Classification of inelastic deformation and material-intrinsic indices about mechanical performance of general solid matter

Abstract

The present article is aimed to detect material-intrinsic indices that can be used to supervise the mechanical performance of general solid matter. The novelty carried in this article can be summarised as follows. Firstly, an inelastic deformation state of almost any solid matter can be treated as the combination of two fundamental modes due to different microscopic causation: Mode I inelastic distortion due to the movement of sliding types of defects and Mode II inelastic dilation due to the evolution of voids/bubbles. Secondly, each inelastic deformation mode is characterised by a single principal inelastic deformation descriptor (PIDD): Mode I by a newly introduced quantity of maximum distortional angle change α and Mode II by the logarithm of dilating magnification ω. In particular, the concept of maximum distortional angle change gives rise to a geometrically intuitive yield criterion of α > α_c, which in situations of small deformation, is shown to asymptote von Mise’s, and to become Tresca’s in cases of plane stress. Thirdly, the deformation process of a solid matter under monotonic and ambient loads is formulated by means of trajectories of thermodynamic equilibria with respect to the PIDD pair. Then a pair of physical quantities which measure the stresses needed to change the local PIDD state are singled out. Being termed as inelastic deformation resistances (IDRs), these two quantities are shown to depend only on the onsite atomic configurations. It is also shown that key descriptive properties about the mechanical behaviours of materials, such as ductility, are encoded in IDRs as functions of PIDDs. Hence the IDR pair may serve as material performance indices that may be more intrinsic than conventional stress-strain relationships.