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In order to evaluate quantitatively the initial mean grain size (do) and the grain size distribution (σo) for the occurrences of the considerable grain growth and abnormal grain microstructure observed in fine grained hardmetals, the grain growth was simulated by numerical calculation based on multi-grain size model where the rate-determining step of Ostwald ripening is the interface reaction (precipitation), following the previous studies based on 2- and 3- grain size models.The results obtained were as follows: (1) The following three equations were derived for the growth of grains except for the smallest grain, the extinction of the smallest grain, and the mean grain size, respectively.di, t+Δt=di, t+(81/32)K(1/dmin, t-1/di, t)Δtdmin, t+Δt-(81/32)⋅K⋅(1/dmin, t2Fmin, t)[NOΣi=min+{di, t2Fi, t(1/dmin, t-1/di, t)}]⋅Δt-dt=NOΣi=min(Fi, t⋅di, t)where K is (32/81)4(2CoσKVm2/vRT) and is the same as K in well-known equation of d12-d02=Kt. The value of K measured for typical fine grained WC-0.5mass%VC-10mass%Co hardmetal is 2.18×10-2μm2/ks in the case of sintering at 1673K for 0-10.8ks.(2) In the case of monomodal (normal) distribution of WC grain size, the abnormal grain microstructure dose not occur even at d0 less than 0.2-0.lμm for the sintering at 1673K for 3.6ks. However, the considerable grain growth occurs and the mean grain size (d3.6) of the sintered alloy becomes above about 0.4μm, irrespective of the value of σo. The result is similar to that obtained by 3-grain size model. (3) In the case of bimodal distribution consisting two kinds of normal distributions, the abnormal grain microstructure occurs when the total number of grains in the second distribution is extremely smaller than that in the first distribution and also the initial ratio of the mean grain size (d02m) in the second distribution to that in the first distribution (d01m) is above about 9, for example in the case of d01m(≅d0)=0.1μm. The d3.6 is nearly the same as that in the monomodal distribution. The result is similar to that obtained by 2-grain size model. (4) From these results, it was suggested that the fine grained hardmetal with mean grain size less than 0.3μm is substantially difficult to be fabricated by controlling the initial distribution of WC powder as well as the initial mean grain size, as far as VC (5mass% to Co) is used as the grain growth inhibitor.

A Consideration on Grain Growth in WC-Co Fine Grained Hardmetal by Numerical Calculation Based on Multi-Grain Size Model.