The experimental evidence for the Hall–Petch dependence of strength on the inverse square-root of grain size is reviewed critically. Both the classic data and more recent results are considered. While the data are traditionally fitted to the inverse square-root dependence, they also fit well to many other functions, both power law and non-power law. There have been difficulties, recognized for half-a-century, in the inverse square-root expression. It is now explained as an artefact of faulty data analysis. A Bayesian meta-analysis shows that the data strongly support the simple inverse or ln d / d expressions. Since these expressions derive from underlying theory, they are also more readily explicable. It is concluded that the Hall–Petch effect is not to be explained by the variety of theories found in the literature, but is a manifestation of, or to be underlain by the general size effect observed throughout micromechanics, owing to the inverse relationship between the stress required and the space available for dislocation sources to operate.

Spider dragline silk exhibits a self-powered torsion actuation driven by humidity, potentially acting as a novel torsional actuator.

This paper reviews the mechanical properties of graphene with particular attention to what is established and what is still uncertain. It clarifies the thickness and the elastic constants, and by also considering also phonon frequencies, it argues that “best values” come from graphite, when available. Properties not available from graphite include bending stiffness; this can be determined from studies of carbon nanotubes as well as graphene. In many ways, nanotubes provide access to fundamental properties of graphene, not least because they are the only form of graphene that can be unsupported (unstrained) in vacuum. Environmental effects are considered, including both interactions with substrates and with other solid and liquid media, which may affect the geometrical parameters defining graphene and associated elastic constants. Major uncertainties persist whether slipping or sticking dominates experimental observation, both between graphene and solid media, and between the layers of bilayer and multilayer graphene. The paper concludes with a short discussion of continuum and atomistic models of graphene.

A theory for the size effect in the strength of wires under torsion is reported and compared with data from thin copper wires. Critical thickness theory is solved rigorously and used to validate a useful approximation which is combined with slip-distance theory modified for a finite structure size. Experimental data with high accuracy around and above the elastic limit show excellent agreement with the theory. The results strongly imply that the physical principle is the constraint that size, whether grain size or structure size, puts on allowed dislocation curvature.

Understanding the strengthening of small-scale materials and structures is one of the key issues in nanotechnology. Many theories exist, each addressing a small domain of experimentally observed size effects and invoking different mechanisms. Measurements of the stress–strain relationship of nickel foils in flexure by the load–unload method provide strikingly accurate data from the elastic region through the yield point and to high plastic strain. The data show that the effects on the rate of work-hardening due to crystallite size and sample size interact, whereas in existing theories they should be independent. Existing theories cannot be complete. The symmetry of the dependence of flow stress on grain size and structure size suggests that strengthening effects are due to a finite strained volume, however this is delimited.

This review explores recent advances in the mechanical reinforcement of polymer nanocomposites using 2D nanofillers, focusing on the mechanisms of reinforcement, evaluation of model and bulk nanocomposites, and the effects of hybrid filler combinations.