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.

Fundamental aspects of hot isostatic pressing: An overview

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.

Yielding of metal powder bonded by isolated contacts

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.

A diffusional creep law for powder compacts

Power-law creep of powder bonded by isolated contacts

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.

Rheology of porous alumina and simulation of hot isostatic pressing

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.

Sensing and modeling of the hot isostatic pressing of copper pressing

Surface melting and solidification with high powered beams can be used for enhancing surface properties. The dimensions of the molten zone define the extent of the modified properties and are critical parameters which must be predicted during process design. The flow field in the molten pool has been reported to be one of the key factors which controls the dimensions of the surface layer. However, the calculation of this is only possible through complex numerical schemes and there is a need to look for simple analytical expressions which may be adequate. One approach for this search involves the precise determination of the steady state stationary profiles and then developing a method for extending these values to include the effect of beam motion for predicting the pool dimensions during processing. In this paper, a study of the flow field and its effect on the depth and width of the steady state pool is presented, based on numerical and analytical methods. To validate the predictions, an experimental study is carried out using surface melting of Al-4.5 wt%Cu alloy an electron beam. The pool shapes are presented through optical micrographs and the depth and width of the pool is measured from these micrographs. The experiments are then simulated using a numerical model which includes fluid flow. The flow field is analyzed using streamline plots and the predicted pool shapes are compared with the micrographs. Further, the results are compared to an analytical method based on pure conduction and the pool depth and width are predicted when the liquid thermal conductivity is modified. The numerical and analytical predictions of the pool depth and width are found to be in good agreement with the experimental measurements (obtained from steady state stationary pools and from dimensions inferred on extrapolating moving beam measurements to zero velocity). The reasons for the success of the analytical model is discussed with reference to the two-dimensional flow fields and vortices predicted by the numerical model.

R.J. Schaefer

Papers

Sensing and modeling of the hot isostatic pressing of copper pressing

Analysis of the steady state molten pool obtained by heating a substrate with an electron beam