PSI - Issue 23

Hector A. Tinoco et al. / Procedia Structural Integrity 23 (2019) 529–534 H.A. Tinoco/ Structural Integrity Procedia 00 (2019) 000 – 000

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opening displacement at the first node reached 0.104 . y u m   The value of 2 u y at the first note is taken as the estimate of CTOD. Residual stresses and the plastic zones can be extracted from the results, defining the area of stresses higher than the yield stress as shown in Figure 3b.

0 x  ); (b) Plastic zone – for loading stage I.

Fig. 3. (a) Opening displacement profile (crack tip at

According to the numerical results, the theoretical relationships written in equations (1) and (2) were calibrated fitting the constants 1 0.194 c  and 2 0.191 c  as well as the values listed in Table 1. In Figure 4a, the results showed that the quadratic dependence of  on the SIF is correct. The true size of  (CTOD) corrected by the factor 1 c is 19.4% of the theoretical estimation and t he ratio of ΔCTOD and CTOD was confirmed to be 1/2.

Fig. 4. Numerical results of the dependence of (a) CTOD and (b) monotonic and cyclic plastic zones with respect to the stress intensity factor during loading and unloading.

The results evidenced that the theoretical quadratic dependence of p r on K corresponds to the theory. The true monotonic plastic zone size is 19.1 % of the value obtained using Eq. (2) with 2 1 c  . Therefore, the ratio between p r and cp r is 1/5.35 instead of 1/4 proposed for an elastic-perfectly plastic material. When these two corrections are combined, the true cp r was only 43% of the theoretical size. These corrections lead to a better estimation of the crack propagation rate which would be too high according to the classical relationships. If the effective threshold loading Δ K eff = 3 0.5 MPa m  reported by Liaw et al. (1983) is considered, then Δ CTOD can be determined using the correction