The viscoplastic compaction of composite powders

A model for the densification of spherical powders is developed for the early stages of cold and hot compaction under general loading. General viscoplastic properties are adopted which reduce to strain hardening plasticity at ambient temperature and to power law creep at elevated temperature. A large strain analysis is carried out to determine the macroscopic compaction behaviour, based on the affine motion of particles with viscoplastic dissipation occurring at the contacts between particles. Random packing is assumed and the model includes the increase in the number of contacts per particle with densification. A general prescription is given for computing the macroscopic stress as a function of strain rate and accumulated strain. Detailed results are presented for yield surfaces and creep dissipation surfaces after isostatic and closed die compaction. A scalar constraint factor is derived for a random mixture of two populations of particles with different sizes and strengths. The predictions include the limiting case of deformable spheres reinforced with rigid spheres of different size.

[1]  N. Fleck,et al.  Hydrostatic compaction of cylindrical particles , 1994 .

[2]  P. Dawson,et al.  An anisotropic continuum model for the sintering and compaction of powder packings , 1988 .

[3]  B. Storȧkers.  Local Contact Behaviour of Viscoplastic Particles , 1997 .

[4]  J. Porter,et al.  Deformation consolidation of metal powders containing steel inclusions , 1991 .

[5]  K. Walton,et al.  The effective elastic moduli of a random packing of spheres , 1987 .

[6]  Norman A. Fleck,et al.  On the cold compaction of powders , 1995 .

[7]  G. Mason.  Radial Distribution Functions from Small Packings of Spheres , 1968, Nature.

[8]  G. D. Scott,et al.  Radial Distribution of the Random Close Packing of Equal Spheres , 1962, Nature.

[9]  E. Arzt.  The influence of an increasing particle coordination on the densification of spherical powders , 1982 .

[10]  N. Fleck,et al.  The viscoplastic compaction of powders , 1997 .

[11]  A. Jagota,et al.  Isotropic Constitutive Model for Sintering Particle Packings , 1990 .

[12]  A. Jagota,et al.  Viscosities and Sintering Rates of Composite Packings of Spheres , 1995 .

[13]  S. Nemat-Nasser,et al.  A Micromechanical Description of Granular Material Behavior , 1981 .

[14]  J. Rice.  On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals , 1970 .

[15]  A. Cocks.  Overview no. 117 The structure of constitutive laws for the sintering of fine grained materials , 1994 .

[16]  Hellmut F. Fischmeister,et al.  Particle Deformation and Sliding During Compaction of Spherical Powders: A Study by Quantitative Metallography , 1978 .

[17]  D. Bouvard.  Modelling the densification of powder composites by power law creep , 1993 .

[18]  S. H. Goods,et al.  Overview No. 1: The nucleation of cavities by plastic deformation , 1979 .

[19]  S. Biwa,et al.  Analysis of cold and hot isostatic compaction of spherical particles , 1996 .

[20]  Per-Lennart Larsson,et al.  Similarity analysis of inelastic contact , 1997 .

[21]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[22]  M. Ashby,et al.  The cold isostatic pressing of composite powders—I. Experimental investigations using model powders , 1996 .

[23]  C. R. Calladine,et al.  Nesting surfaces of constant rate of energy dissipation in creep , 1962 .

[24]  P. Larsson,et al.  On Brinell and Boussinesq indentation of creeping solids , 1994 .

[25]  Norman A. Fleck,et al.  The yield behaviour of metal powders , 1997 .

[26]  Shiro Biwa,et al.  An analysis of fully plastic Brinell indentation , 1995 .

[27]  M. Ashby,et al.  Hot isostatic pressing diagrams : new developments , 1985 .

[28]  Norman A. Fleck,et al.  Transient creep analysis of ball indentation , 1995 .

[29]  Norman A. Fleck,et al.  Yielding of metal powder bonded by isolated contacts , 1992 .

[30]  Hellmut F. Fischmeister,et al.  Densification of Powders by Particle Deformation , 1983 .

[31]  Robert M. McMeeking,et al.  Power-law creep of powder bonded by isolated contacts , 1992 .

[32]  A. F. Bower,et al.  Indentation of a power law creeping solid , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[33]  M. Ashby,et al.  Pressure sintering by power law creep , 1975 .

[34]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[35]  A. Zdunek,et al.  A theoretical study of the Brinell hardness test , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[36]  Susumu Shima,et al.  Plasticity theory for porous metals , 1976 .

[37]  F. Lange,et al.  Relation between percolation and particle coordination in binary powder mixtures , 1991 .

[38]  Norman A. Fleck,et al.  Indentation of porous solids , 1992 .