Mapping ratcheting regimes in ceramic–metal functionally graded (CMFG) beams under cyclic loading

This study presents a comprehensive analysis of the ratcheting behavior in Ceramic–Metal Functionally Graded (CMFG) cantilever beams subjected to cyclic thermal and axial loads. The objective is to investigate the mechanical responses—elastic, shakedown, and ratcheting—of CMFG beams, specifically those with a balanced 50% ceramic and 50% metal composition, under varying temperature and pressure conditions. This unique composition offers an optimized balance between strength and thermal resistance, making the CMFG beam ideal for high-performance applications, particularly in sectors such as aerospace and nuclear engineering. The novelty of this study lies in the development of a Bree diagram that maps the transitions between these mechanical behaviors, providing valuable insights into the beam’s performance across different loading conditions. Numerical results show that for the CMFG beam, the transition from elastic to shakedown occurs at a normalized axial load ratio of approximately 0.4 and a temperature ratio of 0.6, while ratcheting initiates beyond $$\\widehat{p}=0.7$$ and $$\\theta =0.8$$ , with ceramic enrichment increasing the shakedown limit by nearly 15% compared to a fully metallic beam. The Bree diagram derived from this analysis serves as a critical tool for predicting the material's long-term performance in practical applications.