The ideal strength of iron in tension and shear

Abstract

The ideal strength of a material is the stress at which the lattice itself becomes unstable and, hence, sets a firm upper bound on the mechanical strength the material can have. The present paper includes an ab-initio calculation of the ideal shear strength of Fe. It is, to our knowledge, the first such computation for any ferromagnetic material. The paper also elaborates on our earlier calculation of the ideal tensile strength of Fe by studying the effects of strains which break the tetragonal symmetry. The strengths were calculated using the Projector Augmented Wave Method within the framework of density functional theory and the generalized gradient approximation. In <001> tension the ideal strength is determined by an elastic instability of the ferromagnetic phase along the "Bain" strain path from bcc to fcc. An <001> tensile strain also leads to instability with respect to transformation into a face centered orthorhombic structure, and to various magnetic instabilities. However, these are encountered at larger strains and, thus, do not affect the ideal strength. We also investigated the ideal shear strength of bcc iron in two prominent shear systems, <111>{112} and <111>{110}. In both shear systems the ideal strength is determined by the body centered tetragonal structure that defines a nearby saddle point on the energy surface. The ideal shear strengths are thus very similar, though they are not identical since the two shears follow slightly different strain paths from bcc to bct. We investigated the magnetic instabilities encountered during <111>{112} shear. These instabilities do not appear until the strain is significantly greater than the instability strain of the ferromagnetic crystal.Hence while Fe exhibits some novel effects due to magnetism, they do not affect the ideal strength, which is determined by the same elastic instabilities that determine the strengths of most other bcc metals.

Intrinsic hardness of crystalline solids

“…Ideal shear strength calculations have also shown that [42,45] weaknesses in crystallographic planes determine the lattice instability and, therefore, the intrinsic hardness. To this end, the real space orbital correlation approach (e.g., Fig.…”

“…Not surprisingly, the highest tensile strength is predicted along [100] and the lowest peak of the stress is at [011]. A calculated ideal tensile strength in the [011] direction of 25.9 GPa is still higher than that of iron (12.6 GPa) [45]. The covalent Os-B bonds enhance the resistance of OsB 2 to tensile deformation in all stress directions.…”

Ab Initio Predicted Alloying Effects on the Elastic Properties of AlxHf1−xNbTaTiZr High Entropy Alloys

“…As an inherent property of a material, the ideal tensile strength (ITS) does not change with the grain boundaries, cracks, dislocations, and microstructural defects, ITS offers insight into the correlation between the intrinsic chemical bonding and the crystal symmetry [45]. Figure 3 shows the energy difference ΔE and stress σ as a function of relaxed tensile strain and unrelaxed tensile strain along bcc<001> direction, respectively.…”

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

“…The nature of the instability reached at this stress level can provide insights into the intrinsic failure mechanisms for a material. For example, under tensile loading crack initiation requires that the local normal stress perpendicular to the cleavage plane is equal to or larger than the ideal tensile strength [1][2][3][4] . However, when a material yields under tensile loading, it is possible for it to fail through a shear instability [5][6][7][8][9] .…”

“…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.…”