A preliminary multiscale modeling of material failure

Microelectromechanical systems (MEMS) and Nanoelectromechanical systems (NAMS) are on the revolutionary frontier of science and engineering. The development of MEMS and NAMS requires appropriate analysis, design, and fabrication techniques that enable the features such as reliability, repeatability, and high yield, etc., in general systems. To achieve this goal, a better understanding of the materials and mechanics at the micro- and nanodimension levels is imperative. In this paper, a preliminary material strength model, for dealing with the resistance to crack propagation at opposite extremes of material representation, continuum solid and atomic lattice, is described. The development of this model is in two parts: (1) The crack of continuum solids - using a quadric surfaces function to establish the piecewise failure envelope for incorporating the material anisotropy, and the final failure envelope of the quadric surfaces criterion is closed in order to accommodate the physical justification of materials with finite strengths. (2) The failure of atomic lattice - representing solids by many-body assemblages of point atomic masses linked by spring bonds, this simplified mass-spring model will be used to express the sequential bond-rupture picture of brittle fracture, in terms of an interatomic cohesive-force function. In this simplified mass-spring model, the solids are regarded as a simple array of parallel uncoupled linear chains, subject only to longitudinal components of forces, the lattice constraint effects are ignored. By addressing the failure mechanisms and establishing failure theories of not only macroscopic anisotropic composite materials, but also the metal lines at the micro level, results of this preliminary study provide some reference guidelines to do the reliable engineering designs of MEMS and NAMS systems.