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Acoustic anisotropy and localization of plastic deformation in aluminum alloys
Materials Today: Proceedings xxx (xxxx) xxx
Contents lists available at ScienceDirect
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Acoustic anisotropy and localization of plastic deformation in aluminum alloys Dmitry Tretyakov a,⇑, Alexander Belyaev a,b, Nikita Shaposhnikov a a b
Peter the Great St. Petersburg Polytechnic University, 29 Politekhnicheskaya St., St. Petersburg 195251, Russia Institute for Problems in Mechanical Engineering of the RAS, 61 V.O. Bolshoy Ave., St. Petersburg 199178, Russia
a r t i c l e
i n f o
Article history: Received 18 December 2019 Accepted 30 December 2019 Available online xxxx Keywords: Acoustic anisotropy Non-destructive control Autowaves of plastic flow Aluminum-manganese alloy Plastic strain localization
a b s t r a c t The process of uniaxial inelastic tension of 20 mm thickness corset specimens made of aluminummanganese alloy was investigated by ultrasonic non-destructive testing method based on measuring of acoustic anisotropy. The value of acoustic anisotropy defines as the phase shift between velocities of propagation of shear waves with orthogonal polarization. Acoustic measurements were carried out at different stages of stepwise loading of specimens with ultrasonic device used for non-destructive testing of stress-strain state of structures in nuclear and oil and gas industries. Nonlinear dependence of acoustic anisotropy on total axial inelastic deformations of specimens was established. It was found that acoustic anisotropy is an indicator of autowaves of plastic flow localized in surface layer of metal. The obtained results can be used for non-destructive ultrasonic testing of plastic deformations in thick structures made of aluminum alloys. Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry.
1. Introduction Acoustic anisotropy is a characteristic of difference in properties of continuous medium, which uses velocities of propagation of ultrasonic waves. It is based on measuring of phase shift between orthogonally polarized transverse waves [1]. It can be caused by different factors such as change in elastic properties of medium due to mechanical stresses, existence of defects, presence of anisotropic texture of structure, and others. Acoustic anisotropy is used in estimating of stress-strain state of structures in acoustoelasticity method [1]. It is based on the acoustoelastic effect, which establishes a linear relationship between velocities of shear wave propagation and stresses in continuous medium [1,2]. The theoretical foundations of acoustoelasticity method were laid by Bio [3] and Truesdell [4] and developed by Thurston and Bragger [5], Toupin and Bernstein [6] and others. The theory of acoustoplasticity [7] was developed to study case of plastic deformations. It was based on nonlinear elastic Murnaghan model. Linear relationship between acoustic anisotropy and value of plastic deformations (1) was obtained in [7]:
a ¼ a0 þ a1 ðeP1 eP2 Þ þ C A ðr1 r2 Þ
ð1Þ
Where e e are principal plastic deformations; r1, r2 are principal stresses; a1, CA are material constants; a0 is intrinsic acoustic anisotropy caused by influence of anisotropic texture and defects in material. The verification of Equation (1) was carried out for case of small plastic deformations on specially prepared specimens with initially isotropic properties [8]. Recent experimental works indicate a much more difficult dependence for acoustic anisotropy than presented in Equation (1). The influences of corrosion [9] and hydrogen-induced cracking [10] on acoustic anisotropy were detected. However, the influence of cracks on acoustic anisotropy is not taken into account in Equation (1). Also, the surface effect of acoustic anisotropy in rolled steel [11,12] and nonlinear behavior of acoustic anisotropy in the framework of elasto-plastic model [13] were discovered. The aim of this work is to study the behavior of acoustic anisotropy in rolled aluminum specimens. It is necessary to investigate the influence of plastic flow on value of acoustic anisotropy in initial anisotropic metal. P 1,
P 2
2. Methods ⇑ Corresponding author at: Peter the Great St. Petersburg Polytechnic University, 29 Politekhnicheskaya St., St. Petersburg 195251, Russia. E-mail address: [email protected] (D. Tretyakov).
Aluminum specimens were made from corrosion-resistant AMts alloy (in Fig. 1). Specimens were cut across the sheet rolling
https://doi.org/10.1016/j.matpr.2019.12.387 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry.
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
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D. Tretyakov et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 1. The arrangement of points of acoustic anisotropy measuring in destroyed specimen.
direction. They were subjected to mechanical tests for uniaxial rigid stepwise tension until the formation of plastic neck and destruction. Mechanical tests were carried out on INSTRON-8806 hydraulic tensile testing machine. Ultrasonic measurements of acoustic anisotropy using IN5101A device (in Fig. 2) were carried out at all stages of step loading. The device is used to estimate the stress-strain state of structures in nuclear [14] and oil and gas industries [15]. It includes a contact ultrasonic sensor, which generates and receives pulses of longitudinal and transverse waves with a frequency of 5 MHz using piezoelectric transducers (in Fig. 2). It allows to measure time delay between multiple reflected pulses with an accuracy of 109 s. The calculation of acoustic anisotropy was carried out according to Equation (2):
a ¼ 2ðt 2 t 1 Þ=ðt 1 þ t 2 Þ
ð2Þ
where t1 and t2 are time delays between pulses of orthogonally polarized transverse waves. Acoustic anisotropy in the main investigated specimen (in Fig. 1) was measured at points located along its working part at equal distance from each other. The distance between points was equal to 12 mm in the specimen before tests.
3. Results and discussion The distribution of initial acoustic anisotropy a0 in one of aluminum specimens before mechanical tests is presented in Fig. 3. The difference in the values of acoustic anisotropy a0 in the range of 0.562 0.317% was observed. Acoustic anisotropy measurements were taken with opposite sign for convenience of data analysis. The stress-strain curve of main investigated specimen (in Fig. 1) is presented in Fig. 4. Logarithmic deformations in Fig. 4 were plotted along the abscissa axis. Acoustic anisotropy was measured at each of 19 loading stages at n = 10 points. The total axial deformation elog of the specimen was equal to 27.79%. The dependences of acoustic anisotropy a on inelastic deformations elog at points located at different distances from zone of specimen destruction (in Fig. 1) are shown in Fig. 5. The acoustic anisotropy distributions a measured at points 1–10 for different values of inelastic deformations are presented in Figs. 6 and 7. The intermediate distributions at deformation stages 2, 3, 6 and 7 of the specimen are shown in Fig. 6. The distributions of acoustic anisotropy a before loading, at last stage of loading and after destruction of the specimen are shown in Fig. 7. The obtained results allow to investigate three different phenomena: influence of initial acoustic anisotropy on results of
Fig. 2. Ultrasonic analyzer of acoustic anisotropy IN-5101A.
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
D. Tretyakov et al. / Materials Today: Proceedings xxx (xxxx) xxx
3
Fig. 6. Intermediate acoustic anisotropy distributions -a, %after 2-3 and 6-7 stages of specimen deformation.
Fig. 3. The distribution of initial acoustic anisotropy -a0, % in specimen before mechanical tests.
Fig. 7. Distributions of acoustic anisotropy at points 1–10 before testing, at the last stage of loading and after destruction of the specimen.
non-destructive testing (in Fig. 3), behavior of acoustic anisotropy in a wide range of inelastic deformations (in Fig. 5) and dynamics of nonlinear distributions of acoustic anisotropy during the process of plastic flow in metals (in Figs. 6 and 7). Fig. 4. The stress – strain curve of main investigated specimen.
3.1. Influence of initial acoustic anisotropy on results of nondestructive testing Uneven distributions of initial acoustic anisotropy a0 were observed in all aluminum specimens. The maximum difference in the values of a0 measured before mechanical tests was equal to 0.245% (in Fig. 3). At the same time, total contribution of elastic stresses to the value of acoustic anisotropy a measured in main specimen (in Fig. 1) was equal to 0.539%. It suggests that influence of anisotropic texture a0 in rolled aluminum specimens is comparable with contribution of elastic deformations to acoustic anisotropy a. At the same time, initial acoustic anisotropy a0 is considered as a constant in the acoustoelasticity method [14,15]. The obtained distributions (in Fig. 3) show that it can lead to significant errors in results of estimating of mechanical stresses in metals. 3.2. Non-monotonic dependence of acoustic anisotropy on value of plastic deformations Fig. 5. The dependence of -a, % on elog, %for different measuring points in the specimen.
The monotonic dependences of acoustic anisotropy on inelastic deformations for steel specimens were obtained in [16,17]. It
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
4
D. Tretyakov et al. / Materials Today: Proceedings xxx (xxxx) xxx
allowed to approximate experimental curves with high-order polynomials [17]. Estimates of plastic deformations value using measurements of acoustic anisotropy were obtained for different steels with an accuracy of 5%. Simplicity and possibility of developing an industrial method for estimating of inelastic deformations in steel structures are the advantages of this approach. However, the results in Fig. 5 suggest that this approach cannot be applied to aluminum rolled specimens. The nonmonotonic behavior of acoustic anisotropy a was observed at points near the destruction zone (in Fig. 5). It began to weaken only at distance of 150–180 mm from the zone of plastic neck formation. In addition, one more zone of nonmonotonic dependence was observed for all points for deformation elog 2.8% (in Fig. 5). It correlates with beginning of nonlinear behavior of the stress – strain curve (in Fig. 4). Thus, accurate estimation of inelastic deformations value in these zones is impossible. The reason for difference in results of [16,17] and distributions in Fig. 5 may be due to difference in elastic modulus of materials. This assumption requires additional experimental verification.
4. Conclusions The experimental investigations of acoustic anisotropy shown that influence of anisotropic texture in aluminum rolled specimens is comparable to influence of elastic stresses. It can lead to significant errors in results of estimating of stress-strain state by the acoustoelasticity method. The observed nonmonotonic dependence on inelastic axial deformations does not allow to estimate the value of plastic deformations using acoustic anisotropy in aluminum. Its nonmonotonic behavior was observed at all points in the range of 2-3% plastic deformations as well as in points at the distance of less than 150–180 mm from zone of specimen destruction. The discovered relationship between acoustic anisotropy and autowaves of plastic flow is the main result of investigation. It was shown that acoustic anisotropy is an indicator of autowaves of plastic deformation in metals. The propagation of autowaves in metal caused formation of the surface effect of acoustic anisotropy observed in a thin layer of 250–300 mm in metal. The results of investigation can be used in diagnosis of plastic deformations and damage in metals using acoustic anisotropy.
3.3. Acoustic anisotropy and autowaves of plastic flow in metals Declaration of Competing Interest L.B. Zuev investigated the dynamics of localized plastic deformations at macro level in [18]. He proposed an approach that considers plastic flow in metals as process of propagation of solitary deformation waves. The existence of three stages of deformation localization was established [18]. At the first stage, a secluded front of localized deformation is propagated at the yield site. At the second stage, a deformation wave propagates in the case of linear hardening. At the third stage of parabolic hardening, a stationary system of localized flow zones is formed. It does not move along specimen and has a macroscopic character [18]. Unlike elastic waves, process of autowaves propagation leads to change in structure and properties of deformable medium. It was confirmed during the experimental study of aluminum specimens using speckle interferometry method [18,19]. Investigations of deformation localization process are not limited to the approach [18,19]. The significant contributions to study of deformation process at meso, micro and macro structural levels were made in fundamental works [20–25]. Dependence between acoustic anisotropy and concentration of dislocations during inelastic deformation of metals was obtained in [19]. It allows to relate acoustic anisotropy with autowaves of plastic flow in metals. It could be seen that the acoustic anisotropy distributions changed similarly to behavior of plastic deformation autowaves during monotonic tension of metals (in Figs. 6 and 7) [18]. The formation of systems of waves from a single solitary wave at stages 2, 3 and 6 and its breakdown at deformation value elog 9.53% at stage 7 is shown in Fig. 6. The qualitative nature of waves at the last stage of loading and after fracture of the specimen was preserved (in Fig. 7). The changes in location of system of stabilized waves due to movement of the macrowave from destruction zone (in Fig. 7). Thus, it can be supposed that autowaves of plastic flow localized in surface layer of metal have a significant influence on value of acoustic anisotropy. In this case, acoustic anisotropy becomes an indicator of autowaves of plastic deformation [18]. They also cause the surface effect of acoustic anisotropy. The level of acoustic anisotropy a before loading was in the range of 0.455 0.317%, but after destruction it was in the range of 1.667 1.037% (in Fig. 7). Previous investigations shown that acoustic anisotropy returns to its level before mechanical tests after removal of 250– 300 mm of surface layer of metal [10].
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The research was financially supported by the Russian Science Foundation, grant 18-19-00413. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
R.W. Benson, V.J. Raelson, Prod. Eng. 30 (1953) 56–59. D.S. Hughes, J.L. Kelly, Phys. Rev. 92 (1953) 1145–1149. M.A. Biot, J. Appl. Phys. 11 (1940) 522–530. C. Truesdell, Arch. Ration. Mech. Anal. 8 (1961) 263–296. R.A. Toupin, B. Bernstein, J. Acoust. Soc. Am. 33 (1961) 216–225. R.N. Thurston, K. Brugger, Phys. Rev. 133 (1964) A1604–A1610. M. Hirao, Y.H. Pao, J. Acoust. Soc. Am. 77 (1985) 1659–1664. T.T. Wu, M. Hirao, Y.H. Pao, J. Appl. Mech. Trans. ASME 58 (1991) 18–23. D.A. Tretyakov, A.K. Belyaev, A.R. Galyautdinova, V.A. Polyanskiy, D.A. Strekalovskaya, E3S Web Conf. 121 (2019), 01017-1-01017–4. D.A. Tretyakov, A.K. Belyaev, V.A. Polyanskiy, A.V. Stepanov, Y.A. Yakovlev, E3S Web Conf. 121 (2019), 01016-1-01016–5. A.S. Semenov, St. Petersbg. Polytech. Univ. J. Phys. Math. 3 (2017) 271–283. A.S. Semenov, V.A. Polyanskiy, L.V. Shtukin, D.A. Tretyakov, J. Appl. Mech. Tech. Phys. 59 (2018) 1136–1144. A.K. Belyaev, A.M. Lobachev, V.S. Modestov, A.V. Pivkov, V.A. Polyanskiy, A.S. Semenov, D.A. Tretyakov, L.V. Shtukin, Mech. Solids 51 (2016) 606–611. A.V. Kamyshev, S.V. Makarov, L.A. Pasmanik, V.A. Smirnov, V.S. Modestov, A.V. Pivkov, Russ. J. Nondestruct. Test. 53 (2017) 1–8. N.Y. Nikitina, A.V. Kamyshev, V.A. Smirnov, A.V. Borshchevskii, Y.M. Sharygin, Russ. J. Nondestruct. Test. 42 (2006) 185–189. K.V. Kurashkin, Acoust. Phys. 65 (2019) 316–321. A.V. Gonchar, V.V. Mishakin, V.A. Klyushnikov, K.V. Kurashkin, Tech. Phys. 62 (2017) 537–541. L.B. Zuev, Ann. Der Phys. 16 (2007) 286–310. L.B. Zuev, B.S. Semukhin, K.I. Bushmeleva, Tech. Phys. 45 (2000) 50–54. V.A. Popovich, E.V. Borisov, A.A. Popovich, V.S. Sufiiarov, D.V. Masaylo, L. Alzina, Mater. Des. 114 (2017) 441–449. M.A. Matveev, N.G. Kolbasnikov, A.A. Kononov, Met. Sci. Heat Treat. 59 (2017) 197–202. Y.A. Bezobrazov, N.G. Kolbasnikov, A.A. Naumov, Steel Transl. 44 (2014) 71–79. M.A. Skotnikova, G.V. Ivanova, A.A. Popov, O.V. Paitova, Lect. Notes Mech. Eng. (2018) 143–150. M.A. Skotnikova, N.A. Krylov, J.I. Mescheryakov, M.M. Radkevich, E.K. Ivanov, E. V. Mironova, AIP Conf. Proc. 706 (2004) 609–612. R.A. Parshikov, A.I. Rudskoy, A.M. Zolotov, O.V. Tolochko, Rev. Adv. Mater. Sci. 45 (2016) 67–75.
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Acoustic anisotropy and localization of plastic deformation in aluminum alloys Dmitry Tretyakov a,⇑, Alexander Belyaev a,b, Nikita Shaposhnikov a a b
Peter the Great St. Petersburg Polytechnic University, 29 Politekhnicheskaya St., St. Petersburg 195251, Russia Institute for Problems in Mechanical Engineering of the RAS, 61 V.O. Bolshoy Ave., St. Petersburg 199178, Russia
a r t i c l e
i n f o
Article history: Received 18 December 2019 Accepted 30 December 2019 Available online xxxx Keywords: Acoustic anisotropy Non-destructive control Autowaves of plastic flow Aluminum-manganese alloy Plastic strain localization
a b s t r a c t The process of uniaxial inelastic tension of 20 mm thickness corset specimens made of aluminummanganese alloy was investigated by ultrasonic non-destructive testing method based on measuring of acoustic anisotropy. The value of acoustic anisotropy defines as the phase shift between velocities of propagation of shear waves with orthogonal polarization. Acoustic measurements were carried out at different stages of stepwise loading of specimens with ultrasonic device used for non-destructive testing of stress-strain state of structures in nuclear and oil and gas industries. Nonlinear dependence of acoustic anisotropy on total axial inelastic deformations of specimens was established. It was found that acoustic anisotropy is an indicator of autowaves of plastic flow localized in surface layer of metal. The obtained results can be used for non-destructive ultrasonic testing of plastic deformations in thick structures made of aluminum alloys. Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry.
1. Introduction Acoustic anisotropy is a characteristic of difference in properties of continuous medium, which uses velocities of propagation of ultrasonic waves. It is based on measuring of phase shift between orthogonally polarized transverse waves [1]. It can be caused by different factors such as change in elastic properties of medium due to mechanical stresses, existence of defects, presence of anisotropic texture of structure, and others. Acoustic anisotropy is used in estimating of stress-strain state of structures in acoustoelasticity method [1]. It is based on the acoustoelastic effect, which establishes a linear relationship between velocities of shear wave propagation and stresses in continuous medium [1,2]. The theoretical foundations of acoustoelasticity method were laid by Bio [3] and Truesdell [4] and developed by Thurston and Bragger [5], Toupin and Bernstein [6] and others. The theory of acoustoplasticity [7] was developed to study case of plastic deformations. It was based on nonlinear elastic Murnaghan model. Linear relationship between acoustic anisotropy and value of plastic deformations (1) was obtained in [7]:
a ¼ a0 þ a1 ðeP1 eP2 Þ þ C A ðr1 r2 Þ
ð1Þ
Where e e are principal plastic deformations; r1, r2 are principal stresses; a1, CA are material constants; a0 is intrinsic acoustic anisotropy caused by influence of anisotropic texture and defects in material. The verification of Equation (1) was carried out for case of small plastic deformations on specially prepared specimens with initially isotropic properties [8]. Recent experimental works indicate a much more difficult dependence for acoustic anisotropy than presented in Equation (1). The influences of corrosion [9] and hydrogen-induced cracking [10] on acoustic anisotropy were detected. However, the influence of cracks on acoustic anisotropy is not taken into account in Equation (1). Also, the surface effect of acoustic anisotropy in rolled steel [11,12] and nonlinear behavior of acoustic anisotropy in the framework of elasto-plastic model [13] were discovered. The aim of this work is to study the behavior of acoustic anisotropy in rolled aluminum specimens. It is necessary to investigate the influence of plastic flow on value of acoustic anisotropy in initial anisotropic metal. P 1,
P 2
2. Methods ⇑ Corresponding author at: Peter the Great St. Petersburg Polytechnic University, 29 Politekhnicheskaya St., St. Petersburg 195251, Russia. E-mail address: [email protected] (D. Tretyakov).
Aluminum specimens were made from corrosion-resistant AMts alloy (in Fig. 1). Specimens were cut across the sheet rolling
https://doi.org/10.1016/j.matpr.2019.12.387 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the scientific committee of the Materials Science: Composites, Alloys and Materials Chemistry.
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
2
D. Tretyakov et al. / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 1. The arrangement of points of acoustic anisotropy measuring in destroyed specimen.
direction. They were subjected to mechanical tests for uniaxial rigid stepwise tension until the formation of plastic neck and destruction. Mechanical tests were carried out on INSTRON-8806 hydraulic tensile testing machine. Ultrasonic measurements of acoustic anisotropy using IN5101A device (in Fig. 2) were carried out at all stages of step loading. The device is used to estimate the stress-strain state of structures in nuclear [14] and oil and gas industries [15]. It includes a contact ultrasonic sensor, which generates and receives pulses of longitudinal and transverse waves with a frequency of 5 MHz using piezoelectric transducers (in Fig. 2). It allows to measure time delay between multiple reflected pulses with an accuracy of 109 s. The calculation of acoustic anisotropy was carried out according to Equation (2):
a ¼ 2ðt 2 t 1 Þ=ðt 1 þ t 2 Þ
ð2Þ
where t1 and t2 are time delays between pulses of orthogonally polarized transverse waves. Acoustic anisotropy in the main investigated specimen (in Fig. 1) was measured at points located along its working part at equal distance from each other. The distance between points was equal to 12 mm in the specimen before tests.
3. Results and discussion The distribution of initial acoustic anisotropy a0 in one of aluminum specimens before mechanical tests is presented in Fig. 3. The difference in the values of acoustic anisotropy a0 in the range of 0.562 0.317% was observed. Acoustic anisotropy measurements were taken with opposite sign for convenience of data analysis. The stress-strain curve of main investigated specimen (in Fig. 1) is presented in Fig. 4. Logarithmic deformations in Fig. 4 were plotted along the abscissa axis. Acoustic anisotropy was measured at each of 19 loading stages at n = 10 points. The total axial deformation elog of the specimen was equal to 27.79%. The dependences of acoustic anisotropy a on inelastic deformations elog at points located at different distances from zone of specimen destruction (in Fig. 1) are shown in Fig. 5. The acoustic anisotropy distributions a measured at points 1–10 for different values of inelastic deformations are presented in Figs. 6 and 7. The intermediate distributions at deformation stages 2, 3, 6 and 7 of the specimen are shown in Fig. 6. The distributions of acoustic anisotropy a before loading, at last stage of loading and after destruction of the specimen are shown in Fig. 7. The obtained results allow to investigate three different phenomena: influence of initial acoustic anisotropy on results of
Fig. 2. Ultrasonic analyzer of acoustic anisotropy IN-5101A.
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
D. Tretyakov et al. / Materials Today: Proceedings xxx (xxxx) xxx
3
Fig. 6. Intermediate acoustic anisotropy distributions -a, %after 2-3 and 6-7 stages of specimen deformation.
Fig. 3. The distribution of initial acoustic anisotropy -a0, % in specimen before mechanical tests.
Fig. 7. Distributions of acoustic anisotropy at points 1–10 before testing, at the last stage of loading and after destruction of the specimen.
non-destructive testing (in Fig. 3), behavior of acoustic anisotropy in a wide range of inelastic deformations (in Fig. 5) and dynamics of nonlinear distributions of acoustic anisotropy during the process of plastic flow in metals (in Figs. 6 and 7). Fig. 4. The stress – strain curve of main investigated specimen.
3.1. Influence of initial acoustic anisotropy on results of nondestructive testing Uneven distributions of initial acoustic anisotropy a0 were observed in all aluminum specimens. The maximum difference in the values of a0 measured before mechanical tests was equal to 0.245% (in Fig. 3). At the same time, total contribution of elastic stresses to the value of acoustic anisotropy a measured in main specimen (in Fig. 1) was equal to 0.539%. It suggests that influence of anisotropic texture a0 in rolled aluminum specimens is comparable with contribution of elastic deformations to acoustic anisotropy a. At the same time, initial acoustic anisotropy a0 is considered as a constant in the acoustoelasticity method [14,15]. The obtained distributions (in Fig. 3) show that it can lead to significant errors in results of estimating of mechanical stresses in metals. 3.2. Non-monotonic dependence of acoustic anisotropy on value of plastic deformations Fig. 5. The dependence of -a, % on elog, %for different measuring points in the specimen.
The monotonic dependences of acoustic anisotropy on inelastic deformations for steel specimens were obtained in [16,17]. It
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387
4
D. Tretyakov et al. / Materials Today: Proceedings xxx (xxxx) xxx
allowed to approximate experimental curves with high-order polynomials [17]. Estimates of plastic deformations value using measurements of acoustic anisotropy were obtained for different steels with an accuracy of 5%. Simplicity and possibility of developing an industrial method for estimating of inelastic deformations in steel structures are the advantages of this approach. However, the results in Fig. 5 suggest that this approach cannot be applied to aluminum rolled specimens. The nonmonotonic behavior of acoustic anisotropy a was observed at points near the destruction zone (in Fig. 5). It began to weaken only at distance of 150–180 mm from the zone of plastic neck formation. In addition, one more zone of nonmonotonic dependence was observed for all points for deformation elog 2.8% (in Fig. 5). It correlates with beginning of nonlinear behavior of the stress – strain curve (in Fig. 4). Thus, accurate estimation of inelastic deformations value in these zones is impossible. The reason for difference in results of [16,17] and distributions in Fig. 5 may be due to difference in elastic modulus of materials. This assumption requires additional experimental verification.
4. Conclusions The experimental investigations of acoustic anisotropy shown that influence of anisotropic texture in aluminum rolled specimens is comparable to influence of elastic stresses. It can lead to significant errors in results of estimating of stress-strain state by the acoustoelasticity method. The observed nonmonotonic dependence on inelastic axial deformations does not allow to estimate the value of plastic deformations using acoustic anisotropy in aluminum. Its nonmonotonic behavior was observed at all points in the range of 2-3% plastic deformations as well as in points at the distance of less than 150–180 mm from zone of specimen destruction. The discovered relationship between acoustic anisotropy and autowaves of plastic flow is the main result of investigation. It was shown that acoustic anisotropy is an indicator of autowaves of plastic deformation in metals. The propagation of autowaves in metal caused formation of the surface effect of acoustic anisotropy observed in a thin layer of 250–300 mm in metal. The results of investigation can be used in diagnosis of plastic deformations and damage in metals using acoustic anisotropy.
3.3. Acoustic anisotropy and autowaves of plastic flow in metals Declaration of Competing Interest L.B. Zuev investigated the dynamics of localized plastic deformations at macro level in [18]. He proposed an approach that considers plastic flow in metals as process of propagation of solitary deformation waves. The existence of three stages of deformation localization was established [18]. At the first stage, a secluded front of localized deformation is propagated at the yield site. At the second stage, a deformation wave propagates in the case of linear hardening. At the third stage of parabolic hardening, a stationary system of localized flow zones is formed. It does not move along specimen and has a macroscopic character [18]. Unlike elastic waves, process of autowaves propagation leads to change in structure and properties of deformable medium. It was confirmed during the experimental study of aluminum specimens using speckle interferometry method [18,19]. Investigations of deformation localization process are not limited to the approach [18,19]. The significant contributions to study of deformation process at meso, micro and macro structural levels were made in fundamental works [20–25]. Dependence between acoustic anisotropy and concentration of dislocations during inelastic deformation of metals was obtained in [19]. It allows to relate acoustic anisotropy with autowaves of plastic flow in metals. It could be seen that the acoustic anisotropy distributions changed similarly to behavior of plastic deformation autowaves during monotonic tension of metals (in Figs. 6 and 7) [18]. The formation of systems of waves from a single solitary wave at stages 2, 3 and 6 and its breakdown at deformation value elog 9.53% at stage 7 is shown in Fig. 6. The qualitative nature of waves at the last stage of loading and after fracture of the specimen was preserved (in Fig. 7). The changes in location of system of stabilized waves due to movement of the macrowave from destruction zone (in Fig. 7). Thus, it can be supposed that autowaves of plastic flow localized in surface layer of metal have a significant influence on value of acoustic anisotropy. In this case, acoustic anisotropy becomes an indicator of autowaves of plastic deformation [18]. They also cause the surface effect of acoustic anisotropy. The level of acoustic anisotropy a before loading was in the range of 0.455 0.317%, but after destruction it was in the range of 1.667 1.037% (in Fig. 7). Previous investigations shown that acoustic anisotropy returns to its level before mechanical tests after removal of 250– 300 mm of surface layer of metal [10].
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The research was financially supported by the Russian Science Foundation, grant 18-19-00413. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
R.W. Benson, V.J. Raelson, Prod. Eng. 30 (1953) 56–59. D.S. Hughes, J.L. Kelly, Phys. Rev. 92 (1953) 1145–1149. M.A. Biot, J. Appl. Phys. 11 (1940) 522–530. C. Truesdell, Arch. Ration. Mech. Anal. 8 (1961) 263–296. R.A. Toupin, B. Bernstein, J. Acoust. Soc. Am. 33 (1961) 216–225. R.N. Thurston, K. Brugger, Phys. Rev. 133 (1964) A1604–A1610. M. Hirao, Y.H. Pao, J. Acoust. Soc. Am. 77 (1985) 1659–1664. T.T. Wu, M. Hirao, Y.H. Pao, J. Appl. Mech. Trans. ASME 58 (1991) 18–23. D.A. Tretyakov, A.K. Belyaev, A.R. Galyautdinova, V.A. Polyanskiy, D.A. Strekalovskaya, E3S Web Conf. 121 (2019), 01017-1-01017–4. D.A. Tretyakov, A.K. Belyaev, V.A. Polyanskiy, A.V. Stepanov, Y.A. Yakovlev, E3S Web Conf. 121 (2019), 01016-1-01016–5. A.S. Semenov, St. Petersbg. Polytech. Univ. J. Phys. Math. 3 (2017) 271–283. A.S. Semenov, V.A. Polyanskiy, L.V. Shtukin, D.A. Tretyakov, J. Appl. Mech. Tech. Phys. 59 (2018) 1136–1144. A.K. Belyaev, A.M. Lobachev, V.S. Modestov, A.V. Pivkov, V.A. Polyanskiy, A.S. Semenov, D.A. Tretyakov, L.V. Shtukin, Mech. Solids 51 (2016) 606–611. A.V. Kamyshev, S.V. Makarov, L.A. Pasmanik, V.A. Smirnov, V.S. Modestov, A.V. Pivkov, Russ. J. Nondestruct. Test. 53 (2017) 1–8. N.Y. Nikitina, A.V. Kamyshev, V.A. Smirnov, A.V. Borshchevskii, Y.M. Sharygin, Russ. J. Nondestruct. Test. 42 (2006) 185–189. K.V. Kurashkin, Acoust. Phys. 65 (2019) 316–321. A.V. Gonchar, V.V. Mishakin, V.A. Klyushnikov, K.V. Kurashkin, Tech. Phys. 62 (2017) 537–541. L.B. Zuev, Ann. Der Phys. 16 (2007) 286–310. L.B. Zuev, B.S. Semukhin, K.I. Bushmeleva, Tech. Phys. 45 (2000) 50–54. V.A. Popovich, E.V. Borisov, A.A. Popovich, V.S. Sufiiarov, D.V. Masaylo, L. Alzina, Mater. Des. 114 (2017) 441–449. M.A. Matveev, N.G. Kolbasnikov, A.A. Kononov, Met. Sci. Heat Treat. 59 (2017) 197–202. Y.A. Bezobrazov, N.G. Kolbasnikov, A.A. Naumov, Steel Transl. 44 (2014) 71–79. M.A. Skotnikova, G.V. Ivanova, A.A. Popov, O.V. Paitova, Lect. Notes Mech. Eng. (2018) 143–150. M.A. Skotnikova, N.A. Krylov, J.I. Mescheryakov, M.M. Radkevich, E.K. Ivanov, E. V. Mironova, AIP Conf. Proc. 706 (2004) 609–612. R.A. Parshikov, A.I. Rudskoy, A.M. Zolotov, O.V. Tolochko, Rev. Adv. Mater. Sci. 45 (2016) 67–75.
Please cite this article as: D. Tretyakov, A. Belyaev and N. Shaposhnikov, Acoustic anisotropy and localization of plastic deformation in aluminum alloys, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.387