13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- The modeling of the test coupons was performed with the developed VBA program using the metrology results and crack measurements specific to each coupon. Doing so, no interpolation among crack size and crack shape values was performed. The crack growth rates were calculated using the secant method. Both the da/dN- Ka (thickness direction) and dc/dN- Kc (width direction) data points were calculated. The calculated crack growth rate dc/dN vs. K (or Kmax if R is negative) results of the single crack cases are illustrated in Figure 8. The Ka and Kc values were calculated from the StressCheck model at = 85 and = 0 (surface crack) or = 5 (corner crack), respectively. In this paper, only single crack data were used in the K calculation. 2t c 2a Symmetry condition for center surface crack at notch a c a c a > c a < c y x r W L Symmetry condition along crack plane x z Figure 7. Definition of variables and boundary conditions 4. Comparison of precrack and natural small crack data (C(T) vs. SENT) The crack growth rate data, generated from the C(T) tests (with and without ACR correction) and the SENT tests, are presented in Figure 8. The comparisons indicate that, 1) For long crack growth, da/dN>1E-7 in/cycle (2.54E-9 m/cycle), the C(T)-ACR and SENT test results are similar to each other, except for the R=0.05 case, which should include more crack closure than the high R-ratio cases. Without the ACR correction, some of the R=0.05 C(T) results were close to the SENT results, which had no ACR correction for the residual stress and closure effects. Meanwhile some other C(T) results showed negligible ACR correction, which involved very small residual stress, even tensile residual stress effects. 2) In the near-threshold region, da/dN<1E-7 in/cycle (2.54E-9 m/cycle), for R=0.05, the SENT results appear to give higher ΔKth values than the C(T)-ACR results. The R=0.5 SENT tests did not provide enough data in the near-threshold region. But for R=0.8, the SENT results appear to give lower ΔKth values than the C(T)-ACR results, for which the ACR correction is very small. Overall, the SENT results have more scatter than the C(T)-ACR results in the near-threshold region, and the SENT results should include less closure effect induced by small crack plasticity wake, but more machining-induced compressive residual stress on the surface layer (<50m). From the SENT and C(T) test results, a combined NRC short-long crack growth material model was developed as presented in Figure 9. The combined model is largely based on the SENT data, corrected with C(T)-ACR results to remove residual stress effect for R=0.05 and compensated with C(T)-ACR the near-threshold data for R=0.5. Note that the SENT data (ΔK) for R=-0.33 were shifted to the left using the ΔK ratio between the SENT and the C(T)-ACR long crack data for R=0.05, assuming the same residual stress effect in both tests. As a result, the NRC model is deemed to be a ‘residual stress free’ material model.
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