超微粒超硬合金の粒成長に関する多粒子径モデル基数値計算による一考察 [in Japanese] A Consideration on Grain Growth in WCCo Fine Grained Hardmetal by Numerical Calculation Based on MultiGrain Size Model [in Japanese]
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Abstract
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 multigrain size model where the ratedetermining step of Ostwald ripening is the interface reaction (precipitation), following the previous studies based on 2 and 3 grain size models.<BR>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.<BR><I>d</I><I><SUB>i, t+Δt</SUB></I>=<I>d<SUB>i, t</SUB></I>+(81/32)<I>K</I>(1/<I>d</I><SUB>min, <I>t</I></SUB>1/<I>d<SUB>i, t</SUB></I>)Δ<I>t</I><I>d</I><SUB>min, <I>t</I>+Δ<I>t</I></SUB>(81/32)⋅<I>K</I>⋅(1/<I>d</I><SUB>min, <I>t</I></SUB><SUP>2</SUP><I>F</I><SUB>min, <I>t</I></SUB>)[<I>N</I>OΣi=min+{<I>d<SUB>i, t</SUB></I><SUP>2</SUP><I>F<SUB>i, t</SUB></I>(1/<I>d</I><SUB>min, <I>t</I></SUB>1/<I>d<SUB>i, t</SUB></I>)}]⋅Δ<I>t</I><I>d<SUB>t</SUB></I>=<I>N</I>OΣ<I>i</I>=min(<I>F<SUB>i, t</SUB></I>⋅<I>d<SUB>i, t</SUB></I>)<BR>where K is (32/81)4(2C<SUB>o</SUB>σKVm<SUP>2</SUP>/vRT) and is the same as K in wellknown equation of d<SUB>1</SUB><SUP>2</SUP>d<SUB>0</SUB><SUP>2</SUP>=Kt. The value of K measured for typical fine grained WC0.5mass%VC10mass%Co hardmetal is 2.18×10<SUP>2</SUP>μm<SUP>2</SUP>/ks in the case of sintering at 1673K for 010.8ks.<BR>(2) In the case of monomodal (normal) distribution of WC grain size, the abnormal grain microstructure dose not occur even at d<SUB>0</SUB> less than 0.20.lμm for the sintering at 1673K for 3.6ks. However, the considerable grain growth occurs and the mean grain size (d<SUB>3.6</SUB>) of the sintered alloy becomes above about 0.4μm, irrespective of the value of σ<SUB>o</SUB>. The result is similar to that obtained by 3grain 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 (d<SUB>0</SUB><SUP>2m</SUP>) in the second distribution to that in the first distribution (d<SUB>0</SUB><SUP>1m</SUP>) is above about 9, for example in the case of d<SUB>0</SUB><SUP>1m</SUP>(≅d<SUB>0</SUB>)=0.1μm. The d<SUB>3.6</SUB> is nearly the same as that in the monomodal distribution. The result is similar to that obtained by 2grain 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.
Journal

 J. Jpn. Soc. Powder Powder Metallurgy

J. Jpn. Soc. Powder Powder Metallurgy 45(6), 544552, 19980615
Japan Society of Powder and Powder Metallurgy