Establishment and application of grain morphology distribution model for quantitative analysis of titanium alloys with typical microstructures

A novel probability model of grain morphology distribution considering the orientation and size of non-spherical grains, including P₀₁(r),P₁₁(r),P₀₂(r),P₃₃(r),P₁₂(r), is established based on the nearest-surface function, and it is used to reveal the dispersion and uniformity degree of different morphology grains in titanium alloys. Especially, the distribution probability of lamellar α intersection is introduced instead of the distributed relationship of different α lamellae, and the distributed relationship between lamellar and globular grains is transformed into the distribution of globular grains by the equivalent circle method. Then, several corresponding distribution probabilities are selected in terms of describing different microstructure states (equiaxed, basketweave, duplex microstructures). The model is applied to the quantitative analysis of TC4 alloy with different morphology grains. The results show that the distribution of α grains with different morphology in the β matrix becomes more inhomogeneous with increasing height reduction and cooling rate. Moreover, the larger the globular α size is, the greater the aggregation degree and the smaller the uniformity of other α grains around it is. The reliability of probability model is verified by the comparison between the predicted and the measured frequency distributions for the nearest neighbor surface distance r.