M. B. Shtern

Rheological Foundations of Powder Consolidation Processes and the “Mean-Square” Concept

The past, present, and possible future development of basic models for engineering processes in powder metallurgy are examined. Special attention is devoted to the rheological concept of sintering and strain, as well as to the “mean-square” concept which together form the ideological basis for many existing models. Modern generalizations of sintering models to the cases of anisotropy and phase transitions in the matrix material are examined. Models of plastic and nonlinearly viscous flows that follow from the “mean-square concept” concept are correlated with other theories of flow in porous media. The relationship among these is established. The possible use of these ideas for solving current problems in materials science is discussed.

Optimization of the Composition and Geometric Shape of Implants Based on Computer Modeling

We consider typical features in application of computer modeling methods to design implants of optimal shape and composition. Nanostructural medical grade titanium and bioactive ceramic components, synthesized on the basis of hydroxyapatite, are used as material for joint endoprostheses. Studies are based on the assumption that compact bone is an elastic, orthotropic, porous material. The presence of friction and heating in the contact regions is taken into account. The problem is considered in a thermoelastic formulation. The solution of this problem will make it possible to optimize both the geometric characteristics of implants and their composition.

EFFECT OF A THIRD INVARIANT ON THE PROPERTIES AND STRUCTURE OF CONSTITUTIVE RELATIONSHIPS FOR POWDER MATERIALS

The bahavior of powder materials is considered whose properties are sensitive to a third invariants of stress and strain rate. Nonlinear relationships between stress and strain rate tensors for isotropic compactable material are found. Limitations on the material parameters of the model that provide correct determination are formulated. Estimates of axial and radial stress during compaction with a rotating die are presented within the model developed. It is established that three-invariant models describe more accurately the reduction in operating parameters with an increase in rotation rate than models containing the first two variants.

Effect of a Third Invariant on the Effective Reaction of Ductile Porous Bodies. Part 2. Loading Surface of Porous Bodies Whose Properties Are Sensitive to a Triaxial Stressed State

The lower and upper boundary approximation for describing the yield condition of porous bodies whose behavior is sensitive to a third strain rate invariant is obtained. Together with porosity the constitutive equations contain a material parameter that is responsible for the change in pore shape. This approach makes it possible to present the macroscopic yield condition in a compact form convenient for analysis and various applications. In particular, generalization of well-known plasticity conditions of Gurson and Green-Shima is presented. The lower estimate generalizes the Gurson model and the upper estimate corresponds to the Green-Shima model. Octahedral contours of the loading surface are constructed that agree with experimental data for loose materials and porous powder bodies.

Numerical Modeling of the Compaction of Powder Articles of Complex Shape in Rigid Dies: Effect of Pressing Method on Density Distribution. 1. Mechanical Model of Powder Densification

A theory of plasticity of a porous body was formulated taking into account the specifics of powder behavior under pressing. The proposed model of the material under compression is one-parameter with all functions depending on the current density. In order to determine the parameters of the model, use was made of the equilibrium density attained during the compression of an unbonded powder body, that value of density beyond which further deformation is not accompanied by volume change. Methods for determining the material parameters of the model are described.

Determination of the ultimate plastic capacity for powder materials based on the plastic flow model for porous solids. II. Influence of porosity and the stress-strain properties of the solid phase on the ultimate plastic capacity of a porous sintered material

A procedure for theoretical construction of the limiting surface for porous materials is described. The procedure requires the porosity, the stress-strain properties of the solid phase, and decohesion to be predefined. The limiting surface is defined for proportional loading paths. The obtained limiting states are also represented as plasticity diagrams. A satisfactory correspondence of the theoretical results with experimental data is shown for a number of both ferrous and non-ferrous powder materials.

Effect of a Third Invariant on the Effective Reaction of Plastic Porous Bodies. Part 1. Behavior of a Porous Material Unit Cell and a Generalized Rule of Normality

This work is devoted to deriving in general form definitive equations for plastic flow of porous bodies whose behavior is sensitive to a third strain rate invariant. Use of a micromechanical approach, including analysis of the behavior of a unit cell, and also such concepts as energy dissipation and an associated flow rule, make it possible to obtain the structure of macroscopic definitive equations in a general form. However, analysis of them and application gives rise to difficulties since they contain elliptical integrals and they cannot be expressed by means of elementary functions. Therefore the general definitive equations serve as a basis for subsequent analysis, i.e. determination of the lower and upper boundary approximations for the macroscopic stress tensor components and also formulation of macroscopic flow conditions in a convenient and compact form.

Effect of a shell on the change in shape of a porous billet during isostatic pressing. 1. stress deviator with isostatic pressing

Isostatic compaction of a porous billet in an incompressible container is considered. The behavior of the container as well as the matrix phase of a porous billet is assumed to be described by power law equations. Macroscopic deformation of a billet is controlled by flow theory for a compressible body with a smooth potential. It is established that the stressed state in a billet is not isostatic.

Density–Pressure Dependence and Density Distribution During Powder Pressing

The effect of applied load on density–pressure dependence as well as density distribution under axial pressing of powders in closed dies is analyzed. The continuity hypothesis is used for the analysis. The notion of a representative element is introduced. It is established that the size of this element is related to the effective diameter of powder particles. The sensitivity of density–pressure dependence and density distribution to pressing conditions is explained. Some features of axial pressing with a rotating punch are pointed out. The personal contribution of I. D. Radomyselskii to the formulation and solution of basic problems of powder pressing theory is emphasized.

Simulation of the Equal-Channel Angular Extrusion of Porous Blanks using Different Deformation Patterns

The results from simulation of equal-channel angular extrusion of sintered porous blanks with use of different deformation patterns are presented. It is shown that the maximum equidensity and the minimum volume of the poorly compacted area are observed in the pattern with a movable bottom plate of the die horizontal channel and with backpressure on the sample portion being extruded. This deformation pattern is also determined by the maximum values of deformation force.