Consideration of Softening Near Free Surface in the Direct Model of Crystal Plasticity
DOI:
https://doi.org/10.17072/1993-0550-2023-3-31-43Keywords:
crystal plasticity, direct model, single crystalline, polycrystalline, dislocations, slip systems, free surface, softeningAbstract
Current industrial demands require the improvement of existing technologies and the creation of new ones that allow the production of parts and structures with advanced performance properties. Especially important are the issues of design and analysis of thermomechanical treatment of metals and alloys by intensive inelastic deformation methods. The study of manufacturing processes for miniaturized parts deserves special attention. The boundary value problems arising in this case belong to the class of phys-ically and geometrically nonlinear problems of the mechanics of deformable solids, for the solution of which it is necessary to develop appropriate mathematical models. Most classical models are based on the macrophenomenological theory of elastoplasticity. However, in the processes under consideration, significant structural changes occur at the meso- and microscale that have a significant influence on the physical and mechanical characteristics of the processed materials and the performance characteristics of the products. These changes are not described by the mentioned theories. An effective approach to describe these processes is to use multilevel models of crystal plasticity. Despite the tendency to minia-turize products, the parameters of such models are usually determined from the results of experiments on macrosamples. The question arises whether such parameters are valid for the analysis and modeling of real structures with typical length scales below 500 µm, where the internal and external boundaries of crystallites play a special role. In this study, the influence of the free surface on the mechanical proper-ties of single crystalline and polycrystalline materials is considered. Modification of the basic direct crystal plasticity model of elastoviscoplasticity to account for the softening of slip systems near free boundaries due to easier exit of dislocations to the surface is proposed.References
Поздеев А.А., Трусов П.В., Няшин Ю.И. Большие упругопластические деформации: теория, алгоритмы, приложения. М.: Наука, 1986. 232 с.
Ильюшин А.А. Пластичность. Основы общей математической теории. М.: АН СССР, 1963. 272 с.
Трусделл К. Первоначальный курс рациональной механики сплошных сред. М: Мир, 1975. 592 с.
Метлов Л.С., Мышляев М.М. Общие термо-динамические механизмы ИПД и сверхпластичности // Физика и техника высоких дав-лений. 2009. № 4. С. 57–69.
Трусов П. В., Швейкин А. И. Многоуровневые модели моно- и поликристаллических мате-риалов: теория, алгоритмы, примеры применения // Новосибирск: Издательство СО РАН, 2019. 605 с. DOI: 10.15372/MULTILEVEL2019TPV.
Трусов П.В., Волегов П.С. Физические теории пластичности: теория и приложения к описанию неупругого деформирования материалов. Ч. 1. Жесткопластические и упругопластические модели // Вестник ПГТУ. Механика. 2011. № 1. С. 5–45.
Трусов П.В., Волегов П.С. Физические теории пластичности: теория и приложения к описанию неупругого деформирования материалов. Ч. 2. Вязкопластические и упруговязкопластические модели // Вестник ПГТУ. Механика. 2011. № 2. С. 101–131.
Engel U., Eckstein R. Microforming–from basic research to its realization // Journal of Materials Processing Technology. 2002. Vol. 125–126. P. 35–44. DOI: 10.1016/S0924-0136(02)00415-6.
Трусов П.В. Классические и многоуровневые конститутивные модели для описания поведения металлов и сплавов: проблемы и перспективы (в порядке обсуждения) // Известия российской академии наук. Механика твердого тела. 2021. № 1. С. 69–82. DOI: 10.31857/S0572329921010128.
Arzt E. Size effects in materials due to micro-structural and dimensional constrains: a comparative // Acta Materialia. 1998. Vol. 46, Is. 16. P. 5611–5626. DOI: 10.1016/S1359-6454(98)00231-6.
Geiger M., Kleiner M., Eckstein R., Tiesler R., Engel U. Microforming // Annals of the CIRP. 2001. Vol. 5, Is. 50. P. 445–462. DOI: 10.1016/S0007-8506(07)62991-6.
Новиков И.И. Дефекты кристаллического строения металлов. М.: Металлургия, 1975. 208 с.
Фридель Ж. Дислокации. М.: Мир, 1967. 644 с.
Хирт Дж., Лоте И. Теория дислокаций. М.: Атомиздат, 1972. 600 с.
Keller C., Hug E. Hall–Petch behavior of Ni polycrystals with a few grains per thickness // Materials Letters. 2008. Vol. 62, Is. 10–11. P.1718–1720. DOI: 10.1016/j.matlet.2007. 09.069.
Keller C., Hug E., Chateigner D. On the origin of the stress decrease for nickel polycrystals with few grains across the thickness // Materials Science and Engineering: A. 2009. Vol. 500, Is. 1–2. P. 207–215. DOI: 10.1016/j.msea.2008.09.054.
Keller C., Hug E., Retoux R., Feaugas X. TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section // Mechanics of Materials. 2010. Vol. 42, Is. 1. P. 44–54. DOI: 10.1016/j.mechmat. 2009.09.002.
Keller C., Hug E., Feaugas X. Microstructural size effects on mechanical properties of high purity nickel // International Journal of Plasticity. 2011. Vol. 27, Is. 4. P. 637–654. DOI: 10.1016/j.ijplas.2010.08.002.
Hug E., Dubos P. A., Keller C. Temperature dependence and size effects on strain hardering mechanism in copper polycrystals // Materials Science and Engineering: A. 2013. Vol. 574. P. 253–261. DOI: 10.1016/j.msea. 2013.03.025.
Hug E., Keller C., Dubos P.A., Celis M.M. Size effects in cobalt plastically strained in tension: impact on gliding and twinning work hardering mechanisms // Journal of Materials Research and Technology. 2021. Vol. 11. P. 1362–1377. DOI: 10.1016/j.jmrt.2021.01.105.
Hall E.O. The deformation and aging of mild steel. III. Discussion and results // Proc. Phys. Soc. of London. 1951. Vol. B64. P. 747–753. DOI: 10.1088/0370-1301/64/9/303.N.
Petch N.J. The cleavage strength of polycrystalls // J. Iron and Steel Inst. 1953. Vol. 174. P. 25–28.
Jang D., Greer J. R. Size-induced weakening and grain boundary-assisted deformation in 60 nm grained Ni nanopillars // Scripta Materialia. 2011. Vol. 64, Is. 1. P. 77–80. DOI: 10.1016/j.scriptamat.2010.09.010.
Yang B., Motz C., Rester M., Dehm G. Yield stress influenced by the ratio of wire diameter to grain size – a competition between the effects of specimen microstructure and dimension in micro-sized polycrystalline copper wires // Philosophical Magazine. 2012. Vol. 92, Is. 25–27. P. 3243–3256. DOI: 10.1080/14786435.2012.693215.
Shin C., Lim S., Jin H., Hosemann P., Kwon J. Specimen size effects on the weakening of a bulk metastable austenitic alloy // Materials Sci-ence and Engineering: A. 2015. Vol. 622. P. 67–75. DOI: 10.1016/j.msea.2014.11.004.
Теплякова Л.А., Лычагин Д.В., Козлов Э.В. Локализация сдвига при деформации моно-кристаллов алюминия с ориентацией оси сжатия [001] // Физическая мезомеханика. 2002. Т. 5. № 6. С. 49–55.
Теплякова Л.А., Лычагин Д.В., Беспалова И.В. Закономерности макролокализации деформации в монокристаллах алюминия с ориентацией оси сжатия [110] // Физическая мезомеханика. 2004. Т. 7, № 6. С. 63–78.
Лычагин Д.В., Теплякова Л.А., Шаехов Р.В., Конева Н.А., Козлов Э.В. Эволюция деформационного рельефа монокристаллов алюминия с ориентацией оси сжатия [001] // Физическая мезомеханика. 2003. Т. 6, №3. С. 75–83.
Liu W., Liu Y., Cheng Y., Chen L., Yu L., Yi X. Unified model for size-dependent to size-independent transition in yield strength of crystalline metallic materials // Physical Review Letters. 2020. Vol. 124, Is. 23. P. 235501. DOI: 10.1103/PhysRevLett. 124.235501.
Keller C., Hug E., Habraken A.M., Duchene L. Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals // International Journal of Plasticity. 2012. Vol. 29. P. 155–172. DOI: 10.1016/j.ijplas.2011.08.007.
Yants A., Trusov P., Tokarev A. Direct crystal plasticity model for describing the deformation of samples of polycrystalline materials: influence of external and internal grain boundaries // Nanoscience and Technology: An International Journal. 2021. Vol. 12, Is. 2. P. 1–21. DOI: 10.1615/NanoSciTechnolIntJ. 2021036837.
Eshelby J.D., Stroh A.N. CXL. Dislocations in thin plates // The London, Edinburg, and Dublin Philosophical Magazine and Journal of Science. 1951. Vol. 42, Is. 335. P. 1401–1405. DOI: 10.1080/14786445108560958.
Head A.K. Edge dislocations in inhomogeneous media // Proceedings of the Physical Society. Section B. 1953. Vol. 66, Is. 9. P. 793–801. DOI: 10.1088/0370-1301/66/9/309.
Maurissen Y., Capella L. Stress field of a dislocation segment parallel to a free surface // Philosophical Magazine. 1973. Vol. 29, Is. 5. P. 1227–1229. DOI: 10.1080/14786437408 226608.
Maurissen Y., Capella L. Stress field of a dislocation segment perpendicular to a free surface // Philosophical Magazine. 1974. Vol. 30, Is. 3. P. 679–683. DOI: 10.1080/14786439808 206591.
Steketee J.A. On Volterra's dislocations in a semi-infinite elastic medium // Canadian Journal of Physics. 1958. Vol. 36. P. 192–205. DOI: 10.1139/p58–024.
Yoffe E.H. A dislocation at a free surface // Philosophical Magazine. 1961. Vol. 6, Is. 69. P. 1147–1155. DOI: 10.1080/14786436108 239675.
Shaibani S.J., Hazzledine P.M. The displacement and stress fields of a general dislocation close to a free surface of an isotropic solid // Philosophical Magazine A. 1981. Vol. 44, Is. 3. P. 657–665. DOI: 10.1080/01418618108 236168.
Lothe J., Indenbom V.L., Chamrov V.A. Elastic field and self-force of dislocations emerging at the free surfaces of an anisotropic halfspace // Physica Status Solidi (b). 1982. Vol. 111, Is. 2. P. 671–677. DOI: 10.1002/pssb. 2221110231.
Neily S., Dhouibi S., Bonnet R. Threading dislocations piercing the free surface of an anisotropic hexagonal crystal: review of theoretical approaches // Advances in Condensed Matter Physics. 2018. Vol. 2018. P. 1–8. DOI: 10.1155/2018/3038795.
Balusu K., Huang H. A combined dislocation fan-finite element (DF-FE) method for stress field simulation of dislocations emerging at the free surfaces of 3D elastically anisotropic crystals // Modelling and Simulation in Materials Science and Engineering. 2017. Vol. 25, Is. 3. P. 1–14. DOI: 10.1088/1361-651x/aa5a9d.
Crone J. C., Munday L. B., Knap J. Capturing the effects of free surfaces on void strengthening with dislocation dynamics // Acta Materialia. 2015. Vol. 101. P. 40–47. DOI: 10.1016/j.actamat.2015.08.067.
Asaro R. J., Needleman A. Texture development and strain hardening in rate dependent polycrys-tals // Acta Metall. 1985. Vol. 33, N 6. P. 923–953. DOI: 10.1016/0001-6160(85) 90188-9.
Estrin Y., Tóth L. S., Molinari A., Bréchet Y. A dislocation-based model for all hardening stages in large strain deformation // Acta mater. 1998. Vol. 46, N 15. P. 5509–5522. DOI: 10.1016/S1359-6454(98)00196-7.
Kalidindi S. R., Bronkhorst C. A., Anand L. Crystallographic texture evolution in bulk de-formation processing of FCC metals // J. Mech. Phys. Solids. 1992. Vol. 40, N 3. P. 537–569. DOI: 10.1016/0022-5096(92)80003-9.
Kocks U.F., Mecking H. Physics and phenomenology of strain hardening: the FCC case // Progress in Materials Science. 2003. Vol. 48. P. 171–273. DOI: 10.1016/S0079-6425(02)00003-8.
Van Houtte P., Li S., Seefeldt M., Delannay L. Deformation texture prediction: from the Taylor model to the advanced Lamel // Int. J. Plasticity. 2005. Vol. 21. P. 589–624. DOI: 10.1016/j.ijplas.2004.04.011.
Трусов П.В., Швейкин А.И. О разложении движения и определяющих соотношениях в геометрически нелинейной упруговязкопластичности кристаллитов // Физическая мезомеханика. 2016. Т. 19, № 3. С. 25–38.
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