PSI - Issue 14

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

31

L.R.Botvina/ Structural Integrity Procedia 00 (2018) 000 – 000

6

Barenblatt and Botvina (1980, 1985), allowed us to substantiate the empirical choice of the proposed similarity parameter. The dimensional analysis showed that the ratio λ⁄ of the wavelength to the average grain diameter is a similarity parameter characterizing the process of attenuation of ultrasonic waves by the material structure elements, and the process itself practically in the entire region of change in grain size and frequency of ultrasonic waves can be considered self-similar described by the power function of the similarity parameter.

Fig. 3. (a) changes in the attenuation coefficient with frequency in various damage zones of the stainless steel specimen tested for a long-term strength at a temperature of 600° C: + - Ψ = 60.2 %; ● - Ψ = 55.2 %; ■ - Ψ = 7.8 %; ○ - Ψ = 6.7%; □ - Ψ =5.75 % ( Ψ is the reduction of specimen area); (b) the ultrasonic attenuation diagram plotted using the data of (a) The development of these studies by Botvina and Michailov (2000) led to the plotting kinetic diagrams of ultrasonic attenuation in steel specimens with different levels of damage under conditions of tension, creep and fatigue. Fig. 3b shows an ultrasonic attenuation diagram plotted using the data of the measurement of the attenuation coefficient in various zones of damage of a stainless steel specimen tested for long-term strength (Fig. 3 a). Specimen reduction area ( Ψ ) was used as damage parameter. The diagram shows the parameters characterizing the stages of development of damage and allowing to diagnose the state of the material in the conditions of its service on the data of nondestructive testing. Similar diagrams were obtained by evaluating the attenuation of ultrasound in the samples tested in condition of tension and fatigue. 4. Kinetic diagram of swelling at irradiation Process of damage evolution at irradiation called “swelling” is connected to increasing a specimen volume and decreasing in material density as a result of defect formation. It is influenced by many factors: dose ( D ) of irradiation, temperature ( T ), stress ( σ ), preceding cold deformation ( ε ), and concentration of alloying ( C AE ) or trace elements ( C TE ). If radiation swelling ( S ) is taken as a damage measure, and the swelling rate is written as dS/dD (as far as a dose is a function of a time), then swelling rate is the function of the above-mentioned factors: = ( , , , , , , ⁄ ) (9) Analysis of the damage accumulation process during irradiation, which was carried out by Zharkova and Botvina (1998) on the base of the similarity theory, showed that swelling rate ( ⁄ ) is a power - law function of an R parameter suggested which characterizes the swelling in different irradiation conditions and determines the stages and mechanisms of this process: ̇= ⁄ = ( ) = (10)