A.C.F. Cocks

The flow of powder into simple and stepped dies

An experimental study of die filling into constrained cavities of simple and complex geometries is presented. A model shoe system for the study of powder flow in air and vacuum has been developed. Transparent dies and shoes have been used, which allow the flow and rearrangement of the powder to be observed using a high-speed video system. Both qualitative and quantitative estimations of the influence of powder characteristics and shoe kinematics on the die filling process have been made. Measurements of filling rate and filling ratio for various shoe and die geometries are presented. The influence of airflow is revealed by comparison of experiments conducted in air and in vacuum. Possible positive and negative contributions of the entrained air during die filling have been addressed. Results are presented in the context of the Beverloo equation, which was originally developed to characterize hopper flow. The concept of a critical velocity is introduced, below which complete filling of a standard die is achieved. This provides a measure of the flowability of a powder and can be used to gauge the influence of airflow and pressure on the filling process.

A PHENOMENOLOGICAL CONSTITUTIVE LAW FOR THE BEHAVIOUR OF FERROELECTRIC CERAMICS

Abstract A general thermodynamic structure for the constitutive behaviour of ferroelectric ceramics with the Perovskite structure is described. The state of the material is described in terms of the remanent strain and the remanent polarisation. A yield function is identified, such that changes in remanent strain and polarisation can only occur when the yield condition is satisfied. Simple forms of the Helmholtz free energy are presented, based on an understanding of the underlying micromechanical processes. The resulting hysteresis and butterfly loops predicted by this model are in good agreement with the general form of loops observed experimentally.

Transient creep analysis of ball indentation

The effect of transient creep on the indentation behaviour of a creeping solid has been investigated for a strain hardening primary creep law. Numerical analyses have been performed to obtain the full field solution for a frictionless ball indenter. The functional form of the relationship between the uniaxial response of the solid and the indentation behaviour of the material is explored. The implications of the results are discussed with regard to displacement- and load- controlled indentation creep tests, and the time hardening creep law. Experiments on primary creep indentation of lead support the indentation theory.

Constitutive modelling of powder compaction and sintering

Abstract In this paper, the current status of modelling the compaction and sintering of particulate materials is reviewed. Recent theoretical and experimental studies are described. It is argued that models used to design processes must be robust and simple, but they must be based on a sound understanding of the underlying micromechanics. The models can then be extrapolated from the laboratory to the design environment with confidence. An important stage in this process is the identification of the dominant micromechanical events and the development of constitutive relationships which accurately model these events. Where appropriate, deficiencies in the current models are described and areas where additional modelling is required are identified.

A model for the sintering and coarsening of rows of spherical particles

The formation of interparticle contacts and neck growth by grain boundary and surface diffusion during the sintering of rows of spherical particles is modeled. It is shown that rows of identical particles sinter into a metastable equilibrium configuration whereas rows of particles with different sizes evolve continuously by sintering followed by relatively slow coarsening. During coarsening, smaller particles disappear and larger particles grow. The model is based on a variational principle arising from the governing equations of mass transport on the free surface and grain boundaries. Approximate solutions are found through the use of very simple shapes in which the particles are modeled as truncated spheres and neck formation is represented by a circular disc between particles. Free and pressure assisted sintering of rows of identical and different size particles are studied through this numerical treatment. The effect of initial particle sizes, dihedral angles, diffusivities, and applied compressive forces are investigated.

Finite element formulation of coupled grain-boundary and surface diffusion with grain-boundary migration

Finite element formulations are developed to model microstructure evolution by a combination of grain–boundary diffusion, grain–boundary migration and free surface diffusion. The formulations are based on a unified variational principle which allows fully coupled processes to be analysed. For example, a process can be analysed which involves grain–boundary diffusion along a curved and migrating grain–boundary network, coupled with surface diffusion along internal and/or external free surfaces which intersect with the grain–boundary network. The numerical solution provides the velocities of each individual grain and the velocities of grain–boundaries and migrating surfaces. The finite element formulations, when combined with a time integration algorithm, form a numerical technique which can be used to simulate microstructural evolution in polycrystalline materials. The technique can be applied to a wide range of physical problems including: sintering of powder compacts; grain–growth; diffusive void growth and crack propagation; superplastic deformation and the morphological evolution of electronic thin films. Various numerical examples are presented to demonstrate the effectiveness of the numerical technique.

CREEP-BUCKLING OF CELLULAR SOLIDS

) deform by elastic defor-mation, elastic buckling and plastic collapse of their cell wall. At more elevated temperatures, creep con-tributes to the deformation, which becomes time dependant. Deformation by the creep-bending of cellwalls has been analysed in some detail, but deformation by creep-buckling has not. In this paper we ana-lyse for the first time the collapse of cellular structures by creep-buckling, deriving the critical load andtime required for the buckling event to commence. 7 2000 Acta Metallurgica Inc. Published by ElsevierScience Ltd. All rights reserved.Keywords: Cellular solids; Foams; Creep; Creep-buckling1. INTRODUCTION

IUTAM Symposium on Mechanics of Granular and Porous Materials

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Modelling microstructure evolution in engineering materials

Abstract In this paper we describe a general thermodynamically consistent variational principle for the rate of evolution of microstructure, which considers the competition between energy dissipation and the rate of change of Gibbs free energy of the system. We describe how numerical and approximate analytical procedures can be developed from the variational principle. Two examples are presented which demonstrate the utility of the approach: the kinetics of precipitate growth in an elastically strained body and the influence of an elastic strain on interdiffusion in a two-component system. Within these examples we pay particular attention to the effect of changes of elastic stored energy on the evolution process. The sensitivity of the morphology of growing phases to the ratio of the driving forces arising from elastic and chemical considerations is explored.

Isolated contact model of an idealized asphalt mix

The isolated contact modelling approach, first developed for analysis of powder compaction, is applied to model the deformation behaviour of an idealized asphalt mix. The deformation characteristics of thin films of nonlinear viscous bitumen (established elsewhere) are employed as the microscopic contact model. An isolated contact model is derived to describe the deformation of an idealized mix subject to axisymmetric loadings. Results are presented for mixes having isotropic and anisotropic microstructures. The evolution of anisotropy in initially isotropic mixes is also discussed.