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

摘要- Bazant，NWn U.目前，安全系数的强度降低部分被认为是固定的，纯粹从测试数据的统计确定。然而，这仅适用于纯脆性或塑性极限的情况。这里的关键思想是，对于准脆性结构（混凝土结构、纤维复合材料、硬质泡沫、陶瓷、岩石、冰、土壤、木材等）的过渡范围，和那些接近纳米级），安全系数必须依赖于结构的大小和几何形状，并确保tolerablefailure概率，如百万分之一，安全系数必须确定的极值统计的基础上的应力依赖性的激活能的原子间键。材料单元和结构的强度概率分布，偏离幂律尺寸效应，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性，推导并用于验证和校准。 通过对结构性灾害的随机数值分析，证明了相关性和实际应用。主要影响的设计规范和准脆性结构的做法，以及微纳米尺度薄膜和MEMS的可靠性，确定。

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.