A statistical crystal plasticity model based on continuum dislocation dynamics and its application to the comprehensive analysis of microstructure evolution in copper during equal-channel angular pressing

Author details

Kirill A. Romanov
Perm National Research Polytechnic University, Perm, Russian Federation
Alexey I. Shveykin
Perm National Research Polytechnic University, Perm, Russian Federation

https://doi.org/10.15593/perm.mech/2025.4.01

During metal forming processes, especially those involving severe plastic deformation techniques, the grain structure of metals and alloys undergoes significant changes. At low homologous temperatures, the predominant mechanism of microstructural reorganization is fragmentation. This process occurs through the formation of dislocation cell blocks and their gradual evolution into subgrains and new fine grains via mutual rotations during deformation. Advances in computational capabilities over recent decades have increasingly enabled the application of mathematical modeling to analyze and optimize technological forming processes. To investigate microstructural transformations during these processes, multilevel constitutive models grounded in the crystal plasticity are particularly suitable. These models explicitly account for the evolution of internal structure and deformation mechanisms. This work proposes a novel multilevel statistical constitutive model based on continuum dislocation dynamics to describe grain fragmentation in face-centered cubic metals. The developed model comprehensively characterizes the fragmentation process by tracking the evolution of statistically stored dislocation and geometrically necessary dislocation densities, quantifying their influence on key microstructural parameters: average misorientation angle, average fragment size and average grain size in polycrystal. Model verification was performed against experimental data from four passes of equal-channel angular pressing of copper at room temperature via route Bc (workpiece rotation between passes). The model demonstrates satisfactory agreement with experimental results in predicting stress-strain states and critical structural parameters (grain size, crystallographic textures, disorientation angle and fragment size, dislocation densities).

Keywords

statistical crystal plasticity modelscontinuum dislocation dynamicsgrain fragmentationgrain refinementECAPgrain sizefragment sizestatistically stored dislocationsgeometrically necessary dislocationsfragment disorientation angle

МНОГОУРОВНЕВАЯ СТАТИСТИЧЕСКАЯ КОНСТИТУТИВНАЯ МОДЕЛЬ НА БАЗЕ КОНТИНУАЛЬНОЙ ДИСЛОКАЦИОННОЙ ДИНАМИКИ И ЕЕ ПРИМЕНЕНИЕ ДЛЯ КОМПЛЕКСНОГО ОПИСАНИЯ ТРАНСФОРМАЦИИ СТРУКТУРЫ МЕДИ ПРИ РАВНОКАНАЛЬНОМ УГЛОВОМ ПРЕССОВАНИИ

В ходе технологических процессов (ТП) обработки давлением металлов и сплавов, особенно с применением методов интенсивной пластической деформации, происходит изменение их зеренной структуры. При низких гомологических температурах доминирующим процессом перестройки внутренней структуры материала является фрагментация, которая реализуется за счет образования блоков ячеек и постепенной их эволюции в субзерна и новые мелкие зерна за счет разворотов друг относительно друга в ходе деформирования. Развитие вычислительных средств в последние десятилетия позволяет все более эффективно применять для анализа и совершенствования реальных ТП аппарат математического моделирования. При этом для исследования происходящих в ходе ТП изменений внутри материала целесообразно использовать многоуровневые конститутивные модели (КМ), основанные на принципах физической теории пластичности, за счет явного учета в них эволюции внутренней структуры материала и реализующихся механизмов деформирования. В работе предлагается новая многоуровневая статистическая КМ на базе континуальной дислокационной динамики для описания фрагментации зерен металлов с ГЦК-решеткой. Разработанная КМ комплексно описывает процесс фрагментации: учитывает эволюцию плотности статистически накопленных и геометрически необходимых дислокаций, а также её влияние на изменение средних значений углов разориентации, размеров фрагментов и зерен в поликристалле. Верификация результатов моделирования осуществлялась на опытных данных для четырех проходов равноканального углового прессования меди при комнатной температуре по маршруту Вс (с поворотом заготовки). Полученные в КМ результаты предсказания изменения напряженно-деформированного состояния и ключевых параметров структуры (размеров зерен, текстуры, углов разориентации и размеров фрагментов, плотностей дислокаций) находятся в удовлетворительном соответствии с данными экспериментов.

Ключевые слова

многоуровневые статистические конститутивные моделиконтинуальная дислокационная динамикафрагментацияизмельчение зеренРКУПразмер зернаразмер фрагментовстатистически накопленные дислокациигеометрически необходимые дислокацииугол разориентации фрагментов

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Published: 8 December 2025
Issue date: 8 December 2025
Issue: No. 4 (2025)

A statistical crystal plasticity model based on continuum dislocation dynamics and its application to the comprehensive analysis of microstructure evolution in copper during equal-channel angular pressing

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