13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Figure 6. AlMgSi1 fatigue data for the tested specimen geometries The extrapolation to the d22 specimen geometry based on the d3 estimates (Fig. 5c) leads to an underestimation of the data scatter and of the median curve. In this context, it has to be noted that the threshold parameters for the d3 data set were estimated in higher values than those for the d8 and d22 data sets. In fact, the threshold stress exp(C) for the d3 specimens results in 221 MPa which represents a higher value than the lowest stress range in the fatigue results for the d8 and d22 specimens equal to 220 MPa. Therefore, failure data lying below the threshold stress of the estimated model cannot be represented by the model. In contrast, the prediction of the SN field for the d3 geometry based on the d22 estimates (Fig. 5d) results in a noticeable overestimation of mean curve and data scatter. 6. Conclusions A new model for the evaluation of fatigue test results under simultaneous consideration of size effect and variable stress state along the specimens is presented. The model, describing the SN field by means of percentiles, has been applied to three sets of fatigue data for AlMgSi1, each set obtained on specimens with different size. The estimated SN fields fit the experimental data well. As the parameters of the fatigue model are referred to a uni-axially and uniformly tensioned surface element, extrapolation to different specimen geometries can be performed. However, extrapolation to different specimen geometries is only satisfactory from the d8 to the d22 specimens. For the other presented cases, an extrapolation of the model from larger to smaller specimens overestimates the lifetimes of the smaller specimens and vice versa, an extrapolation from smaller to larger specimens tends to underestimate the fatigue behaviour. Thus, further research will be undertaken to get a deeper understanding of the size effect, and the role played by the defect distribution and the statistical independence assumption in order to improve the model. Acknowledgements The authors are indebted to the MICINN (Ministry of Science and Innovation) (Project BIA2010-19920) for financial support of this work. Furthermore, we thank Ing. Ana Teresa Vielma Mendoza for her help in the preparation of the micrographies. 10 5 10 6 10 7 10 8 180 200 220 240 260 280 300 320 340 N [Cycles] Δ σ [MPa] d22 d8 d3
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