Research on TBM Cutterhead Crack Damage and Fatigue Reliability

Based on the research data of hob loads under different rocks [ 28 ], starting with marble geology, the finite element analysis of the cutterhead was carried out. Through static strength analysis, large stress and deformation areas were found. The stress and deformation nephogram are shown in Figure 2 e,f, respectively. It can be seen that the area with higher stress and deformation was distributed in the center of the cutterhead because of the supporting effect of the stiffened plate in the peripheral area. Therefore, cracks were more likely to occur in the central area, which is consistent with the actual engineering data [ 12 ]. Hence, the stress intensity factor calculation and crack fatigue reliability study focused on this area.

The material of the cutterhead was Q345B steel, whose behavior was assumed to be linear-elastic; its properties are shown in Table 1

The focus of this study was the Xinjiang cutterhead with a diameter of 8 m ( Figure 2 a), which was imported into ANSYS (ANSYS 19.1, ANSYS Inc., Canonsburg, PA, USA) for mesh generation and finite element analysis. A node, which was rigidly coupled with the cutterhead, was established at the center of the cutter hole of each hob. The loads were applied on the node ( Figure 2 b) and the back of the cutterhead was fixed as the constraint condition ( Figure 2 c). The finite element model of the TBM cutterhead is shown in Figure 2 d, where there were 248,713 elements and 348,670 nodes.

2.2. Calculation of the Stress Intensity Factor and an Analysis of the Influencing Factors

The stress intensity factor (SIF) is a description of the stress distribution in the crack tip region, which can be used to evaluate whether the structure is in a state of unstable growth [ 29 ] and is an important parameter for evaluating the growth life of structures with cracks [ 30 ]. There are many calculation methods that are used to find the SIF, including stress extrapolation, displacement extrapolation, and interactive integration [ 31 ]. For a simple structure, the SIF can be determined using classic analytical methods, but the cutterhead shape and stress are complex; thus, it requires numerical methods and sophisticated analysis.

With the continuous improvement of computation capacity, the finite element method provides accurate and reliable calculations of the SIF [ 32 ]. However, due to the large volume of the cutterhead, it continues to require a lot of time to simulate the whole model since the calculation efficiency is low. To decrease the computational time, a widely used submodeling technique [ 33 34 ] was applied in this study.

c

1 and the short half-axis was

a

1, and the position angle and parameter diagram are shown in

The crack-prone area of the cutterhead was taken as the submodel, where the selected area and crack insertion point is shown in Figure 3 a,b, respectively. The long half-axis of the crack wasand the short half-axis was, and the position angle and parameter diagram are shown in Figure 3 c. The displacement calculated by the FEM analysis on the global model was applied on the submodel cut surfaces ( Figure 3 d) [ 35 ]. Then, the mesh was refined ( Figure 3 e). The numbers of grids and nodes were 187,113 and 132,995, respectively.

Based on the static strength analysis of the cutterhead, the SIF of the crack was calculated and the influence of the different variables on the SIF was analyzed. In the crack initiation stage, the position angle and the shape ratio were random; this study mainly analyzed the influence of the crack position angle and shape ratio on the SIF, and then investigated the damage characteristics of the crack.

a

1 = 6 mm and

c

1 = 12 mm were selected to calculate the SIF under different position angles, where the results of the stress intensity factors

K

I,

K

II, and

K

III are shown in

First,= 6 mm and= 12 mm were selected to calculate the SIF under different position angles, where the results of the stress intensity factors, andare shown in Figure 4

K

I and

K

III at the deepest crack tip reached the maximum and

K

II was approximately zero, which indicates that the crack propagation in the crack tip was mainly of the open and tearing types and that there were three kinds of propagation modes on the crack surface.

It can be seen from Figure 4 that the absolute values ofandat the deepest crack tip reached the maximum andwas approximately zero, which indicates that the crack propagation in the crack tip was mainly of the open and tearing types and that there were three kinds of propagation modes on the crack surface.

K e a q = ( K I + K II ) 2 + K III 2 / ( 1 − 2 λ ) ,

(1)

λ

is the Poisson’s ratio of the material, which was taken to be 0.3 (

According to the fracture mechanics, the SIF at the front of the crack had a great influence on the crack propagation. Therefore, it is necessary to analyze the relationship between the equivalent SIF and the crack angle, which could be found using the expression of equivalent SIF:whereis the Poisson’s ratio of the material, which was taken to be 0.3 ( Table 1 ).

Under the same loading and constraints, the equivalent SIF of the front end of the crack was calculated by changing the crack position angle and parameters. The calculation results are shown in Figure 5

The results ( Figure 5 ) clearly show that with the change of the crack position angle, the equivalent SIF in the fore-end of the crack also changed, and the closer the position angle is to 80°, the smaller the equivalent SIF was, which indicated that the crack growth trend was relatively weak. When the crack position angle was closer to 0°, the equivalent SIF in the fore-end of crack was larger, which indicated that the crack growth trend was relatively strong, and showed that the damage of the cutterhead caused by such cracks was more serious.

c

1 = 12 mm and calculated the SIF under different crack shape ratios by changing the size of

a

1. The calculation results of

K

I,

K

II, and

K

III are shown in

To study the influence of the crack shape ratio on the SIF of the cutterhead crack, this study fixed= 12 mm and calculated the SIF under different crack shape ratios by changing the size of. The calculation results of, andare shown in Figure 6

K

III was asymmetric, where the absolute value on the left side was larger than that on the right side, which may have been caused by the complex stress state of the cutterhead. In addition, the smaller the shape ratio, the clearer was the difference in

K

I, which indicated that the trend of the crack growth was stronger, which will affect the reliability of the cutterhead. In order to further study the fatigue reliability of the cutterhead crack, a reliability evaluation model was established (discussed in the next section), where the fatigue reliability of the cutterhead crack under different crack parameters is discussed.

It can be seen from Figure 6 that with the decrease in the shape ratio, the value ofwas asymmetric, where the absolute value on the left side was larger than that on the right side, which may have been caused by the complex stress state of the cutterhead. In addition, the smaller the shape ratio, the clearer was the difference in, which indicated that the trend of the crack growth was stronger, which will affect the reliability of the cutterhead. In order to further study the fatigue reliability of the cutterhead crack, a reliability evaluation model was established (discussed in the next section), where the fatigue reliability of the cutterhead crack under different crack parameters is discussed.