Issue 45

G. Gomes et alii, Frattura ed Integrità Strutturale, 45 (2018) 67-85; DOI: 10.3221/IGF-ESIS.45.06

Initially, a FEM analysis with ABAQUS [20] for K I evaluation in a beam with a centered hole as illustrated in Fig. 10, was carried out aiming to calibrate the BC2D program. Three simulations, varying the crack size and the mesh dimension, were carried out to compare the SIF values when the crack tip is located at a distance of the main boundary hole equal to 2.5, 6.4 and around 12 mm, respectively. It is important to note that this procedure have been used in the other examples, where the final meshes presented were obtained after convergence for a given SIF value. The results obtained with the BC2D code using different numbers of elements are compared with those obtained by ABAQUS and are presented in Tab. 3. Bold values correspond to the final convergent values for the respective meshes. For the crack nearest to the hole (≈12 mm), the maximum size allowed by ABAQUS (minimum radius of the J-Integral) to perform the analysis was 12.1 mm, while with BC2D was 12.2 mm.

ABAQUS

BemCracker2D

Crack-tip distance (mm)

Elements

K I

Elements

K I

Crack-tip

Total 981 1075 1218 1865 1885 1964 1049 1389 1489 932 1058 1091

Crack

Total

2.12 1.93 1.83 1.80 1.61 1.47 2.76 2.73 2.62

66 90 156

54 62 74

4/face

1.46

2.5

54 62 74 62 74 86 98

6.4

156

4/face

2.63

10.16 9.94 9.628

9.65 9.71 9.75 9.77

12.1/12.2

156

4/face

Table 3: K I

evaluation with FE and BE methods.

The results in Tab. 3 show that both FEM and BEM produced similar K I values when the crack tip is distant from the inclusion (2.5 and 6.4 mm), although the discrepancy between the numbers of elements containing the crack tip with FEM and BEM should be noted. On the other hand, as the crack approaches the hole (12.1 and 12.2 mm), the values obtained with the FEM are smaller, which justifies the need for a better FEM mesh refinement in the hole region and at the crack tip. Results for modified SEN Fig. 11 shows the initial mesh generated by BC2D with an enlarged detail of the initial crack, where the BEM discretization has 124 nodes and 62 quadratic elements, 24 continuous on the hole boundary and 4 discontinuous on each crack surface.

Figure 11: Initial mesh for CP modified SEN with Bemcracker2D program.

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