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Journal ArticleDOI

Plasticity theory for porous metals

Susumu Shima1, M. Oyane1
01 Jun 1976-International Journal of Mechanical Sciences (Pergamon)-Vol. 18, Iss: 6, pp 285-291
TL;DR: In this paper, a plasticity theory for porous metals is proposed and the stress-strain curves for sintered copper with various apparent densities are calculated by utilizing the basic equations.
About: This article is published in International Journal of Mechanical Sciences.The article was published on 1976-06-01. It has received 766 citations till now. The article focuses on the topics: Stress (mechanics) & Compression (physics).
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Book ChapterDOI
TL;DR: In this paper, a convected coordinate formulation of the field equations is used to describe the material failure by coalescence of microscopic voids, and 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 also elaborated in this chapter.
Abstract: 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.

938 citations

Journal ArticleDOI
TL;DR: In this paper, a promising approach is connected with the use of continuum mechanics, which has been successfully applied to the analysis of compaction of porous bodies, based upon the theories of plastic and nonlinear-viscous deformation of porous body.
Abstract: 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.

581 citations

Journal ArticleDOI
TL;DR: In this paper, the basic science of sintering and hipping is summarized and contrasted, and the current state of understanding and modeling of hipping can be classified either as microscopic or macroscopic in their approach.
Abstract: Hot isostatic pressing (hipping) can be used for upgrading castings, densifying presintered components, consolidating powders, and interfacial bonding. It involves the simultaneous application of a high pressure and elevated temperature in a specially constructed vessel. The pressure is applied with a gas (usually inert) and, so, is isostatic. Under these conditions of heat and pressure, internal pores or defects within a solid body collapse and diffusion bond. Encapsulated powder and sintered components alike are densified to give improved mechanical properties and a reduction in the scatter band of properties. In this article, the basic science of sintering and hipping is summarized and contrasted. The current state of understanding and modeling of hipping is then reviewed. Models can be classified either as microscopic or macroscopic in their approach. In the microscopic approach, the various mechanisms of densification are analyzed in terms of a single particle and its surroundings. In the macroscopic approach, the compact is treated as a continuous medium. In hipping, although the pressure is isostatic, shrinkage is not generally isotropic, particularly if containment is used. However, the shrinkage can now be well predicted, provided that the material and container properties are accurately known.

536 citations

Journal ArticleDOI
Jacques Besson1
TL;DR: In this paper, the authors present a review of the material constitutive equations and computational tools which have been recently developed to simulate ductile rupture and fracture, which are used in structural computations.
Abstract: The past 20 years have seen substantial work on the modeling of ductile damage and fracture. Several factors explain this interest. (i) There is a growing demand to provide tools which allow to increase the efficiency of structures (reduce weight, increase service temperature or load, etc.) while keeping or increasing safety. This goal is indeed first achieved by using better materials but also by improving design tools. Better tools have been provided which consist (ii) of material constitutive equations integrating a physically-based description of damage processes and (iii) of better numerical tools which allow to use the improved constitutive equations in structural computations which become more and more realistic. This article reviews the material constitutive equations and computational tools, which have been recently developed to simulate ductile rupture.

471 citations


Cites background from "Plasticity theory for porous metals..."

  • ...…assumes that isotropic hardening is described by a scalar variable p which is interpreted as the plastic deformation of the matrix material so that (Shima and Oyane, 1976): _"p : ¼ ð1 fÞ _p ð10Þ which expresses that the macroscopic plastic work (left-hand side) is equal to the microscopic plastic…...

    [...]

  • ...One then assumes that isotropic hardening is described by a scalar variable p which is interpreted as the plastic deformation of the matrix material so that (Shima and Oyane, 1976):...

    [...]

  • ...The elliptic form for * was originally developed on a purely phenomenological basis (see, e.g., Green, 1972; Shima and Oyane, 1976; Abouaf et al., 1988) in order to introduce a pressure dependence in the expression of the yield surface....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a new yield function for compressible P M materials has been derived based upon a yield criterion postulated by the authors, which was experimentally verified for the uniaxial state of compressive stress using the P M aluminum alloy X7091 as a model material, and excellent agreement was found between theoretical and experimental results for the density dependence of the yield and geometrical hardening.

350 citations

References
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Journal ArticleDOI
R.J. Green1
TL;DR: In this paper, a deformation theory for a solid weakened by numerous cracks or voids was developed and the treatment is completely isotropic and would be suitable whenever the voids are nearly spherical or where the direction of cracks is completely random.

479 citations

Journal ArticleDOI
TL;DR: In this paper, the basic equations for plastic deformation of porous metals such as sintered metal powders or metal powder compacts are proposed, where the porous metal is assumed to be made up of a homogeneous metallic material and unformly distributed pores.
Abstract: 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.

89 citations

Journal ArticleDOI
TL;DR: In this article, the effects of shape of pores on toughness and ductility of sintered iron were investigated and the results were summarized as follows: 1) The roundness of the pores caused an increase in the charpy shelf energy and made the ductile-brittle transition more evident.
Abstract: It is the purpose of this study to investigate the effects of shape of pores on toughness and ductility of sintered iron.Compacts with a density range of 5.9-7.6 g/cm3 were pressed from electrolytic iron powder and pre-sintered at 1100°C for 10 min in hydrogen. Subsequently they were infiltrated with ferrous chloride by soaking for 4 min in its melt at 750°C.Activated-sintering (or reduction of ferrous chloride) was carried out at 800°C, 950°C and 1100°C for 5 min-3 hr in hydrogen. Impact and tensile properties of these materials with round pores were compared to those of conventionally sintered ones with sharp edged pores.The results were summarized as follows.1. The roundness of the pores caused an increase in the charpy shelf energy and made the ductile-brittle transition more evident.For this reason, the impact strength of the activation-sintered iron was, at 200°C, about two times as large as that of conventionally sintered iron with the same density, but at low temperatures, smaller than that.2. Activated-sintering increased the ultimate tensile strength and the fracture strain by 10-50% over conventional sintering. But the yield strength was hardly affected by the pore shape.3. The relative strength and the fracture strain of porous materials were expressed as functions relating not only to the porosity but also to the notch effect of the pores.

3 citations