Issue 36

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 36 (2016) 201-215; DOI: 10.3221/IGF-ESIS.36.20 212 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. 9 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. 9 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. 10 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), has no significant difference of crack closing stress during crack propagation. In fact it is the most conservative model from the four evaluated. During the fourth and sixth cycle the models SAE2 (crack propagation model 0.50 mm) and SAE3 (crack propagation model 0.75 mm) have no difference in the crack closing stress. The model SAE4 (crack propagation 1.0 mm/cycle) has representative difference in the crack closing stress when compared with others models in the cycles due to more residual plasticity in the crack tip. The last representative differences between crack closing stress levels in the models happen during propagation in the cycles eight to tenth. An increase of the crack propagation rate will also increase the crack closing stress. Fig. 12 shows that depending on the design criterion it is possible to apply a different crack propagation rate. For example if the criterion is to use a conservative crack closing stress it is recommended utilization of the model SAE1 (crack propagation 0.25 mm). The softest model or that one which allows the bigger crack opening and closing stresses is model SAE4 (crack propagation model 1.0 cycle/mm). C ONCLUSIONS n this work it was possible to identify the crack opening and closure using the finite element method. In the literature there are few works covering crack propagation simulation with random loads like FD&E loads histories from SAE data bank. Normally only a few load blocks are used to reduce the complexity; this should provide conservative answers when used to develop structural components. The use of different crack propagation rate in this work shows that for reproducing the effective plastic zone it is possible to use smaller or larger element sizes compared with the Irwin equation. To improve the correlation between numerical and experimental data it is necessary to increase the crack length to obtain the same qualitative results that is estimated by the Irwin equation. The next step in this work will be to perform some analyses with the same model and load history with different crack propagation rates to identify whether or not the retard effect can be observed. These data will be compared with experimental test and, if necessary, adjustment of the crack propagation model will be done to improve the crack propagation model. R EFERENCES [1] Miner, M. A., Cumulative damage in fatigue, Journal of Applied Mechanics, ASME, USA, 12 (1945) A159-A164. [2] Schijve, J., Fatigue crack propagation in light alloy sheet material and structures, NLR, Report MP195, Amsterdam, (1960). I