PSI - Issue 71

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

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Table 1. Experimentally measured and theoretical values of stress amplitude

Power density, GW/сm 2

Pressure (copper samples), GPa

Pressure (Ti-6Al-4V samples), GPa

Equation (9)

Experimental

Equation (9)

Experimental

7 9

3,79 5,36 6,11 7,39

3,52 5,40 5,74 5,91

4,48 5,30 6,10 7,02

3,00 4,00 6,00

13 19

6,50 The experimental pressure amplitude on the specimen surface was obtained by extrapolating results from a zero thickness specimen (Fig. 4b, 4d). The data in Table 1 confirm the existence of a saturation process in pressure impulse generation for copper. Equation (9) shows satisfactory performance up to a power density of ~10 GW/cm², while above this threshold, pressure pulses exhibit minimal variation. For titanium specimens, experiments yielded underestimated and continuously increasing pressure values, likely due to insufficient data on pressure amplitudes for small specimen thicknesses. A critical aspect for verifying the mathematical model is the duration and shape of the pressure impulse. We approximate the pressure impulse as a trapezoid: one side corresponds to plasma heating with rising pressure, the top base represents the initial expansion phase at constant pressure, and the second side reflects hydrodynamic plasma expansion with declining pressure. Comparison with experimental data (Fig. 3) reveals a pressure rise time of 10 ns, a near-zero constant-pressure duration, and a decay time of approximately 60 ns. 5. Simulation of residual stress distribution The verification of the proposed mathematical model is carried out by comparing the results of calculating the CRS profile for Ti-6Al-4V plates with a thickness of 3 mm. An area of 11×11 mm without overlaps with a 1×1 mm square beam profile was processed. Figure 5 shows a photo of the specimen after LSP treatment and a numerical model for simulating the residual stresses.

a

b

Fig. 5: (a) Typical view of the specimen after LSP treatment and (b a numerical model for simulating the residual stresses. The following boundary conditions were used in the numerical simulation: the lower surface of the plate is fixed – there are no vertical movements | Г 1 =0 ; the side surfaces of the plate are free from load ∙ | Г 2 =0 ; in processing zone located on the upper surface, a mechanical pressure is set (duration of pulse is 60 ns) ∙ | Г 3 = ( ) . The meshing is carried out using 8-node hexahedral elements with a linear shape function. To calculate the residual stress profiles, the area in the vicinity of the load application was partitioned into elements with a side size of 20  m. As the distance from the boundary increases, the side size of the finite elements increases to 2000  m. The total number of elements in the calculation area is 15х10 6 . The profiles of residual stress (corresponding components of the stress tensor in the x and y planes orthogonal to the acting load, respectively) after LSP treatment in one pass and after repeated processing in the same mode are shown in Fig. 6.

a

b

Fig. 6: Residual stress profiles: (a) after one pass (b) after two passes