On fracture locus in the equivalent strain and stress triaxiality space

Discrete particle simulation of particulate systems: A review of major applications and findings

Publisher Summary This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.

Material Failure by Void Growth to Coalescence

Plasticity theory for porous metals

Theoretical concepts of sintering were originally based upon ideas of the discrete nature of particulate media. However, the actual sintering kinetics of particulate bodies are determined not only by the properties of the particles themselves and the nature of their local interaction with each other, but also by macroscopic factors. Among them are externally applied forces, kinematic constraints (e.g. adhesion of the sample's end face and furnace surface), and inhomogeneity of properties in the volume under investigation (e.g. inhomogeneity of initial density distribution created during preliminary forming operations). Insufficient treatment of the questions enumerated above was one of the basic reasons hindering the use of sintering theory. A promising approach is connected with the use of continuum mechanics, which has been successfully applied to the analysis of compaction of porous bodies. This approach is based upon the theories of plastic and nonlinear-viscous deformation of porous bodies. Similar ideas have recently been embodied in a continuum theory of sintering. The main results of the application of this theory for the solution of certain technological problems of sintering are introduced including their thermo–mechanical aspects.

Theory of sintering: from discrete to continuum

Criteria for ductile fracture and their applications

The basic equations are proposed for plastic deformation of porous metals such as sintered metal powders or metal powder compacts. The porous metal is assumed to be made up of a homogeneous metallic material and unformly distributed pores. The following equations are obtained from the Levy-Mises equatioins, (de1-de2)/(σ1-σ2)=(de2-de3)/(σ2-σ3)=(de3-de1)/(σ3-σ1)=(3fdeυ)/(2σm/f)=(3deeq)/(2γσeq) where γ is the relative density of the porous metal, f a function of γ, the subscripts 1, 2 and 3 represent the principal directions, σm=(σ1+σ2+σ3)/3 and deυ=de1+de2+de3. The theory shows a good agreement with the experimental results for sintered copper powder compacts.

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Susumu Shima

Papers

Plasticity theory for porous metals

Criteria for ductile fracture and their applications

Thoery of Plasticity for Porous Metals

A study of the one-path deep drawing spinning of cups

Densification behaviour of ceramic powder