PSI - Issue 42

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

1358

9

and miniature specimens:

= ( ∗2 1∗ ) = 2 where β is a constant specific to the geometry and critical stress σ *. This is applied along with the current statistical ASTM correction factor in standard E1921 to yield the combined miniaturization factor k M which should replace the current ASTM correction factor: = . = 2 + 1 4 Curve fitting reveals that β = 0.125 for a Eurofer97 ( σ *=2000 MPa) CT specimen. In the case of the 0.18T-CT and 1T-CT specimens considered in this study, where the miniaturization ratio is 1:0.18, k M would be approximately 2.356. This factor, unlike the current ASTM correction factor in standard E1921 (approximately 1.535 with 0.18T-CT and 1T-CT specimens), includes the effect of constraint loss in miniaturized specimens and avoids undercorrection at high stress intensity. The ASTM correction factor being more than 1 is because looking at the statistical effect of miniaturization alone, it is more difficult for a crack to form in a smaller front in the miniaturized specimen. However, the miniaturized specimen is significantly more susceptible to both forms of constraint loss due to the larger plastic zone compared to the side area and narrower specimen width, so the constraint loss factor strengthens the effect of the current (crack front length) correction factor. The modified fit with the combined miniaturization factor ( = . 0.18 , ) is given in Figures 7 and 8 where K-values obtained from simulated 0.18T-CT specimens with the combined miniaturization factor and K values in simulated 1T-CT specimens are compared over a range of displacement and stress intensity. The current state-of-the-art curve with ASTM correction factor was added for comparison. Clearly, the fit has improved significantly compared to the relationship between simulated 1T specimen and ASTM-corrected 0.18T specimen as shown in the Results section. Some deviation still happens at high loading, but to a much lesser extent than the current state of the art. The exponent β must be determined for different specimen geometries experimentally or computationally, making this factor slightly more complex from a practical standpoint, but the gain in accuracy and range is a significant advantage to help justify the modification. It is, however, important to take into account the limitations of the combined miniaturization factor. Since the critical areas depend on the critical stress selected for the simulations, the entire constraint loss correction factor also depends on the critical stress, which is not always known. Indeed, attempting to curve fit similarly to Figure 9 with an arbitrary incorrect critical stress (e.g. 1500 MPa) yielded a worse fit especially in the lower loading range up to 50 MPa.m 1/2 and a different value for the exponent ( β =0.092). Even though the fit at higher stress intensity levels was acceptable (see Figure 9), the application of our improved correction factor should be reserved to well-defined systems where experimental data pertaining to the critical stress is available. While performing the same simulations at 153K did not make a difference, but the effect of temperature will affect the exponent β , especially when the temperature is significantly different from the temperatures considered in this work.