Three-Level Dislocation-Based Model for Describing the Deformation of Polycrystals: Structure, Implementation Algorithm, Examples for Studying Nonproportional Cyclic Loading

• Published in: Physical mesomechanics Vol. 25; no. 6; pp. 557 - 567
• Main Authors: Gribov, D. S., Trusov, P. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.12.2022; Springer Nature B.V
• Subjects: 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; split dislocations; dislocation barriers; multilevel model; hardening; nonproportional cyclic loading
• ISSN: 1029-9599; 1990-5424
• DOI: 10.1134/S102995992206008X

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.