Indicatory surface of anelastic-elastic properties of Ti alloys

The simultaneous influence of hydrogen H and ultrasound deformation on internal friction Q −1 and dynamic elastic modulus E of intermetallic Ti3Al alloy after cutting and polishing were studied. The relaxation maximum of internal friction Q −1 M1 at temperature Т М1 ≈ 398 К, conditioned by the mechanism caused by reorientation interstitial atoms in dumbbell configurations H-H was discovered. Internal friction maximum Q −1 M2 in intermetallic Ti3Al at temperature T M2 ≈ 439 K was discovered with an activation energy H 2 = 0.86±0.1 eV. 2D and 3D atomic force microscopy microstructure images of Ti (VT8) alloy after mechanical and thermal treatment are presented. Strengthening of Ti alloys is related to the cooperation of dislocations with point defects.


Introduction
Non-destructive internal friction (IF) Q −1 method is related to intermetallic alloy parameter analysis based on the positions of IF maximum - Q , M 1 relaxation time τ, and their contribution to the damping of elastic vibrations [1][2][3][4][5][6][7].Information about the dynamics of structure defects, their distribution, mobility, interaction of defects with each other, processes of nanocomplexes formation and their dissociation contains in measurement of IF Q −1 and modulus defect ΔE/E at different temperatures Т, deformation amplitudes ε and frequencies f.Measuring the elastic characteristic descriptions of crystals can provide information about anharmonic effects.Elastic modulus E can be determined using the second derivative of the quantity from the cooperation energy W between the atoms of the crystalline grate on deformation ε: The moment of separation of the dislocation segments from the stoppers can be determined by measuring the amplitude dependence of IF Q −1 (ε).To determine the variations in anharmonic effects, it is necessary to select high-fidelity measurement methods because these changes are small [8][9][10][11][12][13][14][15][16].To set the spectrum of structural defects in the analysis of positions IF maximums - Q , M 1 the duration of relaxation time τ and their deposit in the attenuation of elastic vibrations can be used as a non-destructive IF method.The structural relaxation criterion can be defined as anelastic structural relaxation, which is caused by structural defects or a system of symmetry below the symmetry of the crystal.However, the value of the relaxation effect could not be determined using this criterion.
The purpose of this work is to show the relationship between three main characteristics (internal friction (IF) Q −1 , dynamic elastic modulus E and temperature T) in the form of 'indicatory surface of anelastic-elastic body' of Ti alloys, which carries additional information about IF dynamics.

Materials and methods
To measure the temperature dependences of IF Q −1 (Т) and elastic modulus E(T), resonance vibrations at frequency f ≈ 2 kHz and the methods of a complete piezoelectric oscillator at frequency f ≈ 117 kHz and during alternative deformation ε ≈ 10 −6 in vacuum P ≈ 10 −3 Pa were used.The measurement error of IF determination was ΔQ −1 /Q −1 ≈ 10%, and the relative change in the elastic modulus was ΔE/E ≈ 0.1% [17][18][19][20][21].
Polycrystal samples were cut from a vane blade made of Ti alloy, which can be used in aircraft engines.First, the samples were polished with fine-grained sandpaper, and then mechanically polished with different diamond pastes.Finishing was performed using a diamond paste with a grain size d G = 14 ÷ 20 μm.The depth of the disturbed layer was h DL ≈ 6 μm.Polycrystal samples were saturated with hydrogen H using an electrolytic method.Platinum Pt foil was used as the anode, and the sample was used as the cathode.One normal solution of H 2 SO 4 was used as the electrolyte.

Results and discussion
Intermetallic Ti 3 Al alloy values of the elastic modulus E and IF Q −1 after mechanical cutting and polishing were simultaneously investigated based on the influence of hydrogen H, temperature T, changing the defect nanostructure and ultrasonic deformation ε.The temperature dependence of IF Q −1 (T) graph is shown in figure 1.
In addition, graphs of the elastic modulus E(T) dependence and ('indicatory surface of anelastic-elastic body') are shown in figures 2 and 3(a).
The use of 3D atomic force microscopy (AFM) allowed us to obtain a static image of the intermetallic Ti 3 Al microstructure after mechanical treatment, as shown in figure 3(b).
Internal friction Q −1 and dynamic elastic modulus E, which were measured at the same room temperature T r , at which 3D AFM was applied, and the cross section of the 'indicatory surface of anelastic-elastic body' of intermetallic Ti 3 Al alloy at the same room temperature T r directly correlate with 3D AFM microstructures.The initial size of IF background was high - Q 0 1 ≈ 7.8 × 10 −3 .The initial IF background - Q 0 1 during the first heating was considerably higher than that of IF background - Q 0 1 during repeated heating.This confirms the presence of a stress field σ i in intermetallic Ti 3 Al.They increased as a result of the mechanical treatment.The anomalous change in IF background - Q 0 1 is shown in figures 1 and 3; in the process of heating, a decrease in these tension values σ i was obtained.Structural defect annealing bends the shape of IF temperature spectrum.The vacancies moved during admixture annealing.Visualization of 'indicatory surface of anelastic-elastic body' after hydrogenization H was performed, as shown in figure 4    The shear modulus G diminishes, and the tension of activation of dislocation sources σ D can be explained by the local increase of conductivity electrons e − concentration in hydrogen H clouds around the dislocations, as described by equation (1) [8]: where L N -distance between the fixing points of the dislocations, G-shear modulus, and b-Burgers vector.The connections of metal atoms are strengthened by hydrogen H, which cannot be the reason for the fragile destruction.The increase of dislocations in the investigated alloy and the tension increase on the leading dislocation σ D are caused by diminishing the distance between dislocations L D in accumulations owing to hydrogen H, which is the reason for the facilitated microcracks.Ti (VT8) (6.5% Al + 3.0% Mo + 0.3% Fe + 0.2% Si) alloy after mechanical and thermal treatment 2D and 3D AFM microstructure images were obtained and are shown in figure 6.A shallowly dispersed smooth surface was observed, the small islands coalesced, and their shape became round.The sites have a highly fragmented structure, which consists of weakly misoriented relative to each other islands with a size of H = 300 ± 80 nm.
Under a mechanical load, the real crystal total deformation consists of elastic and anelastic constituents ε ∑ = ε E + ε IE .The motion of dislocations causes anelastic deformation ε IE [1][2][3][4][5][6][7][8][9][10][11][12].Anelastic deformation depends on temperature ε IE (t) and elastic deformation ε E happens 'instantly'.This is caused by the presence of relaxation times τ, which characterize the motion of crystalline structure defects.There are two maximum values of the elastic modulus: relaxation elastic modulus E R and non-relaxation elastic modulus E NR .With frequency ω in the appendix of the external periodic tension σ(ω), the experimental elastic modulus takes the intermediate value The relaxation of elastic modulus = = where Е R -relaxation elastic modulus, Е NR -non-relaxation elastic modulus, D =  relaxation processes is specified by the considerable width on the temperature range of relaxation of elastic modulus ΔE/E.
The point defect concentration at the boundary was determined by two competing processes: formation of defects during irradiation and their disappearance due to annealing.Let us estimate the stationary concentration of defects C V using equation (2) [10]: where C d -the rate of point defect generation in a single flow, F -flow, αgeometric factor of the sinks, and D V -defect diffusion coefficient.Assuming that the main mechanism is the vacancy V diffusion mechanism, we will understand the concentration of defects as the vacancy concentration C V .Considering that the diffusion coefficient D is proportional to the concentration of vacancies C V , we obtained the ratio of the diffusion coefficients in the irradiated D * and non-irradiated D alloys using equation (3): A reduction in the dislocation source σ D initiates tension, which simplifies dislocation reproduction under the action of the enclosed loading in σ, causing a decrease in elastic modulus E. In addition to the linear dislocation tension σ L , which increases their mobility and distance between dislocations in the accumulations h D , that in the flat accumulations results in an increase in the number of dislocations N D and loading on the leading dislocation σ D .The Debye temperature θ D was determined using equation (4) [8]: where N A -Avogadro number, V ║longitudinal US velocity, V ⊥transverse US velocity, ρdensity, k B -Boltzmann constant, Amiddle gram-molecular mass, and h -Plank's constant.Ratio of relative transversal ε ⊥ compression to relative longitudinal lengthening ε ║ is equal to the Poisson coefficient μ ║ and described by equation (5) [5]: After the protracted ultrasonic deformation ε during t ≈ 3.9 × 10 3 s, a decrease in IF Q −1 was observed.This could be related to the activation of admixtures that diffused into the dislocation segments, besieged them, and fastened them.The decrease in IF value is caused by a decrease in the density of the active dislocation loops.Poisson coefficient μ ≈ 0.3191, velocity of longitudinal elastic waves V ║ = 6210 ± 10 m s −1 , velocity of transverse elastic waves V ⊥ = 3201 ± 10 m s −1 , and Debye temperature θ D ≈ 407.2 К of Ti (VT3-1) alloy were determined.

Conclusions
1.The correlation between elastic modulus Е, internal friction Q −1 , and temperature T may be presented as 'indicatory surface of anelastic-elastic properties' which gives additional information about influence of the mechanical and thermal treatment of Ti alloys.
2. Information about the changes in the fields of thermoelastic strains σ i in Ti alloy was received as a result of internal friction background - Q 0 1 measurements after different heat treatments.
3. The increase in the structural defect concentration was confirmed by the growth of internal friction maximum -Q M 1 heights, and the relaxation process of the new types of structural defects is represented by the spread of internal friction maximum 4. At the same temperature interval ΔT of internal friction maximum -Q M 1 the relaxation of elastic modulus ΔE/E Ti alloy testified to the relaxation process, presumably linked to the vacancy complexes V-V-V excited at the change in number under variable ultrasonic deformation ε, the vacancy-hydrogen V-H complexes, and the reorientation of interstitial hydrogen atoms in dumbbell-shaped configurations H-H. 5.The shape of the temperature spectrum of internal friction Q −1 (Т) is bending out by annealing of structural defects in Ti alloys.From the different continuously changing factors of temperature T and irradiation of the same Ti alloy, it was possible to observe the dependencies of the elastic modulus E(T) and internal friction Q −1 (T).

Figure 2 .
Figure 2. Temperature dependence of intermetallic Ti 3 Al alloy dynamic elastic modulus E of after mechanical treatment.

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the maximal defect of elastic modulus.The anelastic contribution is to deformation ε AE = 0, when Е NR was measured in time of appendix of tension σ; anelastic deformation maximal ε AE = max, when Е R measured after a time Δt ?τ.The amount of microrelaxation of different types and their individual contributions to the anelastic deformation at temperature T determine the value of the maximal defect of the elastic modulus Δ.The contributions of different microrelaxations are summarized.There are relaxation IF maxima - Q M 1 on temperature dependences Q −1 (T) at temperatures when the defect of the elastic modulus Δ sharply increases.The distribution of the activation energy H of the proper