PSI - Issue 2_A

Kenichi Ishihara et al. / Procedia Structural Integrity 2 (2016) 728–735 Kenichi Ishihara, Takeshi Hamada, Naohiro Kikuya and Toshiyuki Meshii / Structural Integrity Procedia 00 (2016) 000–000 7

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6. Discussion The relationship between σ 22 measured at 4 δ t on the x 1 axis, denoted as σ 22d , and J FEA calculated from P - V diagram for each load step are shown in Fig. 7. The solid line in Fig. 7 is the average of σ 22c . From Fig. 7, saturating nature of σ 22d for increasing J FEA is read. The small scatter of σ 22c seemed to be a result that σ 22c is a saturated value of σ 22d . Meshii and Yamaguchi (2016) reported that J when σ 22d reaches σ 22c has the possibility to correspond to the lower bound of J c for a specified specimen geometry. Thus, it was examined whether their finding is applicable to the case considered with residual stress. Although σ 22d in Fig. 7 showed a tendency of convergence with increasing J FEA , there is not a definite way to determine whether σ 22d has converged or not numerically. Hence, we applied a method described below. First, an i -th σ 22d defined as σ 22d i and σ 22d which obviously converged was defined as σ 22d0 . Then a norm S n was defined as below

1 2

   

1 = ∑ = n i    

(

)

2

n S

(2)

σ

σ

−

i

22d

22d0

and J at the value of S n / S n +1 is equal to 0.9999 was defined as the predicted minimum of fracture toughness J s . In this work, J s was 12.7 N/mm, and thus, the predicted lower bound K J s was 53.5 MPam 1/2 when σ 22d0 = 1802 MPa. On the other hand, 2 % tolerance bound K J c(0.02) of the experimental data by the method of ASTM E1921 is 57.3 MPam 1/2 , and thus, K J s was closed but smaller than the 2 % tolerance bound. In summary, although it is necessary to study further for more appropriate method of determining the convergence value of the σ 22d and threshold to J at the value of S n / S n +1 , it seems that J s was able to predicted the lower bound of J c in an engineering sense, even for a case with residual stress.

0 1 2 3 4 5

3.60

σ 22d / σ YS

-5 -4 -3 -2 -1

FEA results JcFEA Js

0 10 20 30 40 50 60 70 80

J [N/mm]

Fig. 7 The relationship between σ 22d and J FEA calculated from P - V diagram

7. Conclusion

In this work, applicability of the modified RKR failure criterion was demonstrated for S45C SE(B) specimen with residual stress due to a mechanical preloading.

References

Wallin, K., 1985. The Size Effect in K IC Results, Engineering Fracture Mechanics, 22, 149-163. Dodds, R. H., Anderson, T. L., Kirk, M. T., 1991. A Framework to Correlate a / W Ratio Effects on Elastic-Plastic Fracture Toughness ( J c ), International Journal of Fracture, 48, 1-22.