Engineering Failure Analysis 93 (2018) 224–240
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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Multiple cracks failure rule for TBM cutterhead based on threedimensional crack propagation calculation
T
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Wei Sun, Ye Zhu, Jun-Zhou Huo , Xiao-Hong Chen Dalian University of Technology, Dalian, China
A R T IC LE I N F O
ABS TRA CT
Keywords: TBM cutterhead Crack propagation Three-dimensional crack Multiple cracks Stress intensity factor Crack propagation path
Practically, there is multiple cracks interpenetrating in TBM cutterhead, which gives rise to its failure prematurely. While the existing theoretical formulas and calculating methods cannot calculate its fatigue failure process under dynamic loading. In view of such situation, crack cutting sampling of TBM cutterhead after service and its fracture failure analysis were performed to clear that its fracture failure is mainly brittle fracture, based on which, A three-dimensional finite element crack propagation model was established to calculate the crack propagation process under dynamic loading. Stress intensity factor of compact test specimens is calculated by standard formula, and the growth paths of crack are got from multiple cracks fatigue tests, compared the two results obtained above to verify respectively the accuracy of the proposed method in calculating stress intensity factor and its growth path. It is confirmed that the two results about the change of stress intensity factor is basically match, and the maximum error of the growth path of the multiples crack model and the test result is about 3.7% within the permissible range. It is proved that the proposed method is feasible to calculate the multiple cracks failure process under the dynamic loading. Finally, the growth processes of collinear multiple cracks, parallel multiple cracks, nonparallel multiple cracks, and penetrating multiple cracks were calculated. The results show that the stress intensity factor at the intersection of collinear cracks decreased by about 26%, compared with a single crack. Parallel and non-parallel multiple cracks are attracted to each other as the cracks propagate in the process of growth and the stress intensity factor gradually decreases. Although the growth path and stress intensity factor do not change, the crack stops expanding, with the crack tip penetrates through another crack. The failure criterion of TBM cutterhead and the rule of interpenetration of multiple cracks proposed in this paper are the theoretical basis and technical support for the its life prediction and risk prediction.
1. Introduction Full face rock tunnel boring machine (TBM) as a key component of the full-face rock tunnel boring machine (TBM), the cutterhead has the roles of crushing rock and stabilizing the tunnel face, which affects the boring performance and efficiency of the whole machine [1].Due to the complicated geological environment and the variability of construction parameters, the risk of cutterhead accidents accounted for more than half of the total risk of TBM accidents, these accidents make TBM excavation efficiency and cutter life greatly reduced [2, 3]. Among them, the fatigue failure is the main reason for the failure of the cutterhead. There are a large
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Corresponding author. E-mail address:
[email protected] (J.-Z. Huo).
https://doi.org/10.1016/j.engfailanal.2018.07.002 Received 28 April 2018; Received in revised form 28 May 2018; Accepted 5 July 2018 Available online 11 July 2018 1350-6307/ © 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Multiple cracks failure of TBM cutterhead.
number of cracks on the cutterhead surface, Moreover, the phenomenon of multiple cracks intersect often occurs, which results in the failure of the cutterhead when it fails to meet the expected requirements. as shown in Fig. 1. Therefore, the research on failure principle of multiple cracks propagation in the TBM cutterhead have an important theoretical value and practical significance in improve the fatigue strength and accurately predict the crack propagation of the TBM cutterhead. (See Fig. 2.) So far, scholars have improved the structure design of the TBM cutterhead by studying the rock fragmentation mechanism, cutterhead coupling layout, Cutter arrangement, dynamic modeling of cutterhead and the evaluation of the cutting efficiency [4–8]. However, there are few studies on the fatigue life prediction of TBM cutterhead, mainly focused on the static finite element simulation and the derivation of theoretical formula of single crack [9], The mechanism of crack damage and the rule of multiple crack propagation of TBM cutterhead have hardly been reported.In the field of simulation and theoretical calculation of multiple crack propagation, Kamaya [10, 11] considered that the multiple cracks can be equivalent to a single crack in the same region, which is the same as that proposed by the Murakami et al. in the early time [12]. Cannizzaro et al. [13] gived the closed form and stress field of crack tip for circular arch multiple cracks.Pang et al. [14]in view of the welding structure, the crack closure effect and the crack polymerization effect were taken into consideration for the welded structures, and the theoretical calculation model of crack propagation was established to predict the fatigue life of multiple cracks in welded structures. Lepore M et al. [15] simulate multiple three-dimensional crack propagation in a welded structure, based on a finite element approach by considering temperature dependent elastic-plastic material properties.Seifi et al. [16] through the comparison and analysis of the experimental and numerical calculation of the aluminum alloy hole plate with multiple site damages (MSD), explored the diameter of the hole, the thickness of the plate and the distance between the hole and the hole, and the path of the crack propagation path of the multi crack hole plate. Galatolo [17] studied the multiple crack propagation of the aircraft porous plate structure, establishes a theoretical prediction model, and uses the experiment to verify the correctness of the theoretical model. Jin et al. [18] proved the difference in the form of single crack and multiple crack propagation through experiments, and introduced the parameter Delta k-n to calculate the interaction of cracks in the common thread.; Dündar et al. [19] through fracture crack propagation analysis system (FCPAS) with finite element software, based on the plate with four hybrid crack, with a central hole and three crack plate and plate with three holes and four crack three different forms of the planar crack plate structure, the experiment of FCPAS analysis result with a large number of literature data, results show that the crack propagation path and the stress intensity factor respect is very precise, which confirmed FCPAS can very good use in predicting the plane crack plate structure crack propagation behavior. Trollé et al. [20] used the extended finite element method to simulate the expansion of two-dimensional rail multi-crack, and analyzed the influence of plastic stress on crack propagation path and stress intensity factor. Sutula D et al. [21] used the principle of minimum total energy to the problem of arbitrary crack growth in 2D. Zhu S P et al. [22] established a probabilistic framework for multiaxial LCF assessment of notched components by using the Chaboche plasticity model and Fatemi-Socie criterion. Qian G et al. [23] research work the effect of
Fig. 2. The overall flow chart. 225
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temperature on the model parameters in local approackes (LAs)to cleavage fracture. Nasri et al. [24] applied the extended finite element method to study the crack propagation path in a single material and the related parameters of the crack propagation. In summing up, the failure law of a certain type of multiple cracks under a single load is researched, based on theoretical derivation, numerical simulation, experimental detection and other methods in different fields. Whereas, there are few reports on the law of multiple crack propagation of large equipment under dynamic load, which causes that there is a lack of clear failure mechanism of TBM cutterhead and a variety of multiple cracks propagation rule. In view of the above problems, the fracture of the TBM cutterhead after service is analyzed to clear its mechanism of crack propagation. Based on it, the calculation method of crack related parameters is determined. Combined with numerical simulation of multiple crack propagation processes using Zencrack to propose the stress intensity factor and the crack propagation path around the crack tip during the process of multiple cracks propagation, and summarize the different forms of multiple crack propagation rule. 2. Study on the mechanism of TBM cutterhead damage Accurately determining the mechanism of crack propagation is the primary condition for calculating the fatigue life of cracks and simulating the cracks propagation. Therefore, In order to exactly determine the mechanism of the TBM cutterhead crack propagation, Cracked failure data was sampled from Zhong Tianshan TBM cutterhead after service and carrying out crack failure analysis to determine the main damage form of TBM cutterhead, and then clarify the mechanism of TBM cutterhead damage. 2.1. Sample collection of fail parts of TBM cutterhead There are a lot of cracks on the Zhong Tianshan TBM cutterhead after serving. The specific failure parts of the crack are determined by processing the surface of the 1/4 TBM cutterhead piece(as shown in Fig. 3(a)), observing the crack morphology and measuring the crack size, which is shown in Fig. 3(b). The failure part is cutted to obtain TBM cutterhead failure sample as shown in Fig. 3(c). 2.2. Analysis of macroscopic and microscopic morphology of crack failure samples Observe and analyze the macro-morphology of the sample (as shown in Fig. 3(d)) and micro-microstructure (as shown in Fig. 3(e)) to provide a basis for determining the mechanism of crack damage in the TBM cutterhead. The macroscopic cracks of all the specimens are relatively straight, with brittle fracture characteristics. The 3# specimen has a significant thickness transition, whose cracks are occured in the stress concentration area of the thick transitional zone. From the micro- microstructure of the sample, it can be seen that the original microstructure of samples 1# and 2# was destroyed due to the high temperature generated during the cutting and sampling, which just do not add up. The 3# and 4# samples exhibit strip segregation and Wechsler tissue respectively, which reduce the plasticity and impact toughness of the metal and make the sample appear brittle. 2.3. Fracture analysis of crack failure sample Crack fracture analysis is carried out for the crack specimen to get the macro-morphology (Fig. 3(f) using 3# sample as an example) and the micro- morphology of the cracks was observed by scanning electron microscopy (SEM). (as shown in Fig. 3(g) using 1# and 2# samples as an example), to analyze the failure characteristics of the fractures. Synthesize the above analysis to determine the crack damage mechanism of the TBM cutterhead. It can be seen from the figure that the macro-fracture of the crack shows a herringbone pattern, with a clear brittle fracture. From the micro-morphology, the fractures are brittle quasi-cleavage fracture, which matches the straight features of the macroscopic appearance of the sample crack. Through the macroscopic and microscopic observation of the above samples and the fracture analysis of the samples, the failure samples show clear brittle behavior. By observing the macro and micro morphology of the sample and analyzing the failure samples with the sample crack fracture, Therefore, the mechanism of crack damage of TBM cutterhead is brittle fracture. According to the previous engineering experience, the linear elastic fracture mechanics(LEFM) can simulate crack brittle fracture well [25]. Therefore, the crack propagation is calculated based on the theory of LEFM. 3. 3D crack growth simulation Because of the complex structure of the TBM cutterhead and the randomness of the external excitation load, it is unrealistic to use the theoretical solution to calculate the variation of the stress intensity factors in the process of crack propagation and to predict the direction of the crack growth. Therefore, based on the damage mechanism of the TBM cutterhead, this paper uses the linear elastic theory and software Zencrack (8.0–1, zentech international Itd,London,U.K.) to calculate the 3D crack propagation process under the complex load. The specific process is shown in Fig. 4(a). 226
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Fig. 3. Failure analysis of crack fracture in TBM cutterhead, (a)The whole TBM cutterhead(b)TBM cutterhead failure data acquisition, (c) Crack failure sample of TBM cutterhead, (d)Sample macromorphology, (e)Microscopic metallographic organization of the sample, (f) Macroscopic morphology of sample fracture, (g) Micromorphology of sample fracture.
3.1. Solution of stress intensity factor around the front of the crack The stress intensity factor K is a parameter that characterizes the strength of the stress field and the singularity of the displacement field around the crack tip. The stress intensity factor in the crack tip directly determines the crack growth rate, which is the key factor for calculating the life.Based on the theory of LEFM, 1/4 node displacement extrapolation method is used to calculate the relationship between the nodal displacement and the stress intensity factor of the crack front [26]. θ
u ⎧ v ⎫ = KI ⎨ 4G ⎭ ⎩w⎬
3θ
⎧ (2k − 1) cos 2 − cos 2 ⎫ ⎪ r ⎪ K θ 3θ + II 2π ⎨ (2k + 1) sin 2 − sin 2 ⎬ 4G ⎪ ⎪ 0 ⎩ ⎭
θ
3θ
⎧ (2k + 3) sin 2 + sin 2 ⎫ ⎪ r ⎪ K θ 3θ + III 2π ⎨ (3 − 2k ) cos 2 − cos 2 ⎬ 4G ⎪ ⎪ 0 ⎩ ⎭ 227
0 r ⎧ 0 ⎫ 2π ⎨ 8 sin θ ⎬ 2⎭ ⎩
(1)
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Fig. 3. (continued)
where r, θ are the coordinate components of local cylindrical coordinates, respectively, u, v, w denote the radial displacement, normal displacement and tangential displacement at any point of the crack front (as shown in Fig.4(b)), respectively, KI,KII and KIII respectively represent the opening mode (Mode I),sliding mode (Mode II), and tearing mode (Mode III) stress intensity factors, G is the shear modulus, and k is the material constant related to the poisson's ratio, which is defines as follows:
3 − 4λ for plane strain k=⎧ 3 − λ /1 + λ for plane stress ⎨ ⎩
(2)
where λ is Poisson's ratio. Because the TBM cutterhead is in the coupling action of spatial multi-point distribution load, the crack location presents a complex multi-directional stress state. For this reason, the effective mixed-mode stress intensity factor is used to be the criterion of crack propagation, which is calculated by the following formula [27]:
K eq =
(KI + KII )2 + KIII2/(1 − 2λ )
(3)
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Fig. 3. (continued)
3.2. Crack-block modeling The crack initiation of the TBM cutter disk accounts for a small part of the whole fatigue life, and the fatigue life of the cutter head is mainly based on the crack propagation [28]. Therefore, The life of TBM cutterhead is mainly focused on the relationship between crack initiation and rapid crack growth. To insert cracks on the whole model and accurately get the data around crack tip, the whole foundation mesh needs to be very dense, resulting in huge computation and low efficiency in solving the problem.Therefore, this paper used the Zencrack finite element software “crack-block” technology to prefabricated crack, insert “crack-block” unit in the initial crack position(as shown in Fig. 4(c)), The crack front can be either semi-circular/semi-elliptical or linear within a crack block. Therefore, either a 3D surface crack or a through crack can be inserted by combining different crack blocks(as shown in Fig. 4(d)),so as to refinement mesh around the crack tip and match the surrounding meshs automatically during the simulated crack propagation process. 3.3. Crack propagation direction The direction of crack propagation is an important factor in the crack propagation. The accurate prediction of the direction of crack propagation has played a key role in studying the law of crack propagation, calculating the life of TBM cutterhead, and improving the structure design of TBM cutterhead.The crack propagation direction is determined to be the direction of the maximum energy release rate describing the formation of new crack surfaces under any state of stress, based on the virtual crack propagation method proposed by Hellen and Bakker [29, 30].at any node on a 3D crack front a “normal plane”can be defined.A series of virtual crack extensions in the normal plane will produce a distribution of energy release rates.This is shown schematically in Fig. 4(e) as energy release rate values G1 to G7.At some angle to the local crack plane the energy release rate will be a maximum.Gmax denotes this maximum energy release rate.The value of Gmax and the corresponding angle must be calculated for use in crack growth prediction. 4. Simulation verification of 3D crack propagation In order to verify the correctness of the simulation crack propagation method by Zencrack software,In this paper, the empirical formula for calculating the stress intensity factor of the compact test (CT) specimen is used to verify the accuracy of Zencrack in calculating the stress intensity factor around the crack tip. Multiple cracks fatigue tests were carried out to verify the accuracy of Zencrack in predicting crack propagation path. 4.1. Validation of stress intensity factor To verify the correctness of the stress intensity factor around crack tip calaulated by Zencrack,in this paper the empirical formula 229
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(caption on next page) 230
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Fig. 4. Crack propagation simulation in Zencrack software, (a) Simulation and calculation of crack growth process by Zencrack software, (b) Local coordinate near crack tip, (c) Crack-block module prefabricated crack tip mesh by crack-block module(d)Shape design of initial crack, (e)Typical energy release rate distribution at a point on a crack front.
Shi [31] for calculating the stress intensity factor of CT specimen is used to validate the correctness of the stress intensity factor calculated by Zencrack,Specimen geometry and material properties are adopted from Shi [31]. The specific formulas are as follows:
K=
P 1 BW 2
2+
a W
(1 − ) a W
3 2
a f⎛ ⎞ ⎝W ⎠
(4)
a a a 2 a 3 a 4 − 13.32 ⎛ ⎞ + 14.72 ⎛ ⎞ − 5.6 ⎛ ⎞ f ⎛ ⎞ = 0.886 + 4.46 W ⎝W ⎠ ⎝W ⎠ ⎝W ⎠ ⎝W ⎠
(5)
where, P is load amplitude, B is the thickness of specimen,a is the distance of tip from the center of loading, W is the height of specimen,as shown in Fig. 5(a). Through the calculation results (as shown in Fig. 5(c)), It can be seen that the simulation results are basically consistent with the formula results. As the number of cycles increases, the difference between them gradually increases, which can meet the calculation error requirement of life prediction in engineering, It is proved that the stress intensity factor of crack tip can be accurately calculated by Zencrack combination formula (1), (3). 4.2. Fatigue tensile test of multiple cracks 4.2.1. Test purpose Tests were carried out on fatigue cracks of multiple cracks specimens and single crack specimens. The crack propagation path during the failure process were recorded, and the test results were compared with simulation results to verify the accuracy of threedimensional crack propagation simulation in the calculation of crack propagation path. The difference between multiple crack propagation behavior and single crack propagation behavior is analyzed, The reasons for the failure of multiple cracks are analyzed, and the failure rules of multiple cracks are summarized.
Fig. 5. Calculation of CT specimen stress intensity factor (a) CT specimen sketch map, (b)Simulation of crack propagation in CT specimen, (c)The simulation results of stress intensity factor of CT specimen are compared with the empirical formula. 231
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Table 1 The material properties of Q345D. Chemical composition /%
Mechanical property
C
Mn
Si
P
S
Al
σs/Mpa
σb/Mpa
δ/%
0.15
1.54
0.34
0.02
0.012
≥0.015
≥345
490–675
≥22
4.2.2. Test equipment Gantry frame Load test-bed (Dalian University of Technology independent research and development, Dalian, China). Hdraulic Servo Actuators (Changchun Actuator Co., Ltd., ZS137035F.11, Changchun, China). Control System (Changchun Actuator Co., Ltd., DsPACE, Changchun, China). Crack depth sounder (RMG4015,Germany). The gantry frame Load test-bed was constructed independently by this research group, the main material was Q345 steel, and the height was 3.4 m. It was used to fix the test piece and servo actuator in the experiment. The crack depth sounder RMG4015 measures the depth of cracks using the principle of AC potential difference method. An alternating current with a known voltage is applied to the left and right probes of the equipment. When the probe contacts a workpiece with cracks, a voltage drop occurs. The value can be converted to the depth of the crack. The maximum static load test force of the hydraulic servo actuator actuator is ± 100 kN, the maximum dynamic test force is ± 80 kN, the displacement stroke is ± 80 mm, the power is 37 kw, and the test frequency is 0.01 to 20 Hz. 4.2.3. Test scheme This test is based on the test equipment of the State Key Laboratory of industrial test structure analysis of Dalian University of Technology. To get the influence of the crack distance and the crack angle on the interpenetration of multiple cracks. In this paper, Q345D is used as the following material for multiple cracks fatigue sample. Q345D Material performance is shown in Table 1. The initial crack ao is got by numerical control electrospark wire-electrode cutting(as shown in Fig. 7(a)), and the parameters of samples list is shown in Table 2. The fatigue test device as shown in Fig. 6(a), Fatigue test is carried out by uniaxial tension. a dSPACE control system is adopted to record the loading cycles and control the input parameters of actuator loadings.And the crack is measured by crack sounder during the test, further to obtain the crack propagation rules and crack propagation path of different test schemes. The test loadings amplitudes are set as constant and pulsating, which keep consistent with the theoretic situation of cutterhead life prediction. The loading frequencies are adjusted to 2 Hz, with the maximum loadings of 22 kN and average loadings of 5 kN. During the test, the crack sizes (length and depth) are monitored by the method of nondestructive inspection, and the crack surface is observed at the appropriate shutdown time, combined the crack depth got by the detector RMG4015 to determine the crack tip location. When the test is interrupted with no-unloading at specied cycle numbers, the fatigue cycles are recorded and the crack sizes are measured. 4.2.4. Test results and analysis It can be seen from the Fig. 7(b), that the propagation path of cracks has changed significantly compared with single cracks, and the multiple cracks attract each other. The results of the crack propagation path simulation in Zencrack (as shown in Fig. 8(a), (b)) are compared with the experimental results of the crack propagation path (as shown in Fig. 8(c), (d)). The maximum error is about 3.7%, which mainly occurs at the late stage of crack propagation. This is due to the fact that the cracks are too large in the late stage, and the actuators have inertial effects in terms of load expansion, which the finite element simulation does not take into account. After analysis, It is proposed that the simulation crack propagation based on linear elastic fracture mechanics can be applied to the prediction and evaluation of crack propagation path. From Fig. 8(b), it can be seen that the multi-crack propagation path significantly changes compared with single cracks, and multiple cracks attract each other. According to the three-dimensional multi-crack simulation process, the stress fields of the two crack tips gradually converge during the process of propagation. And the stress field at the intersection fluctuates with the continuous propagation of the crack. Since the crack propagation direction is mainly affected by the direction of the stress field at the crack tip, the crack path changes accordingly and mutual attraction is induced. Through the verification of the stress intensity factor and the propagation path of the three-dimensional crack propagation model, Table 2 Specific parameters of the specimen. Specimen type
Specimen thickness
Specimen width
Specimen length
Initial crack size (mm)
Single crack Multiple cracks
10 mm 10 mm
100 mm 100 mm
150 mm 150 mm
a0 = 10 mm a0 = 10 mm
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Fig. 6. The test installation.
Fig. 7. Test samples, (a) Single crack and multiple crack sample, (b) Failure sample.
it is proved that the proposed method simulation in Zencrack which based on LEFM can accurately predict the three-dimensional multiple cracks propagation process. 5. Study on the rule of multiple cracks propagation For the TBM cutterhead, the crack propagation is random in the actual project. The effect of different multiple cracks intersection modes on the crack propagation path and crack tip stress intensity factor is different. Therefore, based on the LEFM, this paper simulates the crack propagation process of collinear multiple cracks, parallel multiple cracks, non parallel multiple cracks and penetrate multiple cracks in Zencrack, and extracts the relevant parameters and summarizes the failure rule of multiple cracks. 5.1. Collinear multiple cracks When the two cracks are on the same line, The change rule of stress intensity factor around the crack tip and the propagation path of the crack are calculated by Zencrack and the crack propagation path of crack tip were calculated by Zencrack. the change rule of the stress intensity factor at the crack tip and the propagation path of the crack are calculated. The loading direction and the location of the pre-crack are shown in the Fig. 9(a), The maximum load is 10 KN, the minimum value is 2 KN and the frequency is 10 HZ. In the figure, C0 is the single crack with a length of 10 mm, C1,C2 are two collinear cracks with length of 10 mm respectively, S is the 233
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Fig. 8. Crack propagation path comparisons test results and Zencrack simulation results. (a) Simulation of single crack propagation (b) Simulation of multiple crack propagation(c) Crack propagation paths comparison of test and simulation results about multiple cracks sample and (d) Crack propagation paths comparison of test and simulation results about single sample.
horizontal distance of multiple cracks with length of 60 mm. Tip1 and tip2 are the crack tips of the single crack. tip3, tip4, tip5, tip6 are the crack tips of the multiple cracks tips. The Zencrack simulation are shown in Fig. 9(b), The results of stress intensity factors and crack propagation paths are extracted, and the two propagation forms are compared. The results are shown in Fig. 9(c) and (d). It can be seen from the above figure that in the case of collinear cracks, the crack path does not change obviously compared with single crack. The stress intensity factor around the crack tip decreases compared with the single crack due to the interaction of two cracks in the coalescence process. The other two ends of the crack stress intensity factor and single crack stress intensity factor are basically the same.
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Fig. 9. Zencrack simulation results of collinear multiple cracks, (a) Initial crack prefabrication and load setting(b)Single crack and collinear multiple crack Zencrack simulation, (c) Simulation results of stress intensity factors around crack tip of collinear multiple cracks and single crack, (d) Simulation results of crack propagation paths of collinear multiple cracks and single crack.
5.2. Parallel multiple cracks When the two cracks are parallel, the stress intensity factor at the crack tip and the crack propagation path change with the relative position of the crack, the loading direction and pre-crack position are shown in the Fig. 10(a), The maximum load is 10 KN, the minimum value is 2 KN and the frequency is 10 HZ. In the figure, C1, C2 are two parallel multiple cracks with length of 10 mm,S is the horizontal distance of multiple cracks, H is the vertical distance of multiple cracks, and tip1, tip2, tip3 and tip4 are the crack tips of multiple cracks. Control variable method is used to control one of the parameters in S and H, and the change of another parameter is observed to get their influence on the crack propagation to study the regulations of change of multiple cracks. Keeping S a constant60 mm, the crack propagation is calculated when H is 20 mm, 40 mm, 60 mm, 80 mm, 100 mm respectively. Keeping H a constant20 mm, the crack propagation is calculated when S is 20 mm, 60 mm, 100 mm respectively.The Zencrack simulation are shown in Fig. 10(b), The results of stress intensity factors and crack propagation paths are extracted(as shown in Fig. 10(c), (d), (e), (f)),The 235
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Fig. 10. Zencrack simulation results of Parallel multiple cracks (a) Initial crack prefabrication and load setting, (b)Parallel multiple cracks Zencrack simulation, (c)Simulation results of stress intensity factor around crack tip varying with H, (d)Simulation results of stress intensity factor around crack tip varying with S, (e)Simulation results of crack propagation path varying with H, (f) Simulation results of crack propagation path varying with S,
change of stress intensity factor of tip2 is listed here only, due to the main analysis of something about the change of the stress intensity factor around the crack tip during the intersection of cracks, and the position and loading condition of the cracks at both ends are completely symmetrical. From the above figure, when the parallel multiple cracks meet, the stress intensity factor at the crack tip gradually decreases due to the interaction between the two cracks. When S is a constant, the trend of decrease in stress intensity factor tends to be gentle as the H increases. But when H is a constant, the stress intensity factor does not change significantly as S increases. Two multiple cracks 236
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Fig. 11. Zencrack simulation results of non-parallel multiple cracks, (a) Initial crack prefabrication and load setting, (b) Non parallel multiple cracks Zencrack simulation, (c) Simulation results of stress intensity factors around crack tip, (d) Simulation results of crack propagation path.
attract each other during the propagation of the crack, which is influenced by the change of S and H. With the increase of H, the attraction degree of the crack propagation path tends to be slow, and the crack propagation path has not changed much with the increase of S, which indicate that H has great influence on the stress intensity factor and the path of crack propagation, while S has little effect on multiple cracks, during In the intersecting process of parallel multiple cracks.
5.3. Non-parallel multiple cracks In practical engineering, the multiple cracks patterns are dominated by non-parallel cracks. When the two cracks are non-parallel, the stress intensity factor at the crack tip and the variation of the crack propagation path with the relative position of the crack are calculated. The loading direction and the pre-crack Location as shown In the Fig. 11(a),The maximum load is 10 KN, the minimum value is 2 KN and the frequency is 10 HZ. In the figure C1,C2 are two non-parallel pre-crack, the length is 10 mm. Tip1 and tip2 are the crack tips between two multiple cracks. β is the angle between two cracks. The Zencrack simulation are shown in Fig. 11(b), The results of stress intensity factors and crack propagation paths are extracted(as shown in Fig. 11(c), (d)).The change of stress intensity factor of tip1 is listed here only, due to the main analysis of something about the change of the stress intensity factor around the crack tip during the intersection of cracks. From the above figure, it is known that the stress intensity factor gradually decreases,with the convergence of the crack, and its downward trend tends to be slow as the angle increases. The propagation path of cracks are basically the same as that of parallel multiple cracks, and they tend to be consistent, with the propagation of cracks, which prove that the direction of load plays an important role in the propagation path of cracks. 237
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Fig. 12. Zencrack simulation results of penetrate multiple cracks, (a) Initial crack prefabrication and load setting, (b) Penetrate multiple cracks Zencrack simulation, (c) Simulation results of stress intensity factors around crack tip, (d) Simulation results of crack propagation path.
5.4. Penetrate multiple cracks When the two crack tips do not coalesce, but one crack tip penetrates into another crack, this paper analyzes the change rule of stress intensity factor and propagation path, with the relative position of crack. The loading direction and the pre-crack location are shown in the Fig. 12(a), The maximum load is 10 KN, the minimum value is 2 KN and the frequency is 10 HZ. C1, C2 are two penetrate pre-cracks, the length is 10 mm. tip1, tip2, tip3 and tip4 are the crack tips of two cracks, the β1 is angle between the two cracks. The Zencrack simulation are shown in Fig. 12(b), The results of stress intensity factors and crack propagation paths are extracted(as shown in Fig. 12(c), (d)),The stress intensity factor around the crack tip is mainly analyzed during the intersection of cracks, so here is only listed tip2 stress intensity factor changes. It can be seen from the above figure that when one crack penetrates another crack, the crack propagation direction and crack tip stress intensity factor are basically the same with the case of the single crack. The propagation path of the crack is basically consistent with the crack propagation. It is affected by the loading direction of the load, but the crack does not continue to propagate as one crack penetrates into the other crack. 6. Conclusion In this paper, the fatigue crack propagation mechanism of the TBM cutterhead is determined according to the fatigue failure analysis of the TBM cutterhead, Based on this theory, the crack propagation simulation software Zencrack is applied to calculate the multiple cracks propagation process under dynamic loading. The correctness of the numerical simulation is verified by empirical formula and fatigue test.The rules of multiple cracks failure are summarized to provide the basis for fatigue life calculation of TBM cutterhead. The main work and conclusion are as follows: 1. Through the crack analysis of the TBM cutterhead after service, the results show that the crack failure of the TBM cutterhead belongs to the brittle fracture. Therefore, the LEFM is used as the theoretical basis to calculate the stress intensity factor around crack tip and simulate the crack propagation. 238
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2.The correctness of the crack propagation method proposed in this paper is verified by the crack fatigue testing and empirical formula. The empirical formula for calculating the stress intensity factor of CT specimen was used to verify the accuracy of the proposed method in calculating the stress intensity factor. And the fatigue test was used to verify the correctness of the crack propagation path We can get the result that the error is within the allowable range which proved that the method proposed in this paper is suitable for the fatigue crack propagation calculation. 3. According to the test results, compared with the single crack, the multi-crack propagation path exhibits a mutual attraction phenomenon. Combined with the test and simulation, it was found that the reason of two cracks attract each other during the propagation process is that the stress field around the crack tip is polymerized and tilted, which changes the direction of the principal stress around the crack tip, and the crack propagation. 4.The influence of different forms of crack propagation on crack propagation parameters was analyzed. Through analysis, it can be seen that when the two cracks are collinear, the crack propagation path is basically the same as that of a single crack, and the stress intensity factor around one end of the intersection is smaller about 26% than that of the single crack during the propagation process. When the two cracks are in parallel state, the cracks attract each other during the propagation process and the stress intensity factor will gradually decrease with the overlap of the crack tip. With the increase of vertical distance, the degree of influence between the cracks decreases, and the increase of horizontal distance has little effect on the crack propagation path. When the vertical distance is about 100 mm, there is almost no interaction between multiple cracks.When two cracks are non-parallel, the rule of the propagation path is basically the same as the parallel multiple cracks, which is mainly affected by the direction of loading not relative position between cracks. As the relative crack angle increases, the crack stress intensity factor decreases more smoothly. In the process of the crack penetrating another crack, the stress intensity factor and the propagation path do not have any change, but the crack stop propagating when one crack penetrates the other crack. Acknowledgments This work was supported by the NSFC-Liaoning United Key Fund (Grant No. U1608256 and No. U1708255), the National Key Technologies R & D Program of Liaoning Province (Grant No. 2015106016). Meanwhile, the work was supported by Collaborative Innovation Center of Major Machine Manufacturing in Liaoning, Dalian, China. References [1] A.E. Samuel, L.P. Seow, Disc force measurements on a full-face tunnelling machine, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 21 (2) (1984) 83–96. [2] H. Haeri, M.F. Marji, Simulating the crack propagation and cracks coalescence underneath TBM disc cutters, Arab. J. Geosci. 9 (2) (2016) 1–10. [3] J. Huo, W. Wang, W. Sun, J. Ling, J. Dong, The multi-stage rock fragmentation load prediction model of tunnel boring machine cutter group based on dense core theory, Int. J. Adv. Manuf. Technol. (2016) 1–13. [4] J. Huo, N. Hou, W. Sun, L. Wang, J. 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