rus
Issue #3/2025
V. V. Likhanskiy, K. E. Ulybyshev, N. N. Elkin, M. V. Khorokhorin
Changes in the Polycrystalline Alloy Microstructure Under Impact Action of Short Laser Pulses
Changes in the Polycrystalline Alloy Microstructure Under Impact Action of Short Laser Pulses
DOI: 10.22184/1993-7296.FRos.2025.19.3.210.222
A review of publications devoted to the application of pulsed laser radiation in the field of technologies has been performed. The advantages of laser shock peening of the processed product surfaces have been considered. The developmental model of point defects and dislocations under the shock-wave load of polycrystalline materials has been proposed. The high-quality compliance between the calculated dislocation density and experimental results related to the laser shock peening of AMg6 samples has been obtained.
A review of publications devoted to the application of pulsed laser radiation in the field of technologies has been performed. The advantages of laser shock peening of the processed product surfaces have been considered. The developmental model of point defects and dislocations under the shock-wave load of polycrystalline materials has been proposed. The high-quality compliance between the calculated dislocation density and experimental results related to the laser shock peening of AMg6 samples has been obtained.
Теги: dislocation density laser shock peening point defects лазерное ударное упрочнение плотность дислокаций точечные дефекты
Changes in the Polycrystalline Alloy Microstructure Under Impact Action of Short Laser Pulses
V. V. Likhanskiy 1, 2, K. E. Ulybyshev 1, 2, N. N. Elkin 1, M. V. Khorokhorin 1, 2
Research Center “Kurchatov Institute”, Moscow, Russia
Lebedev PhysicalInstitute of the Russian Academy of Sciences, Moscow, Russia
A review of publications devoted to the application of pulsed laser radiation in the field of technologies has been performed. The advantages of laser shock peening of the processed product surfaces have been considered. The developmental model of point defects and dislocations under the shock-wave load of polycrystalline materials has been proposed. The high-quality compliance between the calculated dislocation density and experimental results related to the laser shock peening of AMg6 samples has been obtained.
Key words: laser shock peening, point defects, dislocation density
Article received: March 06, 2025
Article accepted: April 17, 2025
Introduction
The researches related to the use of lasers to influence the materials being processed in various ways has been conducted for a long period of time [1–2]. An example of laser technologies that are widely applied today is laser-beam welding [3–4]. Another widely used technology is laser surface cleaning [5–6]. The surface of some products requires painting to increase the corrosion resistance of alloys and improve their aesthetic appearance. Thus, to ensure the required service life of aluminum alloys, it is necessary to periodically remove and reapply the surface paint coat. The conventional paint removal methods include mechanical grinding, chemical treatment, and sandblasting. However, they are not only time-consuming and inefficient, but also cause various damage to the aluminum alloy base, while affecting its service life. In addition, the chemical treatment process can lead to environmental pollution and pose a potential hazard to the human health. Laser cleaning has the advantages of being environmentally friendly, precise, and controllable, and is highly efficient compared to the conventional cleaning methods. This paper examines one of the promising areas of laser radiation application in the industry, namely the surface treatment of a finished product in order to improve the material properties.
The up-to-date high-tech industries (aircraft engineering, rocket engineering, nuclear power engineering) impose increased requirements on the performance specifications of the materials used. Among the main parameters that determine the product reliability, the specialists put emphasize on crack resistance, tensile strength, creep-rupture strength, and corrosion resistance. These parameters can be improved by thermal or mechanical action on the sample near-surface layer.
The thermal action is heating of the near-surface layer to the temperatures close to the melting point by plasma or laser radiation with the specially selected parameters. Since the thermal conductivity of metals is quite high, after heating there is a rapid cooling of the heated area (“hardening”), accompanied by the microstructural changes. This technology is the subject of research in the papers [7–10]. The publication [7] considers the processes in iron-carbon steels during laser hardening. In the paper [8], an analysis of the current application level and prospective development of laser hardening technology is performed. One of the advantages of this method is its possible application for brittle materials, such as cast iron. The paper [9] considers numerical modeling of the temperature distribution near the tool cutting edge during the laser hardening process. In the publication [10] the material hardening by a plasma flow generated by an electric arc discharge is considered. The main application results of the described methods, including the laser and plasma hardening are an increased surface layer hardness and, accordingly, an enhanced wear resistance.
As the disadvantages of the thermal laser hardening method, it should be noted that the plastic deformations occurred under the temperature stresses usually lead to the residual tensile stresses in the surface layer that has a negative impact on the product strength and crack resistance. As an addition to this method, designed to minimize the said disadvantage, or as an independent surface treatment technology, a shock peening procedure is often practiced that develops the residual compressive stresses in the surface layer. The basis of this method is generation of a pressure pulse on the product surface leading to a shock wave propagating deep into the material. The stresses developed by the shock wave lead to some changes in the material microstructure and formation of plastic deformations causing the residual stresses.
The plastic deformation resistance of metallic materials in the crystalline state is determined by four essentially different mechanisms, including the solid solution, dislocation, grain boundary, and dispersion peening. In the state-of-the-art structural materials, a combined interaction of several of these mechanisms is usually used, often all four. The mechanisms that determine the mechanical properties and plastic specifications of materials, depending on the crystalline structure type, the material microstructure, and alloying additives in the alloys, are described in detail in the classic monograph by Hirth and Lothe [11].
The resistance to dislocation movement through an ordered dislocation arrangement (substructure) differs from the resistance to movement through a chaotic dislocation distribution. If in the latter case it depends only on the dislocation density, then in the case of substructure formation, the resistance to dislocation movement already depends on the parameters of the latter. This phenomenon is called substructural strengthening. It has a significant contribution in the strength development of hardened steel, sometimes exceeding the contribution of solid-solution hardening.
Most of the materials used are polycrystals. The availability of grain boundaries in the polycrystal leads to its strengthening. At a certain stress value, the dislocations cannot pass through the grain boundary into another grain and begin to slow down. To overcome the boundary, they need additional stress. It has been experimentally proved that with a decrease in the average grain size, the deformation resistance of a polycrystalline material is increased.
Dispersion strengthening, or strengthening by the dispersed particles, consists of the small second-phase precipitates in the matrix of the base metal or alloy. These precipitates can have the same or other crystal lattice, and develop the stress fields. Inclusions of secondary phases lead to the additional obstacles to the dislocation movement and as a result can significantly increase the material strength.
An efficient way to strengthen the finished product is plastic deformation only of the device surface layer. The most common methods of surface plastic deformation are shotblasting and surface rolling.
The up-to-date laser peening technologies based on the effect of short radiation pulses on the material surface seem promising. Thus, in 1963, during the study of short laser pulses on the metal sample surfaces, the effects of shock wave generation were demonstrated for the first time [12]. The laser cold working is currently one of the most popular and widely used methods of surface hardening abroad. In order to complete the laser cold working process, it is necessary to use a laser station that meets the following requirements: average power supply from several hundred watts to several kilowatts, pulse energy of about 0.1–100 J and pulse duration within the range of 10–50 ns.
In many papers, for example, in [13–14], the significant changes in the material microstructure were determined due to the optimization of laser processing modes for the products made of polycrystalline alloys.
Firstly, in the case of short-term laser shock peening, the dislocation density in the surface areas of materials is increased. Secondly, the residual compressive stresses are generated in the surface areas of the processed samples. Thirdly, under the multiple impulse action on the polycrystalline material, the grain size has significant decreases. For example, in the paper [13], attention is drawn to the decreased grain size with an increased multiplicity of laser shock processing in the AZ31B Mg alloy (Fig. 1).
The data provided show a more than fivefold reduction in the average grain size with the fourfold laser exposure.
As another example demonstrating the impact of grain boundaries in the polycrystalline alloys on changes in the mechanical and corrosion metal specifications, it is possible to indicate the dislocation structures observed in the paper [15] in copper and nickel after shock peening. In the publication [15], the dislocation cells were shown being concentrated to a greater extent near the grain boundaries of metals (Fig. 2).
The interesting results were obtained in the publication [16] in relation to the numerical modeling of shock wave propagation in a polycrystalline copper sample using the molecular dynamics (MD) method. The calculation results demonstrated an increased concentration of point defects at the grain boundaries. The results of the paper [16] show a noticeable increase in the microstructural defects in the grains after the shock wave front has passed.
In a number of publications, for example, in [17], the calculations using the MD method have shown that in the area of intergrain boundaries of polycrystalline materials, the migration energies of point defects and their formation energies can be significantly lower than in the bulk of grains. These effects should have an impact on the nucleation processes of interstitial atoms with generation of the dislocation loops and vacancy pores with a sufficiently fast impulse action on materials with the regions supersaturated with defects. The increased dislocation density on the material surface, at the grain boundaries and on other crystal imperfections during the laser shock peening process is a confirmed experimental fact. This provision is discussed in many papers, for example, in the articles [14, 15].
For wide industrial application of the laser shock peening technology, it is desirable to ensure its cost-effectiveness, i. e. to use laser systems that do not require any expensive components and generation of laser pulses with the unique specifications. The laser systems based on the neodymium pulse lasers have proven themselves to be quite good [18]. The main advantages of these systems are portability, high efficiency and relatively low cost. The selection of laser radiation parameters to obtain the required characteristics of the processed materials is a multifactorial task. Let us briefly indicate the main factors.
Firstly, the laser radiation exposure results depend on the composition and properties of the material being processed. The important material specifications include its crystal structure, grain parameters and texture of polycrystals, concentration and volume fraction of secondary phase inclusions, their composition, and dislocation density.
Secondly, any changes in the material specifications are largely determined by the temperature and mechanical fields in the samples. The laser exposure level is determined by the radiation parameters, such as wavelength, pulse duration, laser spot area and intensity.
Thirdly, the processing results depend on the geometric parameters of the sample and the material surrounding the sample, as well as on the laser exposure process mode.
As a rule, almost all of the above factors are interconnected and determined by the nonlinear multiparameter dependencies on the temperature, pressure and material properties. The most appropriate and optimal approach is to develop the separate calculation and theoretical stations for specific materials and for the conditions and sample laser processing process modes required by the industry.
This paper is devoted to the development of a method for predicting changes in the specifications of sample surface areas as a result of laser shock peening on the polycrystalline materials by the example of aluminum alloy AMg6. For this alloy, there is a large amount of experimental data that allows to estimate the physical-kinetic model parameters for describing the non-stationary behavior of defects in the crystal structure.
Basic provisions of the model being developed and evaluation formulas
To obtain the dependencies of the evolution of microstructural changes and residual stresses distributions in the polycrystalline materials under the shock peening of short laser pulses, it is proposed to consider a physical model that accounts for the kinetics of transient processes, time parameters of the shock wave, temperature and initial microstructure of the material.
Let us consider the issue of changing the atom energy specifications in a crystal lattice with a rapid increase in the compressive stresses. During the adiabatic lattice compression under the shock wave action, the atoms, in accordance with the adiabatic invariant preservation, increase its oscillation frequency that corresponds to a local temperature increase in the compressed layer. In the one-dimensional approximation, one atom during compression has an energy of about a3P22E, where a is the crystal lattice parameter, P is the pressure amplitude in the material during the shock wave passage, E is the Young’s modulus. The increased atom energy during the crystal compression process is equivalent to an increase in the local temperature by the value of about ΔT ~ a3P22kE, where k is the Boltzmann constant. When making the estimates, it is necessary to use the published temperature dependences of the self-diffusion coefficients Ds(T) of aluminum atoms and equilibrium dependences of the vacancy concentration cv(T) in aluminum alloys on the temperature [19, 20]:
DS(T) = 1.9 · 10−5 exp − ; (1)
Cv(T) = 7.5 exp − . (2)
Hereinafter the diffusion coefficients are given in [m2/s]. The vacancy concentration dependence in the expression (2) is registered in the dimensionless units relative to n0 that is the initial concentration of aluminum atoms in the alloy, Т – the temperature in Kelvin degrees. It is necessary to consider the generation impact of point defects with due regard to their diffusion and recombination. According to the dependences (1, 2) misesteem of the grain boundary contribution allows to estimate the diffusion coefficient of vacancies Dυ(T) in the bulk of aluminum alloy grains:
Dυ(T) = 2.5 · 10−6 exp − . (3)
To determine the changes in concentrations of point defects over time, we will use a system of diffusion equations describing the dynamics of point defects:
(4)
where: Fv(i)(T) – a bulk source of point defects (vacancies and interstitials, respectively); δFv(i) – an additional bulk source of point defects arising under the action of a shock wave passing through the sample; Rvi – the mutual recombination coefficient of vacancies and interstitials; Δ – Laplacian; Sv(i) – coefficient of defect capture by the wastewater.
If any experimental and calculated results are used, according to which the thermal diffusion coefficients of interstitial atoms significantly exceed the diffusion coefficients of vacancies (Di >> Dv), then for the thermally equilibrium conditions the temperature dependence of the bulk source of point defects can be estimated according to the following formula:
Fv(T) = 2 π a Ds n20 cv. (5)
With due regard to the experimental dependencies (1–3), the bulk source of defects (5) for the aluminum alloy AMg 6 within the framework of the Frenkel model can be represented as follows:
Fv(T) = 1.31 · 1045 exp − , m−3 s−1 (6)
Inclusion of the increased atom energy by the value of a3P22E as a result of the shock wave action on the crystal with a pressure amplitude of up to 5 GPa and a laser pulse duration of less than 10−7 s at a sample temperature of less than 350 K provides any additional concentrations values of point defects that are insufficient to generate the dislocation loops with a dislocation density relevant to the experimental data [21–23]. This is due to the high value of the generation energy of point defects and the low coefficient of their diffusion in the crystal volume.
In the area of grain boundaries and near the dislocation loop cores, the binding energy between the crystal lattice atoms is noticeably lower than in a single crystal. As a consequence, in these areas of a polycrystal, the generation energy of point defects, as well as the diffusion activation energy shall be reduced. An estimated analysis of the processes leading to any changes in the dislocation density in the field of grain boundaries during the pulsed, short-term material compression can be based on the following phenomena. We will assume that the generation processes of extended defects (dislocation loops, pores, secondary phase inclusions) at the grain boundaries under the influence of a shock wave can be described as follows.
During the crystal lattice compression, the excess point defects are generated at the grain boundary and near the dislocation cores. The rate of point defect production and its concentration growth depend on the magnitude and time of changes in the compressive pressure. If the times are shorter than the time of point defect diffusion in the grain and shorter than the time of flow to the intergranular dislocations, these processes can be neglected and the value of excess concentrations of point defects can be estimated. In this approximation, the dependences of increased concentration of point defects near the grain boundaries on the shock peening parameters are quite simply estimated if the generation energy of a pair of Frenkel defects (a vacancy and an interstitial atom) and the growth value of the vibrational energy of atoms located in the lattice points during the adiabatic crystal lattice compression are well-known. These values shall be determined at the verification stage of the developed model parameters based on the available experimental data that is supposed to be done during the subsequent studies.
In the paper [17], the vacancy migration in Al was subject to computer modeling with due regard to the grain boundaries and dislocations. The migration energy values near the grain boundaries were obtained to be significantly lower; when the vacancy moved to the grain boundary or to the dislocation core, the decrease in migration energy was more than 5 times. The similar approach shall be applied to analyze the role of grain boundaries on the microstructural changes under the short-term impact action. Since both the migration of point defects and their development are activation processes, then to make an evaluation the generation energy of a Frenkel pair near the grain boundary and the dislocation core shall be reduced by about 5 times. Then an additional generation source XGb of Frenkel pairs in the grain boundary area, related to one crystal atom, with due regard to the compressive impulse of the shock wave, can be estimated as follows:
XGb = 2.1 · 1016 exp − · β · a3P22k · E · WGbT, s−1 (7)
where: k – the Boltzmann constant, Т – temperature in Kelvin degrees, a3P22E – changes in the elastic energy per atom during the crystal lattice compression, β – dimensionless parameter to be determined on the basis of experiments, WGb = 4762 K – generation energy of point defects at the grain boundary in Kelvin degrees.
In the general case, the time dependence for the vacancy concentration exceeding the equilibrium value at the grain boundary is indicated in the form of an equation:
· n0 − nv, i, Gb · XGb(t) − RGb · nv, i, Gb, (8)
where: n0 is the initial concentration of aluminum atoms in the crystal, nv, i, Gb is the concentration of nonequilibrium (excess) point defects in the intergranular region. According to the published data, for aluminum it is n0 ≈ 6 · 1028 m−3 . The coefficient RGb(t) considers the annihilation processes of vacancies and interstitial atoms at the grain boundaries. This coefficient may depend on many parameters, including temperature, concentrations of point defects, diffusion processes, anisotropy of mechanical stresses, concentrations of alloying elements, etc. Determination of the dependencies that define the annihilation rate of point defects in the grain boundary region is expected to be performed in the subsequent studies.
The preliminary estimates of the diffusion transfer rate of point defects in an aluminum alloy based on information determined in the papers [19, 20] show that during the times of 10−6 sec that are significantly longer than the shock wave pulse action times, the diffusion length from the grain boundary region into the grain at the temperatures below 350 K is less than the crystal lattice parameter. Therefore, when estimating the accumulation of point defects in the intergranular region, it is sufficient to take into account only the first term in the equation (8) at the shock wave pulse propagation times. In this approximation, the integration (8) yields an estimate of the additional concentration of accumulated point defects in the grain boundary region:
nv, i, Gb(t) = n0 · 1 − exp− XGb(τ) dτ. (9)
Based on (9) and with due regard to (8), an estimate is obtained showing a significant increase in the local concentration of point defects. The accelerated intergranular diffusion over relatively short periods of time can lead to the generation of dislocation loops near the grain boundaries and, thus, reduce the excess nonequilibrium concentration of point defects. If it is assumed that the critical radius of stable dislocation loop generation is constant and the compression time duration over the shock wave passage changes slightly along the sample depth, then the dislocation density additionally formed near the grain boundaries is proportional to the concentration of accumulated point defects and, as a consequence, to the pressure amplitude square (see the equation (7)).
To estimate the density of dislocation loops with the radius R based on the excess concentration of point defects obtained according to (9), the following expression can be used:
ρ = RNd = · . (10)
where: Nd is the concentration of dislocation loops that is πR2a2 times less than the concentration of point defects that make up the loop that is resulted from the expression (10).
The factor 4/π in the expression (10) considers the orientation difference of the plane where the dislocation is located to the plane of section made to calculate the dislocation density. If the typical size of dislocation loops is 1.5–2 nm and with due regard to the estimated concentration of point defects (9) from the total aluminum concentration, the values being consistent with the dislocation densities on the sample surface measured during the experiments [21–23] are obtained.
Figure 3 shows a comparison of the experimentally measured [21] distribution of dislocation density along the sample depth after a single laser shock peening with the evaluation approach results obtained by the calculated dependencies for the shock wave amplitude distribution in the sample based on the performed calculation studies on the propagation of shock waves in the samples made of AMg6 alloy [24].
The modelled possible generation mechanism of dislocation loops from the point defects that have left the grain surface is compliant with other experimental facts.
Conclusions
The proposed generation mechanism for dislocation structures under the impact effects of short laser pulses on the surface of polycrystalline alloys, based on the model of physicochemical nucleation of point defects at the excess concentration values near the grain boundaries, will allow to qualitatively explain a number of observed experimental dependences related to the changed specifications of dislocation structures due to the impact effect parameters and temperature conditions. The experiments show that with an increased amplitude of compressive pressure in the shock wave, the dimensions of the dislocation loops being generated near the grain boundaries are decreased. According to the developed model, with an increased amplitude of compressive pressure in the shock wave, the generation of excess point defects near the grain boundaries is enhanced. Moreover, in accordance with the kinetic nucleation theory of new phase nuclei, the dimensions of the dislocation loops being generated near the grain boundaries are reduced with the increased concentration.
In this paper, the key parameters determining the microstructural evolution and formation of residual stresses in the polycrystals, such as the values of the reduced energies of point defect generation and the diffusion activation energy, have not yet been determined. These studies are expected to be performed in the subsequent papers using the published experimental and calculated data.
An entire series of dependencies are scheduled to be considered and included in the developed calculation set to enable the assessments of changes in the mechanical and corrosion specifications of processed products with an increased multiplicity of exposure and the laser beam overlap level.
AUTHORS
Likhanskiy Vladimir Valentinovich, Doctor of Physical and Mathematical Sciences, Research Center “Kurchatov Institute”, lead researcher, Laboratory of Physics of Nonequilibrium Processes in Materials, Troitsk separate subdivision of the Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia; e-mail: likhanskiy2020@mail.ru.
Ulybyshev Konstantin Evgenievich, PhD in Physics and Mathematics, Research Center “Kurchatov Institute”, research engineer, Laboratory of Physics of Nonequilibrium Processes in Materials, Troitsk separate subdivision of the Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia; e-mail: Ulybyshev_KE@nrcki.ru.
Elkin Nikolay Nikolaevich, Doctor of Physical and Mathematical Sciences, Research Center “Kurchatov Institute”, Moscow, Russia; e-mail: elkin_nn@mail.ru.
Khorokhorin Maxim Vasilievich, Research Center “Kurchatov Institute”, research assistant, Laboratory of Physics of Nonequilibrium Processes in Materials, Troitsk separate subdivision of the Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia; e-mail: m.khorokhorin@lebedev.ru.
AUTHORS’ CONTRIBUTIONS
The authors’ contribution to the paper is distributed in accordance with the order of indication in the article title. The authors agree with the manuscript text, its results and contributions.
V. V. Likhanskiy 1, 2, K. E. Ulybyshev 1, 2, N. N. Elkin 1, M. V. Khorokhorin 1, 2
Research Center “Kurchatov Institute”, Moscow, Russia
Lebedev PhysicalInstitute of the Russian Academy of Sciences, Moscow, Russia
A review of publications devoted to the application of pulsed laser radiation in the field of technologies has been performed. The advantages of laser shock peening of the processed product surfaces have been considered. The developmental model of point defects and dislocations under the shock-wave load of polycrystalline materials has been proposed. The high-quality compliance between the calculated dislocation density and experimental results related to the laser shock peening of AMg6 samples has been obtained.
Key words: laser shock peening, point defects, dislocation density
Article received: March 06, 2025
Article accepted: April 17, 2025
Introduction
The researches related to the use of lasers to influence the materials being processed in various ways has been conducted for a long period of time [1–2]. An example of laser technologies that are widely applied today is laser-beam welding [3–4]. Another widely used technology is laser surface cleaning [5–6]. The surface of some products requires painting to increase the corrosion resistance of alloys and improve their aesthetic appearance. Thus, to ensure the required service life of aluminum alloys, it is necessary to periodically remove and reapply the surface paint coat. The conventional paint removal methods include mechanical grinding, chemical treatment, and sandblasting. However, they are not only time-consuming and inefficient, but also cause various damage to the aluminum alloy base, while affecting its service life. In addition, the chemical treatment process can lead to environmental pollution and pose a potential hazard to the human health. Laser cleaning has the advantages of being environmentally friendly, precise, and controllable, and is highly efficient compared to the conventional cleaning methods. This paper examines one of the promising areas of laser radiation application in the industry, namely the surface treatment of a finished product in order to improve the material properties.
The up-to-date high-tech industries (aircraft engineering, rocket engineering, nuclear power engineering) impose increased requirements on the performance specifications of the materials used. Among the main parameters that determine the product reliability, the specialists put emphasize on crack resistance, tensile strength, creep-rupture strength, and corrosion resistance. These parameters can be improved by thermal or mechanical action on the sample near-surface layer.
The thermal action is heating of the near-surface layer to the temperatures close to the melting point by plasma or laser radiation with the specially selected parameters. Since the thermal conductivity of metals is quite high, after heating there is a rapid cooling of the heated area (“hardening”), accompanied by the microstructural changes. This technology is the subject of research in the papers [7–10]. The publication [7] considers the processes in iron-carbon steels during laser hardening. In the paper [8], an analysis of the current application level and prospective development of laser hardening technology is performed. One of the advantages of this method is its possible application for brittle materials, such as cast iron. The paper [9] considers numerical modeling of the temperature distribution near the tool cutting edge during the laser hardening process. In the publication [10] the material hardening by a plasma flow generated by an electric arc discharge is considered. The main application results of the described methods, including the laser and plasma hardening are an increased surface layer hardness and, accordingly, an enhanced wear resistance.
As the disadvantages of the thermal laser hardening method, it should be noted that the plastic deformations occurred under the temperature stresses usually lead to the residual tensile stresses in the surface layer that has a negative impact on the product strength and crack resistance. As an addition to this method, designed to minimize the said disadvantage, or as an independent surface treatment technology, a shock peening procedure is often practiced that develops the residual compressive stresses in the surface layer. The basis of this method is generation of a pressure pulse on the product surface leading to a shock wave propagating deep into the material. The stresses developed by the shock wave lead to some changes in the material microstructure and formation of plastic deformations causing the residual stresses.
The plastic deformation resistance of metallic materials in the crystalline state is determined by four essentially different mechanisms, including the solid solution, dislocation, grain boundary, and dispersion peening. In the state-of-the-art structural materials, a combined interaction of several of these mechanisms is usually used, often all four. The mechanisms that determine the mechanical properties and plastic specifications of materials, depending on the crystalline structure type, the material microstructure, and alloying additives in the alloys, are described in detail in the classic monograph by Hirth and Lothe [11].
The resistance to dislocation movement through an ordered dislocation arrangement (substructure) differs from the resistance to movement through a chaotic dislocation distribution. If in the latter case it depends only on the dislocation density, then in the case of substructure formation, the resistance to dislocation movement already depends on the parameters of the latter. This phenomenon is called substructural strengthening. It has a significant contribution in the strength development of hardened steel, sometimes exceeding the contribution of solid-solution hardening.
Most of the materials used are polycrystals. The availability of grain boundaries in the polycrystal leads to its strengthening. At a certain stress value, the dislocations cannot pass through the grain boundary into another grain and begin to slow down. To overcome the boundary, they need additional stress. It has been experimentally proved that with a decrease in the average grain size, the deformation resistance of a polycrystalline material is increased.
Dispersion strengthening, or strengthening by the dispersed particles, consists of the small second-phase precipitates in the matrix of the base metal or alloy. These precipitates can have the same or other crystal lattice, and develop the stress fields. Inclusions of secondary phases lead to the additional obstacles to the dislocation movement and as a result can significantly increase the material strength.
An efficient way to strengthen the finished product is plastic deformation only of the device surface layer. The most common methods of surface plastic deformation are shotblasting and surface rolling.
The up-to-date laser peening technologies based on the effect of short radiation pulses on the material surface seem promising. Thus, in 1963, during the study of short laser pulses on the metal sample surfaces, the effects of shock wave generation were demonstrated for the first time [12]. The laser cold working is currently one of the most popular and widely used methods of surface hardening abroad. In order to complete the laser cold working process, it is necessary to use a laser station that meets the following requirements: average power supply from several hundred watts to several kilowatts, pulse energy of about 0.1–100 J and pulse duration within the range of 10–50 ns.
In many papers, for example, in [13–14], the significant changes in the material microstructure were determined due to the optimization of laser processing modes for the products made of polycrystalline alloys.
Firstly, in the case of short-term laser shock peening, the dislocation density in the surface areas of materials is increased. Secondly, the residual compressive stresses are generated in the surface areas of the processed samples. Thirdly, under the multiple impulse action on the polycrystalline material, the grain size has significant decreases. For example, in the paper [13], attention is drawn to the decreased grain size with an increased multiplicity of laser shock processing in the AZ31B Mg alloy (Fig. 1).
The data provided show a more than fivefold reduction in the average grain size with the fourfold laser exposure.
As another example demonstrating the impact of grain boundaries in the polycrystalline alloys on changes in the mechanical and corrosion metal specifications, it is possible to indicate the dislocation structures observed in the paper [15] in copper and nickel after shock peening. In the publication [15], the dislocation cells were shown being concentrated to a greater extent near the grain boundaries of metals (Fig. 2).
The interesting results were obtained in the publication [16] in relation to the numerical modeling of shock wave propagation in a polycrystalline copper sample using the molecular dynamics (MD) method. The calculation results demonstrated an increased concentration of point defects at the grain boundaries. The results of the paper [16] show a noticeable increase in the microstructural defects in the grains after the shock wave front has passed.
In a number of publications, for example, in [17], the calculations using the MD method have shown that in the area of intergrain boundaries of polycrystalline materials, the migration energies of point defects and their formation energies can be significantly lower than in the bulk of grains. These effects should have an impact on the nucleation processes of interstitial atoms with generation of the dislocation loops and vacancy pores with a sufficiently fast impulse action on materials with the regions supersaturated with defects. The increased dislocation density on the material surface, at the grain boundaries and on other crystal imperfections during the laser shock peening process is a confirmed experimental fact. This provision is discussed in many papers, for example, in the articles [14, 15].
For wide industrial application of the laser shock peening technology, it is desirable to ensure its cost-effectiveness, i. e. to use laser systems that do not require any expensive components and generation of laser pulses with the unique specifications. The laser systems based on the neodymium pulse lasers have proven themselves to be quite good [18]. The main advantages of these systems are portability, high efficiency and relatively low cost. The selection of laser radiation parameters to obtain the required characteristics of the processed materials is a multifactorial task. Let us briefly indicate the main factors.
Firstly, the laser radiation exposure results depend on the composition and properties of the material being processed. The important material specifications include its crystal structure, grain parameters and texture of polycrystals, concentration and volume fraction of secondary phase inclusions, their composition, and dislocation density.
Secondly, any changes in the material specifications are largely determined by the temperature and mechanical fields in the samples. The laser exposure level is determined by the radiation parameters, such as wavelength, pulse duration, laser spot area and intensity.
Thirdly, the processing results depend on the geometric parameters of the sample and the material surrounding the sample, as well as on the laser exposure process mode.
As a rule, almost all of the above factors are interconnected and determined by the nonlinear multiparameter dependencies on the temperature, pressure and material properties. The most appropriate and optimal approach is to develop the separate calculation and theoretical stations for specific materials and for the conditions and sample laser processing process modes required by the industry.
This paper is devoted to the development of a method for predicting changes in the specifications of sample surface areas as a result of laser shock peening on the polycrystalline materials by the example of aluminum alloy AMg6. For this alloy, there is a large amount of experimental data that allows to estimate the physical-kinetic model parameters for describing the non-stationary behavior of defects in the crystal structure.
Basic provisions of the model being developed and evaluation formulas
To obtain the dependencies of the evolution of microstructural changes and residual stresses distributions in the polycrystalline materials under the shock peening of short laser pulses, it is proposed to consider a physical model that accounts for the kinetics of transient processes, time parameters of the shock wave, temperature and initial microstructure of the material.
Let us consider the issue of changing the atom energy specifications in a crystal lattice with a rapid increase in the compressive stresses. During the adiabatic lattice compression under the shock wave action, the atoms, in accordance with the adiabatic invariant preservation, increase its oscillation frequency that corresponds to a local temperature increase in the compressed layer. In the one-dimensional approximation, one atom during compression has an energy of about a3P22E, where a is the crystal lattice parameter, P is the pressure amplitude in the material during the shock wave passage, E is the Young’s modulus. The increased atom energy during the crystal compression process is equivalent to an increase in the local temperature by the value of about ΔT ~ a3P22kE, where k is the Boltzmann constant. When making the estimates, it is necessary to use the published temperature dependences of the self-diffusion coefficients Ds(T) of aluminum atoms and equilibrium dependences of the vacancy concentration cv(T) in aluminum alloys on the temperature [19, 20]:
DS(T) = 1.9 · 10−5 exp − ; (1)
Cv(T) = 7.5 exp − . (2)
Hereinafter the diffusion coefficients are given in [m2/s]. The vacancy concentration dependence in the expression (2) is registered in the dimensionless units relative to n0 that is the initial concentration of aluminum atoms in the alloy, Т – the temperature in Kelvin degrees. It is necessary to consider the generation impact of point defects with due regard to their diffusion and recombination. According to the dependences (1, 2) misesteem of the grain boundary contribution allows to estimate the diffusion coefficient of vacancies Dυ(T) in the bulk of aluminum alloy grains:
Dυ(T) = 2.5 · 10−6 exp − . (3)
To determine the changes in concentrations of point defects over time, we will use a system of diffusion equations describing the dynamics of point defects:
(4)
where: Fv(i)(T) – a bulk source of point defects (vacancies and interstitials, respectively); δFv(i) – an additional bulk source of point defects arising under the action of a shock wave passing through the sample; Rvi – the mutual recombination coefficient of vacancies and interstitials; Δ – Laplacian; Sv(i) – coefficient of defect capture by the wastewater.
If any experimental and calculated results are used, according to which the thermal diffusion coefficients of interstitial atoms significantly exceed the diffusion coefficients of vacancies (Di >> Dv), then for the thermally equilibrium conditions the temperature dependence of the bulk source of point defects can be estimated according to the following formula:
Fv(T) = 2 π a Ds n20 cv. (5)
With due regard to the experimental dependencies (1–3), the bulk source of defects (5) for the aluminum alloy AMg 6 within the framework of the Frenkel model can be represented as follows:
Fv(T) = 1.31 · 1045 exp − , m−3 s−1 (6)
Inclusion of the increased atom energy by the value of a3P22E as a result of the shock wave action on the crystal with a pressure amplitude of up to 5 GPa and a laser pulse duration of less than 10−7 s at a sample temperature of less than 350 K provides any additional concentrations values of point defects that are insufficient to generate the dislocation loops with a dislocation density relevant to the experimental data [21–23]. This is due to the high value of the generation energy of point defects and the low coefficient of their diffusion in the crystal volume.
In the area of grain boundaries and near the dislocation loop cores, the binding energy between the crystal lattice atoms is noticeably lower than in a single crystal. As a consequence, in these areas of a polycrystal, the generation energy of point defects, as well as the diffusion activation energy shall be reduced. An estimated analysis of the processes leading to any changes in the dislocation density in the field of grain boundaries during the pulsed, short-term material compression can be based on the following phenomena. We will assume that the generation processes of extended defects (dislocation loops, pores, secondary phase inclusions) at the grain boundaries under the influence of a shock wave can be described as follows.
During the crystal lattice compression, the excess point defects are generated at the grain boundary and near the dislocation cores. The rate of point defect production and its concentration growth depend on the magnitude and time of changes in the compressive pressure. If the times are shorter than the time of point defect diffusion in the grain and shorter than the time of flow to the intergranular dislocations, these processes can be neglected and the value of excess concentrations of point defects can be estimated. In this approximation, the dependences of increased concentration of point defects near the grain boundaries on the shock peening parameters are quite simply estimated if the generation energy of a pair of Frenkel defects (a vacancy and an interstitial atom) and the growth value of the vibrational energy of atoms located in the lattice points during the adiabatic crystal lattice compression are well-known. These values shall be determined at the verification stage of the developed model parameters based on the available experimental data that is supposed to be done during the subsequent studies.
In the paper [17], the vacancy migration in Al was subject to computer modeling with due regard to the grain boundaries and dislocations. The migration energy values near the grain boundaries were obtained to be significantly lower; when the vacancy moved to the grain boundary or to the dislocation core, the decrease in migration energy was more than 5 times. The similar approach shall be applied to analyze the role of grain boundaries on the microstructural changes under the short-term impact action. Since both the migration of point defects and their development are activation processes, then to make an evaluation the generation energy of a Frenkel pair near the grain boundary and the dislocation core shall be reduced by about 5 times. Then an additional generation source XGb of Frenkel pairs in the grain boundary area, related to one crystal atom, with due regard to the compressive impulse of the shock wave, can be estimated as follows:
XGb = 2.1 · 1016 exp − · β · a3P22k · E · WGbT, s−1 (7)
where: k – the Boltzmann constant, Т – temperature in Kelvin degrees, a3P22E – changes in the elastic energy per atom during the crystal lattice compression, β – dimensionless parameter to be determined on the basis of experiments, WGb = 4762 K – generation energy of point defects at the grain boundary in Kelvin degrees.
In the general case, the time dependence for the vacancy concentration exceeding the equilibrium value at the grain boundary is indicated in the form of an equation:
· n0 − nv, i, Gb · XGb(t) − RGb · nv, i, Gb, (8)
where: n0 is the initial concentration of aluminum atoms in the crystal, nv, i, Gb is the concentration of nonequilibrium (excess) point defects in the intergranular region. According to the published data, for aluminum it is n0 ≈ 6 · 1028 m−3 . The coefficient RGb(t) considers the annihilation processes of vacancies and interstitial atoms at the grain boundaries. This coefficient may depend on many parameters, including temperature, concentrations of point defects, diffusion processes, anisotropy of mechanical stresses, concentrations of alloying elements, etc. Determination of the dependencies that define the annihilation rate of point defects in the grain boundary region is expected to be performed in the subsequent studies.
The preliminary estimates of the diffusion transfer rate of point defects in an aluminum alloy based on information determined in the papers [19, 20] show that during the times of 10−6 sec that are significantly longer than the shock wave pulse action times, the diffusion length from the grain boundary region into the grain at the temperatures below 350 K is less than the crystal lattice parameter. Therefore, when estimating the accumulation of point defects in the intergranular region, it is sufficient to take into account only the first term in the equation (8) at the shock wave pulse propagation times. In this approximation, the integration (8) yields an estimate of the additional concentration of accumulated point defects in the grain boundary region:
nv, i, Gb(t) = n0 · 1 − exp− XGb(τ) dτ. (9)
Based on (9) and with due regard to (8), an estimate is obtained showing a significant increase in the local concentration of point defects. The accelerated intergranular diffusion over relatively short periods of time can lead to the generation of dislocation loops near the grain boundaries and, thus, reduce the excess nonequilibrium concentration of point defects. If it is assumed that the critical radius of stable dislocation loop generation is constant and the compression time duration over the shock wave passage changes slightly along the sample depth, then the dislocation density additionally formed near the grain boundaries is proportional to the concentration of accumulated point defects and, as a consequence, to the pressure amplitude square (see the equation (7)).
To estimate the density of dislocation loops with the radius R based on the excess concentration of point defects obtained according to (9), the following expression can be used:
ρ = RNd = · . (10)
where: Nd is the concentration of dislocation loops that is πR2a2 times less than the concentration of point defects that make up the loop that is resulted from the expression (10).
The factor 4/π in the expression (10) considers the orientation difference of the plane where the dislocation is located to the plane of section made to calculate the dislocation density. If the typical size of dislocation loops is 1.5–2 nm and with due regard to the estimated concentration of point defects (9) from the total aluminum concentration, the values being consistent with the dislocation densities on the sample surface measured during the experiments [21–23] are obtained.
Figure 3 shows a comparison of the experimentally measured [21] distribution of dislocation density along the sample depth after a single laser shock peening with the evaluation approach results obtained by the calculated dependencies for the shock wave amplitude distribution in the sample based on the performed calculation studies on the propagation of shock waves in the samples made of AMg6 alloy [24].
The modelled possible generation mechanism of dislocation loops from the point defects that have left the grain surface is compliant with other experimental facts.
Conclusions
The proposed generation mechanism for dislocation structures under the impact effects of short laser pulses on the surface of polycrystalline alloys, based on the model of physicochemical nucleation of point defects at the excess concentration values near the grain boundaries, will allow to qualitatively explain a number of observed experimental dependences related to the changed specifications of dislocation structures due to the impact effect parameters and temperature conditions. The experiments show that with an increased amplitude of compressive pressure in the shock wave, the dimensions of the dislocation loops being generated near the grain boundaries are decreased. According to the developed model, with an increased amplitude of compressive pressure in the shock wave, the generation of excess point defects near the grain boundaries is enhanced. Moreover, in accordance with the kinetic nucleation theory of new phase nuclei, the dimensions of the dislocation loops being generated near the grain boundaries are reduced with the increased concentration.
In this paper, the key parameters determining the microstructural evolution and formation of residual stresses in the polycrystals, such as the values of the reduced energies of point defect generation and the diffusion activation energy, have not yet been determined. These studies are expected to be performed in the subsequent papers using the published experimental and calculated data.
An entire series of dependencies are scheduled to be considered and included in the developed calculation set to enable the assessments of changes in the mechanical and corrosion specifications of processed products with an increased multiplicity of exposure and the laser beam overlap level.
AUTHORS
Likhanskiy Vladimir Valentinovich, Doctor of Physical and Mathematical Sciences, Research Center “Kurchatov Institute”, lead researcher, Laboratory of Physics of Nonequilibrium Processes in Materials, Troitsk separate subdivision of the Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia; e-mail: likhanskiy2020@mail.ru.
Ulybyshev Konstantin Evgenievich, PhD in Physics and Mathematics, Research Center “Kurchatov Institute”, research engineer, Laboratory of Physics of Nonequilibrium Processes in Materials, Troitsk separate subdivision of the Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia; e-mail: Ulybyshev_KE@nrcki.ru.
Elkin Nikolay Nikolaevich, Doctor of Physical and Mathematical Sciences, Research Center “Kurchatov Institute”, Moscow, Russia; e-mail: elkin_nn@mail.ru.
Khorokhorin Maxim Vasilievich, Research Center “Kurchatov Institute”, research assistant, Laboratory of Physics of Nonequilibrium Processes in Materials, Troitsk separate subdivision of the Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia; e-mail: m.khorokhorin@lebedev.ru.
AUTHORS’ CONTRIBUTIONS
The authors’ contribution to the paper is distributed in accordance with the order of indication in the article title. The authors agree with the manuscript text, its results and contributions.
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