Mesoscale Mechanisms in Viscoplastic Deformation of Metals and Their Applications to Constitutive Models

Deformation of metals has attracted great interest for a long time. However, the constitutive models for viscoplastic deformation at high strain rates are still under intensive development, and more physical mechanisms are expected to be involved. In this work, we employ the newly-proposed methodology of mesoscience to identify the mechanisms governing the mesoscale complexity of collective dislocations, and then apply them to improving constitutive models. Through analyzing the competing effects of various processes on the mesoscale behavior, we have recognized two competing mechanisms governing the mesoscale complex behavior of dislocations, i.e., maximization of the rate of plastic work, and minimization of the elastic energy. Relevant understandings have also been discussed. Extremal expressions have been proposed for these two mesoscale mechanisms, respectively, and a stability condition for mesoscale structures has been established through a recently-proposed mathematical technique, considering the compromise between the two competing mechanisms. Such a stability condition, as an additional constraint, has been employed subsequently to close a two-phase model mimicking the practical dislocation cells, and thus to take into account the heterogeneous distributions of dislocations. This scheme has been exemplified in three increasingly complicated constitutive models, and improves the agreements of their results with experimental ones.

Dynamics of hybrid hardening and viscoplastic beams under explosive effects

Рассматриваются полиметаллические балки постоянного поперечного сечения из наборов упрочняющихся и вязкопластичных материалов с двухсимметричным их расположением в поперечном сечении. Считается, что балки находятся под воздействием нагрузок взрывного типа. Для всех материалов использована модель жестко-вязкопластического деформирования и приняты классические гипотезы деформирования Кирхгофа. Для биметаллических шарнирно-опертых балок получены общие уравнения деформирования и описан метод их решения. Определены остаточные формы динамического повреждения. We consider polymetallic beams of constant cross-section from sets of hardening and viscoplastic materials with their two-symmetric arrangement in the cross-section. The beams are considered to be subject to explosive loads. For all materials, a rigid-viscoplastic deformation model was used and the classical Kirchhoff deformation hypotheses were adopted. For bimetallic hinged- supported beams, general equations of deformation are obtained and a method for their solution is described. Residual forms of dynamic damage were determined.

ENGINEERING MODEL FOR THE CONSOLIDATION OF OIL SEED MATERIAL DURING VISCOPLASTIC DEFORMATION

Cоставлено модельное уравнение консолидации масличного материала, учитывающее процесс его вязкопластичной деформации для неньютоновской твердожидкой смеси. Использованы параллельные соединения моделей Ньютона с вязкостью ηН и Сен-Венана с пределом текучести σ0. Обе формулы представлены в виде конститутивных реологических уравнений состояния. В процессе расчета использовано прямое и обратное преобразования Лапласа. Рассмотрен одномерный вариант пластической деформации масличного материала. Выведены градиенты смещения и скорости. Полученное уравнение распределения давления по высоте слоя материала позволяет определить изменение давления по толщине прессуемого материала с учетом его вязкопластичной деформации. The aim of the study was to compile a model equation for the consolidation of oilseeds, taking into account the process of its viscoplastic deformation for a non-Newtonian solid/liquid mixture. To compile the equation, we used in parallel a combination of Newton models with viscosity ηН and Saint-Venant with yield strength σ0. Both formulas are constitutive rheological equations of state. In the calculation process, the direct and inverse Laplace transforms were used, and a one-dimensional version of the plastic deformation of the oil material was considered, due to which the displacement gradient and velocity gradients were derived. As a result, the obtained equation of pressure distribution over the height of the material layer allows one to determine the pressure change over the thickness of the pressed material, taking into account its viscoplastic deformation.