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发表于 2005-1-17 11:18:57
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来自 辽宁沈阳
Re:【分类讨论】粉末冶金
In recent years, two approaches, based on ‘porous material’ and ‘granular material’ models respectively, have been developed which describe the effect of stress state on the response of the powder material. The porous material model, generally known as a modified von Mises, has been used for the simulation of metal forming and powder forming processes (Corapcioglu and Uz, 1978; Sluzalec, 1989; Hisatsune et al., 1991). This model includes the influence of the hydrostatic stress component and satisfies the symmetry and convexity conditions required for the development of a plasticity theory. The granular material model which has been used for the modeling of frictional materials such as soil or rock, is adopted to describe the behavior of metal powder (Crawford and Lindskog, 1983; Haggblad, 1991; Riero and Prado, 1994). This model reflects the yielding, frictional and densification characteristics of powder along with strain and geometrical hardening which occur during the compaction process.
The yielding of porous materials is more complicated than that of fully dense materials because the onset of yielding is influenced not only by the deviatoric stress component but also by the hydrostatic stress. It is for this reason that a von Mises yield function cannot be used for the development of a plasticity theory for porous materials. Therefore, a yield function for porous materials, which can be considered as an extension of von Mises’s concept of yielding of fully dense materials, has been considered by many researchers as (Kuhn and Downey, 1971; Green, 1972; Shima and Oyane, 1976; Doraivelu et al., 1984)
AJ′2+BJ12=δY02=Yρ2
Where J1 is the first invariant of the stress tensor, J′2 is the second invariant of the stress deviator and Y0 and Yρ are the yield stress of the solid and aggregate, or partially dense, material having relative density ρ, respectively. The parameters A, B and δ are functions of relative density ρ, expressed by the above equation, has the form of an ellipsoid whose major axis coincides with the σm axis, and is shown in Fig.1. Eq.(1) represents a prolate spheroid in principal stress space which is a smooth, convex, bounded surface of a very simple form. The analogy with the comparable arguments for the use of the von Mises yield criterion for non-porous materials is very compelling.
It has been shown that the yield functions proposed by the various researchers satisfy the required conditions and reduce, as expected, to the von Mises yield function for fully dense materials (rou=1). However, these functions do not predict the dependence of compressive yield stress on relative density, as described by the large discrepancies between experiment and theory given in Doraivelu et al. (1984). Most of the case studies reporting compaction start at a relative density of about 0.7-however, for the powder compaction process, the relative density of the loose powder fill is about 0.25-0.4. Furthermore, this type of material model neglects the hardening factor associated with the densification process where this is one of the main features in the process. Thus, the use of a yield criterion for a porous material is not suitable for loose metal powder and the adoption of a model which represents a frictional granular material is more applicable. |
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