PSI - Issue 19

Marc J.W. Kanters et al. / Procedia Structural Integrity 19 (2019) 698–710 Marc Kanters et al. / Structural Integrity Procedia 00 (2019) 000–000

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4.2.2. Fatigue life estimation While properly considering the influence of local stress (section 4.1.2), fiber orientation (section 4.1.4), stress concentration (section 4.1.5), and local stress ratio (sections 4.1.3 and 4.2.1), the lifetime computations can be completed for the demonstrator part. As shown in Figure 12a, the failure location depends on applied load ratio. In case � < −1 , failure occurs at location 2 and for � ≥ −1 failure occurs at location 1. This is properly identified by the simulations. Next is the comparison between lifetime in experiments and model, as shown in Figure 13. Figure 13a and b display that, when systematically adding complexity (open markers), the overall predictability is within a factor 5 - 30 accuracy, except for � = 0.5 . The latter is caused by the large local stress ratios, unfortunately in a range where the model for crack-growth controlled failure is not optimally calibrated, since this work focused on larger load amplitudes. However, for all other force ratios the benefit of this systematic framework is clearly demonstrated. It also shows that the influence of stress, i.e. the slope of the FN curves, and the dependence on force ratio, i.e. the local stress ratio, are captured very well, suggesting merely a systematic error since the deviations appear consistent for all load ratios and lifetimes.

Figure 13: Comparison of the Digimat material model and experiments for the demonstrator part. Open markers represent accuracy of the model by systematically adding complexity. In (a) the solid markers represent the accuracy of a material model without inclusion of the stress concentration correction, in (b) that of a model that does and is calibrated with prior knowledge on part level.

This systematic error most likely finds its origin in the correction for stress concentrations. Here the local stress is scaled down, depending on the local stress gradient, and a small deviation in load magnitude can have huge effects on lifetime. As already highlighted in Figure 10, the model to compensate for local stress concentrations can easily introduce an error of ± 15% in stress or ± 5 times in life. The necessity for proper stress concentration corrections is evident, once more highlighted by Figure 13a. A model calibrated by including local stress, fiber orientation and local stress ratio, but without recalibration and correction for the stress concentrations (solid markers in Figure 13a) provides a prediction more than a factor 100 - 1000 conservative, and the model based on the systematic approach using the normalized stress gradient presented in this work improves the accuracy with more than a factor 20. Although already a significant improvement, it is important to realize that the normalized stress gradient in the demonstrator part is only 0.65, hence far below the large and ambitious range of stress gradients used to calibrate this model (see Figure 10a). To improve accuracy even further, it might be preferred to focus the calibration of the influence of stress gradients on geometries which have a gradient in the same range as in the application. Alternatively, prior knowledge on part level can allow definition of a correction required for that specific geometry. This would require a single measurement and would allow accurate prediction of the lifetime for any arbitrary load ratio and yields even better results (solid markers, Figure 13b).