# Lifetime Prediction of Single Crystal Nickel-Based Superalloys
## 4 Conclusions  
In this study, the damage-based lifetime prediction model presented by [PERSON] and [PERSON] is modified as an anisotropic lifetime assessment model by considering Mode I crack opening stress to predict the effect of anisotropy on single crystal component lives. This lifetime assessment model is combined with the rate-dependent crystal plasticity model presented in Section 2.2 to achieve the octahedral and cubic slip system behaviour of FCC single crystals. HCF lifetime estimation of Ni-based single crystal CMSX-4 for a notched specimen at 750 \({}^{\circ}\)C for different R ratios is in good agreement with the experimental data. In addition, crack initiation locations are predicted for different crystal orientations of the notched specimen, showing coherent results with the fatigue tests conducted on another Ni-based single crystal SC16 specimen. This proves that the model is coherent in estimating both lifetime values and crack initiation points of geometries with stress concentration zones. Figure 12: Fatigue curves prediction at various temperatures for CMSX-4. Choosing cleavage stress as the critical stress for lifetime estimation considers both crack initiation and propagation contributions to the life of the specimen, even under fast crack propagation loadings and life HCF loadings. These results show that it is possible to achieve correct predictions for real-life geometries, like turbine blades, under both creep and combined fatigue loadings since cleavage systems are more apparent under LCF loadings. Further modifications, such as creep-fatigue interaction (which has already been developed by [PERSON] [16]) and HCF-LCF superimposition, are required for the modified Chaboche model presented in this paper to predict real-life single crystal components with complex geometries. ANNs achieve accurate predictions with low uncertainty for small and moderate perturbations. At 5% perturbation, the average multiplicative uncertainty of approximately 3.5 is acceptable for fatigue lifetime predictions, supported by strong performance metrics with \(R^{2}\) values above 0.99 and MAE near 0.15 on both validation and test datasets. While the parameters of the modified damage model are inherently temperature-dependent, necessitating careful optimization for each specific temperature condition, ANNs present a robust alternative for predicting fatigue curves across varying temperatures. The research highlighted that with a sufficient dataset, ANNs could effectively internalize and replicate the complex behaviors captured by the damage model, adapting to different thermal environments without the need for manual re-parameterization. This capability not only streamlines the predictive process but also enhances the scalability of fatigue life assessments in practical engineering applications. Integrating ANNs with traditional damage models like the Chaboche damage model could significantly improve the efficiency and accuracy of lifetime predictions for critical components under diverse operational stresses and temperatures. Provided fatigue tests with dwell times and HCF-LCF combinations, wide-range lifetime predictions with ANNs for such loading conditions seem attainable. Conceptualization, O.A. ; methodology (crystal plasticity), C.K. ; methodology (lifetime assessment modeling), U.K.; validation, U.K.; writing--original draft preparation, U.K.; writing--review and editing, all of the authors; visualization, U.K.; supervision, O.A. ; funding acquisition, C.K. All authors have read and agreed to the published version of the manuscript. This research was funded by the TUBITAK 2244 Industrial PhD Program under project number [119C037]. Additionally, publication fees were covered by Turkish Aerospace Industries (TAI). Not applicable. Restrictions apply to the availability of these data. Data were obtained from the PREMECCY project (Contract number: AST5-CT-2006-030889) and are available from the author, [PERSON], with the permission of the PREMECCY project.