PSI - Issue 68

Ilia Nikitin et al. / Procedia Structural Integrity 68 (2025) 24–31

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I. Nikitin et al. / Structural Integrity Procedia 00 (2025) 000–000 ∙ | ∈&' !# = )∗ ( , ) : ⨂ # | ∈&' $" = #∗ ( , ) : ⨂ | ∈&' # = − )∗ ( , )

(5)

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The model considers the degradation of the material’s elastic moduli with the accumulation of cyclic damage. The evolution of the damage function is stress-state dependent and is described by the following kinetic equation: (8) where ( , Δ ) is a coefficient depending on the stress state and stress amplitude, γ is a parameter of the model. These coefficients can be obtained by integrating the kinetic equation for the damage function. The integration limits in this case are as follows: failure of the material occurs ( ψ=1 ) at a given number of cycles ( N * ) under a certain stress amplitude ( σ + ). For a given metal material, the integration limits are determined by the full fatigue curve. , = !(-/ - 0)-2 % F〈 34 − 5 〉 〈 6 − 5 〉 ⁄ J -/8 & for 5 + ∆ < 34 < 6 (9) ' = !(-/ - 0)-2 ' F〈 34 − M 5 〉 〈 5 − M 5 〉 ⁄ J -/8 ( for M 5 < 34 ≤ 5 + ∆ (10) where 34 is the equivalent stress, 5 is the fatigue strength at 10 6 cycles (HCF region), 6 is the ultimate tensile strength, M 5 is the fatigue strength at 10 9 cycles (VHCF region) ) , ∆ = 10 /98 & ( 6 − 5 ) . In the framework of the used fatigue failure model, two types of fatigue cracks are considered: cracks with normal opening and shear. The two different equivalent stresses are calculated based on the solution to the elastic problem. The Smith-Watson-Topper (SWT) criterion by Smith (1970) is used to calculate the equivalent stress for normal crack opening (equation 11). The Carpinteri-Vantadori-Spagnoli (CVS) criterion by Carpinteri (2011) is used to calculate the shear crack equivalent stress (equation 12). (11) " # $ % "! $ ! !" # " # # " " $ = % $ The equivalent stress is the driving parameter for damage accumulation. Depending on the dominant role of normal or shear equivalent stress, the corresponding damage is accumulated, leading to the degradation of the elastic moduli. If the degradation of the elastic moduli is due to shear damage accumulation, such quasi-cracks are named ‘shear’. Otherwise, the crack is considered a normal opening crack. The proposed model allows for the prediction of the location of the fatigue crack initiation site, the number of cycles to crack nucleation, the durability of the crack growth stage, and the type of crack opening. 2.2. Heat conduction model for SLM technology The scheme of the heat conduction problem and numerical realization is shown in Fig. 2. The metal powder covers the substrate of solid metal. The laser beam moves in the x-direction and injects the energy into the system. The laser impact is represented by the heat flux q . When the injected energy is sufficient for melting the metal powder, a phase transformation occurs, forming a liquid bath of molten metal. When the laser spot moves away from a given location, the liquid state turns to solid, forming a solidified track. The phase transformation boundary moves with the laser spot. This problem is typically described by the heat conduction equation in temperature terms. ! ! ! !"# $ ! "# ! ! ! ! = = " $ % & ! ! " # !$ %" # !$ !" ! " " # # " ! = = # + # (12)