The ideal strength of gold under uniaxial stress: anab initiostudy

Abstract

We employ an ab initio calculation based on density functional theory to investigate the ideal strength of face-centered cubic crystal Au under uniaxial stress along the [100] direction. We show that the stability of the perfect Au crystal under tensile stress is determined by the tetragonal shear stiffness modulus, with an ideal tensile strength of 4.2 GPa and the corresponding Lagrangian tensile strain of ∼ 0.07. The potential bifurcation from the primary uniaxial loading path is along the tetragonal shear. Under compressive stress, there is a stress-free body-centered cubic phase, which is unstable and ready to transform to a stress-free body-centered tetragonal phase with lower internal energy. The stable region is from - 1.6 to 4.2 GPa in the ideal strength, or from - 0.07 to 0.07 in the Lagrangian strain.

Nonlinear stress-strain relations for crystalline solids in initially deformed state

“…The other is the prediction of phase transitions and mechanical stability of crystalline materials when approaching the instability point. 7,21,22 One can employ the nonlinear theory to obtain the stress-strain relations close to the instability point where either molecular dynamics simulation or other modeling calculation may face difficulties due to large strain fluctuations. Some of these efforts are underway.…”

Nonlinear theoretical formulation of elastic stability criterion of crystal solids

“…This is different from the original Polanyi-Frenkel-Orowan criterion for theoretical strength mentioned above if the strain corresponding to the violation of the stability condition is not along the primary loading path, the [100] direction. This phenomenon is called stability bifurcation 15,16,[19][20][21][22][23] . The corresponding strain along the primary loading path where any one of the above stability conditions is violated sets the strain limit for the materials.…”

“…Continuum model with finite element method 10 , atomistic simulation with embedded atom method (EAM) 11,12 , and ab initio quantum mechanic simulation [13][14][15][16] have been employed extensively in various calculations. All these approaches however require tremendous amount of computational resource, among which the largest fraction is on calculation of the second order elastic constants ijkl C in each deformed state.…”

Ideal strength and ductility in metals from second- and third-order elastic constants

“…Elastic instabilities can be calculated by employing Density Functional Theory (DFT), which has been a common approach in the literature 2,9,[14][15][16][17][18][19][20] . In such studies, typically different amounts of strains are applied to a unit cell and at each strain the internal coordinates and lattice vectors perpendicular to the load are relaxed.…”