Parametric Symbolic Regression for Learning Additive Manufactured Structures’ Unified Crack Growth Models

In aerospace applications, critical metal additive manufacturing (AM) structures require rigorous damage tolerance certification, depending on reliable crack growth analysis. As the bridge from specimen-level experiments to structural assessments, the construction of crack growth models traditionally relied on extensive databases and engineering expertise. Yet the complexity of AM processes hinders the establishment of stable, comprehensive data sets, limiting conventional approaches. To address this challenge, this study proposes a Parametric Symbolic Regression framework for learning crack growth models of AM structures (PSR-AM), in which the symbolic regression is constructed upon parametric candidate models, enabling a unified representation of underlying physical mechanisms while capturing variations across experimental conditions through parameter shifts. Moreover, models’ parameter fitting incorporates both physical and global trend constraints, ensuring reliable and physically consistent modeling even under sparse data conditions. Guided by multiple evaluation metrics, PSR-AM effectively leverages diverse and even sparse AM experimental data sets to derive concise, robust, and generalizable crack growth models. Test on 178 AM Ti-6Al-4V data sets demonstrates that the PSR-AM learned crack growth model captures highly scattered experimental results under multifactor influences with concise mathematical forms and a small set of stable parameters, while outperforming the conventional empirical model in reflecting the intrinsic data characteristics.