Evaluation of the direction-dependent mechanical properties of ideal single crystal metals: a comparative ab initio study

Abstract The anisotropy of crystal structures mandates the direction dependence of materials’ mechanical properties. Key properties of interest are the Young’s modulus and Poisson ratio in the small strain limit, and the ideal tensile strength in the large strain regime. To date, atomistic computations of these properties have been conducted using two approaches. The first approach explicitly calculates the stress–strain response using computational tensile test experiments. The second approach computes the single crystal elastic constants then derives the mechanical properties using analytical equations. The two approaches have been used interchangeably and their equivalence not assessed. This work systematically computes the mechanical properties of 13 BCC and 12 face centered cubic (FCC) metals via the two approaches using first principles density functional theory calculations and hypothesize the robustness of the first approach. Analysis of the results has revealed the shortcomings of the elastic constants method in detecting instabilities in the structures captured by the first principles computational tensile test approach. Large discrepancies in calculations of Young’s moduli using the latter approach are herein reported, as well as auxetic repossess and large Poisson ratio for some metals. Beyond the small strain results, we systematically examined the lateral strain response up to 0.5 applied strain in 3 crystallographic directions and reported large changes in slopes and peculiarities around the Bain transformation strain. From the computational stress–strain results, we validated empirical equations in the literature relating the ideal strength to the direction-dependent Young’s modulus and the Bain strain along [001] in BCC and [110] in FCC but also presented further relations for other crystallographic directions. In conclusion, we believe that the elastic constants approach, while computationally efficient, has to be used with caution and should be validated against the computational tensile tests. In addition, we highlight the importance of examining different crystallographic directions with possibly desirable properties.