ideal position P is defined as the smallest one. The curves of s r1 and s r2 correspond to two different stress distribution curves. The curves of L c1 and L c2 represent the crack-length threshold curves corresponding to s r1 and s r2 respectively. The intersection of L c1 and L r is A 1 and A 2 ; the intersection of L c2 and L r is B 1 and B 2 .
According to Equation (11), the closed shadow region of L c1 and L r is the possible crack-propagation region under the condition of s r1 . Because it satisfies the crack initiation condition of l r ≥ l c in this region. When the crack-length threshold curve is L c2 , the crack-propagation region would add a distance of DY' that is the length between A 1 and B 1 . However, it is difficult to predict A 1 , A 2 , B 1 and B 2 in practice.
To simplify the prediction process of crack-propagation region, D 1 , D 2 , D 3 and D 4 are introduced to replace the A 1 , A 2 , B 1 and B 2 . The determination process and the meaning of these points are as followings: 1. The determination of D 1 , D 2 , D 3 and D 4 : First, obtaining the fluctuation value of crack-length as DL r ; then, drawing upwards a line whose distance from the bottom of curve L c1 and L c2 is DL r ; finally, the interactions between this line and the L c1 and L c2 are D 1 , D 2 , D 3 and D 4 .
2. The meaning of D 1 , D 2 , D 3 and D 4 : D 1 and D 2 are the extreme location for crack initiation corresponding to s r1 , and Y 1 is the maximum crack initiation range corresponding to s r1 . Similarly, D 3 and D 4 are the extreme location for crack initiation to s r2 , and Y 2 is the maximum crack initiation range corresponding to s r2 .
3. Its relationship with A 1 , A 2 , B 1 and B 2 : When the lowest points of L c1 and L c2 are close to position P, D 1 , D 2 , D 3 and D 4 are approximately coincident with A 1 , A 2 , B 1 and B 2 , and the DY (distance between D 1 and D 3 ) is approximately equal to DY'.
By introducing D 1 , D 2 , the step to obtain maximum crack initiation range Y 1 is as following: Frist, s r curve is obtained by stress calculation or simulation; then, the corresponding curve Lc can be fitted using some discrete points calculated by Equation (9). Finally, the D 1 , D 2 is obtained by the above methods, and the Y 1 is achieved.
By using this method, the maximum crack initiation ranges of the four kinds of specimens are gotten and are shown in Figure 8. The s r curve and L c curve are obtained by thermal stress simulation. The length change of microcrack in the edge of each workpiece is defined as Dl max corresponding to Dl rc in Figure 7. This value is obtained by calculating the length difference between the maximum value and the minimum value of the micro-cracks. Due to the different manufacturing methods of workpieces, these values for these four materials are different. After measurement and calculation, the Dl max for glass is approximately 200 mm, as well as 500 mm for SiC, 400 mm for Al 2 O 3 ceramic and 300 mm for ZrO 2 ceramic. As shown in Figure 8, it is found that the Y 1 for glass is approximately 6 mm as well as 12 mm for SiC, 8 mm for Al 2 O 3 and 10 mm for ZrO 2 .
Under the condition of a unilateral crack on a rectangular plate with unit thickness, if the crack length is x and an increment dx is added, according to the theory of Griffith energy release, then the released stress-strain energy dU e can be written as: where s f is the tensile stress perpendicular to the crackfront (Pa), which is balanced with the external load; The generated surface energy dE s (J)is: When the crack propagates, the increment of kinetic energy is: Where k 0 is integral coefficient of displacement component; v s is crack-propagation velocity (m/s); r is the reciprocal of acoustic velocity in the medium (s/m); E k is crack kinetic energy (J).
The above energy meets the following requirements: Introducing Equations (14)- (16) into Equation (17), then vs can be written as: When v s is constant, the crack growth is stable. Then, s f can be written as: where B k is the constant of stress function, which can be written as: In actual thermal-cracking process, k 0 rvs is negligible (because the crack-propagation is far less than acoustic velocity in the medium), so the stress s f can be written as: Equation (21) is an ideal stress condition in which the crack velocity is equal to the heat source velocity of a constant.
Due to the particularity of the boundary conditions of initial crack, the real stress s l in front of the crack is often greater than the ideal stress s f . This will induce the overspeed propagation of the initial crack. In theory, this unstable propagation segment tends to end when the stress-strain energy released by the crack system is equal to the surface energy produced by the newly generated surface. Figure 9 shows the diagram of the relationship of these two stress curves and it can be used as a method to predict the overspeed propagation length. The distance between the specimen edge and the interaction of these two curves is the overspeed propagation length. It is apparent that the increase of the stress gradient in front of the crack tends to reduce the overspeed propagation length.
The prediction value of overspeed propagation length of each material is obtained and is shown in Figure 10. The intersection of s l curve and s f curve is defined as the stable point. The distance between the stable point and the workpiece edge is defined as overspeed propagation length X 1 , which is actually the length of the initial unstable crack-propagation along X-direction (the microwave scanning direction).
Therefore, combining the s l curve and s f curve, the X 1 can be predicted. The s f curve can be obtained by Equation (21), while s l curve can be obtained by microwave cutting simulation. It indicates that X 1 of ZrO 2 ceramic is 10 mm; X 1 of Al 2 O 3 ceramic is smallest, only 2 mm; X 1 of glass and SiC ceramic are 4.5 mm and 6 mm respectively. Figure 11 shows the starting point deviation Y 1 0 and the unstable propagation length X 1 0 in cutting experiments of glass, SiC, Al 2 O 3 and ZrO 2 . The mean value and deviation value were calculated. Due to the different distribution of micro-cracks around workpiece edges and the unique mechanical and thermal properties of different materials, the mean values are different. As shown in Figure 11, it indicates that the results of Y 1 0 and X 1 0 fluctuates in cutting experiment of these materials. Table 3 shows the comparation of experimental and predicted results on parameters in initial unstable propagation. It indicates that the mean values of Y 1 0 are not beyond half of the maximum crack initiation range Y 1 . In the case of ZrO 2 , Y 1 /2 does not exceed 5% of the mean value of Y 1 0 . Combining with Figure 11, it is noteworthy that the maximum values of Y 1 0 do not deviate too much from half of Y 1 . What' more, the mean value of X 1 0 does not deviate too much from the overspeed propagation length X 1 . It indicates that the theoretical model can effectively predict the unstable propagation in the initial stage of microwave cutting ceramics based on TCFM.

Crack-propagation mechanism of middle and end stage
In the cutting experiments, the deviated crack-propagation appears in the middle stage of crack-propagation. In order to understand the mechanism of this phenomenon, the relationship between the tensile stress at the crack front and the propagation state of the crack was investigated. It is found that crack front does not always own the maximum tensile stress in the middle propagation segment. The crack front is sometimes at the front of the maximum tensile tress zone. This is the reason for discontinuous propagation of the intermediate crack. This is caused by the intermittentequilibrium mechanism between the strain energy at the crack front and the newly generated surface energy for the newly propagated crack. Figure 12 shows the relationship between the strain energy release and crack propagation at the crack front. The specific explanation is as follows: as shown in Figure 12a, tensile stress field is generated and concentrated around the crack front to balance with the compressive stress induced by the heat source center. This concentrated tensile stress would increase with the increase of its distance from the heat source. When the concentrated stress is greater than the threshold of the crack-propagation stress, the strain energy releases immediately and converts into surface energy for the generating new surface. At this moment, the new crack front can propagate instantaneously as shown in Figure 12b. Then, with the moving forward of heat source, the tensile stress at the crack front will gradually concentrate to its peak to induce a next propagation as shown in Figure 12c.
Therefore, to keep this cycle going, the maximum concentrated stress at the crack front should yield the tensile stress threshold for crack-propagation. If this maximum value can't reach the threshold in a segment, the tensile stress in the crack front would decrease as the heat source continues to go ahead. So, the crackpropagation would end. To avoid this phenomenon, the output power of microwave should not be less than a certain value.  Figure 13 shows a diagram of the relationship between the crack propagation path and the heat source path. When the heat source moves ahead, the crack will lag behind the heat source for a certain distance based on the intermittent propagation mechanism discussed above. As is shown in Figure 13, the crack always propagates towards the center of the heat source and keeps a distance of D h from it. The actual propagation path of the crack is h 2 and is composed of a series of segments of broken line. When the broken line is short enough, its envelope curve (dotted line in the figure) is the actual crack-propagation path. It can be seen that the actual propagation path always deviates from the actual scanning trace in curve cutting. Figure 14 shows one of the temperature field and tensile stress field contours in the process of curved-cracking of glass. As discussed above, the actual propagation path in curve cutting propagates into the inside of preset trace. This speculation reproduces in the simulation of curve cutting glass as shown in Figure 14. From the temperature   Figure 14a, it indicates that the maximum temperature in microwave cutting glass is about 140°C, which is lower than the temperature value in laser cutting glass based on TCFM reported by Zhao [9]. Figure 14b shows simulation results of the stress distribution in curved-cracking of glass. As is shown in Figure 14b, the tensile stress is asymmetrically distributed along the scanning line.
According to the experimental results, the terminal crack failed to penetrate the workpiece. To reveal the reason for this phenomenon, the stress characteristic nearby crack front is analyzed when the crack propagates near the terminal point. Figure 15 shows the simulation and sketch of the stress characteristic at the end propagation segment. As discussed above, the intermediate crack would undergo a discontinuous propagation caused by the intermittent-equilibrium mechanism between the strain energy at the crack front and the newly generated surface energy. However, this relative equilibrium state would be broken when the crack propagates near the end stage.
As shown in Figure 15a, a compressive stress field s k1 is generated in the heating region. Tensile stress fields s p1 and sp2 would generate behind and in front of this compressive stress field to balance with it. In the middle segment, the tensile stress fields s p1 and s p2 are in equilibrium with the compressive stress field s k1 as the heat source moving. However, this equilibrium no longer holds when the crack approaches the edge of the workpiece. As shown in Figure 15b, the distance between the center of sp2 and workpiece edge is DD k . When the heat source is close to the edge of the workpiece (DD k is close to zero), the front tensile stress area s p2 would produce a large stress concentration. Since the compressive stress in s k1 is kept near constant, the average stress in s p1 should decrease to keep balance. This decreases the stress intensity factor K at the crack front. When K < K IC , the crack would stop propagating and result in non-penetrating propagation.

Conclusion
In conclusion, this paper has revealed the irregular propagation mechanism in the whole crack-propagation stage in microwave cutting ceramics using TCFM by experimental and theoretical study. The following conclusions can be drawn:  -The phenomena of deviated crack propagation at the initial and intermediate segment and the non-penetrating propagation at the end segment were observed through curve cutting experiments. It indicates that the maximum temperature in microwave cutting glass is about 140°C. -The mechanism of the irregular crack-propagation was revealed by the combination of analytical model and finite element model. Through theoretical analysis, the propagation speed of the initial stage is higher than the scanning speed of microwave. -The maximum crack initiation range and the length of the overspeed propagation could be predicted by analytical and finite element models. The microwave cutting experimental results show good agreement with the prediction results, and the relative deviation between them can be <5% in cutting of some ceramics. -The crack front is sometimes in front of the maximum tensile tress. This is caused by the intermittentequilibrium mechanism between the strain energy at the crack front and the newly generated surface energy.
By effectively predicting the unstable propagation offset and understanding the mechanism of irregular propagation, this study is of great significance to avoid and reduce the offset in thermal controlled fracture method using microwave.