PSI - Issue 59

V.V. Lytvynenko et al. / Procedia Structural Integrity 59 (2024) 372–377 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

375

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Fig. 3. (a) Calculated dependency of a melt depth D from the initial surface versus a beam width L ; (b) Calculated profiles of heating speed at a current flux j ~ 3.5 MA/m 2 versus energy release depth into the sample, where 1 – at ~0.1 µs, 2 – 1 µs; 3 – 2 µs after the start of irradiation. The compression stress in the similar titanium alloys are in the range of 150-450 MPA as in Klepikov (2015) and Donets (2022). The local fracture mechanisms are more of brittle nature. In general, the irradiation resulted in embrittlement of the melted layer of the VT1-0 alloy. The quenched surface layer suffers from delamination due to difference of microstructures. In Didyk (2010), the delamination in irradiated targets was discussed to occur when metals are exposed to intense flows of charged particles through the mechanism of locally elevated temperature along the particle tracks. The HCEB irradiation provokes macro-delamination of regions at the boundary of the heated metal – base metal. The heating and cooling process of the target was numerically simulated. This simulation provided insights into the dynamics of the temperature field. The significance of solving the dynamic problem lies in its ability to estimate the actual depth of melting, the total thickness of quenched and heat-affected zones, and approximate boundary between modified and unmodified volumes. Heating and cooling profiles are calculated up to the depth of energy release, to bring light on temperature conditions in the near surface regions of quenched re-melted and heat affected zones. Other profiles are not of interest for the presented research. The evolution of the temperature field in terms of propagation of the melt was calculated and illustrated in Fig. 3a. The melt pool reached depth of around 1 mm from the initial surface at the beginning of irradiation, in the epicenter region. It correlates with the experimental data of the max thickness of quenched and re-melted heat affected zone of ~1 mm. The driving factor of any differences of calculated values and actual values are speculated to be caused by more intense shielding of the target by its ablation products during irradiation, resulting in less than expected depth of melting. In terms of the model, absorption coefficient should be taken around 0.65-0.7 otherwise it leads to significant differences. Heating profiles were calculated and presented in Fig. 3b. As the irradiation duration increases, the heating rate tends to decrease. In Figure 4, the temperature inhomogeneity during cooling of the target was presented. The cooling rate is determined by specific boundary conditions and accumulated heat in the material during irradiation. Rapid cooling of the surface region, as explained by explosive decay and ejection of overheated material, allows to neglect possible features of heat exchange in the simplest case when a constant temperature (room temperature, 20 °C) is assumed at the external boundary, see Fig. 4a. However, that assumption does not account for re-condensation processes happen for some time after irradiation, during which the surface temperature does not decrease abruptly. In this case (Fig. 4b), the boundary condition can be taken as (1):

( , )

T x t



( , )

( , )

T x t

q x t









(1)

x



0

x



0

x



where q is the heat function, α is the thermal conductivity coefficient, and β is the heat exchange coefficient, T – temperature, at initial surface x at time t . We omit here all the details of the model for simplicity.