Quantifying Relationship between Minimum Creep Rate and Microstructure in Metals and Alloys using Symbolic Regression

Quantification of the minimum creep rate in metals is crucial for the design of new creep-resistant materials. The current equations for predicting creep rate are complex, either based on fundamental modeling or empirical relations, which are harder to generalize, and the effect of grain size remains elusive. Since the effect of grain size is complex, a machine learning approach, such as symbolic regression, can be utilized to develop new equations without human bias, revealing hidden trends and patterns in the data. Here, we develop simple, novel equations to explain the effect of grain size in coarse-grained metallic materials using symbolic regression. The use of real-world experimental creep rate data and domain-knowledge-based equation selection led to the discovery of novel equations that can predict the effect of grain size across many types of face-centered-cubic materials. A novel equation developed for the power-law creep regime showed that material properties, stacking fault energy, and excess free volume at grain boundaries can be used to estimate the parameters qualitatively. Another equation developed for the transition region between the power-law and power-law breakdown regimes showed that the effect of grain size is a combination of two mechanisms, extending the previous equation.