Multiscale evaluation of microstructural worthiness based on the physical–analytical matching (PAM) approach

Abstract

By selecting the appropriate spatial and temporal variables, physical abnormalities at the microscale can be limited to the essentials such that effective analytical solutions can be made available and identified with high resolution TEM and SEM micrographs. A catalogue of physical–analytical pairs can be stored electronically for the evolution of material damage from micro (or nano) up to macroscopic failure. High speed digital processing can organize such information and make forecast on potential failure in the cyberspace. The micro/macro line cracking model is used to illustrate the use of the PAM (physical–analytical matching) technique although it is still at the early stage of development. Three essential parameters describing the inhomogeneity of the material serve as the basis of the approach while specific microstructural details can be accounted for by using the incidental variables as programmed by PAM in the future. Demonstration is made by using the dual scale micro/macro line crack model where closed form asymptotic solution can be obtained from singularity representation. No generality is lost from the line crack configuration. This is analogous to taking the shape of an atom to be spherical since the exact shape is not relevant. The essential quantities are the energy density and characteristic length associated with the equivalent crack length defined with reference to the spatial and temporal variables under consideration. For a macroscopic tensile specimen containing a micro/macrocrack, multiple microcracking patterns are generated. A priori assumptions related to the grain geometries and/or cohesive force laws to create branching will not be made. Instead, values of the essential parameters are selected to obtain multiple minima of the volume energy density functions. These minima are very closely spaced. This implies that the initiation of multiple microcracking is probable even though dynamic effects are not present. This is in contrast to macrocrack branching where the crack velocity had to approach that of the Rayleigh wave speed. The formulation also shows that empirical approach blind folds the details of microscopic and scaling effects. The double singularity line crack model is used to illustrate that different multiple microcracking patterns can be predicted from the volume energy density fracture criterion that has been used extensively for examining the initiation of macrocracking. The criterion relies on identifying the locations of the stationary values of the energy density function with the potential threshold sites dominated by dilatation or distortion without assuming that the two energy density components are the linear sum, a condition invoked in linear elasticity. To reiterate, three essential parameters are defined to describe the non-homogeneous behavior of the material while two incidental variables are used for the double singularity line crack to account for specific microstructural effects. It is the ease with which asymptotic closed form solution can be obtained and identified with observed damage patterns that suggests the possibility to develop the PAM technique in the cyberspace.