Crack tip mechanics of multiscale change

Abstract

Singularity representation at the crack tip and/or smaller region will be considered using six scale transitional physical parameters: three assigned for the nano/micro range (*na/mi, *na/mi, d*na/mi) and three assigned for the micro/macro range (*mi/ma, *mi/ma, d* mi/ma). The subscripts nano, micro, and macro are self-evident. Only the ratio of two successive scale sensitive parameters are needed. Although time dependent physical parameters at the lower scale can be found analytical, they regarded as fictitious, mainly because they are not conducible to measurements. The transitional character of multiscale changes according to nano→micro→ macro with the respective singularity strength of  are given by 1.00/0.75/0.50. Since =0.5 corresponds to the inverse square root r-0.5, where r is the distance from the macro singular point. The micro and nano singular point possess the singularities r-0.75 and r-1.00, respectively. For example, a critical device component may be designed to operate at the nano/micro/macro scale with a life distribution of 2.5+ /3.5+ /5.5+ and total life of 11.5 + years. Progressive changes are assumed to occur in the direction of nano→micro→macro.