PSI - Issue 14

L.R. Botvina / Procedia Structural Integrity 14 (2019) 26–33 L.R.Botvina / Structural Integrity Procedia 00 (2018) 000 – 000

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where P is one from the acting factors above noted (under conditions where other parameters kept constant), А , α are constants. The swelling rate dependencies on each governing parameter were plotted. Initial S-D curves were taken from literature. Such initial swelling curves obtained by Pells and Murphy (1992) for aluminum irradiated at different temperatures are shown in Fig. 4, a. Using these curves, the dependencies of swelling rate ⁄ on dimensionless similarity parameter = ( ⁄ ) 1/3 were plotted for each temperature. For different irradiation temperatures the swelling rate curves either coincide or are almost parallel and can be brought to a single curve by normalization to the coordinates of the curve’s knee points which correspond to the end of a stable stage of swelling. It can be seen that this normalization enables us to obtain a unified universal kinetic swelling diagram which is described by power-law dependence of the swelling rate on the relative parameter ∗ (Fig. 4, b). The swelling diagram is similar by the shape to the well-known fatigue fracture diagram and is described in its linear middle part by the power law function.

Fig. 4. (a) initial swelling curves for aluminum at different temperatures of irradiation obtained by Pells and Murphy (1992); (b) kinetic diagram of swelling in universal coordinates plotted by Zharkova and Botvina (1998) ~ ( ) 1 3 (11) ( / ) ∗ = ∗ (12) ∗̇ = ( ∗ ) (13) Similar relationships were obtained for the swelling rates in function of different factors including preceding cold plastic deformation, various stresses, concentration of trace elements and others. It was found that the swelling diagrams for all the studied factors influencing damage accumulation may be described by power law functions characterizing process development at its extended stage. It allows for considering this process as self-similar. The R-parameter changes during irradiation from the threshold ( ℎ ) to the critical value ( ) corresponding to the minimum swelling rate. Accordingly, the R - parameters suggested may be used to choose and compare materials resistant to the radiation damage. Probably, it can be assumed that the obtained kinetic diagrams characterizing the development of damage in different loading conditions and different media are another consequence of the analogy of the approaches of Griffith and Gibbs.

Acknowledgements

This work was supported by the Russian Foundation for Basic Research, project No. 16-58-48008 IND omi and was carried out according to state assignment No. 007-00129-18-00.