PSI - Issue 76

Xabat Orue et al. / Procedia Structural Integrity 76 (2026) 3–10

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1. Introduction Additive Manufacturing (AM) is a layer-by-layer advanced manufacturing technology that enables great geometrical freedom in part design and production. However, the mechanical properties that are obtained are not as high as in Conventional Manufacturing (CM) due to the limited of control under different factors, such as the process temperature and the layer height. This is true irrespective of the AM technology, but it is more pronounced in the case of Direct Energy Deposition (DED) [1]. Consequently, a process optimization is required to obtain zero-defect components and enhance the final properties [2]. In the case of the variant where a laser beam is used to deposit a coaxial wire (DED-LB/CW), this task becomes more critical due to the interaction between parameters and the importance of the layer height control [3]. Additionally, a proper fatigue assessment is essential to ensure reliability, as most failures of structural components are due to this phenomenon where dynamic loads are involved. This is influenced by many factors such as defects and microstructure among others. One of the procedures to consider the influence of defects is using the Kitagawa-Takahashi (K-T) diagram [4], where the fatigue limit range (Δσ w ) is represented with respect to the crack or equivalent defect size ( a ) according to the following expression: ∆ ( ) = ∆ ℎ, · √ · (1) Where ∆ ℎ, is the long crack growth threshold stress intensity factor range and Y is the geometrical factor taking the crack or defect position and the configuration into account. To consider other aspects apart from the size of defects, modifications of K-T diagram are used. One of them was proposed by El Haddad with a smooth transition between the intrinsic fatigue strength and defect-affected region considering a fictious crack size a + a 0 according to the following expression [5]: ∆ ( ) = ∆ ℎ, · √ · ( + 0 ) (2) Where a 0 is a fictitious intrinsic crack length for long cracks, below which no effect from the defects occurs. Its value is calculated as follows: 0 = 1 · ( ∆ ℎ, · ∆ 0 ) 2 (3) Where ∆ 0 is the intrinsic fatigue strength range in absence of defects. Its value for fully reversal stress ratios ( R = -1) is related with the Vickers hardness ( HV ) of the material as follows [6]: ∆ 0 = 3,2 · (4) To consider the influence of mean stresses ( R ≠ -1), different models are employed, such as Walker’s [7]: , =−1 = · (1 −2 ) = · (1 −2 ) (5) Where R stands for the stress ratio ( σ min /σ max ) and γ is Walker’s exponent which is material dependent with HV [6,7]: = 0,226 + −4 (6) Murakami proposed another modification for the K-T diagram considering the HV of the material and the square root of the projected area of the defect in the plane perpendicular to the principal stresses ( √ ) with the following expression [6]: ∆ ( , √ ) = · ( + 120) · (√ ) 1/6 · (1 −2 ) (7) Where C is a material dependent position factor of the defect [6]. Another model was proposed by Chapetti to consider the microstructural effect of the material on the transition from short to long cracks [8]. This model is interesting especially when the size of defects is small and comparable to microstructural features of the material. ∆ ( , )= ∆ ℎ (∆ , ) · √ · (8)