PSI - Issue 28

Andrey Fedorov et al. / Procedia Structural Integrity 28 (2020) 2245–2252 Andrey Fedorov / Structural Integrity Procedia 00 (2020) 000–000

2250

6

As an illustration, Fig. 5 shows the stress distributions along the cylinder axis from the common vertex at ϕ = 30 ◦ , 60 ◦ , 120 ◦ and 180 ◦ . Here r is the distance from the common vertex of two radial cracks. The calculations made it possible to establish that at equal distances from the common vertex, the highest stress level is achieved at an angle equal to 180 ◦ .

160

   

120

 y  

80

40

0

0.0001

0.001

0.01

0.1

r / R

Fig. 5. Distribution of stresses σ y along the cylinder axis from the common vertex at ϕ = 30 ◦ , 60 ◦ , 120 ◦ and 180 ◦ .

A variant of the common vertex of three spatial radial cracks located inside an elastic isotropic half-space is considered. As in the previous problem, to analyze the stress behavior in the vicinity of common vertex of three radial cracks, the cylinder shown in Fig. 6 is used. In this case, the geometry of the cracks is determined by the angles between the cracks. The two angles between the cracks are equal to π − ϕ/ 2 and are determined by the value of the third angle ϕ .

a

b





O

h





R

Fig. 6. (a) Design scheme for three radial cracks; (b) top view of the upper base of the cylinder.

Figure 7 shows the stress distributions along the cylinder axis from the common vertex at ϕ = 30 ◦ , 60 ◦ and 120 ◦ . The calculations made it possible to establish that at equal distances from the common vertex, the highest stress level is achieved at an angle equal to 120 ◦ , that is, when all three angles are equal. The variant of the common vertex of four spatial radial cracks located inside an elastic isotropic half-space is considered. As in the previous problem, to analyze the stress behavior in the vicinity of common vertex of three radial cracks, the cylinder shown in Fig. 8 is used. The geometry of the cracks is also determined by the angles between the cracks. In this case the two opposite angles between cracks are equal to ϕ and the remaining two angles are equal to π − ϕ . The calculations were carried out at di ff erent values of ϕ . Shown in Fig. 9a are the stress distributions along the cylinder axis from the common vertex at ϕ = 30 ◦ , 60 ◦ and 90 ◦ . The calculations made have shown that at equal distances from the common vertex, the highest stress level is achieved at an angle equal to 90 ◦ , that is, when all four angles are equal. Several configurations with arbitrary combinations of