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• Fatigue performance up to VHCF for SLMed Ti-6Al-4 V at R = −1, −0.5, 0.1 and 0.5. • Internal crack initiation dominant in HCF and VHCF with LOF defects as crack origins. • RA formed in CIR in VHCF at R = −1, −0.5 and 0.1, but no RA at R = 0.5. • RA in VHCF for R = −1, −0.5 and 0.1 is a nanograin layer, explained by NCP model. • Δ K th for defects and RAs decrease with the increase of stress ratio in HCF and VHCF. The fatigue behavior of SLMed Ti-6Al-4V has been intensively investigated in recent years. However, the effect of stress ratio has not been comprehensively studied, especially in VHCF regime. In this paper, the fatigue performance and crack initiation characteristics up to VHCF regime for an SLMed Ti-6Al-4V at various stress ratios (R = −1, −0.5, 0.1 and 0.5) were investigated and the effects of stress ratio were substantially discussed. The stress amplitude decreases with the increase of stress ratio with the order of: σ a (R = −1) > σ a (R = −0.5) > σ a (R = 0.1) > σ a (R = 0.5). Internal crack initiation is dominant in HCF and VHCF regimes under the four stress ratios, although surface crack initiation rarely occurs in HCF regime at R = −1 and 0.5. Whether the crack initiates from subsurface or from interior is affected by the applied maximum stress, and the crack initiation is in relation not only to defect size but also to defect location. The nanograins in RA are evidently formed in VHCF regime at R = −1, −0.5 and 0.1, but not at R = 0.5, which is well explained by the NCP model. [ABSTRACT FROM AUTHOR]

• A continuum fatigue damage model incorporating effects of defects was established. • Fatigue in HCF and VHCF regimes under different stress ratios were investigated. • Lower and upper bounds of fatigue life of LPBF Ti-6Al-4V were well predicted. • Failure probabilities of 5%, 50% and 95% in good agreement with the experiments. Defects and microstructural inhomogeneity have been recognized to have a significant impact on the fatigue performance of titanium alloys fabricated by laser powder bed fusion (LPBF). In this work, a modified Chaboche fatigue damage model incorporating the effect of defects was proposed to predict the fatigue life of LPBF-fabricated Ti-6Al-4V under different stress ratios up to very-high-cycle fatigue regime. A nonlinear effect of mean stress observed in LPBF-fabricated Ti-6Al-4V was also considered in the model. The S - N data, critical defect sizes and locations obtained from our previous experimental work were utilized to calibrate and validate the proposed model. The scatter in fatigue life up to 109 cycles was predicted by the model for samples with subsurface and internal defects of size ranging from 30 μm to 150 μm under different stress ratios, and the prediction results agree with the experimental results very well. Based on the statistics of defect sizes and locations, the S - N curves for failure probabilities of 5 %, 50 % and 95 % were obtained for these stress ratios, and shown to be in reasonable agreement with the experimental data. [ABSTRACT FROM AUTHOR]

• FGA of steels and RA of Ti alloys under negative R are nanograin (NG) layers. • NG layer thickness of FGA is 300–600 nm with mean grain size of 50 nm for R = −1. • NG layer thickness of RA is 200–500 nm with mean grain size of 60 nm for equiaxed-Ti. • NG layer thickness of RA is 700–1500 nm with mean grain size of 110 nm for duplex-Ti. • Numerous cyclic pressing explains NG layer characteristics in crack initiation region. The microstructural features underneath the fracture surfaces of high-strength alloys experienced very-high-cycle fatigue were further investigated to show the nanograin layer in crack initiation regions under negative stress ratios due to numerous cyclic pressing (NCP) mechanism. The grain size and the thickness of nanograin layer in fine granular area of high-strength steels and rough area of titanium alloys were measured. A normalized quantity d* was proposed to characterize the distribution of the nanograin size. A new schematic to express NCP process was depicted to describe the contacting actions between crack surfaces, which causes the microstructure refinement of the high-strength alloys. [ABSTRACT FROM AUTHOR]

[Display omitted] • The DBN-BP model presents high precision and strong stability in predicting the fatigue life of LPBF-fabricated Ti-6Al-4V up to VHCF regime. • The DBN-BP model exhibits an excellent performance in predicting the relation between mean stress and stress amplitude in both HCF and VHCF regimes of LPBF-fabricated Ti-6Al-4V. • The DBN-BP model displays great ability in predicting the effect of energy density on the fatigue strength of LPBF-fabricated Ti-6Al-4V up to VHCF regime. Microstructural defects and inhomogeneity of titanium alloys fabricated by laser powder bed fusion (LPBF) make their fatigue behaviors much more complicated than the conventionally made ones, especially in very-high-cycle fatigue (VHCF) regime. Most of traditional models/formulae and currently-used machine learning algorithms mainly concern fatigue behavior of LPBF-fabricated titanium alloys in high-cycle fatigue (HCF) regime, but rarely in VHCF regime. In this paper, a deep belief neural network-back propagation (DBN-BP) model was proposed to predict the fatigue life of LPBF-fabricated Ti-6Al-4V up to VHCF regime. Results obtained in this study indicate that the DBN-BP model exhibits high precision and strong stability in predicting the fatigue life of LPBF-fabricated Ti-6Al-4V in both HCF and VHCF regimes. The primary hyperparameters of the DBN-BP model were optimized to further improve the prediction precision of this innovative model. Finally, the optimal DBN-BP model was applied to predict the relation between mean stress and stress amplitude, and the effect of energy density on the fatigue behavior of LPBF-fabricated Ti-6Al-4V up to VHCF regime. [ABSTRACT FROM AUTHOR]

• Internal defects caused crack initiation in VHCF regime, with RA feature for R = −1. • Equiaxed defects were crack initiation sites for all cases at R = −1 and HCF at R = 0.5. • Defects with large aspect ratio were crack initiation cites for VHCF at R = 0.5. • RA region is a nanograin layer only in crack initiation region for VHCF at R = −1. • A P-S-N model well described fatigue strength and fatigue life up to VHCF. Crack initiation mechanisms under two stress ratios (R = − 1 and 0.5) and up to very-high-cycle fatigue (VHCF) regime of a selective laser melted (SLMed) Ti-6Al-4V were investigated. Type I lack-of-fusion defects (almost equiaxed) induced crack initiation except for the cases of VHCF under R = 0.5 in which type II defects (large aspect ratio) caused facet mode crack initiation. A nanograin layer formed underneath the crack initiation region of rough area for the cases of VHCF at R = − 1, which was explained by the numerous cyclic pressing (NCP) model. A P-S-N approach was introduced to well describe the fatigue life up to VHCF regime under R = − 1 and 0.5 for the SLMed titanium alloy. [ABSTRACT FROM AUTHOR]