Frictionless indentation of dissimilar elastic–plastic spheres

Abstract

A ®nite element study is performed on the frictionless normal contact of elastic±plastic spheres and rigid spheres. The eects of elasticity, strain hardening rate, relative size of the spheres and their relative yield strength are explored. Indentation maps are constructed, taking as axes the contact size and yield strain, for a wide range of geometries. These show the competing regimes of deformation mechanism: elastic, elastic±plastic, fully plastic similarity and ®nite deformation regime. The boundaries of the regimes depend upon the degree of strain hardening, relative size of the bodies in contact and upon their relative yield strengths. The regime of practical importance is the ®nite deformation regime for practical applications such as powder compaction. The contact force±displacement law, to be used as a part of the micromechanical constitutive model for powder compaction, is constructed semi-empirically by scaling the similarity contact law by a factor which depends on the relative size, relative yield strength and the strain hardening exponent of the bodies in contact. The accuracy of the assumption of independent contacts is addressed for the isostatic compaction of an assembly of rigid and deformable spheres, arranged in a B2 unit cell, based on two overlapping simple cubic lattices. Provided that the relative density of the compact is lower than about 0.82, the contacts deform independently. Ó

Towards a mechanistic model for the interaction between plastically deforming particles under confined conditions: A numerical and analytical analysis

“…First, an initial elastic deformation was observed, consistent with the classical Hertzian contact model [11]. Second, local plastic deformation took place in the vicinity of each contact point, as for models of independent contacts [3], yielding a more or less linear increase in force. Third, the coalescence of two or more plastic zones resulted in a reduced stiffness (see below).…”

“…In its usual formulation, the DEM uses a simplified contact description, with forces considered to be functions of the particle "overlap", assuming independent contacts. The assumption of independent contacts is known to limit the applicability of the DEM to moderate strains, corresponding to relative densities up to 0.85-0.90 for nonporous monodisperse spherical particles [3].…”

Yield behaviour of cold compacted composite powders

“…The SFM model assumes a kinematically admissible ®eld, based on the a ne motion of particle centres without rotation; thus, the e ects of particle rearrangement in the initial stages of compaction are neglected, and the model is an upper bound to the true response. Further, recent calculations by Mesarovic and Fleck [20] reveal that the local indentation response between particles (both soft±soft and soft±hard contacts) is less sti than the contact laws assumed by Storakers et al [15] by 30±40%. Thus the predicted macroscopic stresses for compaction are expected to be at least 30±40% less than that given by the original SFM model.…”

On the accurate computation of the true contact-area in mechanical contact of random rough surfaces

“…From experience, it is known that for non-conformal but simple geometries (1D or 2D wave, circle or sphere against a flat surface), a rather dense mesh is required at the contact interface to track the contact area evolution, see e.g. [39,40,31,20,77,63]. We also refer to a study of a bi-wavy surface in contact with a rigid flat [74], in which a very dense grid (4096 points per side per wavelength) was used, which allowed the authors to reveal peculiar mean contact pressure behaviour near the percolation point, which was missed in previous studies.…”