Mathematical model for predicting mechanical properties of Ti-Al alloy with lamellar structures of γ-TiAl +α₂

A mathematical model for calculating some mechanical properties of crystal of titanium alloy was established to study the mechanical behavior of γ-TiAl alloys with lamellar structure. By calculating the numerical solution of the model, the change trend of the mechanical properties of the γ-phase and the γ+α₂ lamellar structure was obtained. The results indicat that, with the increase of the amount of α₂ phase, the maximum load-bearing direction of the γ+α₂ lamellar structure changes gradually to the direction parallel to (0001) of α₂ phase with a critical equivalent volume fraction of λ₂=0.3. This theoretically explaines the traditional point of view that the maximum load-bearing direction of the γ+α_e lamellar structure is parallel to the crystal plane (0001) of α₂ phase. Furthermore, the results suggest that the traditional point of view is true only when λ_e>0.3.