  Micro and nanoscale materials have remarkable mechanical properties, such as
enhanced strength and toughness, but usually display sample-to-sample
fluctuations and non-trivial size effects, a nuisance for engineering
applications and an intriguing problem for science. Our understanding of
size-effects in small-scale materials has progressed considerably in the past
few years thanks to a growing number of experimental measurements on carbon
based nanomaterials, such as graphene carbon nanotubes, and on crystalline and
amorphous micro/nanopillars and micro/nanowires. At the same time, increased
computational power allowed atomistic simulations to reach experimentally
relevant sample sizes. From the theoretical point of view, the standard
analysis and interpretation of experimental and computational data relies on
traditional extreme value theories developed decades ago for macroscopic
samples, with recent work extending some of the limiting assumptions of the
original theories. In this review, we discuss the recent experimental and
numerical literature on micro and nanoscale fracture size effects, illustrate
existing theories pointing out their advantages and limitations and finally
provide a tutorial for analyzing fracture data from micro and nanoscale
samples. We discuss a broad spectrum of materials but provide at the same time
a unifying theoretical framework that should be helpful for materials
scientists working on micro and nanoscale mechanics.
