PSI - Issue 72

138 Mariia Bartolomei et al. / Procedia Structural Integrity 72 (2025) 135–140 the stress intensity at the yield surface, is the equivalent plastic strain, ̇ is the equivalent plastic strain rate, ̇ , 0 is the reference plastic strain rate, A is the yield stress, B is the strengthening coefficient, n is the strain hardening exponent, C defines strain-rate sensitivity Vshivkov et al. (2024). For titanium alloy TC4 the following physical- mechanical constants (the elastic behaviour of the alloy is described by Hooke’s law for isotropic material) and Johnson- Cook model parameters were assumed in the calculation: Young’s modulus E =106.7GPa; Poiss on’s ratio ν=0.341; density ρ=4424 kg/m 3 ; quasi-static yield stress A =978MPa; strengthening coefficient B =826MPa; strengthening coefficient n =0.639; strain rate sensitivity parameter C =0.034; reference strain rate 0̇ =0.005. Verification of the suggested mathematical model was performed by comparing the results of calculation of the residual stress profile measured experimentally with the data of numerical modelling for the samples from TC4 treated by pattern №2 . An automatic system MTS3000-Restan (according to ASTM E837-13a, Rendler et al. (1966)) was used to measure the values of residual stresses as a function of the depth of the treated layer using the hole drilling method. Fig. 4 shows an example of residual stress distribution by depth for the numerical and experimental (hole drilling) profile. where i s

y

Residual stress measurement point x

O

Fig. 4. Residual stress in depth, comparison of numerical solution and measurements obtained by hole drilling method.

The difference in values of residual stresses in depth between experimental and numerical results is less than 10%. Thus, it can be concluded that the above numerical model well describes the distribution of residual stress fields during the processing of 3 mm thick samples. 3. Results and discussion As a result of numerical modeling, the fields of residual stress distribution were obtained under different LSP patterns, as well as their evolution during tension loading was studied. The load value at which fatigue crack initiation and development occurs was established for each pattern of LSP. Since in the conditions of high cycle fatigue crack initiation mainly occurs on the surface of the material, it was necessary to select by means of numerical modeling such a load for tension of the specimen after LSP, at which the stresses at the top of the notch would correspond to the stresses on the specimen without LSP when it is stretched with a force of 10 kN. Thus, we can estimate the load value at which the treated specimen would last the same number of cycles before failure as the untreated (base) specimen. We applied different tension load and calculated the average value of stresses along the thickness of the specimen by direction from notch to the other side. For pattern №1 the load value was 11.7 kN (Fig 5 a). For pattern №2 the load value was 19 kN (Fig 5 b). And for pattern №3 the load value was 16.5 kN (Fig 5 c). Consequently, numerical modeling allowed us to estimate the value of the maximum force in the loading cycle of the specimens after LSP, at which the stresses in the lateral notch would be equivalent to the stresses in the specimen