Refinement of Master Densification Curves for Sintering of Titanium
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SU and Johnson[1] developed the master sintering curve approach for alumina. The thermal history during sintering is reduced to a single parameter, sometimes termed the ‘‘work of sintering.’’[2] This parameter is essentially an integral of the sintering rate over time, with the sintering rate obeying Arrhenius kinetics. Subject to limitations such as the operation of a single dominant sintering mechanism and microstructure being determined solely by density, the sintered density and microstructure evolve along a single path, the master sintering curve, with the work of sintering determining progress along the path. The path is dependent on powder type and compaction method. Master sintering curves and master densification curves have since been used to model many materials including Al2O3,[3,4] TiO2,[5,6] ZnO,[7] BaTiO3,[8] ThO2,[9] WC,[10] CeO2,[11] and several metallic materials[12,13] (17 to 4 PH and 316L stainless steels, W-Ni-Fe, Nb, Mo, Ni, and Re). The basic sintering model has been developed and extended in various ways. An et al.[14,15] proposed a pressure-assisted master sintering surface for alumina and silicon nitride under applied pressure. Blaine et al.[2] normalized the density relative to green density and produced a master densification curve for molybdenum. The sintering of Mo was also considered by Garg et al.[16] German et al.[17] incorporated the effect of particle size on sintering rate into the work of sintering parameter and examined the effects of grain growth on
the form of the master sintering curve for tungsten. The master sintering curve technique has been extended to model grain growth[18] and debinding[19,20] rather than densification. Several other related papers on the sintering of tungsten have been published.[21–23] The more refined formulations of the master sintering curve model incorporate situations in which different sintering mechanisms operate simultaneously or change with increasing temperature, and provide more realistic estimates of activation energies and therefore more accurate identification of mechanisms.[22] In previous work,[24] we attempted to derive an empirical master sintering curve model for Ti by amalgamating data for three powders with different mean particle sizes. While the model reproduced experimental results well, different segments of the master sintering curve were based on results for different powders. Collection of a large amount of additional data now allows refinement of the models for individual Ti powders. Distinct curves are presented for the three different titanium powders, prealloyed Ti6Al4V, and mixed elemental Ti-Ni binary alloys. A basic formulation of the master densification model is employed, which includes the effect of particle size on sintering rate and requires two parameters to be determined from the experimental data: apparent activation energy and particle size exponent. The effect of grain coarsening on saturation of sintered density is considered.
II. I.M. ROBERTSON, formerly Principal Research Fellow, School of Mechanical and Mining Engin
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