Sensing and modeling of the hot isostatic pressing of copper pressing
TL;DR: In this article, a detailed experimental evaluation of mathematical models for densification during hot isostatic pressing (HIP) has been conducted using high purity copper powder as a model system.
Abstract: A detailed experimental evaluation of mathematical models for densification during hot isostatic pressing (HIP) has been conducted using high purity copper powder as a model system. Using a new eddy current sensor, the density of cylindrical compacts has been measured in situ and compared with model predictions for the HIP process. Pressure shielding by the can has been found to influence the densification, and a simple plastic analysis of a thin-walled pressure vessel was used to account for its effects in the models. The existence of a low temperature creep mechanism during consolidation has been found and a formulation to account for its contribution to densification has been developed and implemented in the models. Other effects, believed to be associated with transient creep and the temperature dependence of power law creep parameters, have also been observed in the experiments and suggest the need for further model refinement.
Citations
More filters
TL;DR: In this paper, the basic science of sintering and hipping is summarized and contrasted, and the current state of understanding and modeling of hipping can be classified either as microscopic or macroscopic in their approach.
Abstract: Hot isostatic pressing (hipping) can be used for upgrading castings, densifying presintered components, consolidating powders, and interfacial bonding. It involves the simultaneous application of a high pressure and elevated temperature in a specially constructed vessel. The pressure is applied with a gas (usually inert) and, so, is isostatic. Under these conditions of heat and pressure, internal pores or defects within a solid body collapse and diffusion bond. Encapsulated powder and sintered components alike are densified to give improved mechanical properties and a reduction in the scatter band of properties. In this article, the basic science of sintering and hipping is summarized and contrasted. The current state of understanding and modeling of hipping is then reviewed. Models can be classified either as microscopic or macroscopic in their approach. In the microscopic approach, the various mechanisms of densification are analyzed in terms of a single particle and its surroundings. In the macroscopic approach, the compact is treated as a continuous medium. In hipping, although the pressure is isostatic, shrinkage is not generally isotropic, particularly if containment is used. However, the shrinkage can now be well predicted, provided that the material and container properties are accurately known.
536 citations
TL;DR: In this article, a macroscopic constitutive law for the plastic yielding of a random aggregate of perfectly plastic spherical metal particles is developed, and the results are considered valid for aggregates with densities ranging from about 60% to around 90% of the theoretical fully dense level.
Abstract: A macroscopic constitutive law is developed for the plastic yielding of a random aggregate of perfectly plastic spherical metal particles. The particles are bonded perfectly by isolated contacts and deformation occurs by plastic yielding of material at and near these contacts. The configuration is treated as isotropic and homogeneous as far as particle size and properties are concerned. The results are considered valid for aggregates with densities ranging from about 60% to around 90% of the theoretical fully dense level. The yield surface is obtained from the plastic dissipation at necks between particles given an imposed macroscopically uniform strain rate. The contact yield surface resulting from this analysis is sensitive to pressure as well as to deviatoric stress. The plastic strain rate direction is outwardly normal to the yield surface. Densification takes place when pressure is present, but a notable feature is a vertex on the yield surface at the points of pure positive and negative pressure. Consequently, plastic flow in the presence of pure pressure is nonunique, and deviatoric components may be superposed on densification.
286 citations
TL;DR: In this article, the macroscopic creep of powder due to diffusional mass transport on the interparticle contacts is modelled, where diffusion is very rapid on the free surface of the powder particles.
Abstract: The creep of powder due to diffusional mass transport on the interparticle contacts is modelled. It is assumed that diffusion is very rapid on the free surface of the powder particles so that the critical phenomenon is mass transport on the interparticle boundary. An interparticle shear viscosity is allowed for also. To characterize the creep law, the macroscopic strain rate in the powder aggregate is specified and the energy dissipated in mass transport and interparticle shear is computed. This work rate is used in a potential to determine the macroscopic creep parameters. The effective macroscopic shear and bulk viscosities resulting from this model depend on the relative density of the powder and disappear at random close packed density. The viscosities depend also on parameters controlling mass transport, the size of the powder particles and, in the case of shear viscosity, on the interparticle shear drag. A term driving sintering arises naturally in the model.
189 citations
TL;DR: In this paper, the deformation of powder due to power-law creep near the interparticle contacts is modeled, where the plastic dissipation is dominated by the rate of approach of neighboring particles and the effect of tangential motion can be neglected.
81 citations
TL;DR: In this paper, the effect of porosity on shear and densification behavior is studied and compared to results obtained on metal powders showing similar trends for shear, and a stronger influence in the case of densification.
Abstract: Rheology of a porous alumina was studied using sinter-forging, hot-pressing, and sintering tests. The results are analyzed using constitutive equations for porous materials. The deformation and densification rates are found to follow Coble creep behavior with an eventual control by interface reactions. The effect of porosity on shear and densification behavior is studied and compared to results obtained on metal powders showing similar trends for shear and a stronger influence in the case of densification. Large pores are likely to buckle at low densities when external forces are applied. The sintering pressure is also estimated and lies in the range 0 to 3 MPa. Finally, the constitutive equations are used to simulate hot isostatic pressing of test shapes, showing that the proposed model correctly predicts the deformation of the ceramic preforms.
69 citations
References
More filters
Book•
01 Jan 1950
TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.
Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy
7,810 citations
TL;DR: In this paper, the equations and procedures for constructing hot-isostatic pressing diagrams are greatly simplified and clarified, and two further mechanisms are added: diffusional deformation of the particles themselves when the grain size is much smaller than the particle size, and the separation of pores from boundaries when grain growth occurs.
658 citations
TL;DR: In this article, six or more distinguishable mechanisms contribute to the sintering of an aggregate of particles, even in the absence of applied stresses, and diagrams can be constructed which identify, at a given temperature, particle size and neck size, the dominant mechanism.
563 citations
TL;DR: Sintering-mechanism diagrams are diagrams with axes of neck-size or density, and temperature, which identify the fields of dominance of each of the several mechanisms which contribute to sintering as discussed by the authors.
380 citations
TL;DR: In this article, the relationship between the relative density of the powder compact and the contact area was investigated. But the authors focused on the relation between contact area and the density of powder compact.
Abstract: Model 2 The geometrical considerations used here are, in principle, similar to those of Model 1, with respect to the contacting pairs of spheres considered in the densification process. Now, considering the two contacting spheres shown in Fig. 11 (see Appendix 1), the contact area will be increased necessary for evaluating the experimentally obtained data. The relative density of the powder compact can be experimentally determined and this can be related to the contact area between particles. Another aim of the present work was, therefore, to derive a simple geometrical equation describing the relationship between the relative density of the powder compact and the contact area. A model experiment was carried out on an ideal packing system to confirm the validity of this equation.
23 citations