Generalized stacking fault energies and critical resolved shear stresses of random α-Ti-Al alloys from first-principles calculations

Abstract

The critical resolved shear stress (CRSS) and its related plastic deformation of titanium with hexagonal close packed structure are highly anisotropic, leading to low ductility of the material. Understanding the alloying effect on the CRSS is crucial for the improvement of the mechanical properties through rational composition design. Accurate prediction of the CRSS is not straightforward due to the atomic randomness of the alloy. The generalized stacking fault energies (GSFEs) for the basal and prismatic plane 〈a〉 slips of random α-Ti1−xAlx alloys (0≤x≤0.1875) are calculated by using first-principles methods including exact muffin-tin orbitals (EMTO) and plane-wave psuedopotential (VASP) methods in this work. The random distribution of Al in the alloy is treated by using both coherent potential approximation (CPA) for EMTO and special quasirandom structure (SQS) techniques for VASP. The CRSSs are then evaluated within the frame work of semi-discrete variational Peierls-Nabarro model. The VASP-SQS calculations with atomic relaxation generate reasonably good GSFE and CRSS compared with the EMTO-CPA and VASP-SQS calculations without atomic relaxation. For pure Ti, the unstable stacking fault energy (γusf) and CRSS (τa) for the basal 〈a〉 slip are higher than those for the prismatic 〈a〉 slip. With increasing Al concentration x, γusfb for the basal 〈a〉 slip decreases whereas γusfp for the prismatic 〈a〉 increases. The CRSSs for the basal 〈a〉 slip (τab) and the prismatic 〈a〉 slip (τap) both increase with x while τap increases faster than τab such that τab approaches to τap. The calculated CRSSs explain successfully our recently measured mechanical properties (yield strength, fracture toughness, ultimate strength, and elongation) of the α-Ti1−xAlx alloy against x.