A novel constitutive model emphasizing disclination-induced back stress in strain hardening

Back stress hardening is a component of strain hardening during plastic deformation. Traditionally, the theory of dislocations has attributed the microscopic origin of back stress in polycrystalline metal materials to the long-range stress fields generated by geometrically necessary dislocations (GNDs), which accommodate the translational lattice incompatibility of the crystal. However, the lattice incompatibility also contains a rotational component, associated with disclinations. Similar to GNDs, disclinations also generate long-range internal stress fields, yet their role in back stress remains insufficiently understood. This study introduces a disclination-induced back stress mechanism and proposes a novel single-ended disclination pile-up model, analogous to the single-ended GND pile-up model. This model accounts for the reduction in the average distance of long-range stress fields due to the growth of disclinations within grains. Integrating back stress contributions from both GNDs and disclinations, a new constitutive model is developed. Uniaxial tension simulations of 6061-T5 aluminum alloy sheets demonstrate that the predicted back stress from this model closely aligns with experimental results from tension-compression tests, thereby validating its accuracy. The simulation results show that while GND-induced back stress rapidly increases initially and then stabilizes, disclination-induced back stress continues to rise, constituting 65% of the total back stress at a strain of 0.16. This work not only advances our understanding of the origins of back stress in disclinations but also underscores the significance of incorporating disclinations in back stress calculations, offering new insights into the relationship between microstructure evolution and strain hardening behavior.