Quantitative microstructural characterization–Based calculation of the relationship between regional yield strength and microstructure in back–Extruded Mg–Gd–Y–Zr alloy cups

This study quantitatively investigates the relationship between regional yield strength and microstructure in Mg–9Gd–5Y–0.5Zr (wt.%) alloy cups formed by backward extrusion. A refined GM–HP model was developed, incorporating texture, grain boundary, and dislocation strengthening to accurately predict the compressive yield strength across different regions, accounting for microstructural heterogeneity. The microstructure exhibits significant diversity, driven by variations in the deformation path and dynamic recrystallization (DRX), transitioning from a mixed-grain microstructure with <0001>//ED texture to fully recrystallized fine grains in the corners, followed by grain coarsening in the walls. Microstructural analysis reveals that basal <a> slip is the predominant deformation mechanism, with prismatic <a> slip serving as a secondary contributor. The orientation factor M, strongly influenced by texture, reaches a maximum value of ∼3.3 under the <0001>⊥ED texture. Geometrically necessary dislocations (GNDs) exhibit an inverse correlation with DRX, with values ranging from 0.55 to 2.75 × 10¹⁴ m⁻². The GM–HP model reveals that grain boundary strengthening contributes 50–70 % of total yield strength, and highlights the significant hardening of <0001>⊥ED texture and GNDs. These findings provide valuable insights for optimizing the microstructural design and plastic deformation processing of magnesium alloy.