Model-based feedback control of deformation processing with microstructure goals
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INTRODUCTION
HOT isostatic pressing ("hipping") is a process for consolidating porous materials (such as metal or ceramic powders or some castings) to high relative density. The idea of the process is to apply hydrostatic stress to a heated component to induce plasticity and creep at particle-particle contacts. Under the compressive stresses, contacts deform, internal pores shrink, and the component moves toward full density. Because temperatures higher than 60 pet of the absolute melting temperature (but lower than the melting temperature) are typically used, substantial grain growth and other diffusion-controlled microstructurecoarsening processes can accompany densification during hipping. It has been pointed out that hipping has many potential advantages over casting or forging for near net shape processing of advanced materials.t l] Recently, work by Artz, t2J Ashby and coworkers, I3-5,81 and Eadie et a/. t6,71 has resulted in the development of predictive process models for both densification and microstructural coarsening of powders during hipping. A convenient graphical tool obtainable from the models is a HIP map from which a human operator can obtain estimates of the time, temperature, and pressure necessary to achieve a particular density and grain size. These HIP maps assume a constant pressure and temperature, but one can also use the models to simulate evolution of density and grain size under general (nonconstant, time-varying) pressure and temperature schedules. These simulations show clearly the experimentally observed dependence of final density and grain size on the temperature and pressure schedule used. Until the models were developed, the only Way to determine a temperature and pressure schedule that gave a desired final microstructure was by costly and timeconsuming experimental trial and error. The models have attracted considerable attention, in part because they allow the trial and error to be conducted off-line by (relatively cheap and quick) computer simulation. However, it is nonetheless still trial and error. One aspect of the work DAVID G. MEYER, formerly Assistant Professor with the University of Virginia, is Associate Professor of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425. H A Y D N N.G. W A D L E Y , Professor of Materials Science and Engineering and Mechanical Engineering, is with the University of Virginia, Charlottesville, VA 22901. Manuscript submitted September 19, 1991. METALLURGICAL TRANSACTIONS B
reported here seeks to remove the ad hoc nature of schedule design. We give a procedure for designing a HIP schedule to achieve a given goal density and grain size. The procedure is nearly optimal, at least in a local sense. The hipping sensor techniques based upon eddy currents [9] and dilatometry II~ have been developed for laboratory measurement applications. These techniques allow continuous, in situ measurement of density during a HIP run and have been used tS] to investigate the validity of HIP process models. Research is contin
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