PSI - Issue 71

Oleg Plekhov et al. / Procedia Structural Integrity 71 (2025) 10–17

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The fatigue tests were carried out with titanium specimens only. The test frequency was 10 Hz, R=0,1. The geometry of these specimens is shown in Fig. 1b. 2. Experimental setup LSP was implemented using an experimental setup comprising a six-axis robotic manipulator, a pulsed Nd:YAG laser, and an MTS3000 system for residual stress measurement via hole drilling. The developed system enables power density application ranging from 1 to 90 GW/cm², with the laser and robotic manipulator synchronized via a custom software-hardware complex for remote operation and programmed precision, achieving a beam positioning accuracy of less than 0.25 mm on the specimen surface. The effectiveness of LSP on the specimen critically depends on the laser spot shape and the overlap degree of treated areas. To enable diverse processing regimes, the setup incorporates a proprietary optical system capable of generating square-shaped spots with side lengths of 1 mm and 3 mm, as well as a circular spot with a radius of 2 mm, ensuring adaptability to various technological requirements. 3. Mathematical model of LSP process To simulate the LSP process, the ablation of the material is not considered. Instead, the laser impact is taken into account by setting a time-dependent mechanical pressure function on the specimen surface. The resulting stress-strain state is then calculated in the ANSYS finite element package. The mathematical model of the process for a representative material volume includes the law of conservation of momentum and constitutive equations. In the absence of mass forces, the equation of motion (the law of conservation of momentum) can be expressed as follows: = 2 2 . (1) The total deformation in the approximation of small deformations can be written as follows: = 1 2 ( + ) . (2) According to the principle of additive decomposition, the increment of total deformation can be expressed in terms of the increments of elastic deformation and plastic deformation : = + . (3) In the case of an isotropic material, the Cauchy stress is defined by Hooke's law = + 2 . (4) According to the associated law of plastic flow, the rate of plastic deformation can be defined as = , (5) In the case of isotropic hardening, the yield surface can be written as = − ( ) , (6) To simulate the process, it is necessary to add an equation for the calculation of the value ( ) to the system of equations (1)-(6). For the considered materials, it was determined from the Johnson-Cook model Johnson et al. (1985) = [ + ( ) ] [1 + ̇ ̇ , 0 ][1−( − 0 − 0 ) ] , (7) The model parameters and material constants are A=978 MPa, B=826 MPa, C=0,639, n=0,034, ̇ =0,005. In light of the aforementioned considerations pertaining to the mechanical effects of the LSP treatment process, it was deemed unnecessary to incorporate variables related to temperature effects. The simulation of the treatment process was carried out at ambient temperature without taking into account the influence of the melting point and the coefficient of thermal softening. In numerical modeling, a triangular pulse was considered to account for the pressure changes over time: ( ) = { 1 , 0≤ < 1 , 2 − 1 , 1 ≤ < 2 , (8) where 1 and 2 are the pressure rise and decrease times, respectively. The peak pressure amplitude could be calculated based on one-dimensional ablation model Fabbro et al. (1990) or PDV experiments: