Segmented multiscale approach by microscoping and telescoping in material science

Abstract

Scaling in size and time has led to the establishment of a hierarchy of length scale for identifying the material damage process that can be described in terms of physical inhomogeneities and boundary conditions via the order of stress singularities. The scale dependent nature of some of these parameters such as stress, strain, energy density, etc., however, needs to be recognized. Based on the scale invariant property of “force”, scale segments other than those known as macro-stress, micro-stress and dislocation-stress. They correspond to characteristic lengths of 10 cm and 10 cm and can be, but not necessarily, related to pile of dislocations and subgrain boundary precipitates. This provides a full range of imperfections ranked by the lineal dimension from 10 cm to 10 cm. The corresponding stress-like quantities referred to as “primary” take the units of MPa, GPa, TPa, PPa and EPa which are separated by three orders of magnitude in Pascal. The open slots involving TPa and PPa fill in the gap between GPa and EPa that were not recognized previously. The intermediate orders of the stress singularities connected with TPa and PPa follow accordingly. The full range of stress singularity considered is for a macrocrack and for an edge dislocation. Here, r denotes the distance from the singular point. Indeed, the intermediate singularity models can be shown to exist by the Fadle eigenfunction expansion technique. Their solutions satisfy the axioms in mechanics such that the stresses can be discontinuous but the displacements are required to be finite and continuous at the singular points. The singularity representation approach has worked well in linear fracture mechanics and there is no reason why the concept cannot be extended to include other orders of singularities, either stronger or weaker than the The combination of stress singularities, characteristic lengths and physical inhomogeneities serves as the basis of the proposed scaling scheme. By the same token, similar features of size scaling can be found by observing larger objects that are cosmic in size. Instead of using a characteristic length, a characteristic particle size of 10 42 cm in lineal dimension can be used. This offers a scaling scheme for the size of the universe, galaxy, solar system and earth with the respective dimensions of 10, 10, 10 and 10 cm. This corresponds to 10, 10, 10 and 10 particles. The same particle size, however, will not yield a reasonable size spectrum for objects smaller than the macroscopic. This observation suggests not only a discontinuity in the process of scaling but also the possibility of not being able to reconcile the difference between organic and inorganic substances by shifting time and size scales. That is the establishment of a common ground for material and life science in terms of scaling remains as an unexplored possibility.