Simulation of the material behaviour of metal powder during compaction

Abstract

This article describes a direct numerical homogenization method for investigating the deformation mechanisms in, and the material behaviour of metal powder during and after compaction. An assembly of elasto-plastic spherical particles in frictional contact with one another is considered, and the stress response to some prescribed deformation history as well as the resulting yield surface of the aggregate is computed with the finite-element method. This is done by applying periodic boundary conditions to the assembly, in a manner that allows arbitrary stress or strain control, and by monitoring the dissipated energies during re-loading simulations with prescribed stress space directions. Closed die and isostatic compaction are considered in particular; the resulting yield surfaces are compared and the role of plastic deformation and frictional sliding on the micro-scale is investigated. Significant deviations from isotropic phenomenological models are found and the development of anisotropy is demonstrated

Numerical homogenisation of an elasto-plastic model-material with large elastic strains: macroscopic yield surfaces and the Eulerian normality rule

“…9 for the 2.5% yield surface of Fig. 8 and are seen to be indeed normal to the yield surface as predicted by (18). Note that the elastic stiffness at the yield points varies by up to 20% which cannot be neglected in the computation of the inelastic strain increment.…”

“…Other cases where this is an issue include the situation where internal contact phenomena lead to a non-linear elastic behaviour at small elastic strains. A technologically important example for this is the cold compaction of metallic powders which is analysed in [18]. Here the possibility of computing the direction of the inelastic strain rate may be particularly useful because, due to frictional sliding effects, associative plastic behaviour cannot be expected on the macro scale and the formulation of the flow rule presents a problem.…”

“…To obtain (18) from (17), one proceeds as described above and expresses the results in terms of the Cauchy stress. With this in mind, the left hand side of (17) is transformed to…”

“…In order to verify the normality rule (18), the deformation dependent elastic tangent tensorH must be computed. To this end, the referential elastic stiffness…”

A comparative study of different sintering models for Al₂O₃

“…These methods can be used to study sintering characteristics such as influence of initial powder distribution on densification, grain coarsening, neck size, etc. Plankensteiner et al, 6) Schmidt et al, 7) Wang et al 8) used various DEM software codes to investigate sintering behavior and various sintering mechanisms for a collection of particles. Monte Carlo models are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.…”