Probabilistic distribution model of grain boundary α phase length in titanium alloys
Huizhi Peng, Wan Ye, Jianwen Liu, Shun Wu, Yichi Zhang, Yichi Zhang, Yuman Zhu, Alberto Boretti, Aijun Huang
Abstract
The grain boundary α phase (GB-α) is a crucial microstructure feature in many titanium alloys, significantly impacting their mechanical properties and performance in various applications. This work developed a probabilistic model for GB-α phase. In this model, the size of individual GB-α precipitates and centre-to-centre distance between nearby precipitates are defined by lognormal distributions. Then, considering the physical process of GB-α formation involving nucleation, growth, linkage, and coarsening, a probabilistic distribution was derived for GB-α lengths using the law of total probability. Validation across various heat-treated Ti–6Al–2Sn–4Zr–6Mo samples confirms that the GB-α lengths follow the proposed distribution. Additionally, based on limited characterization inputs, the probabilities of GB-α having specific lengths are predicted by our model within an error margin of 4 %. Furthermore, this model is extended to the size of crept-induced voids in Inconel 718 superalloy, demonstrating its potential applicability to microstructure features governed by similar physical process.