Three-Level Dislocation-Based Model for Describing the Deformation of Polycrystals: Structure, Implementation Algorithm, Examples for Studying Nonproportional Cyclic Loading
A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and the introduction of internal variables. The structure, mathematical formulation, and implementation algorithm of the model are discussed. The...
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| Published in | Physical mesomechanics Vol. 25; no. 6; pp. 557 - 567 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.12.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1029-9599 1990-5424 |
| DOI | 10.1134/S102995992206008X |
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| Abstract | A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and the introduction of internal variables. The structure, mathematical formulation, and implementation algorithm of the model are discussed. The element of the upper structural-scale level is the representative macrovolume. The elements of mesolevels 1 and 2, which are identical in scale, are crystallites (grains, subgrains, fragments, depending on the required element size). The description at mesolevel 1 is performed in terms of thermomechanical variables (stresses, strains, strain rates). The behavior of meso-2 elements is described in terms of dislocation densities and velocities. Particular attention is paid to the formation of barriers on split dislocations. As an example, the model is applied to study proportional and nonproportional cyclic loading of samples with substantially different stacking fault energies. It is shown that barriers are more readily formed in materials with low stacking fault energy, leading to their additional cyclic hardening under nonproportional loading. |
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| AbstractList | A three-level constitutive model is proposed for describing the deformation of polycrystalline materials, which is based on crystal elasto-viscoplasticity and the introduction of internal variables. The structure, mathematical formulation, and implementation algorithm of the model are discussed. The element of the upper structural-scale level is the representative macrovolume. The elements of mesolevels 1 and 2, which are identical in scale, are crystallites (grains, subgrains, fragments, depending on the required element size). The description at mesolevel 1 is performed in terms of thermomechanical variables (stresses, strains, strain rates). The behavior of meso-2 elements is described in terms of dislocation densities and velocities. Particular attention is paid to the formation of barriers on split dislocations. As an example, the model is applied to study proportional and nonproportional cyclic loading of samples with substantially different stacking fault energies. It is shown that barriers are more readily formed in materials with low stacking fault energy, leading to their additional cyclic hardening under nonproportional loading. |
| Author | Trusov, P. V. Gribov, D. S. |
| Author_xml | – sequence: 1 givenname: D. S. surname: Gribov fullname: Gribov, D. S. organization: Perm National Research Polytechnic University – sequence: 2 givenname: P. V. surname: Trusov fullname: Trusov, P. V. email: tpv@matmod.pstu.ac.ru, tpv@pstu.ru organization: Perm National Research Polytechnic University |
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| Cites_doi | 10.1016/j.mechrescom.2015.06.00 10.1016/J.PMATSCI.2010.12.001 10.1080/14786445108561065 10.1134/S1029959919040052 10.1108/eb023742 10.1016/0029-5493(89)90112-x 10.3390/ma15030760 10.1016/S1566-1369(03)80022-5 10.1016/0956-7151(93)90325-M 10.1016/j.ijplas.2010.02.008 10.1063/1.1711937 10.1016/0022-5096(71)90010-X 10.1016/0025-5416(86)90281-8 10.1557/jmr.2018.333 10.1080/14786444108561385 10.1134/S1029959917040026 10.1016/0001-6160(85)90154-3 10.1016/j.ijplas.2005.02.004 10.1016/S0022-5096(01)00134-X 10.1016/j.ijplas.2016.12.004 10.1088/0959-5309/52/1/303 10.1016/j.jmatprotec.2019.04.029 10.1007/978-94-009-3439-9_1 10.1007/978-90-481-2687-3_4 10.1016/j.matchemphys.2022.125997 10.1115/1.2897188 |
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| Keywords | split dislocations dislocation barriers multilevel model hardening nonproportional cyclic loading |
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| SubjectTerms | Algorithms Classical Mechanics Constitutive models Crystallites Cyclic loads Deformation Dislocation density Materials Science Mathematical models Nonproportional loads Physics Physics and Astronomy Polycrystals Solid State Physics Stacking fault energy Viscoplasticity |
| Title | Three-Level Dislocation-Based Model for Describing the Deformation of Polycrystals: Structure, Implementation Algorithm, Examples for Studying Nonproportional Cyclic Loading |
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