Issue 43

L.C.H. Ricardo, Frattura ed Integrità Strutturale, 43 (2018) 57-78; DOI: 10.3221/IGF-ESIS.43.04 74 Figure 16 : Crack Closing Stress (σ yy- ) model SAE0.50 [70]. D ISCUSSION OF RESULTS n the present work was identified how difficult is to determine with proper precision the crack opening or closure. It was necessary to use the iterative process in the crack surface step by step during loading and unloading to find the crack opening or closing as shown in details in Ricardo [80]. The retard effect is present in some cycles in special cases where there are overloads. In constant amplitude loading, the effective plastic zone increases with the extension of the crack length; the crack propagation rate has no influence in the quality of results, assuming that it is in respect to the Newman [47] recommendation with four elements yielded in the reverse plastic zone. In variable amplitude loading the crack length can not progress until a new overload occurs or the energy spent during cyclic process creates a new plastic zone and the driving force increases the crack length. The researchers normally work with simple overloads or specific load blocks; this approach can induce some mistakes in terms of results that can be conservative or nonrealistic. Fig. 13 shows the effect of different crack propagation rates in opening stress,  op. This graph starts in the second cycle because it was not possible identify the crack opening in all models evaluated when the crack opens, because all stresses in the first cycle were positive. In the beginning there is no representative difference in the four first cycles in all crack propagation models. In the fourth to fifth cycle it is possible identify a difference of crack open stress level from model SAE2 (crack propagation 0.5 mm/cycle) and the others models. The difference of the crack opening stress level from model SAE2 from the others may be related with the overload that the specimen had in the fifth cycle causing the increase of the crack opening stress level to be more representative than in others that suffered the same overload. From the sixth to eight cycles it is possible to identify again little difference in the crack opening stress of the models. The model SAE1 (crack propagation 0.025 mm/cycle) has the lower crack opening stress. In the cycles 8 to 10 there is some difference in the crack opening stress, having as principal cause the different plasticity that the models suffered, due to different crack propagation rate models. Model SAE2 has the bigger crack opening stress; caused like in the fifth cycle by an overload as in the fifth cycle and again this model had different behavior when compared with others models. The model SAE3 (crack propagation rate 0.75 mm) has no significant difference in the crack opening stress level during all cycles. This could be a good indication that for a first approach in similar conditions the utilization of this crack propagation rate will provide the behavior material faster under similar load history and specimen. Fig. 14 also shows that it is possible to have more different kinds of criteria design. For example for a conservative approach it is possible the utilization of the model SAE1 (crack propagation rate 0.25 mm/cycle). Fig. 15 presents the results from the crack closing stress against numbers of cycles evaluated for the four different crack propagation models considered. It is possible to observe that in the first four cycles there are no significant difference in the crack closing stress in the models studied. In the other cycles the model SAE1 (crack propagation 0.25 mm/cycle), I Surface Crack Crack Tip  y = - 85 MPa