PSI - Issue 13

Yinghao Dong et al. / Procedia Structural Integrity 13 (2018) 1714–1719 Yinghao Dong, Xiaofan He, Yuhai Li / Structural Integrity Procedia 00 (2018) 000–000

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5. Comparison of Eq. (2) with Newman-Raju solution

Fig. 4 illustrates a direct comparison between the K n values numerically determined and those evaluated by Eq. (2) and Newman-Raju solution. The cracks involved in Fig. 4 have a a / ( lt ) value of 0.8. At such a large value, both Eq. (2) and Newman-Raju solution have accuracy lower than that at smaller a / ( lt ) values. For surface crack (a), although the maximum error in Eq. (2) is larger than that in Newman-Raju solution, the accuracy of Eq. (2) at Point A (see Fig. 1 (b)) is better than that of Newman-Raju solution. When the t / W and c / a values of a surface crack fall within the ranges specified in Section 4, e.g. those of surface cracks (b) and (c), the accuracy of Eq. (2) is better at both Point A and B, the improvement at Point A of deep cracks being significant.

(a)

(b)

(c)

Fig. 4. Comparison between the K n values numerically determined and those evaluated by Eq. (2) and Newman-Raju solution for surface cracks with (a) t / W = 0 . 05 , c / a = 3 . 4 , a / t = 0 . 8, (b) t / W = 0 . 20 , c / a = 3 . 4 , a / t = 0 . 594 and (c) t / W = 0 . 45 , c / a = 1 . 0 , a / t = 0 . 8.

6. Conclusions

By fitting assumed functions to the numerical K I results, we obtained an empirical K I expression for a semi elliptical surface crack in a finite plate subjected to remote uniform tension. Two application ranges were determined, respectively allowing for the accuracy of the K I expression better than 3% and 5%. The application ranges cover most surface crack configurations with 0 . 05 ≤ t / W ≤ 0 . 5, 1 . 0 ≤ c / a ≤ 5 . 0, a / t ≤ 0 . 8 and 2 c / W ≤ 0 . 8. Within those ranges, the K I expression yields better accuracy than does Newman-Raju solution, and the accuracy of Newman-Raju solution has been significantly improved at the crack depth point.

Acknowledgements

The authors gratefully acknowledge the support from National Natural Science Foundation of China (No. 11772027), National Key Research and Development Program of China (No. 2017YFB 1104003) and Aeronauti cal Science Foundation of China (No. 28163701002).

References

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