Change in texture-dependent acoustic birefringence in α-Fe and γ-Fe polycrystalline aggregates due to plastic deformation Текст научной статьи по специальности «Физика»

УДК 539.3, 534.2

Изменение текстурно-зависимого акустического двулучепреломления в a-Fe и y-Fe поликристаллах, вызванное пластической деформацией

К.В. Курашкин, В.В. Мишакин, С.В. Кириков, А.В. Гончар, В. А. Клюшников

Институт проблем машиностроения РАН - филиал Федерального государственного бюджетного научного учреждения «Федеральный исследовательский центр Институт прикладной физики Российской академии наук», Нижний Новгород, 603024, Россия

Данная работа посвящена исследованию эволюции кристаллографической текстуры и связанного с ней изменения акустического двулучепреломления в процессе пластической деформации при одноосном растяжении металлического сплава. Результаты компьютерного моделирования для ортотроп-ных a-Fe и y-Fe поликристаллов сравниваются с экспериментальными данными для различных сталей. Установлено, что приращение акустического двулучепреломления сдвиговых упругих волн, вызванное изменением упругих свойств вследствие пластической деформации, является положительным для поликристалла a-Fe с ОЦК-решеткой и отрицательным для поликристалла y-Fe с ГЦК-решеткой. Делается вывод, что этот эффект связан с различием между ОЦК- и ГЦК-решетками, имеющими разные плоскости скольжения и направления скольжения. Установлено, что рассеяние исходной орто-тропной текстуры и критическое напряжение сдвига также влияют на изменение эффективных упругих свойств и, соответственно, на количественный прирост акустического двулучепреломления. Указанные факторы следует учитывать при оценке повреждения металлического сплава методом акустического двулучепреломления.

Ключевые слова: пластическая деформация, поликристалл, акустическое двулучепреломление, кристаллографическая текстура, компьютерное моделирование

DOI 10.24412/1683-805X-2021-3-76-78

Change in texture-dependent acoustic birefringence in a-Fe and y-Fe polycrystalline aggregates due to plastic deformation

K.V. Kurashkin, V.V. Mishakin, S.V. Kirikov, A.V. Gonchar, and V.A. Klyushnikov

Mechanical Engineering Research Institute of the Russian Academy of Science - Branch of Federal Research Center "Institute of Applied Physics of the Russian Academy of Science", Nizhny Novgorod, 603024, Russia

This paper deals with investigation of crystallographic texture evolution and associated change in acoustic birefringence during plastic deformation under uniaxial tension of metal alloy. Results of computer simulation for orthotopic a-Fe and y-Fe polycrystalline aggregates are compared with experimental data for different steels. The increment in acoustic birefringence of shear elastic waves caused by changes in the elastic properties due to plastic deformation is found to be positive for a-Fe polycrystalline aggregate with bcc lattice and negative for y-Fe one with fcc lattice. This effect is concluded to be associated with the difference between bcc and fcc lattices, having different slip planes and slip directions. Scattering of initial orthotopic texture and critical shear stress also are found to affect the changes in the effective elastic properties and, accordingly, the quantitative increment in acoustic birefringence. The mentioned factors should be taken into account when assessing damage of metal alloy by the acoustic birefringence technique.

Keywords: plastic deformation, polycrystalline aggregate, acoustic birefringence, crystallographic texture, computer simulation

© Курашкин К.В., Мишакин В.В., Кириков С.В., Гончар А.В., Клюшников В.А., 2021

KyparnKun K.B., MurnaKun B.B., KupuKoe C.B. u dp. / OusunecKan MesoMexanuKa 24 3 (2021) 76-78 77

1. Introduction

One of the actual topics in the field of physical mesomechanics is the development of non-destructive engineering methods for diagnostics of materials and structures at the stage prior to failure, on the basis of fracture physical mesomechanics.

Ultrasonic technique based on the birefringence effect can be a promising tool for monitoring the state of metal structures subjected to exploitation loads. Acoustic birefringence is relative difference between velocities of two orthogonally polarized shear waves propagating in the same direction. Change in acoustic birefringence is a quite sensitive indicator of material degradation [1-5].

For a metal alloy experiencing plastic deformation, the change in acoustic birefringence is primarily associated with rotation of grains [1-3]. At the early stage of plastic deformation, reorientation of grains occurs due to easy slipping of dislocations [3]. In metal alloys with different types of crystal lattice, different slip systems operate during plastic deformation, so changes in acoustic birefringence may differ drastically. This requires consideration when developing a method, based on measurements of acoustic birefringence, for assessing degradation of metal alloy due to plastic deformation.

In this work, the subject of interest is the effect of plastic deformation on the increment of acoustic birefringence in a-Fe and y-Fe polycrystalline aggregates with bcc and fcc lattices, respectively.

2. Theoretical and experimental background

Consider a statistically orthotropic aggregate consisting of many cubic crystallites, for example, a sheet-type specimen of rolled steel. Let 0xyz be the Cartesian coordinate system with coordinate axes fixed at the specimen. It is convenient to take 0z axis along the direction through the thickness of the specimen, and 0x axis along the rolling direction. Let's introduce the orthonormal basis (e1; e2; e3) associated with this coordinate system. The elastic properties of the specimen will be characterized by the elastic constants of the second order. To denote the tensor components, we will use Voigt notation Cj.

It is generally accepted that acoustic birefringence is defined in terms of velocities of two orthogonally polarized shear waves propagating along the same path. If Vzx and Vzy are velocities of two shear waves propagating in the 0z direction (through the thickness of specimen) and polarized in the 0x and 0y directions (rolling and transverse), respectively, then acoustic birefringence B is defined as [6, 7]

V - V

B _ 2

V + V '

zx zy

(1)

It can also be expressed in terms of the elastic constants of the orthotopic specimen [8, 9]:

C55 - C44 (2)

B = ■

44

C55 + C44

Thus, it is clear that changes in the effective elastic constants affect acoustic birefringence.

Note that from practical viewpoint, the acoustic birefringence technique has several advantages. This technique provides an informative parameter averaged over the thickness of material, without the need to know the thickness. In practice, to determine acoustic birefringence, it is sufficient to measure the propagation times of two shear waves with mutually orthogonal polarizations propagating along the same path. So measurements can be carried out using the ultrasonic echo-method with access to only one side of the flat element, while both contact piezoelectric and non-contact EMA transducers can be used. Also, acoustic birefringence does not depend on temperature, because temperature velocity factor is actually the same for both shear waves. These advantages make the acoustic birefringence technique a promising tool for monitoring material degradation.

During plastic deformation of metal alloy, which is a polycrystalline aggregate consisting of many grains, its crystallographic texture changes. Crystal-lographic texture (preferred orientation of grains) affects all of elastic constants [9-12] and, accordingly, velocities of elastic waves and acoustic birefringence [3, 4, 11]. Acoustic birefringence changes mainly due to reorientations of grains, which tend to set the easy slip directions parallel to the axis of maximum shear stress [1]. In general, plastic deformation may have drastically different effects on acoustic birefringence in bcc and fcc metal alloys. Experimentally observed change in acoustic birefringence, for various steels, during plastic deformation under uniaxial tension is shown in Fig. 1. The data were obtained by us earlier in [3, 4, 13, 14]. As can be seen, acoustic birefringence linearly depends on the degree of plastic deformation at the early stage. Such behavior is consistent with dislocation motion, which causes the grains to rotate.

Funding

This work was supported by the Russian Science Foundation (grant No. 19-19-00637).

References

1.

2.

3.

Makowska K., Piotrowski L., Kowalewski Z.L. Prediction of the mechanical properties of P91 steel by means of magneto-acoustic emission and acoustic birefringence // J. Nondestruct. Eval. - 2017. - V. 36. -P. 43. - https://doi.org/10.1007/s10921-017-0421-9 Szelqzek J., Mackiewicz S., Kowalewski Z.L. New samples with artificial voids for ultrasonic investigation of material damage due to creep // NDT E. Int. -2009. - V. 42. - P. 150-156.

Mishakin V.V., Gonchar A.V., Kirikov S.V., Klyushni-kov V.A. Evaluation of condition of low-carbon steels experiencing plastic deformation using the effect of acoustic birefringence // Nondestruct. Test. Eval. -2020.

Mishakin V.V., Klyushnikov V.A., Kassina N.V. Research on the fracture process of steels by the acoustic method and the pitch net method // J. Mach. Manuf. Reliab. - 2009. - V. 38. - P. 443. Krysztofik J., Kukla D., Manaj W., Socha G. Evaluation of damage degree of inconel 718 alloy with the use of non-destructive methods // Russ. J. Nondestruct. Test. - 2019. - V. 55. - P. 299-307. Allen D.R., Sayers C.M. The measurement of residual stress in textured steel using an ultrasonic velocity combinations technique // Ultrasonics. - 1984. -V. 22. - P. 179-188.

Hirao M., Pao Y. Dependence of acoustoelastic birefringence on plastic strains in a beam // J. Acoust. Soc. Am. - 1985. - V. 77. - P. 1659-1664. Sayers C.M., Allen D.R. The influence of stress on the principal polarisation directions of ultrasonic shear waves in textured steel plates // J. Phys. D. Appl. Phys. - 1984. - V. 17. - P. 1399-1413. Hirao M., Hara N., Fukuoka H. Anisotropy measured with shear and Rayleigh waves in rolled plates // Ultrasonics. - 1987. - V. 25. - P. 107-111. 10. Sullivan P.F., Papadakis E.P. Ultrasonic double refraction in worked metals // J. Acoust. Soc. Am. 33. -1961. - V. 1622-1624.

4.

5.

6.

7.

9.

11. Sayers C.M. Ultrasonic velocities in anisotropic polycrystalline aggregates // J. Phys. D. Appl. Phys. -V. 15. - 1982. - P. 2157-2167.

12. HuangM., Lan Z., Liang H. Constitutive relation of an orthorhombic polycrystal with the shape coefficients // Acta Mech. Sin. - 2005. - V. 21. - P. 608-618.

13. Kurashkin K.V. Study of the acoustoelastic effect in an anisotropic plastically deformed material // Acoust. Phys. - 2019. - V. 65. - P. 316-321.

14. Klyushnikov V.A. Influence of plastic deformation temperature on ultrasonic and electromagnetic properties of austenitic steel // Mater. Today. Proc. - 2019. -V. 19. - P. 2320-2322.

15. Rybin V.V., Perevezentsev V.N., Kirikov S.V. Formation of strain-induced broken dislocation boundaries at faceted grain boundaries // Phys. Met. Metallogr. -2018. - V. 119. - P. 421-429.

16. Trusov P. V., Shveykin A.I. Multilevel crystal plasticity models of single- and polycrystals. Statistical models // Phys. Mesomech. - 2013. - V. 16. - No. 1. - P. 2333. - https://doi.org/10.1134/S1029959913010037

17. Trusov P. V., Shveykin A.I. Multilevel crystal plasticity models of single- and polycrystals. Direct models // Phys. Mesomech. - 2013. - V. 16. - No. 2. - P. 99124. - https://doi.org/10.1134/S1029959913020021

18. Kim S.A., Johnson W.L. Elastic constants and internal friction of martensitic steel, ferritic-pearlitic steel, and a-iron // Mater. Sci. Eng. A. - 2007. - V. 452-453. -P. 633-639.

19. Kupperman D.S., Reimann K.J. Ultrasonic wave propagation and anisotropy in austenitic stainless steel weld metal // IEEE Trans. Sonics Ultrason. - 1980. -V. 27. - P. 7-14.

20. Ledbetter H.M. Predicted single-crystal elastic constants of stainless-steel 316 // Brit. J. Non-Destr. Test. - 1981. - V. 23. - P. 286-287.

Received 13.04.2021, revised 24.05.2021, accepted 26.05.2021

This is an excerpt of the article "Change in Texture-Dependent Acoustic Birefringence in a-Fe and y-Fe Polycrystalline Aggregates due to Plastic Deformation". Full text of the paper is published in Physical Mesomechan-ics Journal. DOI: 10.1134/S102995992201009X

Сведения об авторах

Курашкин Константин Владимирович, к.т.н., снс ИПМ РАН, [email protected], [email protected]

Мишакин Василий Васильевич, д.т.н., зав. лаб. ИПМ РАН, [email protected]

Кириков Сергей Владимирович, мнс ИПМ РАН, [email protected]

Гончар Александр Викторович, к.т.н., снс ИПМ РАН, [email protected]

Клюшников Вячеслав Александрович, к.т.н., снс ИПМ РАН, [email protected]