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

目前，安全系数的强度折减部分被认为是固定的，完全由试验数据的统计确定。然而，这只适用于纯脆性或延性受限的情况。这里的关键思想是，对于过渡范围的准脆性结构(混凝土结构、纤维复合材料、刚性泡沫、陶瓷、岩石、冰、土壤、木材等，以及那些接近纳米尺度的结构)，安全系数必须取决于结构的尺寸和几何形状，并且为了确保可容忍的失效概率，例如百万分之一，安全系数必须从基于原子间键激活能的应力依赖的极值统计中确定。推导了材料和结构的强度概率分布、偏离幂规律尺寸效应、强度直方图上的扭结以及对温度、加载速率和持续时间的依赖关系，并用于验证和校准。通过对记录在案的结构灾害的随机数值分析，证明了其相关性和实际应用。确定了对准脆性结构的设计规范和实践以及微纳薄膜和MEMS的可靠性的主要影响。

Abstract - Bazant, NWn U.Currently the strength reduction parts of safety factors areconsidered as fixed, determined purely from statistics of testdata. However, this is adequate only for purely brittle or ductilelimiting cases. Here the key idea is that, for the transitionalrange of quasibrittle structures (concrete structures, fibercomposites, rigid foams, ceramics, rocks, ice, soils, wood, etc.,and those on approach to nanoscale), the safety factor must dependon structure size and geometry, and that to ensure tolerablefailure probability, such as one in a million, the safety factormust be determined from extreme-value statistics based on stressdependence of activation energy of interatomic bonds. The strengthprobability distributions of material elements and of structure,deviations from power-law size effect, kinks on strengthhistograms, and dependence on temperature, loading rate andduration, are derived and exploited for verification andcalibration. Relevance and practical applications aredemonstrated by stochastic numerical analysis of documentedstructural disasters. Major implications for design codes andpractices for quasibrittle structures, as well as reliability ofmicro-nano-scale thin films and MEMS, are identified.