PSI - Issue 2_A

Enrico Salvati et al. / Procedia Structural Integrity 2 (2016) 3772–3781 Author name / Structural Integrity Procedia 00 (2016) 000–000

3779

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4.3. The Walker-Wheeler models integration So far, the model we described is able to predict fatigue crack retardation at low loading ratio R. Since we want to extend this model further to high values of R, we propose to assemble the two models described above. This can be readily implemented considering the Wheeler model that uses the eSIF evaluated according to Walker. In this way any combination of load ratio and overload retardation can be modelled by replacing the FCGR evaluated by Walker (5) into the Wheeler retardation model (9). The final formulation becomes: � � � � � ∅ � ∅ � �� � ��� �� � � � � � ∅ � ∅ � �� � ����� � �� ��� � � � � (14) 4.4. Results and Discussion The proposed calculation framework for the modelling of the overload effect on the FCGR retardation was applied to the experimental data. It is noted that regarding for the load ratio R=0.7, the crack arrested its propagation right after the OL, and no delay part was detected. Therefore, since the proposed model is not able to account for the arrest effect, for this specific case we did not attempt the modelling of the delay part of propagation after OL. On the other hand, in the case of R=0.1, the delay was observed and the full modelling procedure was implemented. The matching process aimed at the evaluation of the model’s coefficients produced the values showed in Table 2.

� �� � ��� � � 1.25 1.95

� �

Table 2. Wheeler model coefficients. R

0.1 0.7

0.742 0.218

0.199

0.40 - The results of the Walker-Wheeler model application are graphically represented on the Paris diagram of equivalent SIF evaluated using Walker �� �� against the FCGR � � � � , as shown in Fig.4. Overall, the application of the model provided satisfactory matching with the experimental data. Fig. illustrates that good agreement is achieved with a very low level of scatter and deviation. -

Fig. 4. Modelled and experimental FCGR (a) Loading Ratio R=0.1 (b) Loading Ratio R=0.7.

We note that the values of the shaping exponent and the plastic zone coefficients differ in the two loading conditions. It is important to make this observation because the Wheeler model is built on the correlation between the plastic radius and the extent of the OL effect. This means that theoretically the two loading cases should show the same values, since the OL load level is the same. However, at the high loading ratio R the effective plastic radius