Statistical Mechanics of Safety Factors: From Atomic Scale to Structural Scale

Northwestern University, Evanston IL

Investigators

Abstract

Abstract - Bazant, NWn U. Currently the strength reduction parts of safety factors are considered as fixed, determined purely from statistics of test data. However, this is adequate only for purely brittle or ductile limiting cases. Here the key idea is that, for the transitional range of quasibrittle structures (concrete structures, fiber composites, rigid foams, ceramics, rocks, ice, soils, wood, etc., and those on approach to nanoscale), the safety factor must depend on structure size and geometry, and that to ensure tolerable failure probability, such as one in a million, the safety factor must be determined from extreme-value statistics based on stress dependence of activation energy of interatomic bonds. The strength probability distributions of material elements and of structure, deviations from power-law size effect, kinks on strength histograms, and dependence on temperature, loading rate and duration, are derived and exploited for verification and calibration. Relevance and practical applications are demonstrated by stochastic numerical analysis of documented structural disasters. Major implications for design codes and practices for quasibrittle structures, as well as reliability of micro-nano-scale thin films and MEMS, are identified.