13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- coupon tests under transport spectra [7], using the NRC in-house crack growth code CanGROW [9]. At first, a legacy material model of 7075-T7351 (Figure 10-(a)), based on the Forman equation, was used in association with the Hsu retardation model [8] using the default parameter value of M0 = 0.6 and Rcut = 0.3. Both M0 and Rcut are fitting parameters, and M0 = 1.0, Rcut = 0.0 would create the most possible retardation and the longest life. As shown in Figure 10-(b), the fatigue life estimation using the legacy model were considered overly conservative, even when maximizing the Hsu retardation and considering that the legacy model was developed for a relative humidity of 90%. As shown in Figure 10-(b), using NRC Forman model converted from the R=0.5 curve in Figure 9, the life estimation was greatly improved, especially with the Hsu parameters calibrated at M0 = 0.2 and Rcut = 1.0. Note that the spectrum was counted using the rainflow method in the above analyses. 1.E‐09 1.E‐08 1.E‐07 1.E‐06 1.E‐05 1.E‐04 1.E‐03 1.E‐02 1.E‐01 1.E+00 1 10 100 da/dN (in/cycle) K(ksi in) NRC Forman R=‐0.1 NRC Forman R=0.72 Legacy Forman R=‐0.1 Legacy Forman R=0.72 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 5 10 15 20 25 30 35 Crack half length (in) Flight Hours (X1000) NRC; Calibrated Hsu (0.2, 1.0) NRC; Default Hsu (0.6, 0.3) Legacy; Max Hsu (1.0, 0.0) Legacy; Default Hsu (0.6, 0.3) Test data range (a) 7075-T73 material model, legacy and NRC (b) Coupon life estimation using legacy and NRC models Figure 10. Coupon life estimation using CanGROW (1-in=25.4 mm, 1.0 ksiin=1.1 MPam) It was also noted that one weakness of the Forman equation is lack of flexibility to correctly describe and shift the da/dN-K curves between different stress ratios (R), because the shifting solely depends on a fitting parameter (KC) that controls the K-factor near the fracture region. The mismatched shifting was also reported at the low- K region [11]. Using the tabular data in Figure 9 should avoid this issue. In another preliminary study, the NRC model at R=0.8 was simply used as a Keff baseline model in FASTRAN3.8 for the coupon life estimation. As shown in Figure 11-(b), good agreement was achieved between the FASTRAN analysis and tests. Two previous 7075-T73 material models from [4,10] were also compared to the NRC model in Figure 11-(a), which resulted in one poor (blue, before calibration) and one good (yellow after calibrating) life estimations. The FASTRAN analysis used a crack closure model with more parameters (e.g. constraint factors), which calibrating details are beyond the scope of this paper. Note that the spectrum was used in the FASTRAN analysis without a cycle counting process. 1.0E‐10 1.0E‐09 1.0E‐08 1.0E‐07 1.0E‐06 1.0E‐05 1.0E‐04 1.0E‐03 1.0E‐02 1.0E‐01 0.1 1 10 dc/dN (in/cycle) ΔKeff or ΔK@R0.8 (ksi√in) NRC model (7075‐T73, R0.8, TL2 with SENT) Newman (EFM2004, 7075‐ T7351, 0.25", LT) Newman (FAA AR0749, 7075‐T7351, 0.25", LT) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 Half crack length (inch) Flight hours (x1000) Test data range Newman 7075‐T7351 EFM2004 ‐ NMAX=1000 Newman 7075‐T7351 FAA‐AR0749 ‐ NMAX=1000 NRC model (7075‐T73, HF, R0.8, with SENT, NMAX=1000) (a) 7075-T73 material models (b) Coupon life estimation Figure 11. Coupon life estimation using FASTRAN (1-in=25.4 mm, 1.0 ksiin=1.1 MPam) Note Kc is a fitting parameter here
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