An equation for the plasticity of a porous solid allowing for true strains of the matrix material

Powder Metallurgy and Metal Ceramics -     

Effect of Structure and Composition on the Hardness of Sintered Composites Based on Stainless Steels

A phenomenological model is constructed to describe the hardness of a composite material based on stainless steels. The effect of the structure and the content of dispersed inclusions on the hardness of such composites is studied. The adequacy of the model is checked on test specimens made of stainless steel Kh18N15 containing 0.6% carbon and 10-30% dispersed inclusions of chromium carbide. The model makes it possible to not only evaluate the reinforcing effect of fine inclusions, but also to optimize that effect.     

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 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.     

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.