PSI - Issue 13

Fuminori Yanagimoto et al. / Procedia Structural Integrity 13 (2018) 116–122 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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5

Figure 6 shows the relationship between the crack tip position and time. The time starts from the first peak of strains. These data were obtained from the peak of strains obtained by strain gauges. It is worth noting that the crack velocity was nearly constant in Wide2017. This constant crack velocity was about 486 m/s.

1000 1200 1400

0 200 400 600 800 Crack length [mm]

Fig. 6 Crack length and time Wide2016 Wide2017 time from a peak of first strain gauge [μs] 500

0

1000 1500 2000 2500

3.1. Finite element analyses In order to analyze the crack behavior, the experiments were simulated by using 2D elastic finite element analyses. Fig. 7(a) shows the finite element model, which was a half model considering symmetry. Abaqus 6.14 was employed in these analyses (SIMULIA, 2014). The analyses employed implicit dynamic analyses. The thickness of the test plate and tab plate was expressed by an element thickness. The employed elements are plain strain and full integration elements. The mesh size along the crack path was 1.0 mm. Force displacement was applied to the nodes around the pin hole. The displacement was determined so as to make the average tensile stress 315 MPa along the crack path. In the analyses, the static loading was applied at first, and then, the implicit dynamic analysis started using nodal force release technique to express the crack propagation. Stress intensity factors were calculated from the local stress fields in front of the crack tip.

Displacement

y

x

+ 6 . 0 E + 0 8 + 2 . 5 E + 0 8 + 3 . 0 E + 0 8 + 3 . 2 E + 0 8 + 3 . 4 E + 0 8 + 3 . 6 E + 0 8 + 4 . 0 E + 0 8 + 5 . 0 E + 0 8 M a x P r i n c i p a l s t r e s s [ P a ] + 0 . 0 E + 0 8

y symmetry

(a) Finite element model

(b) Static loading in FE analyses

Fig. 7 Finite element analyses It is worth noting that the static tensile stress along the crack path was not uniformly distributed as shown in Fig. 7(b). Around the center of the width, the tensile stress was higher than that near the edge of the specimen width. This was because the distance between the pin hole and the crack path was not long enough to make the stress distribution uniform. Therefore, arrest was calculated from static finite element analyses in Wide2016 test. On the other hand, the transition of static SIF in Wide2017 is shown in Fig. 8. The maximum SIF, 637 MPa√m , can be found when the crack length was 1,055 mm. According to the model calculation in Section 2, the predicted arrest was 415 MPa√m under −13℃ . Therefore, based on the conventional model prediction, the crack should be arrested. As shown in above discussion, the conventional model cannot explain the brittle crack propagation and arrest behaviors in the condition under extremely high SIF. Therefore, it is needed to reconsider the assumption employed by the conventional model.