A systematic study of disclination-induced internal stress associated with multiple types of twin-twin reactions in Mg alloys: Analytical solutions and numerical calculations

Deformation twinning plays an important role in enhancing the mechanical properties of metals and alloys by mechanisms such as twinning-induced plasticity and strain hardening. However, internal stress concentration associated with the interactions and reactions of twins may also lead to the degradation of ductility and fracture toughness. While the elastic behavior of individual twin types has been extensively studied, the crystallographic reactions among multiple types of twins have not been well recognized, which could produce high-index or irrational twins as well as byproduct disclinations. A theoretical framework to predict twin-twin reaction products and quantify associated internal stress is still unavailable. Here we suggest a general approach to investigate twin-twin reactions through symmetry-dictated characteristic defect analyses and stress field calculations based on disclination theory. By using Mg as an example, a systematic study of multiple types of twin-twin reactions has been conducted. The product defects arising from the reactions and associated internal stress fields have been determined analytically, which are validated by numerical simulations and experimental measurements. This work not only establishes a theoretical foundation for quantifying defect-induced internal stress concentration from complicated twin-twin interactions/reactions, but also offers new insights into the impact of deformation twins on mechanical properties.