Modeling Brittle and Ductile Behavior of Solids from First-Principles Calculations

Abstract

A broad classification of solids in terms of their mechanical behavior would characterize them as brittle or ductile. While there is no doubt that ultimately this behavior is due to processes at the atomistic level, the link between these processes and their macroscopic manifestation is difficult to establish. Phenomenological theories that try to address this link must rely on microscopic parameters, the values of which are beyond their scope. Here we review recent efforts to employ firstprinciples electronic structure calculations in order to determine important physical quantities which, in conjunction with phenomenological theories, can provide insight into brittle versus ductile behavior. We apply this approach to cases of intrinsic interest, such as silicon, the prototypical brittle solid, as well as in cases of practical interest, such as the improvement of ductility in molybdenum disilicide, a material of potential usefulness in improved turbine blades. Current indications are that this combination of techniques can serve as powerful qualitative predictive tool for the dependence of mechanical behavior on the microscopic structure and chemical composition of a solid.

On configurational compatibility and multiscale energy momentum tensors

“…A more refined theory of dislocation nucleation based on the Peierls-Nabarro model (Peierls, 1940;Nabarro, 1952) was later proposed by Rice (1992). Subsequent experimental findings (Jokl et al, 1989;Huang and Gerberich, 1992;Zielinski et al, 1992;Marsh et al, 1992;George and Michot, 1993) and recent results of large scale atomistic simulations (Grujicic and Du, 1995;Cleri et al, 1997;Zhou et al, 1997;Bulatov et al, 1998;Cleri et al, 1998;Farkas, 1998;Waghmare et al, 2000;Farkas, 2000;Farkas et al, 2001;Bernstein and Hess, 2003;Guo et al, 2003;Mattoni et al, 2005;Farkas, 2005) have suggested that the fracture of brittle materials is a multiscale phenomenon involving cleavage, dislocation emission, and a host of grain and grain boundary dependent mechanisms such as twinning, recrystallization, or phase transformation. Today, it has become a general consensus that fracture is an archetype of multiscale phenomena in condensed solid state physics.…”

Mechanical Properties of Silicon Microstructures

“…On the basis of this concept and adopting the view that dislocation nucleation is a necessary precursor to dislocation motion, Kaxiras et al [276] proposed a ductility condition that depends only on two energies, γ and γ us , and defined a "disembrittlement parameter" determining to which class a solid belongs:…”

“…Even then, it is not clear for which slip system or for which cleavage plane these quantities must be evaluated [276].…”

First-principles study of the ideal cleavage fracture of Cr2Nb microalloyed by X (Al, Ni, Co, Ti)

“…the solubility and the interaction of dopants. At present, the first-principles method has been widely used to study material fracture, and provide microscopic insights into the mechanical behavior of solid materials at the atomic level [26][27][28][29][30].…”