Evaluating the Spatial and Size Distributions of Flat Precipitates in Diffusion-Controlled Precipitation Processes

This study presents a modeling of spatial and size distributions of precipitates in diffusion-controlled phase transitions in metals. These data are essential for estimating the probability of critical cluster formation, leading to brittle fracture. The practical significance of the current research includes demonstrated ability to estimate the probability of zirconium hydrogen embrittlement based on obtained stochastic characteristics of δ-hydrides (ZrH1.6) morphology. The model includes a statistical analysis of serial calculations based on classical heterogeneous nucleation and growth of plate-shaped inclusions in 3D domain. The approach was verified with experimental data in modeling of θ’-phase (Al2Cu) nucleation and growth in Al–4 wt % Cu alloy. Also the paper includes an appendix with an analytical approach for evaluating the distribution function of inclusions in cluster length and mean projection length, which is the morphology metric correlating with mechanical properties. This analytical solution was also used for the verification of the numerical model.