Mechanical hardness and elastic stiffness of alloys: semiempirical models

Abstract

An atomic-level mechanical hardness model that is based on screened electrostatics and elastic shear (SEES) is generalized to single-phase substitutional annealed alloys, and a semiempirical method is derived to quantify elastic property composition effects in single-phase binary substitutional alloys. The SEES model is adapted to include interactions between dislocations and alloying-elements, and it is applied to eight binary and three ternary alloys. Calculated hardnesses are within 10% (30%) of measured values for 45% (73%) of the materials. Composition effects in the elastic stiffness coefficients c 11( x), c 12( x) and c 44( x) are evaluated for 12 binary alloys, and in the shear modulus G( x) and the bulk modulus B( x) for 22 binary alloys. These elastic properties are within 3.0% of measurement for the following percentages of materials studied: G( x), 90%; B( x), 86%; c 11( x), 100%; c 12( x), 92%, and c 44( x), 83%. The theoretical elastic behavior is bilinear for BCC materials, and variably non-linear for FCC materials. The generalized mechanical hardness equation and its previously published (non-general) analog are equivalent for 70 of the 71 materials previously studied. A discrepancy between the two equations occurs for TiB 2 which, when corrected, moves the TiB 2 hardness 15% closer to measurement and yields fitting parameters corrected by −1.9%: A=0.2992, and γ B =6.2595 for simple metals.