Statistical Crystal Plasticity Model Advanced for Grain Boundary Sliding Description

Abstract

Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model of polycrystalline metals and alloys, which takes into account intragranular dislocation sliding, crystallite lattice rotation and grain boundary sliding. A key advantage of our model over the classical Taylor-type models is that it also includes a consideration of grain boundaries and possible changes in their mutual arrangement. The constitutive relations are defined in rate form and in current configuration, which makes it possible to use additive contributions of intragranular sliding and grain boundary sliding to the strain rate at the macrolevel. In describing grain boundary sliding, displacements along the grain boundaries are considered explicitly, and changes in the neighboring grains are taken into account. In addition, the transition from displacements to deformation (shear) characteristics is done for the macrolevel representative volume via averaging, and the grain boundary sliding submodel is attributed to a separate structural level. We have also analyzed the interaction between grain boundary sliding and intragranular inelastic deformation. The influx of intragranular dislocations into the boundary increases the number of defects in it and the boundary energy, and promotes grain boundary sliding. The constitutive equation for grain boundary sliding describes boundary smoothing caused by diffusion effects. The results of the numerical experiments are in good agreement with the known experimental data. The numerical simulation demonstrates that analysis of grain boundary sliding has a significant impact on the results, and the multilevel constitutive model proposed in this study can be used to describe different inelastic deformation regimes, including superplasticity and transitions between conventional plasticity and superplasticity.

Трехуровневая Модель Для Описания Сверхпластического Деформирования Алюминиевых Сплавов

“…Предлагается статистическая трехуровневая конститутивная модель [4][5][6], основанная на применении внутренних переменных и физической теории упруговязкопластичности. В модель включено описание следующих основных механизмов и процессов: внутризеренного дислокационного скольжения, поворотов решеток кристаллитов, изменения зеренной структуры, зернограничного скольжения, лидирующего при структурной СП, и сопровождающих его аккомодационных механизмов -зернограничной диффузии и динамической рекристаллизации.…”

“…Учитывается взаимодействие механизмов зернограничного и внутризеренного скольжения, а также изменение их ролей при деформировании, что отражено в соответствующих законах упрочнения. Соотношения ранее разработанной версии модели [4][5][6] модифицированы детальным учетом влияния легирующих добавок на действие основных механизмов на разных стадиях сверхпластического деформирования.…”

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

“…In statistical models aimed at describing the behavior of representative macrovolumes, consideration is given to a sample of uniformly deformed grains (reviews of the models of this class are provided in [10][11][12]. The application of modified statistical models makes it possible to take into account the interaction of neighboring grains, e.g., during the explicit description of the motion of dislocations across the boundary [13]. Self-consistent models are used to investigate the behavior of uniformly deformed grains in a matrix representing the Crystals 2021, 11, 1392 2 of 19 effective characteristics of polycrystals.…”

“…In our opinion, it is important to undertake a thorough analysis of these relations, which will enable their comparison in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements. This is especially important given the fact that an intensively developing direction in crystal plasticity is related to the application of constitutive models for describing other, side by side with intragranular dislocation sliding, significant mechanisms and processes, such as twinning [8,[25][26][27], phase transitions [8,28,29], grain boundary sliding [13,[30][31][32], recrystallization [33][34][35]. In order to create advanced models, it is necessary to make a reasonable choice of a platform (the basic structure of the model).…”

Crystal Plasticity

“…Ou et al [7] have incorporated a crystal plasticity finite element model for predicting a crack initiation in additively manufactured IN718 alloy, while Kosuge et al [8] have utilized strain gradient plasticity theory based on the finite element method to estimate a behavior of steel structures subjected to large complicated pre-strains. Further examples on crystal plasticity modeling involve a reaction stress model (Zhang et al [9]), statistical crystal plasticity constitutive models of polycrystalline metals and alloys (Shveykin et al [10]) or 3D representative volume element approach (Qayyum et al [11]). Furthermore, a theoretical work related to yield surfaces and slip systems has been provided by Holmedal [12].…”