PSI - Issue 42

B.Aydin Baykal et al. / Procedia Structural Integrity 42 (2022) 1350–1360 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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correlation. Ideally, this plot would be linear. This means that the divergence of real and simulated values, i.e. the overestimation of the fracture toughness of the larger specimen, increases as the K value on the miniaturized specimen increases. Even in the relatively small K range depicted on Figure 6, it is clear that the linearity is disrupted around 35-40 MPa.m 1/2 , where the divergence in Figure 5 also occurs. Having clearly established that adjusting only for crack front length is not valid beyond a very limited K range, it becomes apparent that a new correction factor must be added into the process of relating the equivalent K values between a miniaturized 0.18T-CT specimen and a full-size 1T-CT specimen, which will be discussed in the next section.

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 K(ASTM) (MPa.m^0.5)

0 5 10 15 20 25 30 35 40 45 50 55 60 0 5

K (MPa.m^0.5)

Fig. 6: Comparison of real K values and ASTM predictions based on miniaturized 0.18T specimen 4. Discussion 4.1 Evaluation of ASTM correction factor Considering that the  *-V* criterion of the local approach model is appropriate for Eurofer97, the aforementioned results clearly establish that the ASTM correction factor is valid only for a relatively narrow K Jc range, up to about 40 MPa.m 1/2 . Since the ASTM correction factor only accounts for statistical size effect associated with the difference in crack front length, the effect of in-plane or out-of-plane constraint loss is not considered. In-plane constraint loss occurs when the plastic zone ahead of the crack tip is too large compared to ligament length. However, out-of-plane constraint loss is linked to the width of the specimen (along the z-axis in our simulation) being insufficient to reach plane strain condition inside the specimen, which depends directly on specimen size. This can become an issue in miniaturization, particularly with large miniaturization ratios. Therefore, the current state-of-the-art ASTM correction factor needs to be modified in order to account for constraint loss effects in such applications. 4.2 Constraint loss correction Modeling the effect of constraint loss can be accomplished as a simple approximation by adding a second correction factor accounting for constraint loss. As we have seen in the description of constraint loss, the plastic area around the crack tip is an important factor. By using the ratio of critical areas as the base variable in curve fitting, it is possible to devise a power law relationship in order to fit the corrected 0.18T data to the simulated 1T data. We propose the following simple constraint loss correction factor k CL based on the ratio of critical areas between full-size