Micro- and nanoscale materials have remarkable mechanical properties, such as enhanced strength and toughness, but they usually display sample-to-sample fluctuations and size effects. These variations are a nuisance for engineering applications and an intriguing problem for science. Our understanding of size effects in small-scale materials has progressed in the past few years thanks to experimental measurements of carbon-based nanomaterials, such as graphene and carbon nanotubes, and of crystalline and amorphous micro- and nanopillars and micro- and nanowires. At the same time, increased computational power has allowed atomistic simulations to reach experimentally relevant sample sizes. From a theoretical point of view, the standard analysis and interpretation of experimental and computational data rely on traditional extreme value theories developed decades ago for macroscopic samples, with recent work extending some of the limiting assumptions of these theories to the micro- and nanoscale. In this Review, we discuss experimental and computational studies of size effects on the fracture in micro- and nanoscale materials, point out the advantages and limitations of existing theories and, finally, provide a pedagogical guide to the analysis of fracture data from micro- and nanoscale samples.

微米和纳米级材料具有出色的机械性能，例如增强的强度和韧性，但它们通常会显示出样品间的波动和尺寸效应。这些变化对于工程应用是令人讨厌的，对于科学来说是一个有趣的问题。由于对碳基纳米材料（例如石墨烯和碳纳米管）以及晶体和无定形的微柱和纳米柱以及微线和纳米线的实验测量，在过去几年中，我们对小尺寸材料的尺寸效应的理解已有所进步。同时，更高的计算能力使原子模拟能够达到实验相关的样本大小。从理论上讲 实验和计算数据的标准分析和解释依赖于数十年前针对宏观样品开发的传统极值理论，而最近的工作将这些理论的某些局限性假设扩展到了微米和纳米尺度。在这篇综述中，我们讨论了尺寸和尺寸对微观和纳米级材料中断裂的影响的实验和计算研究，指出了现有理论的优点和局限性，最后，为从微观和微观角度分析断裂数据提供了教学指导。纳米样品。