Open access peer-reviewed chapter

Characteristics of the Dissipation of Energy at Hot Plastic Deformation of Near-Alpha Titanium Alloy

Written By

Mikhail Mikhaylovich Radkevich, Nikolay Rafailovich Vargasov and Boris Konstantinovich Barakhtin

Submitted: July 9th, 2018 Reviewed: July 26th, 2019 Published: September 12th, 2019

DOI: 10.5772/intechopen.88845

Chapter metrics overview

687 Chapter Downloads

View Full Metrics


Change of mechanical properties of near-alpha titanium alloy is experimentally investigated at stretching in the conditions of variation of temperature and high-speed parameters of deformation. It is established that characteristics of mechanical properties, a structural state influence processes of dissipation of the spent energy. Studying of microstructure of samples before deformation by stretching allowed to install the main mechanisms of dissipative processes and to confirm a possibility of realization of superplasticity in the studied alloy.


  • titanium alloy
  • tensile deformation
  • dissipation
  • superplasticity
  • microstructure

1. Introduction

Structural and phase transformations in metal alloys at deformation in the conditions of plasticity and superplasticity are a subject of long-term and systematic researches.

In scientific literature there are physical and mathematical models of deformation describing structural transformations in process as plastic and superplastic deformation of structural materials [1, 2].

However we have very few materials of publications in which results of the thermodynamic analysis directly correspond to researches of structural transformations. Authors of works [3, 4, 5] showed that one of the effective methods of studying of mechanisms of hot plastic deformation is the thermodynamic approach based on use of dynamic model of deformation of material.

According to the model of the elasto-visco-plastic environment, for any timepoint the power of the mechanical energy P coming to a deformable body is defined by the sum composed by G and J. Both are connected with production of entropy. However first (G) considers dissipation of energy through forming and hardening. Second (J) is connected with the adapting reorganizations in structure of grains of a polycrystal directly in the course of action of the deforming tension. Hence it is connected with production of entropy in material:

P = G + J = σε ; = T ds / dt 0 , E1

where σ is tension, ε; is strain rate, T is temperature, and dS/dt is the speed of production of entropy.

Division of power of dissipation between G and J is defined by strain rate sensitivity m:

dJ / dG = ∆log σ / ∆log ε = m . E2

It is shown that for quantitative assessment of nature of dissipative processes and practical application, it is convenient to use effectiveness ratio of dissipation of energy (η):

η = 2m / m + 1 . E3

The coefficient η characterizes ability of structure of material to dissipate the brought mechanical energy in the course of hot deformation.

Size η changes in the range from zero to unit and is interpreted as the relative speed of production of entropy.

In the present article, results of the research characteristics of dissipation of energy in industrial alloys in the course of uniaxial stretching and compression on the example of near-alpha titanium alloy are stated.

During the planning and implementation, the present article used system approach which included the detailed analysis of structure of alloy before deformation and comparison of results of structural researches to results of mechanical tests and calculation of coefficient of dissipation of energy.


2. Materials and experimental methods

Mechanical tests of samples of titanium alloy cut from hot-rolled sheet products with thickness of 40 mm, the chemical composition of which is given in the Table 1, were made at different temperatures and speed parameters.

Element content, % wt.
Al V Mo Fe Si C O H N Ti
5.4 2.0 1.2 0.25 0.3 0.1 0.15 0.08 0.04 The rest

Table 1.

Chemical composition of the studied alloy.

The initial microstructure of titanium alloy corresponded to a two-phase state which was created in the course of hot rolling.

The received structure is characterized by the large initial size of grains of a β-phase (~300 μm) and represents mix of the α-plates divided by β-phase layers (Figure 1).

Figure 1.

Initial microstructure of alloy.

Mechanical tests on stretching at room temperature were carried out on the tensile testing machine UEN30 “Shimadzu.” At increased temperatures, the modernized universal testing machine UM5 was used.

In an experiment, standard explosive samples with a diameter of 6 mm were used. For tests for compression cylindrical samples with a diameter of 5 and 10 mm on the high-temperature dilatometer DIL 805 were used.

At the same time deformation equaled ε = 0.3, and temperature of heating corresponded 800–1040°С. Average strain rate ε; was 10−3–10 s−1.

Calculation of effectiveness ratio of dissipation of energy at deformation of samples under various temperature and high-speed conditions consisted in formation of a matrix of values of true tension at the set extent of deformation and their logarithms.

Calculation of coefficients of m and η and calculation of intermediate values of effectiveness ratio of dissipation of energy were made by a method of spline interpolation.

Results of calculation can be presented in the tabular, analytical, or graphic style.

The most evident is representation of results of calculation η in the form of 3D plot and cards of constant levels of effectiveness ratio of dissipation of energy. Calculation and creation of cards were carried out with the use of the Mathcad 15 program.

Microstructural researches were carried out on the polished samples of the deformed samples, which are cut out in the cross-sectional and longitudinal direction with application of modern methods [5, 6].

To get images, information technologies and specialized programs have been used (“Expert Pro”, “Fractal”) [7, 8].


3. Results of researches and discussion

According to results of mechanical tests, dependences are constructed σ = f(ε).

The received dependences and their look do not contradict the settled ideas of behavior of metal polycrystals in the conditions of hot plastic deformation. So, in the course of process of plastic deformation of metal, tension smoothly increases and reaches a certain maximum (saturation) in which value is defined at the same time proceeding competing processes—hardenings and a weakening [9]. The growth rate of tension depends on temperature of heating and speed of deformation. At low temperatures and high speeds of deformation, flow stress continuously increases with deformation growth that is caused by the prevailing process of deformation hardening.

At the increased temperatures and low speeds of deformation, flow stress reaches a maximum and then goes down, reaching a certain constant value. In such type of charts, tension deformation is characteristic of the majority of the metals and alloys deformed at temperatures exceeding half the temperature of melting [10, 11].

Current tension size (σs) of the studied alloy depending on temperature and the speed of deformation is presented in Table 2.

Т, °C σs, MPa
10−4 s−1 10−3 s−1 10−2 s−1 10−1 s−1
800 60 100 160 240
840 44 75 130 195
880 24 53 94 149
920 14 28 60 95
960 8.0 16 30 60
1000 5.8 10 18 32

Table 2.

The flow stress of examined alloy at various temperatures and strain rate values for tensile strain of ε = 0.2.

Values of tension of a current at the set temperature and high-speed parameters of deformation were used for the subsequent calculation of effectiveness ratio of dissipation of energy η.

Change of coefficient η from temperature and high-speed parameters of deformation are presented in the form of the volume chart (Figure 2) and also in the form of the card of constant levels of effectiveness ratio of dissipation of energy (Figure 3).

Figure 2.

3D plot of effectiveness ratio dissipations of energy at ε = 0.2.

Figure 3.

Processing map for titanium alloy. Constant levels of coefficient efficiency of dissipation at ε = 0.2.

Analyzing the results of change of effectiveness ratio of dissipation of energy presented on 3D plot and the map of constant levels of effectiveness ratio of dissipation depending on temperature and high-speed parameters of deformation, it is possible to note:

Temperature dependence η = f(t, ε;): It is characterized by a maximum at temperatures 900–940°С. And with increase in speed of deformation, maximum shift toward big speeds of deformation is observed.

  • The studied alloy is characterized by high efficiency of dissipation of energy in the studied range of temperature and high-speed parameters of process of hot deformation. Efficiency of energy of dissipation significantly does not change with increase in extent of deformation from 0.1 to 0.3.

  • Mechanical properties of alloy at hot plastic deformation substantially depend on initial structure and temperature and high-speed parameters of deformation.

  • In an initial state the studied alloy has the coarse-grained (not recrystallized) structure and the increased maintenance of a β-phase in comparison with an equilibrium state.

When heating alloy to temperature of 800°С, the first signs of recrystallization are observed, and further heating to temperatures of 920–940°С and endurance of 15 min. Process of recrystallization proceeds completely.

To process recrystallization, α → β phase transformation is followed. An increase of the β-phase contents in the alloy when heated is represented in Table 3.

Т, °С 750 800 850 900 950 1000 1040
β-phase, % 15 20 28 40 65 82 100

Table 3.

Change of volume fraction of a β-phase when heating alloy.

Increasing the heating temperature of the alloy leads to an increase in the phase change rate due to an increase in self-diffusion. The largest speed of phase transformation is observed at a temperature of heating of 900–950°C. The quantity of α- and β-phases decreases with temperature increase and increase in hold time. The quantity of a phase decreases with temperature increase and increase in hold time. At alloy heating temperatures (1040°С), the phase transformation which is followed by sharp integration of grains of a β-phase completely comes to the end (Table 3).

It follows from the provided data that the microstructure and phase composition of alloys undergo significant changes at a temperature of heating to temperatures more than 950°С owing to full completion of process of recrystallization and phase αβ transformations.

Results of researches on the change of structure of alloy in the course of deformation at various temperatures and extent of deformation 0.4 are presented in Table 4.

Т, °C Grain size, μm Phase composition, %
ε = 0 ε = 0.4 ε = 0 ε = 0.4
α β α β α β α β α β α β
840 12.7 4.7 6.8 2.4 6.6 5.5 3.6 2.5 70 30 54 46
900 11.0 4.9 6.6 3.0 7.9 7.7 4.3 4.2 60 40 42 58
960 10.4 6.7 6.8 5.1 9.9 12.5 6.7 6.9 35 65 22 78

Table 4.

The size of grain and phase composition of alloy before deformation at various temperatures.

Note: I, longitudinal section of a sample; II, the cross-section of a sample.

Grain size change in phase αβ transformation is characteristic for structure at hot deformation of alloy. If the size of grains α-phases decreases, then the size of grains β-phases on the contrary increases.

As appears from the data provided in Table 4 in the course of deformation of alloy, there is an increase in quantity of β-phases. The considerable difference in the number of phases of composition of alloy is observed at deformation speeds 10−3 s−1. Further increase in speed of deformation practically does not lead to significant change of quantity of β-phases in comparison with an initial condition of alloy. Increased rate of deformation results in intensive phase transformation in alloy at small degrees of deformation.

So, at extent of deformation ε = 0.4, quantity of β-phases reaches 12–20%, and at extent of deformation from 0.4 to 1.0, it reaches only 3–4%.

Change of phase composition in the course of deformation is often connected with intensity of diffusive processes. The authors of [11] note that heating to the temperature of deformation of the titanium alloy does not lead to the achievement of phase equilibrium. The reason for this phenomenon is the relatively low diffusion mobility of β-stabilizing elements. For example, the β-phase content is 49% at a strain temperature of 950°C and 30 minutes.

Practically the same quantity of β-phases is observed at 2.5 min. Endurance with extent of deformation ε = 0.5. This circumstance allows to make the assumption that not only the increase in diffusive mobility of atoms is caused by deformation but also temperature change of phase balance is the reason of phase transformation at action of external tension.

The phase αβ transformation is accompanied by a volumetric effect. It is known that various authors estimate this value to be about 0.15% [12]. Transformation of α↔β is accompanied by a volumetric effect and α→β transformation-negative volumetric effect. Therefore with an external pressure, there is a temperature change of polymorphic transformation. The speed of phase transformations generally depends on the difference of free energy of an initial and final state and also the size of change of volume upon this transition. As the size of free energy and volume depend on pressure, it is possible to expect that the speed of phase transformations will also depend on pressure.

In that case when phase transformations are carried out in the diffusive way, the kinetics of phase transformations is defined by change of speed of the course of diffusive processes with a pressure.

The driving force of phase β→α transformation in titanium alloys is shift of phase equilibrium temperature under action of external tensions. The rate of phase change is determined by the diffusion mobility of the β stabilizing elements’ atoms. The interesting fact established when studying changes of a microstructure of alloys at hot deformation is transformation of initial lamellar structure in granular, which is most brightly shown at a temperature of deformation of 920°C and strain rate of 1.1∙10−3 s−1 (Figure 4).

Figure 4.

An alloy microstructure after deformation at 920°С and speeds of deformation 1,1.10−3 s−1. (a) δ = 55%, (b) δ = 200%. ×1000.

Grain shape coefficient was determined by quantitativemetallography method Кф = lα/dα; where lα is the length of the plates and dα is the width of the plates α-phases. The results of the calculations showed that intensive change of grain shape occurs up to deformation of 100%; at higher deformation, Kf stabilizes at values of ≈ 1.2–1.5.

Equiaxial grains of structure 200÷ 300 microns in size are observed in the field of temperatures of β-phases (t ≥ 1040°С).

The nature of dissipative processes described above finally defines indicators of plasticity of alloy. Maximum stability of plastic deformation of alloy is observed at compliance of temperature-speed deformation parameters and maximum coefficient of energy dissipation efficiency [10]. All signs of superplasticity state are observed at temperature of 920-960°C and deformation rate of 10−3–10−2 s−1.

Thus, on the basis of the analysis of structural changes when heating and plastic deformation of alloy, it is possible to draw the following conclusions.


4. Conclusions

  1. At hot plastic deformation of the studied titanium alloy, there are, at least, two dissipative processes—dynamic recrystallization and phase transformation.

  2. The maximum of efficiency of dissipation corresponds to the simultaneous balanced course of these two processes.

  3. The temperature and high-speed extremum of effectiveness ratio of a dissipation of energy corresponds to conditions of the maximum stability at a plastic strain of alloy.

  4. Results of researches about development and speed of dissipative processes at a hot plastic strain of the studied alloy can be used for optimization of the technological modes of hot treatment by pressure.


  1. 1. Kaibyshev OA. Superplasticity of Industrial Alloys. Moscow: Metallurgy; 1984. 284 p. (in Russian)
  2. 2. Poirier JP. High Temperature Plasticity of Metallic Bodies. TRANS. FR. Moscow: Metallurgy; 1982. 273 p. (in Russian)
  3. 3. Prasad YVRK, Sasidhara S, editors. Hot Working Guide A Compendium of Processing Maps. Bangalore: Department of Metallurgy, Indian Institute of Science; 2004. 560 p
  4. 4. Vargasov NR, Rybin VV. Optimization of temperature-rate modes of plastic deformation on the criterion of dissipation of mechanical energy. Metallography and Heat Treatment of Metals. 1999;9:52-56. (in Russian)
  5. 5. Vargasov NR, Rybin VV. Accumulation and dissipation of energy by hot plastic deformation of titanium alloy. Materials Science. 1999;1(18):63-69. (in Russian)
  6. 6. Barakhtin BK, Nemets AM. Metals and alloys. Analysis and research. Physicoanalytical methods of study of metals and alloys. Nonmetallic Inclusions NPO “Professional”, St. Petersburg; 2006. 490 p. (in Russian)
  7. 7. Barahtin BK, Chashnikov VF. A computer program for multifractal analysis of images of structures of metals and alloys. Problems of Materials Science. 2001;N4(28):5-8. (in Russian)
  8. 8. Barahtin BK, Vargasov NR. New approaches in assessing the structural and mechanical condition of the low alloy rail steel during thermal treatment. Materials Science and Engineering. 2014;12:8-14. (in Russian)
  9. 9. Radkevich MM. Technology Strengthening Programme Mechanics and Heat Treatment. St. Petersburg: Technical Publishing, St. Petersburg State Technical University; 2011. 263 p. (in Russian)
  10. 10. Vargasоv NR, Barahtin BK. New approach to the assessment of the structural condition of rail steel during hot deformation. In: Materials of 4th International Scientific-Practical Conference. The Modern Mechanical Engineering. Science and Education. Peter the Great, St. Petersburg Polytechnic University. 2014. pp. 1095-1104. (in Russian)
  11. 11. Radkevich MM. Peculiarities of structure and mechanical properties of soft mechanical and thermal processing of scientific and technical statements of St. Petersburg. Science and Education, St. Petersburg; 2008. Peter the Great, St.Petersburg Polytechnic University No. 1; 2012. p. 142 (in Russian)
  12. 12. Titanium alloys. Metallography of titanium alloys. Moscow: Metallurgy; 1980. 464 p. (in Russian)

Written By

Mikhail Mikhaylovich Radkevich, Nikolay Rafailovich Vargasov and Boris Konstantinovich Barakhtin

Submitted: July 9th, 2018 Reviewed: July 26th, 2019 Published: September 12th, 2019