Phonon Instabilities and the Ideal Strength of Aluminum

Abstract

We have calculated the phonon spectra of aluminum as a function of strain using density functional perturbation theory for <110>, <100>, and <111> uniaxial tension, as well as relaxed <112>[111] shear. In all four cases, phonon instabilities occur at points away from the center of the Brillouin zone and intrude before the material becomes unstable according to elastic stability criteria. This is the first time the ideal strength of a metal has been shown to be dictated by instabilities in the acoustic phonon spectra. We go on to describe the crystallography of the unstable modes, all of which are shear in character. This work further suggests that shear failure is an inherent property of aluminum even in an initially dislocation-free perfect crystal.

Strain Shielding from Mechanically Activated Covalent Bond Formation during Nanoindentation of Graphene Delays the Onset of Failure

“…The assumption that elastic instability corresponds to the peak Cauchy stress along an assumed deformation path is not always true -in general, a homogeneously-deformed material can become elastically unstable before reaching this point. In particular, when the unstable eigenmode is orthogonal to the loading path, an elastic instability can precede the maximum in the stress-strain curve [6,7]. By means of acoustic tensor analysis based on a rigorously tested hyperelastic constitutive model, we show that this is indeed the case for graphene.…”

Ideal strength and structural instability of aluminum at finite temperatures

“…Consequently, the stress-strain relations of Al generated by empirical MD (at T=0 K) cannot reproduce the results by first-principles methods in the peak stresses and/or the critical strains where the peak stresses appear 3,8,12,21,25 . This situation underscores the urgent need for a first-principles approach that can set key benchmarks on fundamental mechanical…”

“…Despite numerous past studies 1,3,8,9,12,[16][17][18][19][20][21][22][23][24][25] , there remain questions on the fundamental properties of Al, such as how the temperature would affect the strength under various loading conditions and whether the lattice instability behaviors predicted at T=0 K would change with rising temperature. Previous first-principles calculations (at T=0 K) predict that under the <001>, <011>, <111> uniaxial tension and the {111} <112> shear deformation, dynamic phonon instabilities always precede the elastic instabilities determined by the peak stresses in ideal strength calculations 12 . More interestingly, all the unstable phonon modes in Al at T=0 K are shear in nature, which suggests that inhomogeneous shear failure may be an intrinsic property of Al under plastic deformations 12 .…”

“…Meanwhile, dynamic instability of a crystal lattice has been studied via separate calculations of the phonon spectra of the crystal lattice at each step along every deformation pathway. The appearance of imaginary frequencies in the phonon spectra indicates the beginning of the dynamic instability of the crystal lattice [12][13][14][15] . These calculations, however, are all performed at T=0 K, thus ignoring thermodynamic effects that are expected to alter material behavior at high temperatures.…”

Indentation strength of ultraincompressible rhenium boride, carbide, and nitride from first-principles calculations

“…26,27 The limit of structural stability of the specimen in these hardness tests is closely related to its maximum shear strength, which precedes the initiation of cracks and dislocations that lead to plastic deformation. Recent advances in computation physics have made it possible to calculate directly the ideal shear strength of a perfect crystal, [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] i.e., the lowest shear stress peak at which a perfect crystal becomes mechanically unstable, that can be compared to the shear strength derived from nano-indentation measurements. 42 These ideal strength calculations, using accurate first-principles methods, also provide atomistic deformation patterns and full range stress-strain relations which offer key insights into the mechanisms responsible for the fracture modes at incipient plasticity.…”