Connecting atomistic and experimental estimates of ideal strength

Abstract

The ideal strength is the minimum stress required to plastically deform an infinite defectfree crystal and is an upper bound to the strength of a real crystal. Disturbingly, however, the best available experimental estimates of the ideal strengths of tungsten and molybdenum are 25-50% above the values predicted by recent ab initio density-functional calculations. This work resolves this discrepancy by extending the theoretical calculations to account for the triaxial state of stress seen in the nanoindentation experiments and by adjusting the experimental values to account for the crystallography of loading and the nonlinearity of the elastic response at large strains. Although an implicit assumption in many discussions of mechanical properties is that the ideal strength is not experimentally observable, as the true strength of most materials is limited by lattice defects, the close agreement between corrected experimental and theoretical estimates of ideal strength suggests that the ideal strength of some materials can be observed directly using nanoindentation.

Intrinsic hardness of crystalline solids

“…This sets the upper bound on the mechanical strength of a material. Detailed analysis [39] of the mechanics of nanoindentation has shown that after proper consideration of the crystallography of loading and the correction of the nonlinearity of the elastic response at large strains, the measured values can be compared quantitatively to the results of the first-principles calculations. In the calculations, the ideal strength is defined as the maximum stress in the stress-strain curve in the weakest tensile stretch or shear slip direction [40,41].…”

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

“…This suggests that the hardness is not at all determined by the elastic constant solely. Qualification of the hardness by DFT is barely to begin recently [16][17][18][19][20]. Accordingly, the mechanical properties descried in this paper are limited to a level of elastic properties and phonon properties.…”

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

“…The ideal shear strength calculations can provide an estimation of the asymptotic (i.e., load independent) hardness by comparing the calculated ideal shear strength with those of benchmark materials, such as diamond and c-BN whose hardness are well established. However, most previous ideal shear strength calculations did not consider normal compressive pressure beneath the indenter, [28][29][30][31][32][33][34][35][36][37][38][41][42][43][44][45][46][47][48] which makes them appropriate primarily to describe the scratching hardness of materials where normal pressures on scratching surfaces are not high.…”

“…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.…”

“…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. [43][44][45][46][47][48] It represents a significant advance in computational materials research despite that some aspects, such as the load-sensitive hardness or the indentation size effect, which mainly stems from the generation and propagation of dislocations and cracks under large indentation loading, are still beyond the available computing capacity.…”