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

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Based on the damage function value at a new time layer, the elastic moduli of the entire model are reinitialized according to the following rule (16) where ( ) is the Heaviside step function, k is a model parameter. When the damage function is below a critical value ∗ the elastic modulus continuously decreases, simulating the natural loss of bearing capacity of the material due to cyclic damage accumulation. As soon as the damage function reaches a critical value, the elastic modulus falls to a very small value (~0.001 of its initial state), simulating a crack (volume of the material without bearing capacity). To make the procedure less sensitive to mech cell size, the delocalization of the damage function is applied (17) - (18). S ( ) = ∫ ( ) W ( , ) :;- , W ( , ) = 2 ( , )/ ∫ 2 ( , ) :;- (17) 2 ( , ) = 〈1 − < ( , )〉 ! , ! ( , ) = | − | ! / 2 ! (18) where ( , ) is the delocalization operator, and 2 is the radius of delocalization. The delocalization of the damage function ensures the convergence of the solution at different mesh size parameters, which is crucial for local zones of stress concentration. 4. Results and discussions The results of numerical simulations for the heat transfer problem are shown in Fig. 3 for different laser beam parameters. Fig.3-a shows the case of a high scanning rate simulation, where the material is not fully melted during the laser beam pass. The material builds up starting from the lower-left corner and continues from left to right, layer by layer. The blue color indicates the volume not affected by the melting process. As clearly seen, the resulting structure has numerous not-melted areas. The overall temperature of the model plays an important role. At the beginning of the procedure (lower-left corner, Fig.3-a), the temperature of the model is low, resulting in large not melt zones. As energy is absorbed by the structure, the temperature increases, reducing the size and number of not melt zones. The VHCF fatigue tests on the material with not-melt zones (Fig. 3-b) show the critical role of such microstructural features on the structural integrity of the material. The fatigue strength and life of the materials with not-melt areas are several times lower compared to regular structures. Fig. 3-b shows the VHCF fracture pattern of the aluminum alloy AlSi10Mg with a crack passing through the neighboring layers. At the free surface, spherical particles are clearly seen. Fig. 3-c shows the results of the heat transfer simulations with a relatively low laser beam rate. The colours in the figure indicate the number of times the material has been re-melted, from 0 times (blue) to 4 times (red). As can be clearly seen, the low scanning rate with the same laser power produces deeper heat penetration. The material has no not-melted zones but contains numerous large re-melt areas. The re-melting process affects the microstructure of the material and, in addition to other transformations, changes the phase fraction, which influences the cyclic strength of the material. Depending on the material, the re-melting process leads to different microstructure transformations, the formation of additional residual stresses, limitations in plasticity, and other effects. Fig. 3-d shows the local change in phase transformation in a titanium alloy. The heat treatment produces coarse alpha-phase platelets, which have lower plasticity and lead to strain incompatibility between this region and the surrounding material during cyclic loading. The strain incompatibility manifests as a local area with deviated deformation behavior (different elastic moduli). ( ) ( ) ! ! ! " # ! "$""! ! ! ! " " " # # $ !" " " + + + # $ = % % + & ' ! !