PSI - Issue 19

Shinji Hashimura et al. / Procedia Structural Integrity 19 (2019) 204–213 Author name / Structural Integrity Procedia 00 (2019) 000–000

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% proof stress of raw material. The FE analysis for A5056 bolts was conducted for Q m =4 kN and 6 kN. The stress amplitude  a was 22.7 MPa corresponding to the fatigue strength for Q m =4 kN. Young's modulus for A6056 was E =72 GPa, Poisson's ratio was ν =0.33. 0.2 % proof stress was  0.2 =358 MPa. The strain hardening coefficient H of A6056 bolt was set H =72 MPa in order to simulate an elastic perfectly plastic material (Schwerdt et al., 2010). The FE analysis was conducted for Q m =2 kN, 4 kN, 6 kN and 8 kN. The stress amplitude  a was 49.2 MPa corresponding to the fatigue strength for Q m =4 kN. In the FE analysis, the nut materials for A5056 and A6056 were set the same material as the bolt. The analysis was conducted based on kinematic hardening rule. We focused on behaviors of the principal stress  1 at the root of the first thread and at the root of the incomplete thread which are the fracture points in the FE analysis. The local mean stress  1 -mean of the principal stress at the fracture points were calculated by the following equation. where  1 -max is the maximum value of the maximum principal stress at the root of the first thread or at the root of the incomplete thread.  1 -min is the minimum value of the maximum principal stress at the root of the first thread or at the root of the incomplete thread. 5.2. Results of FE analysis Figure 8 shows behaviours of the local mean principal stress  1 -mean at the root of the incomplete thread for A5056 bolts. In Fig. 8, the ordinate is the local mean principal stress  1 -mean at the root of the incomplete thread and the abscissa is number of cycle N . The square symbols show the behaviour of  1 -mean for Q m =4 kN. The triangle symbols show the behavior of  1 -mean for Q m =6 kN. The contours of equivalent plastic strain at the root of the incomplete thread are shown in right side of Fig.8. It can be seen that the mean stress  1 -mean became constant after decreased at the first cycle. The difference of  1 -mean at ten cycles between Q m =4 kN and Q m =6 kN was 46 MPa. Since the difference of the nominal mean stress after the bolt was applied the cyclic load was 55 MPa from Table 3, it can be seen that the mean stress has not almost released for A5056. Figure 9 shows behaviours of the local mean principal stress  1 -mean at the root of the first thread for A6056 bolts. In Fig. 9, the ordinate is the local mean principal stress  1 -mean at the root of the first thread and the abscissa is number of cycle N . The circle symbol shows the behaviour of  1 -mean for Q m =2 kN. The square symbols show the behaviour of  1 -mean for Q m =4 kN. The triangle symbols show the behaviour of  1 -mean for Q m =6 kN. The rhomboid symbols show the behaviour of  1 -mean for Q m =8 kN. The contours of equivalent plastic strain at the root of the first thread are shown in right side of Fig. 9. It can be seen that the amount of reduction of the mean stress  1 -mean at the first cycle is ) ( 2 1 1  1  1  min max mean      (2)

Fig. 8 Behaviours of the local mean principal stress  1 -mean at the root of the incomplete thread for A5056 bolts