Issue 48

A. Takahashi et alii, Frattura ed Integrità Strutturale, 48 (2018) 473-480; DOI: 10.3221/IGF-ESIS.48.45 476 are aligned parallel to the surface. The rectangular shape of the specimen is modeled with a global mesh. 10-noded tetrahedral elements are used for the global mesh. The numbers of elements and nodes are 115,200 and 171,245, respectively. On the other hand, the two cracks are modeled with two local meshes separately. 20-noded hexahedral elements are used for the local meshes. The initial numbers of elements are nodes are 13,680 and 61,210, respectively. The half-depth and length of crack is denoted by a and c . The initial horizontal and vertical distance of the two cracks are denoted by S and H . In the FFS code, the alignment rule is compiled with the horizontal and vertical distance of two cracks, the horizontal and vertical distance are changed to study how the two cracks grow under cyclic loading. The maximum tensile stress of the cyclic loading is assumed to be 127 MPa, and the stress ratio R is set to 0.1. The tensile stress is applied to the finite element model by giving corresponding traction to the top surface of the specimen. The displacement of the bottom surface is fully constraint. The material is assumed to be a steel, and 1.67 × 10 -12 and 3.23 are used as the coefficient and exponent of the Paris law [5]. In the Paris law, the units of stress intensity factor range  K and crack growth rate d a /d N are MPamm 0.5 and m/cycle, respectively. (a) Fatigue crack growth patterns (b) JSME criterion Figure 3 : (a) Fatigue crack growth patterns of two non-coplanar cracks and (b) the alignment rule given by the Japan Society for Mechanical Engineers (JSME). The red bold line in the right figure is determined by the experiments of the fatigue crack growth of surface cracks. Finite element mesh for the fatigue crack growth simulation of two non-coplanar embedded cracks. Each crack. The alignment rule is defined by the horizontal separation S and the vertical height H . The JSME criterion fully covers the area defined by the bold red line. Ando et al. performed experiments of the fatigue crack growth of surface cracks, and categorized the fatigue crack growth behavior into five patterns as shown in Fig. 3 [3]. In the pattern A, the crack tips meet each other, and the cracks are naturally combined. In the pattern B, the crack tip direction is within the spacing between the initial crack tips. In the pattern C, the crack tips go to the initial crack. In the pattern D, the crack tips pass the initial cracks. In the pattern E, only one of cracks grows horizontally, and never meet the other crack. Ando et al. determined that the alignment rule must be applied if the fatigue crack growth behavior is patterns A, B and C [3]. The border of the application and non-application of the alignment rule shown in Fig. 3 with the bold red line is obtained by the experiments of surface cracks; therefore, in order to clarify the applicability of the alignment rule to embedded cracks, the fatigue crack growth behavior of two non-coplanar embedded cracks must be observed, and the crack growth behavior must be categorized into the five patterns. The fatigue crack growth behavior of two non-coplanar embedded cracks is simulated. The crack size is fixed to a =2.5 mm and c =2.5 mm. The initial crack tip distance parameters S and H are changed in a range from 2.5 mm to 25 mm. The fatigue crack growth behaviors obtained by the s-FEM simulations for S =10 mm are shown in Fig. 4. Because the location of the two cracks is non-coplanar, the fatigue crack growth behavior is also non-planar, and the s-FEM simulation technique successfully reproduces such a complex fatigue crack growth behavior. The fatigue crack growth behaviors can be categorized into pattern B, C and D as shown in the figure. Fig. 5 shows the interaction map of the two non-coplanar embedded cracks obtained by the s-FEM simulations. Ando et al. discussed about the criteria of the application of the alignment rule based on the experiments of the fatigue crack growth of surface crack. The border of the application